Patent Publication Number: US-2023141094-A1

Title: Automatic generation of load design

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 16/777,498, filed Jan. 30, 2020, which is a continuation-in-part of U.S. patent application Ser. No. 16/712,783, filed Dec. 12, 2019, which claims the benefit of U.S. Provisional Application No. 62/798,911, filed Jan. 30, 2019. U.S. patent application Ser. Nos. 16/777,498 and 16/712,783, and U.S. Provisional Application No. 62/798,911 are incorporated herein by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     This disclosure relates generally to automatic generation of load and route design. 
     BACKGROUND 
     Delivery trailers are often used to transport orders. Generally, the items in an order are prepared into stacks for transport. Stacks typically involve items stacked on pallets, and the stacks are often wrapped to keep the items from falling out from the stack. Such stacks can be loaded into the delivery trailer for transport, then unloaded at a destination. Some delivery routes involve multiple destinations. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       To facilitate further description of the embodiments, the following drawings are provided in which: 
         FIG.  1    illustrates a front elevational view of a computer system that is suitable for implementing an embodiment of the system disclosed in  FIG.  3   ; 
         FIG.  2    illustrates a representative block diagram of an example of the elements included in the circuit boards inside a chassis of the computer system of  FIG.  1   ; 
         FIG.  3    illustrates a block diagram of a load and route design system that can be employed for automatic generation of load and route design, according to an embodiment; 
         FIG.  4    illustrates a block diagram of acts, modules, and outputs, which can be employed for automatic generation of load and route design, according to an embodiment; 
         FIG.  5    illustrates a flow chart for a method, according to another embodiment; 
         FIG.  6 ( a )  illustrates a top, rear, right side perspective view of a lengthwise loading pattern for a trailer; 
         FIG.  6 ( b )  illustrates a top plan view of a pinwheel loading pattern for a trailer; 
         FIG.  7    illustrates a top, left side perspective view of a semi-trailer truck including a tractor and a trailer; 
         FIG.  8    illustrates a top, rear, left side perspective view of a load in a trailer in which the largest and heaviest stacks are positioned in the middle of the trailer, closest to the center point between the axles; 
         FIG.  9    illustrates a flow chart for a block of route optimizing, according to the embodiment of  FIG.  4   ; 
         FIG.  10    illustrates a flow chart for a block of Hours of Service (HOS) validation, according to the embodiment of  FIG.  9   ; 
         FIG.  11    illustrates a flow chart for a method, according to another embodiment; 
         FIG.  12    illustrates a flow chart for a method, according to another embodiment; 
         FIG.  13    illustrates top plan views of a load design for a dry trailer and a load design for a tri-temp trailer; 
         FIG.  14    illustrates top plan views of load designs for a dry trailer showing a swap in a first simulated annealing; 
         FIG.  15    illustrates top plan views of load designs for a dry trailer, showing swaps in a second simulated annealing; and 
         FIG.  16    illustrates a flow chart for a method, according to another embodiment. 
     
    
    
