# Dynamic Job and Conveyor-Based Transport Joint Scheduling in Flexible Manufacturing Systems
## 2 Background and Related Work  
**Production line with a conveyor belt**: The manufacturing system, taken as a reference, consists of a set of machines dedicated to specific tasks disposed in a general _layout_. Each machine is connected with the others through a transport system that moves the materials between the machines circularly. Both raw and finished materials are stored in a vertical warehouse. The production line available at our research facility, _the ICE Laboratory_[18], follows the same layout. Figure 1 shows the plant configuration. It is composed of a set of \"production cells\", specifically tailored to a specific manufacturing process. Starting from the right, the laboratory includes a multi-tool milling machine, a robotic assembly station, a quality control cell, and a vertical warehouse. The conveyor belt moves materials on top of 10 pallets across various _belt segments_. Each pallet is identified by an RFID tag, which is detected by RFID sensors located near the switching mechanisms (blue squares in Figure 1). In particular, the belt segments can be differentiated into the following:  
* _The four machine segments_: These are in charge of loading and unloading materials from the machines (i.e., moving pallets toward and away from the processing area). Sincethese segments are the only access route to the machines, they can contain only one pallet at a certain time instance;
* _The main belt segments_: These are in charge of moving a pallet near the machine when it is ready to process a new task. The pallets waiting for a machine to become free must loop near the destination machine, implementing a circular buffer, while free pallets loop along the long main segments. The main belt is composed of two long belts running in opposite directions. Along these main segments, it is possible to traverse from one to the other by exploiting the switching mechanisms placed in certain positions. The two types of belt segments differ in terms of their control policy. Machine segments are activated in the desired direction to perform loading or unloading pallet operations, and the main belt segments are always active, pushing in the same direction. A switching mechanism can move a pallet by choosing one of the following directions: (1) forward, following the direction of the actual belt; (2) backward, changing direction by switching onto the opposite conveyor; and (3) towards a machine working area. If two pallets must move in the same direction at the same time, the pallet exiting from an unloading segment or moving forward along the main belt has precedence. **Literature review**: In the last decades, the JSS problem has been extensively analyzed by the research community, along with the different variants, such as DJSS and FJSS. The solutions that have been proposed over the years are summarized in [4; 5] and [19]. Our work differs from the standard problem because it specifically addresses the transport time between machines and the impact of this on the schedule. Therefore, we concentrated our analysis of the related works on this specific topic. The transfer time between two machines is a variable delay that depends on the distance between the two machines and the availability of the destination machine. A solution proposed in [20] handles variable delays as sequence-dependent setup times. However, this solution considers the machines busy during the setup time, whereas, in our case, the destination machine can process other tasks while the materials of the next task are moving toward the machine. The authors in [10; 21; 22; 23] proposed a solution for the problem of job scheduling combined with transport time, but they consider only automated guided vehicles (AGVs) as a means of transportation. The limit of considering AGVs is that until a vehicle picks up a task from a machine, the machine itself cannot execute other activities. Similarly, when an AGV is waiting to perform a pick operation from a machine, it wastes transport resources.