# Multiobjective Planning for Logistics Distribution of Consumer Electronic Items Based on Improved Genetic Algorithm

Authors: Rongming Tian; Yan Tang
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

With the increasing uncertainty of customer demand, order management that takes into account the uncertainty of customer demand is important in the supply chain between distribution bases (distribution centers, RDCs, etc.) and large retailers. A multisite delivery planning system is recommended to scale past to handle a single product. Aiming at the logistics distribution problem of consumer electronic products, the problem is attributed to a multiobjective optimization problem, and an improved genetic algorithm is used to deal with it. Combined with the situation, this paper proposes a multiproject (multiproject delivery mass production planning system) and studies the narrative problem description, formula, solution sequence, and case analysis results. The experimental results show that this method can effectively improve the logistics distribution efficiency by 18% and reduce the distribution cost by 34%, by finding the optimal distribution path, reducing the total cost of low-carbon distribution of fresh products, improving customer satisfaction, reducing energy consumption, and achieving economic and social benefits for enterprises.


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## Body

## 1. Introduction

The rapid development of logistics is the third source of profit after resources and labor. However, behind the vigorous development of logistics, there are many problems [1]. With a large population, it is easy to affect the life and work of residents in the process of logistics and distribution. At the same time, there are many motor vehicles, resulting in road congestion and poor traffic flow, resulting in untimely distribution and increased difficulty in distribution [2]. At the same time, the development time of logistics in my country is short, the infrastructure is not perfect, the management level is not high, and the development of informatization is slow, which are obstacles to the development of urban logistics and distribution [3]. Improving the urban logistics distribution system is important in the economic development of China, and at the same time, it can provide better distribution services for residents [4]. Relevant scholars have investigated and analyzed the distribution of agricultural products, petroleum products, fireworks, and other different industries. Some scholars have discussed the optimization of distribution paths and the advantages and disadvantages of logistics models. There are few comparative studies on logistics distribution from an international perspective [5].Uncertainty about customer needs is constantly evolving. In a supply chain between a large retailer’s distribution base (distribution center, RDC, etc.) and multiple locations (e.g., stores), managing orders is important given the uncertainty of customer demand [6]. There is a plan for the joint distribution of household appliances in Kyushu by 20 manufacturers and mass retailers [7]. Traditionally, manufacturers ship products to Kyushu by visiting distribution facilities set up by mass retailers individually, but after a joint distribution system, they only need to ship products to joint facilities [8]. In addition, from a joint distribution facility, different chains will be able to jointly supply dealers in a certain region. The Multicommodity Point Delivery Planning System (MCPS-D), which handles a single commodity, has been extended to a Multicommodity Point Delivery Planning System (MCPS-D), which handles multiple commodities and takes into account lead times between locations and daily loading and unloading capacity limitations. “Multi-item Delivery Mass Customization Production Planning System (MCPS-D),” which can take into account loading and unloading capacity constraints, has been proposed [9, 10]. Problem description, formulation, resolution procedures, and outcomes are described. The effectiveness of this solution is shown.This paper comprehensively considers the three factors of environment, satisfaction, and economic benefits and analyzes the variables of driving speed and time based on real-time road conditions. With the goal of minimizing the total cost of distribution and maximizing customer satisfaction, a multivehicle belt time model considering carbon emissions is constructed. Window product distribution path optimization model designs and improves the hybrid genetic algorithm solution to find the optimal distribution path, reduce the total cost of low-carbon distribution of fresh products, improve customer satisfaction and reduce energy consumption, and achieve economic and social benefits for enterprises.


## 2. Related Work

### 2.1. Analysis of Logistics Distribution in Typical Cities

#### 2.1.1. Japan’s Urban Logistics Distribution Mostly Adopts the Common Distribution Mode

Japan is a big and powerful country in logistics in Asia. Japan’s logistics-related technologies and management ideas are very advanced, which makes its logistics develop extremely rapidly. Urban logistics distribution is an important part of the whole urban logistics, and it is also at the end of the logistics. At present, in Japan, the main mode of urban logistics distribution is joint distribution, and most of its retail industries basically use joint distribution. And the proportion of joint distribution reached 55.4%, of which 41.4% were carried out by distribution centers [11].