     For simplicity and clarity of illustration, the drawing figures illustrate the general manner of construction, and descriptions and details of well-known features and techniques may be omitted to avoid unnecessarily obscuring the present disclosure. Additionally, elements in the drawing figures are not necessarily drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help improve understanding of embodiments of the present disclosure. The same reference numerals in different figures denote the same elements. 
     The terms “first,” “second,” “third,” “fourth,” and the like in the description and in the claims, if any, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances such that the embodiments described herein are, for example, capable of operation in sequences other than those illustrated or otherwise described herein. Furthermore, the terms “include,” and “have,” and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, device, or apparatus that comprises a list of elements is not necessarily limited to those elements, but may include other elements not expressly listed or inherent to such process, method, system, article, device, or apparatus. 
     The terms “left,” “right,” “front,” “back,” “top,” “bottom,” “over,” “under,” and the like in the description and in the claims, if any, are used for descriptive purposes and not necessarily for describing permanent relative positions. It is to be understood that the terms so used are interchangeable under appropriate circumstances such that the embodiments of the apparatus, methods, and/or articles of manufacture described herein are, for example, capable of operation in other orientations than those illustrated or otherwise described herein. 
     The terms “couple,” “coupled,” “couples,” “coupling,” and the like should be broadly understood and refer to connecting two or more elements mechanically and/or otherwise. Two or more electrical elements may be electrically coupled together, but not be mechanically or otherwise coupled together. Coupling may be for any length of time, e.g., permanent or semi-permanent or only for an instant. “Electrical coupling” and the like should be broadly understood and include electrical coupling of all types. The absence of the word “removably,” “removable,” and the like near the word “coupled,” and the like does not mean that the coupling, etc. in question is or is not removable. 
     As defined herein, two or more elements are “integral” if they are comprised of the same piece of material. As defined herein, two or more elements are “non-integral” if each is comprised of a different piece of material. 
     As defined herein, “approximately” can, in some embodiments, mean within plus or minus ten percent of the stated value. In other embodiments, “approximately” can mean within plus or minus five percent of the stated value. In further embodiments, “approximately” can mean within plus or minus three percent of the stated value. In yet other embodiments, “approximately” can mean within plus or minus one percent of the stated value. 
     As defined herein, “real-time” can, in some embodiments, be defined with respect to operations carried out as soon as practically possible upon occurrence of a triggering event. A triggering event can include receipt of data necessary to execute a task or to otherwise process information. Because of delays inherent in transmission and/or in computing speeds, the term “real-time” encompasses operations that occur in “near” real-time or somewhat delayed from a triggering event. In a number of embodiments, “real-time” can mean real-time less a time delay for processing (e.g., determining) and/or transmitting data. The particular time delay can vary depending on the type and/or amount of the data, the processing speeds of the hardware, the transmission capability of the communication hardware, the transmission distance, etc. However, in many embodiments, the time delay can be less than 1 millisecond (ms), 10 ms, 50 ms, 100 ms, 500 ms, or 1 second (s). 
     DESCRIPTION OF EXAMPLES OF EMBODIMENTS 
     Turning to the drawings,  FIG.  1    illustrates an exemplary embodiment of a computer system  100 , all of which or a portion of which can be suitable for (i) implementing part or all of one or more embodiments of the techniques, methods, and systems and/or (ii) implementing and/or operating part or all of one or more embodiments of the non-transitory computer readable media described herein. As an example, a different or separate one of computer system  100  (and its internal components, or one or more elements of computer system  100 ) can be suitable for implementing part or all of the techniques described herein. Computer system  100  can comprise chassis  102  containing one or more circuit boards (not shown), a Universal Serial Bus (USB) port  112 , a Compact Disc Read-Only Memory (CD-ROM) and/or Digital Video Disc (DVD) drive  116 , and a hard drive  114 . A representative block diagram of the elements included on the circuit boards inside chassis  102  is shown in  FIG.  2   . A central processing unit (CPU)  210  in  FIG.  2    is coupled to a system bus  214  in  FIG.  2   . In various embodiments, the architecture of CPU  210  can be compliant with any of a variety of commercially distributed architecture families. 
     Continuing with  FIG.  2   , system bus  214  also is coupled to memory storage unit  208  that includes both read only memory (ROM) and random access memory (RAM). Non-volatile portions of memory storage unit  208  or the ROM can be encoded with a boot code sequence suitable for restoring computer system  100  ( FIG.  1   ) to a functional state after a system reset. In addition, memory storage unit  208  can include microcode such as a Basic Input-Output System (BIOS). In some examples, the one or more memory storage units of the various embodiments disclosed herein can include memory storage unit  208 , a USB-equipped electronic device (e.g., an external memory storage unit (not shown) coupled to universal serial bus (USB) port  112  ( FIGS.  1 - 2   )), hard drive  114  ( FIGS.  1 - 2   ), and/or CD-ROM, DVD, Blu-Ray, or other suitable media, such as media configured to be used in CD-ROM and/or DVD drive  116  ( FIGS.  1 - 2   ). Non-volatile or non-transitory memory storage unit(s) refer to the portions of the memory storage units(s) that are non-volatile memory and not a transitory signal. In the same or different examples, the one or more memory storage units of the various embodiments disclosed herein can include an operating system, which can be a software program that manages the hardware and software resources of a computer and/or a computer network. The operating system can perform basic tasks such as, for example, controlling and allocating memory, prioritizing the processing of instructions, controlling input and output devices, facilitating networking, and managing files. Exemplary operating systems can include one or more of the following: (i) Microsoft® Windows® operating system (OS) by Microsoft Corp. of Redmond, Wash., United States of America, (ii) Mac® OS X by Apple Inc. of Cupertino, Calif., United States of America, (iii) UNIX® OS, and (iv) Linux® OS. Further exemplary operating systems can comprise one of the following: (i) the iOS® operating system by Apple Inc. of Cupertino, Calif., United States of America, (ii) the Blackberry® operating system by Research In Motion (RIM) of Waterloo, Ontario, Canada, (iii) the WebOS operating system by LG Electronics of Seoul, South Korea, (iv) the Android™ operating system developed by Google, of Mountain View, Calif., United States of America, (v) the Windows Mobile™ operating system by Microsoft Corp. of Redmond, Wash., United States of America, or (vi) the Symbian™ operating system by Accenture PLC of Dublin, Ireland. 
     As used herein, “processor” and/or “processing module” means any type of computational circuit, such as but not limited to a microprocessor, a microcontroller, a controller, a complex instruction set computing (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, a graphics processor, a digital signal processor, or any other type of processor or processing circuit capable of performing the desired functions. In some examples, the one or more processors of the various embodiments disclosed herein can comprise CPU  210 . 
     In the depicted embodiment of  FIG.  2   , various I/O devices such as a disk controller  204 , a graphics adapter  224 , a video controller  202 , a keyboard adapter  226 , a mouse adapter  206 , a network adapter  220 , and other I/O devices  222  can be coupled to system bus  214 . Keyboard adapter  226  and mouse adapter  206  are coupled to a keyboard  104  ( FIGS.  1 - 2   ) and a mouse  110  ( FIGS.  1 - 2   ), respectively, of computer system  100  ( FIG.  1   ). While graphics adapter  224  and video controller  202  are indicated as distinct units in  FIG.  2   , video controller  202  can be integrated into graphics adapter  224 , or vice versa in other embodiments. Video controller  202  is suitable for refreshing a monitor  106  ( FIGS.  1 - 2   ) to display images on a screen  108  ( FIG.  1   ) of computer system  100  ( FIG.  1   ). Disk controller  204  can control hard drive  114  ( FIGS.  1 - 2   ), USB port  112  ( FIGS.  1 - 2   ), and CD-ROM and/or DVD drive  116  ( FIGS.  1 - 2   ). In other embodiments, distinct units can be used to control each of these devices separately. 
     In some embodiments, network adapter  220  can comprise and/or be implemented as a WNIC (wireless network interface controller) card (not shown) plugged or coupled to an expansion port (not shown) in computer system  100  ( FIG.  1   ). In other embodiments, the WNIC card can be a wireless network card built into computer system  100  ( FIG.  1   ). A wireless network adapter can be built into computer system  100  ( FIG.  1   ) by having wireless communication capabilities integrated into the motherboard chipset (not shown), or implemented via one or more dedicated wireless communication chips (not shown), connected through a PCI (peripheral component interconnector) or a PCI express bus of computer system  100  ( FIG.  1   ) or USB port  112  ( FIGS.  1 - 2   ). In other embodiments, network adapter  220  can comprise and/or be implemented as a wired network interface controller card (not shown). 
     Although many other components of computer system  100  ( FIG.  1   ) are not shown, such components and their interconnection are well known to those of ordinary skill in the art. Accordingly, further details concerning the construction and composition of computer system  100  ( FIG.  1   ) and the circuit boards inside chassis  102  ( FIG.  1   ) are not discussed herein. 
     When computer system  100  in  FIG.  1    is running, program instructions stored on a USB drive in USB port  112 , on a CD-ROM or DVD in CD-ROM and/or DVD drive  116 , on hard drive  114 , or in memory storage unit  208  ( FIG.  2   ) are executed by CPU  210  ( FIG.  2   ). A portion of the program instructions, stored on these devices, can be suitable for carrying out all or at least part of the techniques described herein. In various embodiments, computer system  100  can be reprogrammed with one or more modules, system, applications, and/or databases, such as those described herein, to convert a general purpose computer to a special purpose computer. For purposes of illustration, programs and other executable program components are shown herein as discrete systems, although it is understood that such programs and components may reside at various times in different storage components of computing device  100 , and can be executed by CPU  210 . Alternatively, or in addition to, the systems and procedures described herein can be implemented in hardware, or a combination of hardware, software, and/or firmware. For example, one or more application specific integrated circuits (ASICs) can be programmed to carry out one or more of the systems and procedures described herein. For example, one or more of the programs and/or executable program components described herein can be implemented in one or more ASICs. 
     Although computer system  100  is illustrated as a desktop computer in  FIG.  1   , there can be examples where computer system  100  may take a different form factor while still having functional elements similar to those described for computer system  100 . In some embodiments, computer system  100  may comprise a single computer, a single server, or a cluster or collection of computers or servers, or a cloud of computers or servers. Typically, a cluster or collection of servers can be used when the demand on computer system  100  exceeds the reasonable capability of a single server or computer. In certain embodiments, computer system  100  may comprise a portable computer, such as a laptop computer. In certain other embodiments, computer system  100  may comprise a mobile device, such as a smartphone. In certain additional embodiments, computer system  100  may comprise an embedded system. 
     Turning ahead in the drawings,  FIG.  3    illustrates a block diagram of a load and route design system  300  that can be employed for automatic generation of load and route design, according to an embodiment. Load and route design system  300  is merely exemplary and embodiments of the system are not limited to the embodiments presented herein. The load and route design system can be employed in many different embodiments or examples not specifically depicted or described herein. In some embodiments, certain elements, modules, or systems of load and route design system  300  can perform various procedures, processes, and/or activities. In other embodiments, the procedures, processes, and/or activities can be performed by other suitable elements, modules, or systems of load and route design system  300 . Load and route design system  300  can be implemented with hardware and/or software, as described herein. In some embodiments, part or all of the hardware and/or software can be conventional, while in these or other embodiments, part or all of the hardware and/or software can be customized (e.g., optimized) for implementing part or all of the functionality of load and route design system  300  described herein. 
     In many embodiments, load and route design system  300  can be a computer system, such as computer system  100  ( FIG.  1   ), as described above, and can each be a single computer, a single server, or a cluster or collection of computers or servers, or a cloud of computers or servers. In another embodiment, a single computer system can host load and route design system  300 . Additional details regarding load and route design system  300  are described herein. 
     In some embodiments, load and route design system  300  can be in data communication through a communication network  330  with physical stores  360 , which can include physical stores  361 - 363 , for example, and distribution centers, such as distribution center  350 . In several embodiments, each of the physical stores (e.g.,  360 ) and each of the distribution centers (e.g.,  350 ) can be a physical, brick-and-mortar location that are associated (e.g., operated by a common business entity or entities under common control) with load and route design system  300 . In many embodiments, the physical stores (e.g.,  360 ) and the distribution centers (e.g.,  350 ) each can include one or more computer systems. 
     In a number of embodiments, each of physical stores  360  can be a retail store, such as a department store, a grocery store, or a super store (e.g., both a grocery store and a department store). In many embodiments, the distribution centers (e.g.,  350 ) can provide the items sold at the physical stores (e.g.,  360 ). For example, a distribution center (e.g.,  350 ) can supply and/or replenish stock at the physical stores (e.g.,  360 ) that are in a region of the distribution center. In many embodiments, a physical store (e.g.,  361 - 363 ) can submit an order to a distribution center (e.g.,  350 ) to supply and/or replenish stock at the physical store (e.g.,  361 - 363 ). In many embodiments, distribution center  350  can be referred to as a warehouse or other facility that does not sell products directly to a customer. 
     In some embodiments, load and route design system  300  can be a distributed system that includes one or more systems in each of the distribution centers (e.g.,  350 ). In other embodiments, load and route design system  300  can be a centralized system that communicates with computer systems in the physical stores (e.g.,  360 ) and distribution centers (e.g.,  350 ). In some embodiments, communication network  330  can be an internal network that is not open to the public, which can be used for communications between load and route design system  300 , physical stores (e.g.,  360 ), and distribution centers (e.g.,  350 ). In other embodiments, communication network  330  can be a public network, such as the Internet. In several embodiments, operators and/or administrators of load and route design system  300  can manage load and route design system  300 , the processor(s) of load and route design system  300 , and/or the memory storage unit(s) of load and route design system  300  using the input device(s) and/or display device(s) of load and route design system  300 , or portions thereof in each case. 
     In several embodiments, load and route design system  300  can include one or more input devices (e.g., one or more keyboards, one or more keypads, one or more pointing devices such as a computer mouse or computer mice, one or more touchscreen displays, a microphone, etc.), and/or can each include one or more display devices (e.g., one or more monitors, one or more touch screen displays, projectors, etc.). In these or other embodiments, one or more of the input device(s) can be similar or identical to keyboard  104  ( FIG.  1   ) and/or a mouse  110  ( FIG.  1   ). Further, one or more of the display device(s) can be similar or identical to monitor  106  ( FIG.  1   ) and/or screen  108  ( FIG.  1   ). The input device(s) and the display device(s) can be coupled to load and route design system  300  in a wired manner and/or a wireless manner, and the coupling can be direct and/or indirect, as well as locally and/or remotely. As an example of an indirect manner (which may or may not also be a remote manner), a keyboard-video-mouse (KVM) switch can be used to couple the input device(s) and the display device(s) to the processor(s) and/or the memory storage unit(s). In some embodiments, the KVM switch also can be part of load and route design system  300 . In a similar manner, the processors and/or the non-transitory computer-readable media can be local and/or remote to each other. 
     Meanwhile, in many embodiments, load and route design system  300  also can be configured to communicate with and/or include one or more databases. The one or more databases can include a product database that contains information about products, items, or SKUs (stock keeping units), for example, among other data as described herein, such as described herein in further detail. The one or more databases can be stored on one or more memory storage units (e.g., non-transitory computer readable media), which can be similar or identical to the one or more memory storage units (e.g., non-transitory computer readable media) described above with respect to computer system  100  ( FIG.  1   ). Also, in some embodiments, for any particular database of the one or more databases, that particular database can be stored on a single memory storage unit or the contents of that particular database can be spread across multiple ones of the memory storage units storing the one or more databases, depending on the size of the particular database and/or the storage capacity of the memory storage units. 
     The one or more databases can each include a structured (e.g., indexed) collection of data and can be managed by any suitable database management systems configured to define, create, query, organize, update, and manage database(s). Exemplary database management systems can include MySQL (Structured Query Language) Database, PostgreSQL Database, Microsoft SQL Server Database, Oracle Database, SAP (Systems, Applications, &amp; Products) Database, and IBM DB2 Database. 
     Meanwhile, communication between load and route design system  300 , physical stores  360 , distribution center  350 , and/or the one or more databases can be implemented using any suitable manner of wired and/or wireless communication. Accordingly, load and route design system  300  can include any software and/or hardware components configured to implement the wired and/or wireless communication. Further, the wired and/or wireless communication can be implemented using any one or any combination of wired and/or wireless communication network topologies (e.g., ring, line, tree, bus, mesh, star, daisy chain, hybrid, etc.) and/or protocols (e.g., personal area network (PAN) protocol(s), local area network (LAN) protocol(s), wide area network (WAN) protocol(s), cellular network protocol(s), powerline network protocol(s), etc.). Exemplary PAN protocol(s) can include Bluetooth, Zigbee, Wireless Universal Serial Bus (USB), Z-Wave, etc.; exemplary LAN and/or WAN protocol(s) can include Institute of Electrical and Electronic Engineers (IEEE) 802.3 (also known as Ethernet), IEEE 802.11 (also known as WiFi), etc.; and exemplary wireless cellular network protocol(s) can include Global System for Mobile Communications (GSM), General Packet Radio Service (GPRS), Code Division Multiple Access (CDMA), Evolution-Data Optimized (EV-DO), Enhanced Data Rates for GSM Evolution (EDGE), Universal Mobile Telecommunications System (UMTS), Digital Enhanced Cordless Telecommunications (DECT), Digital AMPS (IS-136/Time Division Multiple Access (TDMA)), Integrated Digital Enhanced Network (iDEN), Evolved High-Speed Packet Access (HSPA+), Long-Term Evolution (LTE), WiMAX, etc. The specific communication software and/or hardware implemented can depend on the network topologies and/or protocols implemented, and vice versa. In many embodiments, exemplary communication hardware can include wired communication hardware including, for example, one or more data buses, such as, for example, universal serial bus(es), one or more networking cables, such as, for example, coaxial cable(s), optical fiber cable(s), and/or twisted pair cable(s), any other suitable data cable, etc. Further exemplary communication hardware can include wireless communication hardware including, for example, one or more radio transceivers, one or more infrared transceivers, etc. Additional exemplary communication hardware can include one or more networking components (e.g., modulator-demodulator components, gateway components, etc.). 
     In several embodiments, load and route design system  300  can receive an order for a physical store (e.g.,  361 - 363 ) and can automatically design how the order will be fulfilled from a distribution center to delivery at the store. In a number of embodiments, load and route design system  300  can determine pallets to be used for items in the order, how to build stacks of the pallets to be shipped in trailers, designing and/or obtaining routes to be used for the trailers, and designing loads within the trailers for these routes. In several embodiments, the trailers each can be any form of road haulage shipping container or compartment, such as a semi-trailer, a full trailer, etc. For example, the trailers can be similar or identical to trailer  720  which is attached to tractor  710 , as shown in  FIG.  7    and described below. 
     In many embodiments, load and route design system  300  can include a communication system  301 , an order initiation system  302 , a stacking building system  303 , a routing system  304 , and/or a load design system  305 . In many embodiments, the systems of load and route design system  300  can be modules of computing instructions (e.g., software modules) stored at non-transitory computer readable media that operate on one or more processors. In other embodiments, the systems of load and route design system  300  can be implemented in hardware. Load and route design system  300  can be a computer system, such as computer system  100  ( FIG.  1   ), as described above, and can be a single computer, a single server, or a cluster or collection of computers or servers, or a cloud of computers or servers. In another embodiment, a single computer system can host load and route design system  300 . Additional details regarding load and route design system  300  and the components thereof are described herein. 
     Turning ahead in the drawings,  FIG.  4    illustrates a block diagram  400  of acts, modules, and outputs, which can be employed for automatic generation of load and route design, according to an embodiment. Block diagram  400  is merely exemplary and embodiments of the acts, modules, and outputs are not limited to the embodiments presented herein. The acts, modules, and outputs can be employed in many different embodiments or examples not specifically depicted or described herein. In some embodiments, certain elements of block  400  can perform, involve, and/or be generated by involve various procedures, processes, and/or activities. In other embodiments, the procedures, processes, and/or activities can be performed by, and the outputs can be generated by, other suitable elements of block  400 . In many embodiments, block  400  can be implemented by load and route design system  300  ( FIG.  3   ). 
     In many embodiments, block diagram  400  can begin at block  410  of receiving orders and performing initial processing. For example, the orders can be partitioned into the different distribution centers (e.g.,  350  ( FIG.  3   )) to be used to fulfill the orders. As another example, the different types of items in the order can be determined in order to determine what categories of items are included in the order. The types of items (also referred to as “commodity types”) can include (a) “MP,” which can include meats and produce, which can involve temperature control; (b) “FDD,” which can include food, dairy, and deli, which can involve temperature control; and (c) “dry,” which can include any other items that do not require temperature control. As another example, the order can include a requested delivery date, which can be the day that the physical store (e.g.,  361 - 363  ( FIG.  3   )) requests to receive the shipment of the order. In many embodiments, an order filling date can be calculated based on the requested delivery date. The order filling date can be the date that the order is filled at the distribution center (e.g.,  350  ( FIG.  3   )) and placed on a trailer. 
     In several embodiments, block diagram  400  also can include a block  420  of stack building. In many embodiments, each of the types of items in the order can be stored in the distribution center (e.g.,  350  ( FIG.  3   )) on separate pallets. For example, the order can include an order for one pallet of a particular brand of flour, and two pallets of a particular brand of sugar. In several embodiments, the pallets can be arranged into stacks at the distribution center (e.g.,  350  ( FIG.  3   )). Block  420  can involve designing how the pallets should be stacked into a customized (e.g., optimized) arrangement, which can limit the amount of floor spots that will be used in the trailer when the stacks are shipped to the physical store (e.g.,  361 - 363  ( FIG.  3   )). 
     In many embodiments, block diagram  400  additionally can include a block  430  of route optimization and load building. In many embodiments, block  430  can include a block  440  for a route optimizer and a block  450  for a load designer. In many embodiments, the number of stacks that will be built to fill an order can be determined once block  420  of stacking building is completed. Each of these stacks can have a weight, which can be determined based on the weights of the pallets in the stacks. Each order has a destination at a physical store (e.g.,  361 - 363  ( FIG.  3   )). Block  440  of route optimizing can determine a route for each trailer to go to deliver the orders. In many cases, a trailer can carry more than one order, such as two order or three orders, so the routes can be designed such that the trailer carries multiple orders to limit total distances traveled and/or total transit time across all the trailers involved in delivering the orders. In a number of embodiments, block  440  can be implemented as shown in  FIG.  9    and described below. In many embodiments, blocks  440  and  450  are grouped in block  430  because route determination can involve determining an initial load design, the determining the stops at physical stores (e.g.,  361 - 363  ( FIG.  3   )) on a route can involve determining the orders that will be included in a load that will leave the distribution center (e.g.,  350 ) in a trailer. In many embodiments, route optimizer also can consider rest constraints on drivers to allow drivers delivering the trailers to have sufficient rest. 
     In a number of embodiments, block  430  can generate initial load designs, which can be stored in a block  460  of storing initial load design, and/or can generate delivery routes, which can be stored in a block  470  of storing the delivery routes. The initial load designs can include the orders that will be included in a trailer. The delivery routes can include the schedule of stops for the trailer. 
     In several embodiments, block diagram  400  further can include a block  480  of completing the load design, which can include a stack distribution and axle adjustment. In many embodiments, completing the load design can involve using the initial load designs, such as those generated in block  430  and stored in block  460 , and determining how the stacks in the orders will be assigned to floor spots in the trailer in order to satisfy the schedule of stops and weight distribution requirements. 
     In a number of embodiments, block  480  can generate final load designs, which can be stored in a block  490  of storing the final load designs. These final load designs can then be used, together with the delivery routes stored in block  470  to fulfill and/or physically deliver the orders from the distribution centers (e.g.,  350  ( FIG.  3   )) to the physical stores (e.g.,  361 - 363  ( FIG.  3   )) using the trailers according to the plans in the final load designs and the delivery routes. 
     Turning ahead in the drawings,  FIG.  5    illustrates a flow chart for a method  500 , according to another embodiment. In some embodiments, method  500  can be a method of automatically generating load and route design. Method  500  is merely exemplary and is not limited to the embodiments presented herein. Method  500  can be employed in many different embodiments or examples not specifically depicted or described herein. In some embodiments, the procedures, the processes, and/or the activities of method  500  can be performed in the order presented. In other embodiments, the procedures, the processes, and/or the activities of method  500  can be performed in any suitable order. In still other embodiments, one or more of the procedures, the processes, and/or the activities of method  500  can be combined or skipped. 
     In many embodiments, load and route design system  300  ( FIG.  3   ) can be suitable to perform method  500  and/or one or more of the activities of method  500 . In these or other embodiments, one or more of the activities of method  500  can be implemented as one or more computing instructions configured to run at one or more processors and configured to be stored at one or more non-transitory computer readable media. Such non-transitory computer readable media can be part of a computer system such as load and route design system  300  ( FIG.  3   ). The processor(s) can be similar or identical to the processor(s) described above with respect to computer system  100  ( FIG.  1   ). 
     In some embodiments, method  500  and other blocks in method  500  can include using a distributed network including distributed memory architecture to perform the associated activity. This distributed architecture can reduce the impact on the network and system resources to reduce congestion in bottlenecks while still allowing data to be accessible from a central location. 
     Referring to  FIG.  5   , method  500  can include a block  505  of receiving orders from physical stores for fulfillment from a distribution center. The physical stores can be similar or identical to physical stores  360  ( FIG.  3   ). The distribution center can be similar or identical to distribution center  350  ( FIG.  3   ). In several embodiments, each of the orders can include a set of items and a requested delivery date. In many embodiments, an order filling date can be determined for each of the orders based at least in part on the requested delivery date of each respective one of the orders. In many embodiments, block  505  can include various acts of block  410  ( FIG.  4   ). 
     In several embodiments, method  500  also can include a block  510  of generating a stack building plan for each of the orders using simulated annealing. In many embodiments, the stack building plan can minimize the number of stacks created for an order using the pallets that will be used to fulfill the order. By limiting the number of stacks created for the order, the number of floor spots used in the trailer can be minimized, which can allow more orders to be fulfilled in fewer total loads. In many embodiments, generating the stack building plan for each of the orders using simulated annealing can include, for each of the orders, determining the stack building plan for the order using simulated annealing to minimize a quantity of stacks to be built from pallets for the items in the order subject to a stack height limit, pallet stacking rules, and temperate range rules. In many embodiments, block  510  can include various acts of block  420  ( FIG.  4   ). 
     A typical pallet is a frame (often a wood frame, but sometimes a plastic frame or metal frame) measuring approximately 40 inches by approximately 48 inches, with layers of products above the frame. For example, a pallet of sugar can include packages of sugar in piled in layers above the frame for a certain height, such as 4 feet, for example. A pallet is often wrapped with a plastic wrap to secure the products to the pallet and prevent the products from falling and/or spilling off of the pallet. 
     Pallets can be stacked to create a stack. A stack can be a sequence of pallets from bottom to top. A number of constraints can apply when building stacks from pallets. For example, the inside height of the trailer can limit the height of stacks, which can impose a stack height limit. For example, if the inside height of a trailer is approximately 111 inches, there can be a stack height limit of approximately 108 inches, for example, for that particular trailer. Depending on the stack height limit and the height of the individual pallets a stack can include one pallet, two pallets, three pallets, or four or more pallets. 
     Additional constraints for building stacks can include pallet stacking rules. In many embodiments, the pallet stacking rules can restrict certain types of pallets from being stacked above or below other types of pallets. For example, lighter pallets are typically stacked above heavier pallets within the same stack, and a pallet containing chemicals typically are not stacked above other pallets within the same stack. An exemplary set of pallet stacking rules is shown in Table 1, below. 
     
       
         
           
               
               
             
               
                   
                 TABLE 1 
               
             
            
               
                   
                   
               
               
                   
                 Up 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 Self 
                   
               
               
                 Down 
                 Any 
                 Bottom 
                 Chemical 
                 Intact 
                 Normal 
                 Stack 
                 Top 
               
               
                   
               
               
                 Any 
                 999 
                   
                   
                 X 
                 X 
                   
                 X 
               
               
                 Bottom 
                 X 
                 1 
                   
                 X 
                 X 
                   
                 X 
               
               
                 Chemical 
                 X 
                   
                 999 
                 X 
                 X 
                   
                 X 
               
               
                 Intact 
                 X 
                   
                   
                 999 
                 X 
                   
                 X 
               
               
                 Normal 
                 X 
                   
                   
                   
                 999 
                   
                 X 
               
               
                 Self 
                   
                   
                   
                   
                   
                 999 
                 X 
               
               
                 Stack 
               
               
                 Top 
                   
                   
                   
                   
                   
                   
                 999 
               
               
                   
               
            
           
         
       
     
     The rows in Table 1 indicate what types of pallets can be below the types of pallets in the columns, and the columns indicate what types of pallets can be above the types of pallets in the rows. A number indicates how many pallets are allowed, an X means unlimited, and a blank means not allowed. For example, the row for chemical indicates that a chemical pallet cannot be placed below the bottom pallet or below a self-stack pallet. The column for chemical indicates that a chemical pallet cannot be placed above any pallet except a chemical pallet. 
     Further constraints for building stacks can include temperature range rules. For example, a pallet that includes items at a certain temperature range (e.g., frozen, refrigerated, dry (non-refrigerated)) will be stacked with other pallets that include items at the same temperature range, not with pallets that include items at other temperature ranges. 
     Based on the order, the number of pallets and types of pallets (e.g., chemical, refrigerated, etc.) to be used to fill the order can be determined. Based on these inputs, an arrangement of the pallets in stacks can be generated to minimize the number of stacks that will include all the pallets in the order, subject to the stack height limit, the pallet stacking rules, and the temperate range rules. In some embodiments, constraint programming can be used to generate the arrangements of the pallets in the stacks for the order, such as by modelling mathematically with integer programming. 
     In many embodiments, simulated annealing can be used to determine the stacking building plan. Simulated annealing can be used to determine a global minimum despite local minimums. In greedy heuristic algorithms, local minimums can be achieved, but the actual best solution, a global minimum, often is not achieved. In simulated annealing, a local minimum can be overcome by allowing worse outcomes to get out of the local minimum. Eventually, with a view of other options outside of the confines of local minimums, the algorithm can become greedy to achieve the global minimum. For example, initially, each computer representation of a pallet can be assigned to a separate computer representation of stack. A pallet can then be randomly selected to be moved to another stack, at a random position within the stack. If the move is feasible, based on the constraints, the move can be made in the computer representation. If there are fewer stacks than before the move, then the move can be viewed as a positive outcome. A greedy heuristic algorithm would test whether the move results in a positive outcome, and if so, the move would be made, and if not, the move would not be made. By contrast, simulated annealing can allow moves to be made for non-positive (negative or neutral) outcomes in an effort to escape a local minimum to achieve a lower global minimum. In many embodiments, after exploration of moves that are non-positive to escape one or more local minimum, the simulated annealing can become greedy to achieve the global minimum. 
     In a number of embodiments, method  500  additionally can include a block  515  of obtaining routes for delivering the orders in trailers from the distribution center to the physical stores based at least in part on the stack building plan. The trailers can be similar or identical to trailer  720 , as shown in  FIG.  7    and described below. In many embodiments, a route can include a single order, multiple orders, or part of an order. In several embodiments, the routes can split an order across two of the trailers when a quantity of stacks in the order exceeds a floor spot capacity for one of the trailers, such as one of the trailers that has the highest floor spot capacity that is available to the distribution center. For example, if there are 32 floor spots in a trailer, and the number of stacks in an order is 40, the order can be split among two different routes for two different trucks. In many embodiments, block  515  can include various acts of block  430  ( FIG.  4   ), block  440  ( FIG.  4   ), block  450  ( FIG.  4   ), block  460  ( FIG.  4   ), and/or block  470  ( FIG.  4   ). In some embodiments, the routes can be obtained from another system or another module of the system. In other embodiments, the routes can be determined, as described below. 
     In a number of embodiments, the routes for the trailers can be obtained using simulated annealing based at least in part on the stack building plan to determine routes that minimize distances subject to a weight constraint for each of the trailers and a floor spot capacity for each of the trailers. In many embodiments, the stack building plan can include the number of stacks in the order and the total weight of all of the stacks in the order. Each trailer can have a weight constraint, which can be the total amount of weight that the trailer can carry in a load. Each trailer also can have a floor spot capacity. Each floor spot can be an area of the trailer floor that can hold a stack. For example, because pallets are typically approximately 40 inches by approximately 48 inches in area, the stacks can have a bottom surface area of approximately 40 inches by approximately 48 inches. Each floor spot can hold a single stack, and can be approximately 40 inches by approximately 48 inches. The floor spot capacity of a trailer can be dependent on the inside length of the trailer and the inside width of the trailer. 
     The inside width of the trailer can determine the type of loading pattern used in the trailer. For example,  FIG.  6 ( a )  illustrates a top, rear, right side perspective view of a lengthwise loading pattern  610  for a trailer, which can include stacks, such as stacks  611  and  612 . A trailer can allow a lengthwise loading pattern, which means positioning the stacks with the lengths along the cross-sectional width of the trailer, when the inside width of the trailer is greater than or equal to approximately 98 inches, which can fit two stacks lengthwise at approximately 48 inches a piece plus approximately 2 inches additional for buffer. For a trailer having an inside length of approximately 53 feet, the lengthwise loading pattern can allow a floor spot capacity of 30 stacks. 
       FIG.  6 ( b )  illustrates a top plan view of a pinwheel loading pattern  620  for a trailer, which can include stacks, such as stacks  621  and  622 . When the inside width of the trailer is less than approximately 98 inches, two lengthwise stacks will not fit across the inside width. Instead, if the inside width of the trailer is greater than or equal to approximately 90 inches, the stacks can be arranged in the trailer in a “pinwheel” manner, in which one of the stacks across the inside width of the trailer is positioned lengthwise and the other stack is positioned widthwise. For a trailer having an inside length of approximately 53 feet, the pinwheel loading pattern can allow a floor spot capacity of 28 stacks. 
     When the inside width of the trailer is less than approximately 90 inches, the pinwheel loading pattern will not fit. Instead, as long as the inside width of the trailer is at least approximately 82 inches, a widthwise loading pattern can be used, in which the stacks are positioned with the widths of the stacks along the cross-sectional width of the trailer. For a trailer having an inside length of approximately 53 feet, the widthwise loading pattern can allow a floor spot capacity of 26 stacks. 
     In many embodiments, simulated annealing can be used to determine the routes. Simulated annealing can be used to determine a global optimum despite local optimums. As explained above, in greedy heuristic algorithms, local optimums can be achieved, but the actual best solution, a global optimum, often is not achieved. In simulated annealing, a local optimum can be overcome by allowing worse outcomes to get out of the local optimum. Eventually, with a view of other options outside of the confines of local optimums, the algorithm can become greedy to achieve the global optimum. For example, initially, each computer representation of an order can be assigned to a separate computer representation of a route using a computer representation of a trailer. An order can then be randomly selected to be moved to another route, at a sequence within the route. If the move of the order to the route with the trailer is feasible, based on the constraints of the number of stacks in the order, the total weight of the stacks in the order, the floor spot capacity of the trailer, and the weight constraints of the trailer, then the move can be made in the computer representation. If the total distances traveled and/or total transit time for all the orders is decreased, then the move can be viewed as a positive outcome. A greedy heuristic algorithm would test whether the move results in a positive outcome, and if so, the move would be made, and if not, the move would not be made. By contrast, simulated annealing can allow moves to be made for non-positive (negative or neutral) outcomes in an effort to escape a local minimum to achieve a lower global minimum. In many embodiments, after exploration of moves that are non-positive to escape one or more local minimum, the simulated annealing can become greedy to achieve the global minimum. 
     In several embodiments, the routes, as obtained and/or determined, can include a sequence of delivery for the orders in the load of the trailer that will be used for the route. The sequence of delivery can be viewed as sequence-of-delivery constraints to be satisfied when generating a load design in block  530 , described below. 
     In many embodiments, the routes can include a driving schedule generated subject to rest constraints. Rest constraints can be based on legal regulations, company policies, and/or driver specifications, for example. For example, in the United States, the U.S. Department of Transportation (DOT) requires that drivers have 10 hours or rest for every 10 hours of driving. In a number of embodiments, the schedule can be generated based on cumulative driving time and rest time. For example, if the number of hours to be driven in a day will exceed 10 hours, an additional ten hours can be added to the transit time to allow for rest. For example, if the following condition is satisfied, then an additional ten hours can be added to the driving time: 
       (origin&#39;s cumulative time+driving time to destination)%20&gt;10, 
     where origin&#39;s cumulative time is the driving time for the day for the driver at the start of the trip, the driving time to destination is the remaining driving time to reach the destination, and the % is the mod (modulo) operator. 
     In several embodiments, method  500  further can include a block  520  of generating a load design for each of the routes to deliver in a trailer of the trailers a load for one or more of the orders, such that floor spot assignments for stacks for each of the one or more of the orders in the load carried by trailer satisfy sequence-of-delivery constraints and center-of-gravity constraints. In many embodiments, the center-of-gravity constraints of the trailer can be determined as a range of positions of the trailer based on a weight of the load carried by the trailer, positions of axles of the trailer, and weight limits for the axles of the trailer. In many embodiments, block  520  can include various acts of block  450  ( FIG.  4   ), block  460  ( FIG.  4   ), block  480  ( FIG.  4   ), and/or block  490  ( FIG.  4   ). 
     For example,  FIG.  7    illustrates a top, left side perspective view of a semi-trailer truck  700  including a tractor  710  and a trailer  720 . Semi-trailer truck  700  shown in  FIG.  7    can be modified from the actual semi-trailer truck, as the actual tractor typically will include a front axle with two wheels, one on each side, and two rear axles, each having four wheels, two on each side for each rear axle, which are positioned under a front portion of the actual trailer, and the actual trailer typically will have two rear axles, each having four wheels, two on each side for each rear axle, which are positioned under a rear portion of the actual trailer. As shown in  FIG.  7   , semi-trailer truck  700  is simplified such that the two front axles of the actual tractor are modeled as a single axle, specifically, axle  731 , and the two rear axles of the actual trailer are modeled as a single axle, specifically, axle  732 . Trailer  720  can have a length L, a height H, and a width W, as shown in  FIG.  7   . The length L can extend from a front  721  of trailer  720  to a rear  722  of trailer  720 . Axle  731  can have a position  741 , which is a distance δ 1  from front  721  of trailer  720 , and axle  732  can have a position  742 , which is a distance δ 2  from front  721  of trailer  720 . As used herein, the axles of the trailer can include axle  731  and axle  732 , even when axle  731  is actually part of the tractor. 
     In many embodiments, as modeled in  FIG.  7   , axle  731  can be located at a midpoint between the two rear axles of the actual tractor, and axle  732  can be located at a midpoint between the two rear axles of the actual trailer. Axle  731  can have a weight limit, which can be based on the weight limits of the two rear axles of the actual tractor, and axle  732  can have a weight limit, which can be based on the weight limits of the two rear axles of the actual trailer. In many embodiments, the routes determined in block  515  ( FIG.  5   ) above were subject to the weight constraint of the trailer, meaning that the total weight of the stacks is less than the sum of the weight limits for axle  731  and axle  732 . However, these weight constraints assume a perfectly balanced load, such as a center of gravity at the exact center between axle  731  and axle  732  of trailer  720 . In practice, the center of gravity can be frontward or rearward of the center point between axles  731  and  732  of trailer  720 . A range of positions for the center of gravity can be determined in order to satisfy the weight limits of the axles. This range of positions can be based on the total weight of the load, which can be the total weight of all the stacks in the all the orders in the load carried in the trailer (e.g.,  720 ), the positions of the axles, and the weight limits for the axles, as follows: 
     
       
         
           
             
               
                 max 
                 ⁢ 
                 COG 
               
               = 
               
                 
                   AxlePos 
                   1 
                 
                 + 
                 
                   
                     max 
                     ⁢ 
                     
                       Weight 
                       1 
                     
                     × 
                     
                       ( 
                       
                         
                           AxlePo 
                           ⁢ 
                           
                             s 
                             2 
                           
                         
                         - 
                         
                           AxlePo 
                           ⁢ 
                           
                             s 
                             1 
                           
                         
                       
                       ) 
                     
                   
                   
                     t 
                     ⁢ 
                     otalWeight 
                   
                 
               
             
             , 
           
         
       
       
         
           
             
               
                 min 
                 ⁢ 
                 COG 
               
               = 
               
                 
                   AxlePo 
                   ⁢ 
                   
                     s 
                     2 
                   
                 
                 - 
                 
                   
                     max 
                     ⁢ 
                     
                       Weight 
                       2 
                     
                     × 
                     
                       ( 
                       
                         
                           AxlePo 
                           ⁢ 
                           
                             s 
                             2 
                           
                         
                         - 
                         
                           AxlePo 
                           ⁢ 
                           
                             s 
                             1 
                           
                         
                       
                       ) 
                     
                   
                   
                     t 
                     ⁢ 
                     otalWeight 
                   
                 
               
             
             , 
           
         
       