#### 2.1.2. Common Distribution Mode

In producer-led codistribution, its predecessor can be understood as planned distribution. The process is mainly based on the out-of-stock list written in advance by each retail store and then according to the type of product, delivery area, delivery date, etc., to implement planned distribution. In wholesaler-led joint distribution, large-scale wholesale enterprises will jointly establish distribution centers. Wholesale companies first gather commodities from manufacturers to distribution centers, then manage and store them, and then deliver them quickly to stores that are out of stock. Joint distribution of third-party logistics is the basic mode of modern logistics and distribution in Japan. The degree of logistics distribution in Japan is high.


#### 2.1.3. Reasons for Implementing Joint Distribution to Reduce Environmental Load

Japan promulgated the “Kyoto Protocol” to reduce greenhouse gas emissions [12]. Since the CO2 emissions of freight vehicles in Japan account for 7% of the country’s total, it is a responsibility and obligation to build a micrologistics distribution system, and joint distribution is undoubtedly a very suitable distribution method [13]. The revision of the “Urban Construction Law” requires accelerating the formation of “compact cities” [14]. The Ministry of Land, Infrastructure, Transport and Tourism of Japan revised the “Urban Construction Law,” namely, the “Urban Planning Law,” the “Central Block Activation Law,” and the “Measures for Site Selection of Large-Scale Retail Shopping Malls,” and put forward restrictions on the location selection of large-scale retail stores in the suburbs [15]. In order to restore the prosperity of the central block and strengthen the construction of “compact city,” new requirements are put forward for urban logistics and distribution, and the temporary loading and unloading and parking places of freight vehicles are perfected, and multiparty cooperation is required [16]. The revised “Road Traffic Law” in 2007 put forward new requirements for illegal parking, and the punishment is stronger [17]. Therefore, for urban logistics and distribution, vehicle parking, loading, and unloading problems are very big, and joint distribution can reduce the number of distribution vehicles.


### 2.2. The Distribution Center in the United States Is Developing Rapidly

#### 2.2.1. Types of U.S. Distribution Centers

(1) Wholesale distribution center mainly relies on computer management. The business office of the distribution center receives the order information of the retail store through the computer system and immediately informs the manufacturer and freight forwarder. Manufacturers and warehouses issue orders for product assembly and delivery based on order information. (2) In retail distribution center, the distribution centers established by large retail enterprises ensure the timely delivery of their networks. Walmart has established a distribution center, which is a typical retail distribution center in the United States. (3) In storage and distribution center, Fleming distribution center is a typical warehouse distribution center. It accepts orders from the headquarters of the alliance of independent grocery stores in the United States and distributes products to the alliance stores.


#### 2.2.2. Reasons for the Development of Distribution Centers in the United States

The improvement of distribution facilities is the key to its success. A flexible and efficient logistics distribution system can achieve the largest sales volume and the lowest cost [18]. The Walmart distribution center is based on more than 100 retail stores and is established in its central location to reduce distribution time and cost [19]. In addition, Walmart’s unique cross-distribution operation mode makes the incoming and outgoing goods basically at the same time, reducing unnecessary processes such as warehousing, storage, and sorting, so as to speed up the circulation of goods. This efficient and flexible operation mode makes it possible. It has more advantages in the competition of the same industry [20]. Powerful logistics information technology is an important guarantee for Walmart’s success. The operation of efficient distribution centers and distribution methods is inseparable from the support of information technology [21, 22]. At the same time, Walmart has also launched its own satellites to provide guarantee for its powerful information system, and advanced technologies such as EDI, EOS, and POS are widely used, which improves the distribution efficiency and enhances the decision-making ability [23]. The tight and smooth operation of the logistics distribution system is also an important factor for Walmart’s success. The purpose of the “seamless point-to-point” logistics system established by Walmart is to make the connection of the entire supply chain smoother, so as to provide services faster [24]. The second is the automatic replenishment delivery system. Every Walmart store has such a system; it can know the inventory quantity of each store’s goods, how many are in transit, and which products are selling fast and can predict the sales situation in the next week or month based on these data. It saves a lot of time and effort for reshipping [25]. The third is the retail link system. Let suppliers come in, let them know how the product is selling, and make updates.