     
     where maxCOG is the upper bound of the range of positions, minCOG is the lower bound of the range of positions, AxlePos 1  is position  741  (δ 1 ) of axle  731 , AxlePos 2  is position  742  (δ 2 ) of axle  732 , maxWeight 1  is the weight limit for axle  731 , maxWeight 2  is the weight limit for axle  732 , and totalWeight is the total weight of the load. The position of the center of gravity can be between the positions of minCOG and maxCOG, which can provide the range of positions for the center-of-gravity constraints. For heavier loads, the range of positions is smaller, converging on the center point between axles  731  and  732  of trailer  720 . For lighter loads, the range of positions is larger, and for loads that are light enough, the position can be anywhere in the trailer. 
     Once the center-of-gravity constraints have been determined for the trailer for the load based on the orders for the route, the load design can be generated, which can generate floor spot assignments for the stacks in the orders. For example, each stack can be assigned a particular floor spot in the trailer. These floor spot assignments for the stacks can be subject to satisfying the sequence-of-delivery constraints and center-of-gravity constraints. These floor spot assignments can be based on the type of trailer. For example, some trailers are “dry” trailers, which a single compartment trailers that can carry “dry” (non-refrigerated and non-frozen) items. Other trailers are tri-temp trailers, which can include three compartments that can each be at a different temperature range. For many of the tri-temp trailers, the size of each compartment is variable, within ranges, based on separators that can be adjusted to different positions. Adjusting the separators to increase the size of one of the compartments can affect range of sizes available for one or more of the other compartments. For many of the tri-temp trailers, the temperature range for each of the compartments can be adjusted to the desired temperature range, such as frozen, refrigerated, or “dry.” 
     In many embodiments, when the trailer is a dry trailer, the floor spot assignments for the stacks can be assigned based at least in part on a quantity of the one or more of the orders in the load. For example, when the quantity of the one or more of the orders in the load is equal to one, the floor spot assignments can place the stacks that are heaviest in a middle of the trailer.  FIG.  8    illustrates a top, rear, left side perspective view of a load  800  in a trailer. The trailer can include a front region  810 , a middle region  820 , and a rear region  830 . Load  800  can include stacks, such as stack  801 . The largest and heaviest stacks of load  800  are positioned in middle region  820 , closest to the center point between the axles, between front region  810  and rear region  830  of the trailer. 
     When the quantity of the one or more of the orders in the load is equal to two, the floor spot assignments place the stacks associated with a first stop in descending weight order and can place the stacks associated with a last stop in ascending weight order. The first stop can be the first stop in the sequence of deliveries, and the stacks associated with the order associated with the first stop can be placed in the rear portion (e.g., approximately rear half) of the trailer, in a manner such that the weight of the stacks is descending when moving front-to-rear in the trailer (e.g., heaviest to lightest). The last stop can be the last stop in the sequence of deliveries, and the stacks associated with the order associated with the last stop can be placed in the front portion (e.g., approximately front half) of the trailer, in a manner such that the weight of the stacks is ascending when moving front-to-rear in the trailer (e.g., lightest to heaviest). 
     When the quantity of the one or more of the orders in the load is equal to three, the floor spot assignments can place the stacks associated with a first stop (e.g., in the rear of the trailer) in descending weight order, can place the stacks associated with a second stop that are heaviest in a middle of the trailer, and place the stacks associated with a last stop (e.g., in the front of the trailer) in ascending weight order. In several embodiments, when the load design results in empty floor spots at the front and/or the rear of the trailer, padding can be added in these floor spots to secure the load and prevent frontward or rearward shifting of the load during transit. 
     By arranging the positions of the stacks based on the individual weights of the stacks, while center-of-gravity can be positioned near the center point between the axles. As part of generating the load design, the load design can be verified that the floor spot assignments in fact keep the center of gravity of the trailer within the center-of-gravity constraints for the trailer. Additionally, the load design can be verified that the floor spots assignments maintaining the sequence of deliveries, so that the stacks associated with order are positioned in a manner that the stacks for the order to be delivered at the first stop on the route are at the rear of the trailer, and the stacks for the orders for each subsequent stop are positioned immediately frontward of the stacks for the previous stop. This approach can handle the first-in-first-out manner of loading and unloading from the rear for the trailers. 
     In some embodiments, when the trailer is a tri-temp trailer, the floor spot assignments for the stacks can be determined based at least in part on a quantity of different temperature ranges associated with the one or more of the orders in the load. For example, when all of the stacks in the load are for a single temperature range (e.g., all frozen, or all refrigerated, or all dry), the load design can be treated the same as a “dry” trailer, as there is effectively a single compartment, even if there are multiple actual compartments, because each of the actual compartments will be at the same temperature range. 
     When there are two different temperature ranges for the stacks in the load, the stacks are separated into the three compartments with a first group of the stacks for a first temperature range in one or two of the compartments, and a second group of the stacks (e.g., those remaining after removing the first portion) in the other one or two compartments. Both compartments can be set to the same temperature range for the group that is in two compartments. Generally, in a tri-temp trailer, the compartment with the largest possible capacity is smaller than the combined capacity of the second-largest and third-largest compartments. With these types of tri-temp trailers, as long as the number of stacks in the larger of the two groups of stacks fits within the combined capacity of the second-largest and third-largest compartments, the load design can satisfy compartment capacity constraints. 
     When there are three different temperature ranges for the stacks in the load, the stacks are separated into the three compartments with a first group of the stacks for a first temperature range in one of the compartments, a second group of the stacks in a second one of the compartments, and a third group of the stacks in the remaining compartment. As long as the number of stacks in the largest of the three groups of stacks fits within the capacity of the largest compartment, the number of stacks in the second-largest of the three groups of stacks fits within the capacity of the second-largest compartment, and the number of stacks in the third-largest of the three groups of stacks fits within the capacity of the third-largest compartment, the load design can satisfy compartment capacity constraints. For a tri-temp trailer with one, two, or three different temperature ranges, the load also can be verified to satisfy the center-of-gravity constraints for the trailer. 
     Turning ahead in the drawings,  FIG.  9    illustrates a flow chart for a block  440  of route optimizing, according to the embodiment of  FIG.  4   . Block  440  is merely exemplary and is not limited to the embodiments presented herein. Block  440  can be employed in many different embodiments or examples not specifically depicted or described herein. In some embodiments, the procedures, the processes, and/or the activities of block  440  can be performed in the order presented. In other embodiments, the procedures, the processes, and/or the activities of block  440  can be performed in any suitable order. In still other embodiments, one or more of the procedures, the processes, and/or the activities of block  440  can be combined or skipped. 
     Referring to  FIG.  9   , block  440  can include a block  910  of route construction. In many embodiments, block  910  of route construction can involve receiving an input the stack building plan output from block  420  ( FIG.  4   ) of stack building. For example, the input can be a set of orders to be delivered to physical stores from a distribution center, and the stacks that will be used to deliver the orders. In a number of embodiments, the stack building plan can specify stack groups, which can be sets of stacks that are to be delivered in the same load. For example, an order can be split for delivery across multiple loads to be delivered on different routes, but stacks in the same stack group can be kept in the same load. 
     In several embodiments, splitting orders across multiple loads can beneficially result in using fewer overall loads to deliver the orders. For example, for trailers that have a floor capacity of 30, meaning they can carry 30 stacks, there can be three trailers used to ship three orders in which the first of the three orders contains 16 stacks, the second of the three orders contains 17 stacks, and the third of the three orders contains 18 stacks. A single trailer with a floor capacity of 30 cannot carry any two of these orders in their entirety, so if none of the orders are split, the fewest number of trailers (with a floor capacity of 30) used to delivery these three orders is 3 trailers. By splitting these order, such as splitting the first order into a first suborder of 9 stacks and a second suborder of 7 stacks, splitting the second order into a first suborder of 9 stacks and a second suborder of 8 stacks, and splitting the third order into a first suborder of 9 stacks and a second suborder of 9 stacks, the three orders can be delivered using 2 trailers with a floor capacity of 30, as the first trailer can include the first suborder of each order, which would include a total 27 stacks, and the second trailer can include the second suborder of each order, which would include of 24 stacks. Although two trailers would be used to deliver the orders to each of the physical stores, the number of total trailers used can be reduced. Splitting loads can beneficially save on total delivery costs, particularly when most of the orders include around 16-20 stacks. 
     In many embodiments, block  910  of route construction can include a block  911  of instance categorization. In many embodiments, block  911  of instance categorization can include categorizing the orders into (a) orders in which route construction for the orders can be handled using greedy algorithms, in which case the flow of block  910  can proceed to a block  912  of greedy algorithms, and (b) orders in which route template generation using mixed integer programming can be beneficial, in which case the flow of block  910  can proceed to a block  913  of route template generation. In a number of embodiments, orders that can be handled using greedy algorithms can be smaller orders (e.g., less than half of the floor spots of a trailer) in which the routes for delivering the orders can be determined using conventional greedy algorithms. In many embodiments, orders that can be handled using route template generation can be routes that are larger (e.g., more than half of the floor spots of a trailer), which can benefit, in some cases, from splitting the orders. 
     In a number of embodiments, block  912  of greedy algorithms can perform conventional greedy algorithms that are used to address the class of problems known as the vehicle routing problem (VRP) to assign orders to routes. 
     In many embodiments, block  913  of route template generation can generate a set of feasible route templates that can be used, based on the physical stores that have submitted the orders. In many embodiments, block  913  of route template generate can be similar or identical to block  1110  ( FIG.  11   , described below). 
     In some embodiments, the flow of block  910  can proceed after block  913  to either a block  914  of stack group to route template assignment MIP (mixed integer programming), or instead to a block  915  of order to route template assignment MIP, followed by a block  916  of order splits. These two separate flow paths can be different approaches of assigning orders to route templates. In several embodiments, block  914  of stack group to route template assignment MIP can involve using the stack groups of the orders as inputs, and assigning the stack groups to route templates. By contrast, block  915  of order to route template assignment MIP can involve assigning entire orders to route templates, then proceeding to block  916  of order splits to split the orders and adjust the assignments to achieve improvements. In some embodiments, block  914  can be used for orders that involve dry trailers, and blocks  915  and  916  can be used for orders that involve tri-temp trailers. Blocks  914  and  915  can both use MIP formulations, but these formulations can be different. In many embodiments, block  914  of stack group to route template assignment MIP can be similar or identical to blocks  1115  and  1120  ( FIG.  11   , described below). 
     In a number of embodiments, the flow of block  910  can proceed, after block  912 , block  914  and/or block  916  to a block  917  of route construction, which can involve assembling the routes and/or route template assignments generated in block  912 , block  914  and/or block  916 , to be used as output of block  910  of route construction. 
     In several embodiments, block  440  also can include a block  920  of route improvement. In many embodiments, the route template assignments generated in block  910  of route construction can be input into block  920  of route improvement, which can involve using various approaches to improve the route template assignments created in block  910  of route constructions. For example, block  920  of route improvement can include a block  921  of meta-heuristic framework, which can involve using a simulated annealing approach to improve the route template assignments. As another example, block  910  of route improvement can include a block  922  of neighborhood search, which can involve performing conventional neighborhood search algorithms to improve the route template assignments. 
     In a number of embodiments, block  440  additionally can include a block  930  of services. In a number of embodiments, various elements of block  440  can make a call to block  930  of services, which can include a block  931  of heuristics for load design and/or a block  932  of hours of service (HOS) validation. In some embodiments, block  931  of heuristics for load design can include various heuristics that can be called to assist with determining various aspects, such as what type of trailer to use, loading pattern selections, and/or other suitable heuristics. In many embodiments, block  932  of HOS validation can involve determining whether a route template is feasible based on rules, such as HOS rules promulgated by various agencies, such as the U.S. DOT. In a number of embodiments, block  932  of HOS validation can involve customizing (e.g., optimizing) route templates to be feasible, which can be similar or identical to implementation of block  932  shown in  FIG.  10    and described below, and/or method  1200  ( FIG.  12   , described below). In many embodiments, block  932  of HOS validation can be called many times, such as each time a route is considered while performing block  913  of route template generation, and/or by other suitable blocks of block  440 . 
     Turning ahead in the drawings,  FIG.  10    illustrates a flow chart for a block  932  of HOS validation, according to the embodiment of  FIG.  9   . Block  932  is merely exemplary and is not limited to the embodiments presented herein. Block  932  can be employed in many different embodiments or examples not specifically depicted or described herein. In some embodiments, the procedures, the processes, and/or the activities of block  932  can be performed in the order presented. In other embodiments, the procedures, the processes, and/or the activities of block  932  can be performed in any suitable order. In still other embodiments, one or more of the procedures, the processes, and/or the activities of block  932  can be combined or skipped. 
     Referring to  FIG.  10   , block  932  can include a block  1010  of receiving inputs, such as a pickup and delivery sequence  1011 , driving times  1012 , delivery time windows  1013 , rules  1014 , and/or other suitable inputs. In a number of embodiments, pickup and delivery sequence  1011  can specify the sequence of pickups and deliveries in the route template. For example, the route template can start at a distribution center, such as Distribution Center 1 (DC1), then proceed to a physical store Store 1 (S1), then proceed to a physical store Store 3 (S3), then return to DC1. Each of pickup and delivery sequence  1011  can be a separate route template generated in block  913  ( FIG.  9   ) of route template generation. 
     In several embodiments, driving times  1012  can be include about how long it takes to drive between each pair of stops in pickup and delivery sequence  1011 . For example, driving times  1012  can include peak (e.g., rush hour) and/or off-peak (non-rush hour) driving times for driving between DC1 and S1, between S1 and S3, and between S3 and DC1, for example. 
     In a number of embodiments, delivery time windows  1013  can include information about when each of the physical stores allows the delivery to be made, which can be specified by the physical stores. For example, S1 can have a delivery time window of 14:00-19:00, and S3 can have a delivery time window of 11:00-17:00. 
     In several embodiments, rules  1014  can be HOS rules specified by a compliance authority, business rules, and/or other suitable rules. In a number of embodiments, rules  1014  can specify which set of rules to use when the service has already pre-processed one or more sets of rules. 
     In several embodiments, block  932  also can include a block  1020  of processing. In a number of embodiments, block  1020  of processing can provide a response in real-time to determine if a route template is feasible for delivery sequence  1011 , when provided with driving times  1012 , delivery time windows  1013 , and rules  1014 . If the route template is feasible, in a number of embodiments, block  1020  of processing can generate a sequence of driver states with associated times for the route template. 
     In many embodiments, block  1020  can include a block  1021  of rule abstraction. In a number of embodiments, a set of rules, such as HOS rules provided by the DOT, can be abstracted to create drive rules, which can be based on driver states. In some embodiments, types of driver states can be defined hierarchically, such as follows:
     NON-SLEEP (ANY)
       ON-DUTY (NON-SLEEP)
           SERVICE (ON-DUTY)   DRIVE (ON-DUTY)   WAIT (ON-DUTY)   
           BREAK (NON-SLEEP)   
       LAYOVER (ANY)   

     On each row, a driver state type can be followed by a parenthetical, which can specify the driver state type that is the parent of the driver state type on that row, based on the hierarchy of driver state types. These driver state types can be defined hierarchically to accommodate the rules provided by the DOT, which also are hierarchical. For example, a DOT rule can be that a driver must take a break after 8 hours on duty. Any of the driver state types of service, drive, and wait would qualify as being on duty under the hierarchical definition above. 
     In several embodiments, one or more drive rules can be used to represent the DOT rules. In a number of embodiments, a drive rule can include a rule identifier, a minimum duration, a maximum duration, a, applied driver state type, and/or a stop driver state type. In several embodiments, the drive rules can be duration rules and/or cumulative rules. In many embodiments, a duration rule does not include a stop driver state type, but a cumulative rule does include a stop driver state type. As an example, a DOT rule can be that “if more than 8 consecutive hours have passed since the last off-duty (or sleeper berth), you must take an off-duty break of at least 30 minutes before driving.” This DOT rule can be represented as the following two drive rules, each of which are duration rules: 
     Drive Rule 1
         Rule Identifier: “ON-DUTY-LIMIT”   Minimum Duration: 0   Maximum Duration: 8 hours   Applied Driver State Type: ON-DUTY       

     Drive Rule 2
         Rule Identifier: “BREAK”   Minimum Duration: 30 minutes   Maximum Duration: max   Applied Driver State Type: BREAK       

     As another example, another DOT rule can be that a driver is “allowed a period of 14 consecutive hours in which to drive up to 11 hours after being off duty for 10 or more consecutive hours. This DOT rule can be represented as the following three drive rules, the first two of which are duration rules, and the last of which is a cumulative rule: 
     Drive Rule 1
         Rule Identifier: “NON-SLEEP-LIMIT”   Minimum Duration: 0   Maximum Duration: 14 hours   Applied Driver State Type: NON-SLEEP       

     Drive Rule 2
         Rule Identifier: “LAYOVER”   Minimum Duration: 10 hours   Maximum Duration: max   Applied Driver State Type: LAYOVER       

     Drive Rule 3
         Rule Identifier: “CUMULATIVE-DRIVE-LIMITS”   Minimum Duration: 0   Maximum Duration: 11 hours   Applied Driver State Type: DRIVE   Stop Driver State Type: LAYOVER       

     In several embodiments, block  1021  of rule abstraction can be performed offline in pre-processing, such that the set of drive rules can be selected and used in later online processing, such as in blocks  1023  and/or  1024 , described below. 
     In a number of embodiments, block  1020  of processing can include a block  1022  of rule validation. In many embodiments, block  1022  of rule validation can include defining how a drive rule can be validated. For example, for a drive rule that is a cumulative rule, the validation can involve iterating through each driver state, and determining a cumulative duration 0 while the driver state is within the Applied Driver State Type, until the driver state is the Stop Driver State Type. The drive rule can be validated when θ∈[θ min , θ max ], where θ min  is the Minimum Duration defined by the drive rule, and θ max  is the Maximum Duration defined by the drive rule. For a drive rule that is a duration rule, the validation can involve iterating through each driver state, and determining a cumulative duration 0 while the driver state is within the Applied Driver State Type, until the driver state is not within the Applied Driver State Type. The drive rule can be validated when θ∈[θ min , θ max ], where θ min  is the Minimum Duration defined by the drive rule, and θ max  is the Maximum Duration defined by the drive rule. 
     In several embodiments, block  1022  of rule validation can be performed offline in pre-processing, such that the validation procedures can be used in later online processing, such as in blocks  1023  and/or  1024 , described below. 
     In a number of embodiments, block  1020  of processing can include a block  1023  of action recommendation. In many embodiments, block  1023  of action recommendation can include apply process each segment of a pair of driver states that occurs in pickup and delivery sequence  1011 . For example, pickup and delivery sequence  1011  for a route template can be DC1, S1, S3, DC1, as described above. Pickup and delivery sequence  1011  can be converted into a sequence of driver states that will be involved in implementing pickup and delivery sequence  1011 . For example, the sequence of driver states can be Drive (0), Service (DC1, load), Drive (DC1 to S1), Service (S1, unload), Drive (S1 to S3), Service (S3, unload), Drive (S3 to DC1), Service (DC1). A segment can be a sequential pair of driver states, such as Service (DC1, load), Drive (DC1 to S1). 
     In many embodiments, block  1023  also can involve receiving pre-drive conditions for each segment. For example, the pre-drive conditions can include a Pre-Drive condition (D prev ), which can indicate how long the driver has been in the driver state of DRIVE when the segment begins. As another example, the pre-drive conditions can include a Pre-On-Duty condition (OD prev ), which can indicate how long the driver has been in the driver state of ON-DUTY when the segment begins. As yet another example, the pre-drive conditions can include a Pre-Non-Sleep condition (NS prev ), which can indicate how long since the driver has been in the driver state of LAYOVER when the segment begins. 
     In a number of embodiments, block  1023  can involve outputting a recommendation of a driver state to add at a time t. For example, the driver state to add can be one of BREAK (B), LAYOVER (L), or WAIT (W). In many embodiments, the recommendations to add one of these driver states can be made to satisfy the drive rules when a drive rule is violated, for example. For example, block  1023  can include applying logic rules based on the drive rules. As an example, a state time st D  for a driver state of DRIVE (D) and/or a start time st s  for a driver state of SERVICE (S) can be calculated for the segment, a recommendation can be generated to add a wait W if necessary in order to satisfy the service time window for associated with the service driver state. As another example, the ON-DUTY-LIMIT rule can be applied to the segment, and if the rule is violated, a recommendation can be generated to add a break B at a time t, where t=st D +(θ max −OD prev ). As yet another example, a DRIVE rule can be applied to the segment, and if the rule is violated, a recommendation can be generated to add a layover L at a time t, where t=st D +(θ max −D prev ). As a further example, the NON-SLEEP-LIMIT rule can be applied to the segment, and if the rule is violated, a recommendation can be generated to add a layover L at a time t, where t=st D +(θ max −NS prev ). 
     In a number of embodiments, block  1020  of processing can include a block  1024  of action implementation. In many embodiments, block  1024  of action implementation can include determining whether a recommendation to add a new state (NS) at a time t that was generated in block  1023  can be implemented, and if so, adding the new state at the time t. In many embodiments, the input to block  1024  can include the set of driver states in the segment, the new state NS that is recommended, and the time t. In several embodiments, the output can be an updated set of driver states. In some embodiments, if the new state NS cannot be added at time t, block  1024  can determine whether a different new state NS can be added that can be feasible under the drive rules. 
     For example, block  1024  can include applying logic rules based on the driver states in the segment and the recommended new state NS. As an example, if time t is in the middle of a driver state of DRIVE (D), the driver state of D can be split into two parts, in which a duration for the first part, D1 duration =X−st D , and a duration for the second part, D2 duration =X+NS duration , where NS duration  is the duration of the new state NS, where X is time t. As another example, if time t is in the middle of a driver state of WAIT (W), let X′=min(st NS , max(st W ,(et W −NS duration )), where X′ is a temporary variable, st NS  is a start time of the new state NS, st W  is a start time of the W driver state, and et W  is an end time driver state W. As an additionally example, if time t is in the middle of a driver state of SERVICE (S), let X′=et previous state of drive state S ), and et previous state of driver state S  is the end time of the previous state of driver state S. As a further example, if time t is in the middle of a driver state of BREAK (B), and the new state NS is B, the action can be to do nothing. As an additional example, if time t is in the middle of a driver state of BREAK (B), and the new state NS is L, the action can be replace the B with L. As a further example, if time t is in the middle of a driver state of LAYOVER (L), the action can be to do nothing. 
     In a number of embodiments, block  1024  can improve the route template by adding new states in an intelligent manner. In several embodiments, block  1023  and block  1024  can be performed for each of the segments in a pairwise analysis of driver states. In a number of embodiments, block  1023  and block  1024  can be performed iteratively. In many embodiments, when a new state NS is added in a segment, there can be two new pairs, which can then be analyzed under block  1023  of action recommendation. In many embodiments, if a drive rule is violated, and there is no action recommendation made in order to satisfy the drive rule, then the route template can be infeasible. In a number of embodiments, there can be multiple iterations of attempts to make a segment feasible. In several embodiments, the number of iterations can be limited at a threshold, such as 100 iterations, after which the segment can be determined to be infeasible. 
     In a number of embodiments, block  932  additionally can include a block  1030  of responding with an output. The output can be that the route is not feasible, or if the route is feasible, including the sequence of driver states that are associated with the route template. For example, an output can be similar to the output shown in Table 2 below. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                   
                 Service 
                 Service 
               
               
                   
                 Start 
                 End 
                 Window 
                 Window 
               
               
                 Driver State 
                 Time 
                 Time 
                 Start 
                 End 
               
               
                   
               
             
            
               
                 SERVICE (DC1) 
                  9:00 
                 10:00 
                   
                   
               
               
                 DRIVE (DC1 to S1) 
                 10:00 
                 12:00 
               
               
                 WAIT 
                 12:00 
                 14:00 
               
               
                 SERVICE (S1) 
                 14:00 
                 14:50 
                 14:00 
                 19:00 
               
               
                 DRIVE (S1 to S3) 
                 14:50 
                 15:00 
               
               
                 SERVICE (S3) 
                 15:00 
                 15:50 
                 11:00 
                 17:00 
               
               
                 DRIVE 
                 15:50 
                 17:00 
               
               
                 BREAK 
                 17:00 
                 17:30 
               
               
                 DRIVE 
                 17:30 
                 18:00 
               
               
                 BREAK 
                 18:00 
                 19:00 
               
               
                   
               
            
           
         
       
     
     Table 2 shows that various driver states, such as WAIT and BREAK, have been added to the route template to make it feasible under the rules. As another example, an output can be similar to the output shown in Table 3 below. Table 3 shows an example of an intelligent wait that was added in conjunction with a break between 14:00 and 16:00. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                   
                   
                   
                 Service 
                 Service 
               
               
                   
                 Start 
                 End 
                 Window 
                 Window 
               
               
                 Driver State 
                 Time 
                 Time 
                 Start 
                 End 
               
               
                   
               
             
            
               
                 WAIT 
                  8:00 
                  9:00 
                   
                   
               
               
                 SERVICE (S1) 
                  9:00 
                 10:00 
                  9:00 
                 10:00 
               
               
                 DRIVE (S1 to S3) 
                 10:00 
                 14:00 
               
               
                 WAIT 
                 14:00 
                 15:30 
               
               
                 BREAK 
                 15:30 
                 16:00 
               
               
                 SERVICE (S3) 
                 16:00 
                 17:00 
                 16:00 
                 19:00 
               
               
                 DRIVE 
                 17:00 
                 22:00 
               
               
                 LAYOVER 
                 22:00 
                  8:00 
               
               
                 DRIVE 
                  8:00 
                  9:00 
               
               
                 SERVICE (DC1) 
                  9:00 
               
               
                   
               
            
           
         
       
     
     In a number of embodiments, block  932  of HOS validation can advantageously provide a fast heuristic algorithm to check for feasibility and generate driver states to make the route template feasible, if possible. In many embodiments, the HOS validation can be performed in real-time, which can make it possible to evaluate thousands or even millions of possible route templates. In a number of embodiments, the wait time can be minimized under the rules which can lower cost. In several embodiments, the processing framework in block  1020  of processing can use a generalized design that can apply for multiple different sets of rules, and/or can be used to readily adapt to ever-changing rules. In many embodiments, the HOS validation can perform the pairwise comparison and generate new states in a greedy way, which may not be optimal, but can validate feasible route templates and customizations that provide some intelligence to lower overall durations and/or wait times, while being performed in real-time. 
     Turning ahead in the drawings,  FIG.  11    illustrates a flow chart for a method  1100 , according to an embodiment. In some embodiments, method  1100  can be a method of constructing route templates for trailers that include an assignment of stack groups, according to an embodiment. Method  1100  is merely exemplary and is not limited to the embodiments presented herein. Method  1100  can be employed in many different embodiments or examples not specifically depicted or described herein. In some embodiments, the procedures, the processes, and/or the activities of method  1100  can be performed in the order presented. In other embodiments, the procedures, the processes, and/or the activities of method  1100  can be performed in any suitable order. In still other embodiments, one or more of the procedures, the processes, and/or the activities of method  1100  can be combined or skipped. 
     In many embodiments, system  300  ( FIG.  3   ), load and route design system  300  ( FIG.  3   ) can be suitable to perform method  1100  and/or one or more of the activities of method  1100 . In these or other embodiments, one or more of the activities of method  1100  can be implemented as one or more computing instructions configured to run at one or more processors and configured to be stored at one or more non-transitory computer readable media. Such non-transitory computer readable media can be part of system  300 . The processor(s) can be similar or identical to the processor(s) described above with respect to computer system  100  ( FIG.  1   ). 
     In some embodiments, method  1100  and other blocks in method  1100  can include using a distributed network including distributed memory architecture to perform the associated activity. This distributed architecture can reduce the impact on the network and system resources to reduce congestion in bottlenecks while still allowing data to be accessible from a central location. 
     Referring to  FIG.  11   , method  1100  can include a block  1105  of obtaining orders for fulfillment to physical stores from a distribution center. The physical stores can be similar or identical to physical stores  360  ( FIG.  3   ). The distribution center can be similar or identical to distribution center  350  ( FIG.  3   ). In many embodiments, there can be one or more respective stack groups associated with each of the orders. Each stack group can include one or more stacks, such that the stacks in a stack group can be kept together in a single load for delivery. For example, an order for a physical store can indicate that various items and/or pallets ordered are to be kept together. The stacks can be the output from the stack building, such as block  420  ( FIG.  4   ) of stack building, for example. in many embodiments, the orders can be the orders received at a distribution center for next day delivery to physical stores, for example. 
     In a number of embodiments, method  1100  also can include a block  1110  of generating a set of feasible route templates for delivering the orders to the physical stores. 
     In several embodiments, block  1110  of generating a set of feasible route templates for delivering the orders to the physical stores optionally can include a block  1111  of generating a set of routes having one stop for the each first physical store, wherein the set of routes having one stop comprises a respective single route having the each first physical store. For example, there can be a set S of physical stores that have submitted orders. For each physical store S i  in set S, a one-stop route, r1, can be created such that r1={D→S i →D}, where D represents the distribution center, such that route r1 is a route from the distribution center D to physical store S i , then back to the distribution center D. there can be one route for each physical store S i . 
     In a number of embodiments, block  1110  of generating a set of feasible route templates for delivering the orders to the physical stores additionally and optionally can include a block  1112  of iterating through a respective number of stops from 2 up to a predetermined limit of stops by generating a set of routes each having the respective number of stops by adding, to one or more respective routes in a set of routes having one fewer stop than the respective number of stops, respective additional physical stores that satisfies a distance condition. In a number of embodiments, the distance condition can be based at least in part on a distance of a respective additional physical store of the respective additional physical stores to the distribution center being greater than a distance of the each first physical store to the distribution center. In several embodiments, the distance condition can be based at least in part on a distance of a respective additional physical store of the respective additional physical stores to the respective route having one fewer stop than the respective number of stops. 
     In many embodiments, a respective quantity of the respective additional physical stores to add to respective routes can be based on a respective predetermined limit for the respective number of stops. In some embodiments, the predetermined limit of stops can be 2, 3, 4, 5, or another suitable number. 
     For example, for adding a second physical store S; to create a two-stop route, any store S n  in which Dist{D,S n }&lt;Dist{D,S j } can be excluded, where Dist{ } is the distance between the two inputs. In many embodiments, excluding such stores can ensure that the first store in the route is the closest store to the distribution center among the stores in the route, which can satisfy a business condition. 
     In a number of embodiments, after excluding such stores, a first iteration can involve generating two-stop routes using the one-stop routes. In several embodiments, for each store S i , the K1 th closest stores S j  to route r1 j  can be determined, and K1 two-stop routes r2 j ={D→S i →S j →D} can be generated. K1 can be a design parameter. In many embodiments, the closest store S j  to route r1 j  can be the store with minimal distance defined as follows: 
       Dist{ S   j   ,r 1}=Dist{ D,S   i }+Dist{ S   i   ,S   j }−Dist{ D,S   j }
 
     Similarly, the iterations can continue. For example, for each store S j , the K2 th closest stores S k  to route r2 j  can be determined, and K1×K2 three-stop routes r3 k ={D→S i →S j →S k →D} can be generated. K2 can be a design parameter. Similarly, for each store S k , the K3 th closest stores S m  to route r3 k  can be determined, and K1×K2×K3 four-stop routes r4 m ={D→S i →S j →S k →S m →D} can be created. K1 can be a design parameter. In many embodiments, these iterations can continue to the predetermined limit of stops. 
     In various embodiments, block  1110  of generating a set of feasible route templates for delivering the orders to the physical stores further can include, for each route of the sets of routes for the respective numbers of stops from 1 to the predetermined limit of stops, determining if the each route is feasible based at least in part on a respective sequence of stops for respective physical stores of the physical stores in the each route, respective service time windows for the respective physical stores in the each route, and hours-of-service rules. In many embodiments, block  932  ( FIGS.  9 ,  11   ) and/or of HOS validation method  1200  ( FIG.  12   ) can be used to determine if the route is feasible. In many embodiments, block  1110  can create many possible routes for the physical stores, such as a set of routes R i  for each physical store S i . 
     In several embodiments, method  1100  also can include a block  1115  of formulating a MIP formulation for an assignment of the respective stack groups associated with the orders to the set of route templates. Some of the route templates generated in block  1110  can be matched to stack groups, based on the MIP formulation. In some embodiments, the mixed integer programming formulation for the assignment can be based at least in part on a predetermined quantity limit of the two or more respective routes for splitting an order of the one or more orders. In several embodiments, the mixed integer programming formulation for the assignment can be based at least in part on a predetermined size threshold for each respective split order of the each of the one or more orders. In many embodiments, the mixed integer programming formulation for the assignment can be based at least in part on a quantity of trailers that are available to deliver the orders, a respective floor spot capacity for each of the trailers, a respective weight capacity for each of the trailers, respective dimension limits for each of the trailers, and/or other suitable inputs. In a number of embodiments, the assignment can include splitting each of one or more orders of the orders across two or more respective routes of the set of feasible routes. 
     In some embodiments, the MIP formulation can determine an assignment of stack groups to route templates with the objective of minimizing route cost. For example, in some embodiments, the following a first decision variable X s   r  can be defined as follows:
         X s   r  is 1 if stack group s∈S is assigned to route r∈R s ; 0 otherwise.       

     A second decision variable Y O   r  can be defined as follows:
         Y O   r  is 1 if order o∈O is assigned to route r∈R o ; 0 otherwise.       

     A third decision variable Z r  can be defined as follows:
         Z r  is 1 if route r∈R is open—has stack group assigned to it; 0 otherwise.       

     A fourth decision variable U r   t  can be defined as follows:
         U r   t  1 if route r∈R chooses to use trailer type t∈T r ; 0 otherwise.       

     A fifth decision variable L s  can be defined as follows:
         L s  is 1 if stack group s∈S is not assigned to any route; 0 otherwise.       

     In a number of embodiments, an objective function for the MIP formulation can be defined as follows, which can minimize an overall cost of the routes plus a penalty for any stack groups that are not assigned to a route: 
       Minimize Σ r∈R   C   r   ×Z   r +Σ s∈S Penalty s   ×L   s  
 
     In several embodiments, various constraints can be applied in the MIP formulation, such as the following constraints: 
         Z   r∈R     s     X   s   r   +L   s =1 ∀ s∈S   (1)
 
       Σ s∈S   X   s   r   ≤M×Y   o   r  ∀ o   ∈O,r∈R   o   (2)
 
       Σ o∈O     r      Y   o   r   ∥O   r   ∥×Z   r    ∀r∈R   (3)
 
         Z   r∈R     s     X   s   r ≤MaxSplitNumber o    ∀o∈O,s∈S   o   (4)
 
         Z   s∈S     o   Cube s   ×X   s   T ≥MinSplitSize o    ∀O∈O,r∈R   o   (5)
 
       Σ t∈T     r     U   t   r =1 ∀ r∈R   (6)
 
         Z   r∈R     t      U   t   r ≤MaxNumber t    ∀t∈T   (7)
 
       Σ s∈S     r      FS   s   ×X   s   r ≤Σ t∈T     r    CapSpot t   ×U   t   r    ∀r∈R   (8)
 
         Z   s∀S     r    Weight s   ×X   s   r ≤Σ t∈T     r    CapWeight t   ×U   t   r    ∀r∈R   (9)
 
       Σ sES     r     Cub   s   ×X   s   r ≤ t∈T     r     ×U   t   r    ∀r∈R   (10)
 
     where the sets are defined as follows:
 
S=Set of stack groups,
 
O=Set of orders (a stack groups placed by the same store and potential can ride on the same routes),
 
R=Set of routes,
 
S o =Set of stack groups belongs to the same order o,
 
S r =Set of stack groups can potentially ride on route r,
 
R s =Set of routes a stack group s can potential ride on,
 
R o =Set of routes an order o can potential ride on,
 
R t =Set of routes a trailer type t can use (e.g., different lengths of trailers),
 
O r =Set of orders on a route r,
 
∥O r ∥=size of the set O r ,
 
R=Set of trailer types, and
 
T r =Set of trailer types a route r can potentially use,
 
and where the parameters are defined as follows:
 
C r  is the cost of a route r∈R,
 
FS s  is the floor spots a stack group s∈S takes,
 
Penalty s  is the penalty cost of not assigning a stack group s∈S to any route,
 
MaxSplitNumber o  is the maximum number of splits for each order o∈O,
 
MinSplitSize o  is the minimum size of the sub-orders if order o∈O is split,
 
MaxNumber t  is the available number of trailers with trailer type t,
 
CapSpot t  is the floor spot capacity of trailer type t,
 
CapWeight t  is the weight capacity of trailer type t,
 
CapCube t  is the cubic volume capacity of trailer type t,
 
Cube s  is the cube volume of a stack group s, and
 
Weight s  is the weight of a stack group s,
 
     In many embodiments, constraint 1 above can impose a constraint such that each stack group is only assigned to one route. In several embodiments, constraint 2 above can be used to derive the second decision variable, Y O   r . In a number of embodiments, constraint 3 above can be used to derive the third decision variable, Z r , and if a route is open (e.g., selected for assignment), used to ensure that the orders use this route. In various embodiments, constraint 4 above can be used to constrain split orders such that a maximum number of splits for each order, which can be configurable as a design parameter, such as 2, 3, or 4, for example. In several embodiments, constraint 5 above can constrain split order such that there is a minimal split size for each sub-order, such as 3, 4, 5, 6, 7, 8, 9, or 10 stacks, for example. In a number of embodiments, constraint 6 above can impose a constraint such that each route can choose a single trailer type. In some embodiments, constraint 7 above can impose a constraint such that a trailer type has a finite number of trailers available. In some embodiments, constraint 8 above can impose a capacity constraint on floor spots. In various embodiments, constraint 9 above can impose a capacity constraint on weight. In many embodiments, constraint 10 above can impose a capacity constraint on cubic volume. 
     In a number of embodiments, method  1100  further can include a block  1120  of using an optimization solver for the mixed integer programming formation to determine the assignment that minimizes an overall cost of delivering the orders to the physical stores from the distribution center. In many embodiments, a conventional optimization solver can be used to determine the assignment. For example, the CPLEX Optimization Solver developed by International Business Machines, Inc. of Armonk, N.Y., can be used to solve the MIP formulation. In many embodiments, the optimization solver can be run until convergence or for a present amount of time, such as 3 minutes, 5 minutes, 10 minutes, 15 minutes, or another suitable amount of time. In a number of embodiments, the MIP formulation, when solved can generate an assignment that includes order splits. For example, for an order S100 from a physical store, stack groups 1, 5, and 6 can be assigned to a route template  11 , and stack groups 2, 3, and 4 can be assigned to a route template  23 , which can indicate that order S100 is split across multiple loads on two separate routes. 
     In several embodiments, method  1100  also can include a block  1125  of outputting the assignment. In many embodiments, the assignment can be an assignment of each of the stack groups to a route template. In several embodiments, the assignment can be used as an input for block  920  ( FIG.  9   ) of route improvement, as input for load designer  450  ( FIG.  4   ). 
     Turning ahead in the drawings,  FIG.  12    illustrates a flow chart for a method  1200 , according to an embodiment. In some embodiments, method  1200  can be a method of determining a feasible sequence of driver states for a route template, according to an embodiment. Method  1200  is merely exemplary and is not limited to the embodiments presented herein. Method  1200  can be employed in many different embodiments or examples not specifically depicted or described herein. In some embodiments, the procedures, the processes, and/or the activities of method  1200  can be performed in the order presented. In other embodiments, the procedures, the processes, and/or the activities of method  1200  can be performed in any suitable order. In still other embodiments, one or more of the procedures, the processes, and/or the activities of method  1200  can be combined or skipped. 
     In many embodiments, system  300  ( FIG.  3   ), load and route design system  300  ( FIG.  3   ) can be suitable to perform method  1200  and/or one or more of the activities of method  1200 . In these or other embodiments, one or more of the activities of method  1200  can be implemented as one or more computing instructions configured to run at one or more processors and configured to be stored at one or more non-transitory computer readable media. Such non-transitory computer readable media can be part of system  300 . The processor(s) can be similar or identical to the processor(s) described above with respect to computer system  100  ( FIG.  1   ). 
     In some embodiments, method  1200  and other blocks in method  1200  can include using a distributed network including distributed memory architecture to perform the associated activity. This distributed architecture can reduce the impact on the network and system resources to reduce congestion in bottlenecks while still allowing data to be accessible from a central location. 
     Referring to  FIG.  12   , method  1200  can include a block  1205  of obtaining a sequence of stops and service time windows for the stops. The sequence of stops can be similar or identical to pickup and delivery sequence  1011  ( FIG.  10   ). The service time windows can be similar or identical to delivery time windows  1013  ( FIG.  10   ). 
     In a number of embodiments, method  1200  also can include a block  1210  of generating a sequence of driver states that satisfies the sequence of stops. For example, as described above in connection with block  1023  ( FIG.  10   ), a sequence of stops can be DC1, S1, S3, DC1. The sequence of driver states can for this sequence of stops can be Drive (0), Service (DC1, load), Drive (DC1 to S1), Service (S1, unload), Drive (S1 to S3), Service (S3, unload), Drive (S3 to DC1), Service (DC1). 
     In several embodiments, method  1200  also can include a block  1215  of determining, for each pair of respective sequential driver states from the sequence of driver states, whether to generate a respective recommendation to add a respective additional driver state within the respective sequential driver states in order to satisfy a set of rules. Block  1215  can be similar or identical to block  1023  ( FIG.  10   ) of action recommendation. A pair of sequential driver states can be the pair of Service (DC1, load), Drive (DC1 to S1), for example. 
     In several embodiments, driver state types that apply to the set of rules can be defined hierarchically based on hours of service rules. In a number of embodiments, the respective additional driver state can include one of a break state, a layover state, or a wait state. 
     In many embodiments, the set of rules can include one or more duration rules and one or more cumulative rules. In several embodiments, each of the one or more duration rules can include a respective rule identifier, a respective minimum duration, a respective maximum duration, and a respective applied driver state type. In a number of embodiments, each of the one or more duration rules can include a respective rule identifier, a respective minimum duration, a respective maximum duration, a respective applied driver state type, and a respective stop driver state type. 
     In several embodiments, block  1215  of, determining, for each pair of respective sequential driver states from the sequence of driver states, whether to generate the respective recommendation to add the respective additional driver state within the respective sequential driver states in order to satisfy the set of rules further can include applying a respective duration rule of the one or more duration rules and/or applying a respective cumulative rules of the one or more cumulative rules by perform blocks  1216  and  1217 , described below. 
     In several embodiments, block  1215  of determining, for each pair of respective sequential driver states from the sequence of driver states, whether to generate the respective recommendation to add the respective additional driver state within the respective sequential driver states in order to satisfy the set of rules optionally can include a block  1216  of iterating through the sequence of driver states to determine a cumulative duration for the respective applied driver state type. In a number of embodiments, for the one or more duration rules, the iterating can continue until a respective driver state of the driver sequence of driver states is not within the respective applied driver state type. In several embodiments, for the for the one or more cumulative rules, the iterating can continue until a respective driver state of the driver sequence of driver states is within the respective applied stop driver type. 
     In a number of embodiments, block  1215  of determining, for each pair of respective sequential driver states from the sequence of driver states, whether to generate the respective recommendation to add the respective additional driver state within the respective sequential driver states in order to satisfy the set of rules additionally can include a block  1217  of validating the respective duration rule and/or the respective cumulative rule when the cumulative duration is between the respective minimum duration and the respective maximum duration. 
     In a number of embodiments, method  1200  further can include a block  1220  of updating the sequence of driver states based on the respective recommendations, such that the sequence of driver states is feasible in view of the service time windows and the set of rules. Block  1220  can be similar or identical to block  1024  ( FIG.  10   ) of action implementation. In several embodiments, block  1220  of updating the sequence of driver states based on the respective recommendations further can include, for each of the respective recommendations, determining whether the respective additional driver state can be added at a specified time, and if not, whether to replace the respective additional driver state with a different respective additional driver state. 
     In several embodiments, method  1200  also can include a block  1225  of outputting the sequence of driver states. In a number of embodiments, block  1225  of outputting the sequence of driver states further can include outputting a respective start time and a respective end time for each driver state of the sequence of driver state. The output can be similar or identical to the output returned in block  1030  ( FIG.  10   ) of responding with an output. 
     Jumping ahead in the drawings,  FIG.  16    illustrates a flow chart for a method  1600 , according to an embodiment. In some embodiments, method  1600  can be a method of determining a load design, according to an embodiment. Method  1600  is merely exemplary and is not limited to the embodiments presented herein. Method  1600  can be employed in many different embodiments or examples not specifically depicted or described herein. In some embodiments, the procedures, the processes, and/or the activities of method  1600  can be performed in the order presented. In other embodiments, the procedures, the processes, and/or the activities of method  1600  can be performed in any suitable order. In still other embodiments, one or more of the procedures, the processes, and/or the activities of method  1600  can be combined or skipped. In many embodiments, method  1600  can be similar to block  520 , and can include various acts of block  450  ( FIG.  4   ), block  460  ( FIG.  4   ), block  480  ( FIG.  4   ), and/or block  490  ( FIG.  4   ). 
     In many embodiments, system  300  ( FIG.  3   ), load and route design system  300  ( FIG.  3   ) can be suitable to perform method  1600  and/or one or more of the activities of method  1600 . In these or other embodiments, one or more of the activities of method  1600  can be implemented as one or more computing instructions configured to run at one or more processors and configured to be stored at one or more non-transitory computer readable media. Such non-transitory computer readable media can be part of system  300 . The processor(s) can be similar or identical to the processor(s) described above with respect to computer system  100  ( FIG.  1   ). 
     In some embodiments, method  1600  and other blocks in method  1600  can include using a distributed network including distributed memory architecture to perform the associated activity. This distributed architecture can reduce the impact on the network and system resources to reduce congestion in bottlenecks while still allowing data to be accessible from a central location. 
     Referring to  FIG.  16   , method  1600  can include a block  1605  of obtaining a route for delivering one or more orders in a trailer from a distribution center to physical stores in a sequence of stops. In a number of embodiments, the route can have an associated assignment of stack groups comprising stacks of pallets. For example, the assignment can be similar to the assignment output in block  1225  ( FIG.  12   ). 
     In a number of embodiments, method  1600  also can include a block  1610  of determining a load design for the stacks in the trailer based on the sequence of the stops in the route. In several embodiments, block  1610  of determining the load design for the stacks in the trailer further can include, when the trailer is a dry trailer, determining the load design such that each of the stacks can be unloaded a single time when the trailer delivers the orders to the physical stores. For example, the load design for the dry trailer can be similar or identical to load design  1310  ( FIG.  13   , described below). In many embodiments, block  1610  of determining the load design for the stacks in the trailer further can include, when the trailer is a tri-temp trailer, determining the load design such that unloading each of the stacks is minimized when the trailer delivers the orders to the physical stores. For example, the load design for the tri-temp trailer can be similar or identical to load design  1330  ( FIG.  13   , described below). 
     Turning back in the drawings,  FIG.  13    illustrates top plan views of a load design  1310  for a dry trailer and a load design  1330  for a tri-temp trailer. As shown in load design  1310  in  FIG.  13   , a dry trailer can include various stacks, such as stacks  1311 - 1324 . Stacks  1311 - 1324  can be in a single compartment of the trailer at the same temperature. In many embodiments, stacks  1311 - 1324  can be from separate orders, to be delivered at different physical stores (e.g.,  360  ( FIG.  3   )). For example, stacks  1311 - 1313  can be for part or all of an order A, stacks  1314 - 1318  can be for part or all of an order B, and stacks  1319 - 1324  can be for part or all of an order C. In order to eliminate unloading and reloading of stacks, stacks  1311 - 1313  for order A can be loaded first (at the front of the trailer, which is on the left side of  FIG.  13   ) because these stacks will be delivered at the last stop of the route, stacks  1314 - 1318  for order B can be loaded second because these stacks will be delivered at the second to last stop of the route, and stacks  1319 - 1324  for order C can be loaded last because these stacks will be delivered at the first stop of the route. In a number of embodiments, the number of stacks that can fit in a trailer can be based on the number of floor spots in the trailer, the dimensions (e.g., width, length, height) of the trailer, the number of stacks, and/or the dimensions of the stacks. 
     As shown in load design  1330  in  FIG.  13   , a tri-temp trailer can include various stacks, such as stacks  1331 - 1354 , which can be loaded in three separate compartments  1351 - 1353  in the trailer, each set for a different temperature. The compartments (e.g.,  1351 - 1351 ) can be separate by bulkheads, such as bulkheads  1354 - 1355 . The bulkheads (e.g.,  1354 - 1355 ) can be adjustable in position, such that a front-to-rear position of bulkhead  1354  can be located within a range  1356 , and a front-to-rear position of bulkhead  1355  can be located within a range  1357 . The adjustability of the position of the bulkheads (e.g.,  1354 - 1355 ) can result in different sized compartments (e.g.,  1351 - 1352 ), depending on the number of stacks to be transported at each of the temperature settings. For example, stacks  1331 - 1336  can be loaded into compartment  1351  at a first temperature setting, stacks  1337 - 1341  can be loaded into compartment  1352  at a second temperature setting, and stacks  1342 - 1345  can be loaded into compartment  1353  at a third temperature setting. 
     In many embodiments, stacks  1331 - 1345  can be from separate orders, to be delivered at different physical stores (e.g.,  360  ( FIG.  3   )). For example, stacks  1331 - 1333  and  1338  can be for part of an order A, stacks  1334 - 1337  ad  1343  can be for part of an order B, and stacks  1339 - 1341 ,  1342 , and  1345  can be for part of an order C. In order to minimize unloading and reloading of stacks,  1331 - 1333  and  1338  for order A can be loaded at the front of compartments  1351  and  1352 , and stacks  1339 - 1341 ,  1342 , and  1345  for order C can be loaded at the rear of compartments  1352  and  1353 . 
     Returning to  FIG.  16   , in several embodiments, method  1600  also can include a block  1615  of updating the load design using a first simulated annealing to adjust a front-to-rear center-of-gravity of the load design. In a number of embodiments, block  1615  of updating the load design using a first simulated annealing to adjust the front-to-rear center-of-gravity of the load design further can include minimizing a distance between the front-to-rear center-of-gravity of the load design and an optimal front-to-rear center-of-gravity for the trailer, as described below. 
     Turning back in the drawings,  FIG.  14    illustrates top plan views of load designs  1401  and  1402  for a dry trailer, showing a swap in a first simulated annealing. In many embodiments, as described above in connection with  FIG.  7   , a trailer can have weight limits for its axles (e.g.,  731 - 732  ( FIG.  7   )). In a number of embodiments, the center of gravity (COG) in the frontward-to-rearward direction of a load can be variable, and can be controlled by the load design. In a number of embodiments, the optimal COG can be half way between the maxCOG, described above, and the minCOG, described above, such as: 
     
       
         
           
             K 
             = 
             
               
                 1 
                 2 
               
               ⁢ 
               
                 ( 
                 
                   
                     min 
                     ⁢ 
                     COG 
                   
                   + 
                   
                     max 
                     ⁢ 
                     COG 
                   
                 
                 ) 
               
             
           
         
       
     
     where K is the optimal COG. 
     By designing the actual COG of the load design to be close to the optimal COG, if there is shifting (frontward or rearward) during a load, the load likely can remain within the COG constraints, minCOG and maxCOG, so as to not violate the weight limits on the axles. 
     In a number of embodiments, for a given route for a dry trailer with o orders, each order can include n i  stacks, where i is an index, such that i=1, . . . , o. There can be a total number of stacks m=Σ i=1   o n i , with w i  as the weights of an index i, such as i=1, . . . , m. The middle point (COG) of a jth floor spot to the front-most position can be denoted by a j , in which j is an index such that j=1, . . . , m. The total weight of the stacks in the route can be denoted by g=Σ i=1   m w i . The location of axle  731  ( FIG.  7   ) can be denoted δ 1 , and the location of axle  732  ( FIG.  7   ) can be denoted δ 2 . The max weight (weight limit) of axle  731  ( FIG.  7   ) can be denoted g 1 , and the max weight (weight limit) of axle  732  ( FIG.  7   ) can be denoted g 2 . 
     The lower bound of the COG, minCOG, also denoted as COG lb , can be calculated as follows: 
     
       
         
           
             
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     and an upper bound of the COG, maxCOG, also denoted as COG lb  can be calculated as follows: 
     
       
         
           
             
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     In a number of embodiments, stacks can be loaded to the front-most position. In several embodiments, decision variables x ij , (i, j)∈  can represent an ith stack put in jth floor spot in the trailer, in which   represents a set of the combination of all stacks to floor spots in the trailer. In several embodiments, an optimal COG of a dry trailer can be approached using a minimization function, as follows: 
     
       
         
           
             	 
             
               
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     where  (n) is a mapping of an index into a set  (n)={Σ i=1   k−1 n i ++1, . . . , Σ i=1   k n i }, when n∈[Σ i=1   k−1 n i +1, Σ i=1   k n i ]. 
     In a number of embodiments, for a given route for a tri-temp trailer with o orders, the tth order can have n kt  (k=1, . . . , 3, t=1, . . . , o) stacks in kth compartment of the tri-temp trailer. There can be a total number of stacks in the kth compartment of m k =Σ t=1   o n kt , with w ik  (i=1, . . . , m k , k=1, . . . , 3) representing the weight of stack i in the kth compartment. The middle point (COG) of a jth floor spot to the front-most position of the kth compartment can be a jk  (j=1, . . . , m k , k=1, . . . , 3). The total weight of the stacks in kth compartment can be denoted by w (k) =Σ i=1   m     k   w ik  (k=1, . . . , 3). The lower bound of the kth bulkhead can be denoted by b lb   k , and the upper bound of the kth bulkhead can be denoted by b ub   k , where k=1, 2. The length of stacks in the kth compartment can be denoted by    s   k , k=1,2,3. The total weight of the route can be denoted by g=Σ k=1   3 w (k) . The location of axle  731  ( FIG.  7   ) can be denoted δ 1 , and the location of axle  732  ( FIG.  7   ) can be denoted g 2 . The max weight (weight limit) of axle  731  ( FIG.  7   ) can be denoted g 1 , and the max weight (weight limit) of axle  732  ( FIG.  7   ) can be denoted  92 . 
     The lower bound of the COG, minCOG, also denoted as COG lb , can be calculated as follows: 
     
       
         
           
             
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     and an upper bound of the COG, maxCOG, also denoted as COG ub  can be calculated as follows: 
     
       
         
           
             
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             = 
             
               
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     In several embodiments, decision variables x ijk , (i, j)∈   k , k=1, 2, 3 can represent an ith stack put in jth floor spot in the kth compartment in the trailer, in which   represents a set of the combination of all stacks to floor spots in the kth compartment. In several embodiments, an optimal COG, (COG opt ) of a dry trailer can be approached using a minimization function, as follows: 
     
       
         
           
             
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     where  (⋅):{1, . . . , m k }→ {1, . . . , m k } is a mapping a given stack/floor spots to all feasible floor spots/stacks, and    k (n)={Σ t=1   s−1 n kt +1, . . . , Σ t=1   s  n kt }, when n∈[Σ t=1   s=1 n kt +1, E t=1   s n kt ], and    1 =(w (2)  max{b lb   1 , l s   1 }+w (3) max{b lb   1 +l s   2 , l s   1 +l s   2 , b lb   2 })/g, which can account or the gap at the rear-most section of a compartment frontward of the bulkhead. 
     Referring to load design  1401  in  FIG.  14   , a dry trailer can include various stacks, such as stacks  1411 - 1424 . Stacks  1411 - 1413  can be for part or all of an order A, stacks  1414 - 1418  can be for part or all of an order B, and stacks  1419 - 1424  can be for part or all of an order C. The optimal COG for the trailer can be at an optimal COG location  1432 . The actual COG for load design  1401  can be at an actual COG location  1431 . In order to improve the load plan to minimize the distance between the actual COG and the optimal COG, the first simulated annealing can be used to swap stacks within a neighborhood. In many embodiments, the first simulated annealing can use a neighborhood defined by separate rows within a delivery group. The delivery group can be stacks that will be delivered at the same physical store. For example, stacks  1419 - 1424  can be in order C, and can be in a delivery group. Stacks  1423  and  1424  can be on a same row (front-to-rear), which would not be in the neighborhood, but stacks  1422  and  1423  can be on a different row (front-to-rear), which can be in the neighborhood. The different rows can be used to change the front-to-rear COG. The delivery group can be used to not create or increase unloading and reloading of stacks at stops. In several embodiments, the first simulated annealing can involve a series of iterations and a set of swaps within the neighborhood at each of the iterations. In many embodiments, the second simulated annealing can be performed in less than 800 ms, 500 ms, or 200 ms, for example. 
     For example, stack  1422  and stack  1423  can be in a same neighborhood for the first simulated annealing, and can be swapped in an iteration, among other pairs of stacks meeting the neighborhood constraint (e.g.,  1412  and  1413 , or  1416  and  1418 ). In simulated annealing, individual swaps may cause the distance between the actual COG and the optimal COG to increase, but at the end of an iteration involving multiple swaps, the distance will decrease, in order to use that iteration. In many embodiments, the minimization functions described above can be used for a dry trailer or a tri-temp trailer, as applicable. In a number of embodiments, the series of the iterations can end when an improvement at an iteration over an immediately previous iteration is smaller than a predetermined convergence threshold (e.g., the distance is converging on the minimum) and/or a quantity of the iterations meets a predetermined iteration limit. As shown in load design  1402 , actual COG location  1431  can be adjusted by a swap of the position of stacks  1422  and  1423  from load design  1401  to load design  1402 , such that the distance between actual COG location  1431  and optimal COG location  1432  for the optimal COG can be decreased from the distance in load design  1401 . 
     Returning to  FIG.  16   , in a number of embodiments, method  1600  further can include a block  1620  of updating the load design using a second simulated annealing to adjust a side-to-side center-of-gravity of the load design. In several embodiments, block  1620  of updating the load design using the second simulated annealing to adjust the side-to-side center-of-gravity of the load design further can include minimizing a distance between the side-to-side center-of-gravity of the load design and an optimal side-to-side center-of-gravity for the trailer. 
     Turning back in the drawings,  FIG.  15    illustrates top plan views of load designs  1501  and  1502  for a dry trailer, showing swaps in a second simulated annealing. In many embodiments, the center of gravity can be heavier on the curbside (toward the top of  FIG.  15   ) or on the roadside (toward the bottom of  FIG.  15   ) of the trailer. For example, the actual COG can be at an actual COG position  1531  for load design  1501  that includes stacks  1511 - 1524 . 
     In a number of embodiments, a number of rows (front-to-rear) of stacks in the container can be r, in which r&gt;0, and the weight different of stacks in the ith row can be w i   d , in which w i   d ≥0, i=1, . . . , r. In several embodiments, there can be defined x i , i=1, . . . , r: 0/1 decision variables, which can be binary variables that indicate whether to put heavier stack to the curbside for ith row (x i =1) or put the heavier stack to the roadside for the ith row ((x i =0). A variable W can be defined, which is half of the total weight difference, such that: 
     
       
         
           
             W 
             = 
             
               
                 1 
                 2 
               
               ⁢ 
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   r 
                 
                 
                   w 
                   i 
                   d 
                 
               
             
           
         
       
     
     In order to minimize the difference between Σ i=1   r w i   d x i  and W, the formulate can be expressed in an equivalent form of finding the largest possible Σ i=1 w i   d x i  less than W, which changes the formulation to a 0/1 knapsack problem (with item value and weight being the same), as follows: 
             max   ⁢       ∑     i   =   1     r         w   i   d     ⁢     x   i               such that Σ i=1   r   w   i   d   x   i   ≤W, x   i ∈{0,1}.
 
     When there are 16 rows in a container, there can be at most 16 decision variables. 
     Referring to load design  1501  in  FIG.  15   , stacks  1511 - 1513  can be for part or all of an order A, stacks  1514 - 1518  can be for part or all of an order B, and stacks  1519 - 1524  can be for part or all of an order C. In order to improve the load plan to move the actual COG position  1531  closer to the center between the curbside and roadside, the second simulated annealing can be used to swap stacks within a neighborhood. In many embodiments, the second simulated annealing uses a neighborhood defined by a same row. The same row can be used to keep the front-to-rear COG constant and keep not create or increase unloading and reloading of stacks at stops, but instead to adjust the side-to-side COG. In several embodiments, the second simulated annealing can involves a series of iteration and a set of swaps within the neighborhood at each of the iterations. The second simulated annealing can use the maximization function described above. 
     For example, stack  1513  and stack  1514  can be in a same neighborhood for the second simulated annealing, and stack  1521  and stack  1522  can be in a same neighborhood for the second simulated annealing, and can be swapped in an iteration to update load design  1501  to become load design  1502 . These swaps can adjust actual COG location  1531  to be closer to the side-to-side center in load design  1502  than in load design  1501 . In many embodiments, the maximization function described above can be used for both dry trailers and tri-temp trailers, as the compartments in the tri-temp trailer and front-to-back, not side-to-side. In a number of embodiments, the series of the iterations can end when an improvement at an iteration over an immediately previous iteration is smaller than a predetermined convergence threshold (e.g., the distance is converging on the minimum) and/or a quantity of the iterations meets a predetermined iteration limit. In many embodiments, the second simulated annealing can be performed in less than 50 ms, 10 ms, or 5 ms, for example. 
     Returning to  FIG.  16   , in a number of embodiments, method  1600  also can include a block  1625  of outputting the load design, as updated by the first simulated annealing and the second simulated annealing. In several embodiments, the load design can specify a respective floor spot assignment for each of the stacks. 
     For example, an exemplary load design can is shown in Table 4 below, which can show stacks for two orders, with order identifiers  2040  and  2068 . The height in inches and weight in pounds in shown for the stacks on each row on the left side (roadside) and the right side (curbside). In some cases, such as the left stack in row 5, the right stack in row 4, and the right stack in row 14, there can be two pallets in the stack, as opposed to the one pallet in the stack for the other stacks. The total weight of the load is 43,183 pounds. The total weight on axle 1 is 21,591.49 pounds, and the total weight on axle 2 is 21,591.51 pounds, which can indicate that the front-to-rear COG is close to the optimal COG. The total weight roadside weight is 21,589 pounds, and the total curbside weight is 21,594 pounds, which can indicate that the side-to-side COG is close to the side-to-side center. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                   
                 Left 
                   
                   
                 Right 
                   
                   
               
               
                   
                 Side 
                 Left 
                 Left 
                 Side 
                 Right 
                 Right 
               
               
                   
                 Order 
                 Side 
                 Side 
                 Order 
                 Side 
                 Side 
               
               
                 Row 
                 No. 
                 Height 
                 Weight 
                 No. 
                 Height 
                 Weight 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 1 
                 2040 
                 72 
                 846 
                 2040 
                 72 
                 2474 
               
               
                 2 
                 2040 
                 71 
                 1190 
                 2040 
                 30 
                 798 
               
               
                 3 
                 2040 
                 71 
                 1783 
                 2040 
                 72 
                 587 
               
               
                 4 
                 2040 
                 72 
                 565 
                 2040 
                 65 + 8  
                 2575 + 106 
               
               
                 5 
                 2040 
                 65 + 10 
                 2507 + 302 
                 2040 
                 65 
                 1906 
               
               
                 6 
                 2040 
                 72 
                 543 
                 2040 
                 65 
                 348 
               
               
                 7 
                 2040 
                 65 
                 614 
                 2040 
                 72 
                 2841 
               
               
                 8 
                 2040 
                 65 
                 2400 
                 2040 
                 71 
                 697 
               
               
                 9 
                 2068 
                 72 
                 985 
                 2068 
                 72 
                 3071 
               
               
                 10 
                 2068 
                 72 
                 1274 
                 2068 
                 72 
                 674 
               
               
                 11 
                 2068 
                 65 
                 2281 
                 2068 
                 71 
                 534 
               
               
                 12 
                 2068 
                 65 
                 2474 
                 2068 
                 71 
                 589 
               
               
                 13 
                 2068 
                 64 
                 2456 
                 2068 
                 64 
                 370 
               
               
                 14 
                 2068 
                 65 
                 785 
                 2068 
                 72 + 13 
                 2370 + 150 
               
               
                 15 
                 2068 
                 71 
                 584 
                 2068 
                 66 
                 1504 
               
               
                   
               
            
           
         
       
     
     In a number of embodiments, the load design can provide a balanced front-to-rear weight, a balanced side-to-side weight, and/or provide for no or minimal unloading and reloading at stops. 
     Returning to  FIG.  3   , in several embodiments, communication system  301  can at least partially perform block  505  ( FIG.  5   ) of receiving orders from physical stores for fulfillment from a distribution center. 
     In several embodiments, order initiation system  302  can at least partially perform block  410  ( FIG.  4   ) of receiving orders and performing initial processing, and/or block  505  ( FIG.  5   ) of receiving orders from physical stores for fulfillment from a distribution center. 
     In a number of embodiments, stack building system  303  can at least partially perform block  420  ( FIG.  4   ) of stack building, and/or block  510  ( FIG.  5   ) of generating a stack building plan for each of the orders using simulated annealing. 
     In several embodiments, routing system  304  can at least partially perform block  430  ( FIG.  4   ) of route optimization and load building, block  460  ( FIG.  4   ) of storing initial load design, block  470  ( FIG.  4   ) of storing the delivery routes, block  515  ( FIG.  5   ) of obtaining routes for delivering the orders in trailers from the distribution center to the physical stores based at least in part on the stack building plan, block  910  ( FIG.  9   ) of route construction, block  920  ( FIG.  9   ) of route improvement, block  930  ( FIG.  9   ) of services, block  1010  ( FIG.  10   ) of receiving inputs, block  1020  ( FIG.  10   ) of processing, block  1030  ( FIG.  10   ) of responding with an output, block  1105  ( FIG.  11   ) of obtaining orders for fulfillment to physical stores from a distribution center, block  1110  ( FIG.  11   ) of generating a set of feasible route templates for delivering the orders to the physical stores, block  1115  ( FIG.  11   ) of formulating a mixed integer programming formulation for an assignment of the respective stack groups associated with the orders to the set of route templates, block  1120  ( FIG.  11   ) of using an optimization solver for the mixed integer programming formation to determine the assignment that minimizes an overall cost of delivering the orders to the physical stores from the distribution center, block  1125  ( FIG.  11   ) of outputting the assignment, block  1205  ( FIG.  12   ) of obtaining a sequence of stops and service time windows for the stops, block  1210  ( FIG.  12   ) of generating a sequence of driver states that satisfies the sequence of stops, block  1215  ( FIG.  12   ) of determining, for each pair of respective sequential driver states from the sequence of driver states, whether to generate a respective recommendation to add a respective additional driver state within the respective sequential driver states in order to satisfy a set of rules, block  1220  ( FIG.  12   ) of updating the sequence of driver states based on the respective recommendations, such that the sequence of driver states is feasible in view of the service time windows and the set of rules, and/or block  1225  ( FIG.  12   ) of outputting the sequence of driver states. 
     In a number of embodiments, load design system  305  can at least partially perform block  480  ( FIG.  4   ) of completing the load design, block  490  ( FIG.  4   ) of storing the final load designs, block  520  ( FIG.  5   ) of generating a load design for each of the routes to deliver in a trailer of the trailers a load for one or more of the orders, block  1605  ( FIG.  16   ) of obtaining a route for delivering one or more orders in a trailer from a distribution center to physical stores in a sequence of stops, block  1610  ( FIG.  16   ) of determining a load design for the stacks in the trailer based on the sequence of the stops in the route, block  1615  ( FIG.  16   ) of updating the load design using a first simulated annealing to adjust a front-to-rear center-of-gravity of the load design, block  1620  ( FIG.  16   ) of updating the load design using a second simulated annealing to adjust a side-to-side center-of-gravity of the load design, and/or block  1625  ( FIG.  16   ) of outputting the load design, as updated by the first simulated annealing and the second simulated annealing 
     In many embodiments, the techniques described herein can provide a practical application and several technological improvements. In some embodiments, the techniques described herein can provide for automatic generation of load and route designs using specific inputs and machine-implemented simulated annealing to determine stacks, routes, and loads that minimize travel distance and/or time and comply with applicable constraints. These techniques described herein can provide a significant improvement over conventional approaches of building stacks, designing routes, and/or designing loads without considering the breadth of possible options. Further, when considering these aspects collectively, additional improvements can be derived. Moreover, these designs are improvements over other possible approaches, such as subjective estimates, greedy heuristic approaches, and constraint programming. 
     In many embodiments, the techniques described herein can be used continuously at a scale that cannot be handled using manual techniques. For example, the number of loads from each distribution center per day can exceed a hundred or more. 
     In a number of embodiments, the techniques described herein can solve a technical problem that arises only within the realm of computer networks, as automatic solutions do not exist outside the realm of computer networks. Moreover, the techniques described herein can solve a technical problem that cannot be solved outside the context of computer networks. Specifically, the techniques described herein cannot be used outside the context of computer networks, in view of a lack of data, and because the simulated annealing approach cannot be performed without a computer. 
     Various embodiments include a system. The system can include one or more processors and one or more non-transitory computer-readable media storing computing instructions configured to run on the one or more processors and perform certain acts. The acts can include receiving orders from physical stores for fulfillment from a distribution center, each of the orders comprising a set of items and a requested delivery date. The acts also can include generating a stack building plan for each of the orders using simulated annealing. The acts additionally can include obtaining routes for delivering the orders in trailers from the distribution center to the physical stores based at least in part on the stack building plan. The acts further can include generating a load design for each of the routes to deliver in a trailer of the trailers a load for one or more of the orders, such that floor spot assignments for stacks for each of the one or more of the orders in the load carried by the trailer satisfy sequence-of-delivery constraints and center-of-gravity constraints. 
     Several embodiments include a method. The method can be implemented via execution of computing instructions configured to run at one or more processors and stored at one or more non-transitory computer-readable media. The method can include receiving orders from physical stores for fulfillment from a distribution center, each of the orders comprising a set of items and a requested delivery date. The method also can include generating a stack building plan for each of the orders using simulated annealing. The method further can include obtaining routes for delivering the orders in trailers from the distribution center to the physical stores based at least in part on the stack building plan. The method additionally can include generating a load design for each of the routes to deliver in a trailer of the trailers a load for one or more of the orders, such that floor spot assignments for stacks for each of the one or more of the orders in the load carried by trailer satisfy sequence-of-delivery constraints and center-of-gravity constraints. 
     Various embodiments include a system. The system can include one or more processors and one or more non-transitory computer-readable media storing computing instructions configured to run on the one or more processors and perform certain acts. The acts can include obtaining a sequence of stops and service time windows for the stops. The acts also can include generating a sequence of driver states that satisfies the sequence of the stops. The acts further can include determining, for each pair of respective sequential driver states from the sequence of driver states, whether to generate a respective recommendation to add a respective additional driver state within the respective sequential driver states in order to satisfy a set of rules. The acts additionally can include updating the sequence of driver states based on the respective recommendations, such that the sequence of driver states is feasible in view of the service time windows and the set of rules. The acts further can include outputting the sequence of driver states. 
     Several embodiments include a method. The method can be implemented via execution of computing instructions configured to run at one or more processors and stored at one or more non-transitory computer-readable media. The method can include obtaining a sequence of stops and service time windows for the stops. The method also can include generating a sequence of driver states that satisfies the sequence of the stops. The method further can include determining, for each pair of respective sequential driver states from the sequence of driver states, whether to generate a respective recommendation to add a respective additional driver state within the respective sequential driver states in order to satisfy a set of rules. The method additionally can include updating the sequence of driver states based on the respective recommendations, such that the sequence of driver states is feasible in view of the service time windows and the set of rules. The method further can include outputting the sequence of driver states. 
     Various embodiments include a system. The system can include one or more processors and one or more non-transitory computer-readable media storing computing instructions configured to run on the one or more processors and perform certain acts. The acts can include obtaining a route for delivering one or more orders in a trailer from a distribution center to physical stores in a sequence of stops. The route can have an associated assignment of stack groups comprising stacks of pallets. The acts also can include determining a load design for the stacks in the trailer based on the sequence of the stops in the route. The acts additionally can include updating the load design using a first simulated annealing to adjust a front-to-rear center-of-gravity of the load design. The acts further can include updating the load design using a second simulated annealing to adjust a side-to-side center-of-gravity of the load design. The acts additionally can include outputting the load design, as updated by the first simulated annealing and the second simulated annealing. The load design can specify a respective floor spot assignment for each of the stacks. 
     Several embodiments include a method. The method can be implemented via execution of computing instructions configured to run at one or more processors and stored at one or more non-transitory computer-readable media. The method can include obtaining a route for delivering one or more orders in a trailer from a distribution center to physical stores in a sequence of stops. The route can have an associated assignment of stack groups comprising stacks of pallets. The method also can include determining a load design for the stacks in the trailer based on the sequence of the stops in the route. The method additionally can include updating the load design using a first simulated annealing to adjust a front-to-rear center-of-gravity of the load design. The method further can include updating the load design using a second simulated annealing to adjust a side-to-side center-of-gravity of the load design. The method additionally can include outputting the load design, as updated by the first simulated annealing and the second simulated annealing. The load design can specify a respective floor spot assignment for each of the stacks. 
     Various embodiments include a system. The system can include one or more processors and one or more non-transitory computer-readable media storing computing instructions configured to run on the one or more processors and perform certain acts. The acts can include obtaining orders for fulfillment to physical stores from a distribution center. There can be one or more respective stack groups associated with each of the orders. The acts also can include generating a set of feasible route templates for delivering the orders to the physical stores. The acts additionally can include formulating a mixed integer programming formulation for an assignment of the respective stack groups associated with the orders to the set of route templates. The acts further can include using an optimization solver for the mixed integer programming formation to determine the assignment that minimizes an overall cost of delivering the orders to the physical stores from the distribution center. The acts additionally can include outputting the assignment. 
     Several embodiments include a method. The method can be implemented via execution of computing instructions configured to run at one or more processors and stored at one or more non-transitory computer-readable media. The method can include obtaining orders for fulfillment to physical stores from a distribution center. There can be one or more respective stack groups associated with each of the orders. The method also can include generating a set of feasible route templates for delivering the orders to the physical stores. The method additionally can include formulating a mixed integer programming formulation for an assignment of the respective stack groups associated with the orders to the set of route templates. The method further can include using an optimization solver for the mixed integer programming formation to determine the assignment that minimizes an overall cost of delivering the orders to the physical stores from the distribution center. The method additionally can include outputting the assignment. 
     Various embodiments include a system. The system can include one or more processors and one or more non-transitory computer-readable media storing computing instructions configured to run on the one or more processors and perform certain acts. The acts can include obtaining a route for delivering one or more orders in a tri-temp trailer from a distribution center to physical stores in a sequence of stops. The route can have an associated assignment of stack groups comprising stacks of pallets. The acts also can include determining a load design for the stacks in the tri-temp trailer based on the sequence of the stops in the route, such that unloading each of the stacks is minimized when the tri-temp trailer delivers the orders to the physical stores. The acts additionally can include outputting the load design to cause the stacks to be loaded in the tri-temp trailer according to the load design for delivery to the physical stores in the sequence of stops. The load design can specify a respective floor spot assignment for each of the stacks. 
     Several embodiments include a method. The method can be implemented via execution of computing instructions configured to run at one or more processors and stored at one or more non-transitory computer-readable media. The method can include obtaining a route for delivering one or more orders in a tri-temp trailer from a distribution center to physical stores in a sequence of stops. The route can have an associated assignment of stack groups comprising stacks of pallets. The method also can include determining a load design for the stacks in the tri-temp trailer based on the sequence of the stops in the route, such that unloading each of the stacks is minimized when the tri-temp trailer delivers the orders to the physical stores. The method additionally can include outputting the load design to cause the stacks to be loaded in the tri-temp trailer according to the load design for delivery to the physical stores in the sequence of stops. The load design can specify a respective floor spot assignment for each of the stacks. 
     Although the methods described above are with reference to the illustrated flowcharts, it will be appreciated that many other ways of performing the acts associated with the methods can be used. For example, the order of some operations may be changed, and some of the operations described may be optional. 
     In addition, the methods and system described herein can be at least partially embodied in the form of computer-implemented processes and apparatus for practicing those processes. The disclosed methods may also be at least partially embodied in the form of tangible, non-transitory machine-readable storage media encoded with computer program code. For example, the steps of the methods can be embodied in hardware, in executable instructions executed by a processor (e.g., software), or a combination of the two. The media may include, for example, RAMs, ROMs, CD-ROMs, DVD-ROMs, BD-ROMs, hard disk drives, flash memories, or any other non-transitory machine-readable storage medium. When the computer program code is loaded into and executed by a computer, the computer becomes an apparatus for practicing the method. The methods may also be at least partially embodied in the form of a computer into which computer program code is loaded or executed, such that, the computer becomes a special purpose computer for practicing the methods. When implemented on a general-purpose processor, the computer program code segments configure the processor to create specific logic circuits. The methods may alternatively be at least partially embodied in application specific integrated circuits for performing the methods. 
     The foregoing is provided for purposes of illustrating, explaining, and describing embodiments of these disclosures. Modifications and adaptations to these embodiments will be apparent to those skilled in the art and may be made without departing from the scope or spirit of these disclosures. 
     Although automatic generation of load and route designs has been described with reference to specific embodiments, it will be understood by those skilled in the art that various changes may be made without departing from the spirit or scope of the disclosure. Accordingly, the disclosure of embodiments is intended to be illustrative of the scope of the disclosure and is not intended to be limiting. It is intended that the scope of the disclosure shall be limited only to the extent required by the appended claims. For example, to one of ordinary skill in the art, it will be readily apparent that any element of  FIGS.  1 - 16    may be modified, and that the foregoing discussion of certain of these embodiments does not necessarily represent a complete description of all possible embodiments. For example, one or more of the procedures, processes, or activities of  FIGS.  4 - 5 ,  9 - 12 , and  16    may include different procedures, processes, and/or activities and be performed by many different modules, in many different orders, and/or one or more of the procedures, processes, or activities of  FIGS.  4 - 5 ,  9 - 12 , and  16    may include one or more of the procedures, processes, or activities of another different one of  FIGS.  4 - 5 ,  9 - 12   , and  16 . As another example, the systems within load and route design system  300  ( FIG.  3   ) can be interchanged or otherwise modified. 
     Replacement of one or more claimed elements constitutes reconstruction and not repair. Additionally, benefits, other advantages, and solutions to problems have been described with regard to specific embodiments. The benefits, advantages, solutions to problems, and any element or elements that may cause any benefit, advantage, or solution to occur or become more pronounced, however, are not to be construed as critical, required, or essential features or elements of any or all of the claims, unless such benefits, advantages, solutions, or elements are stated in such claim. 
     Moreover, embodiments and limitations disclosed herein are not dedicated to the public under the doctrine of dedication if the embodiments and/or limitations: (1) are not expressly claimed in the claims; and (2) are or are potentially equivalents of express elements and/or limitations in the claims under the doctrine of equivalents.