## 2.1. Analysis of Logistics Distribution in Typical Cities

### 2.1.1. Japan’s Urban Logistics Distribution Mostly Adopts the Common Distribution Mode

Japan is a big and powerful country in logistics in Asia. Japan’s logistics-related technologies and management ideas are very advanced, which makes its logistics develop extremely rapidly. Urban logistics distribution is an important part of the whole urban logistics, and it is also at the end of the logistics. At present, in Japan, the main mode of urban logistics distribution is joint distribution, and most of its retail industries basically use joint distribution. And the proportion of joint distribution reached 55.4%, of which 41.4% were carried out by distribution centers [11].


### 2.1.2. Common Distribution Mode

In producer-led codistribution, its predecessor can be understood as planned distribution. The process is mainly based on the out-of-stock list written in advance by each retail store and then according to the type of product, delivery area, delivery date, etc., to implement planned distribution. In wholesaler-led joint distribution, large-scale wholesale enterprises will jointly establish distribution centers. Wholesale companies first gather commodities from manufacturers to distribution centers, then manage and store them, and then deliver them quickly to stores that are out of stock. Joint distribution of third-party logistics is the basic mode of modern logistics and distribution in Japan. The degree of logistics distribution in Japan is high.


### 2.1.3. Reasons for Implementing Joint Distribution to Reduce Environmental Load

Japan promulgated the “Kyoto Protocol” to reduce greenhouse gas emissions [12]. Since the CO2 emissions of freight vehicles in Japan account for 7% of the country’s total, it is a responsibility and obligation to build a micrologistics distribution system, and joint distribution is undoubtedly a very suitable distribution method [13]. The revision of the “Urban Construction Law” requires accelerating the formation of “compact cities” [14]. The Ministry of Land, Infrastructure, Transport and Tourism of Japan revised the “Urban Construction Law,” namely, the “Urban Planning Law,” the “Central Block Activation Law,” and the “Measures for Site Selection of Large-Scale Retail Shopping Malls,” and put forward restrictions on the location selection of large-scale retail stores in the suburbs [15]. In order to restore the prosperity of the central block and strengthen the construction of “compact city,” new requirements are put forward for urban logistics and distribution, and the temporary loading and unloading and parking places of freight vehicles are perfected, and multiparty cooperation is required [16]. The revised “Road Traffic Law” in 2007 put forward new requirements for illegal parking, and the punishment is stronger [17]. Therefore, for urban logistics and distribution, vehicle parking, loading, and unloading problems are very big, and joint distribution can reduce the number of distribution vehicles.


## 2.1.1. Japan’s Urban Logistics Distribution Mostly Adopts the Common Distribution Mode

Japan is a big and powerful country in logistics in Asia. Japan’s logistics-related technologies and management ideas are very advanced, which makes its logistics develop extremely rapidly. Urban logistics distribution is an important part of the whole urban logistics, and it is also at the end of the logistics. At present, in Japan, the main mode of urban logistics distribution is joint distribution, and most of its retail industries basically use joint distribution. And the proportion of joint distribution reached 55.4%, of which 41.4% were carried out by distribution centers [11].


## 2.1.2. Common Distribution Mode

In producer-led codistribution, its predecessor can be understood as planned distribution. The process is mainly based on the out-of-stock list written in advance by each retail store and then according to the type of product, delivery area, delivery date, etc., to implement planned distribution. In wholesaler-led joint distribution, large-scale wholesale enterprises will jointly establish distribution centers. Wholesale companies first gather commodities from manufacturers to distribution centers, then manage and store them, and then deliver them quickly to stores that are out of stock. Joint distribution of third-party logistics is the basic mode of modern logistics and distribution in Japan. The degree of logistics distribution in Japan is high.


## 2.1.3. Reasons for Implementing Joint Distribution to Reduce Environmental Load

Japan promulgated the “Kyoto Protocol” to reduce greenhouse gas emissions [12]. Since the CO2 emissions of freight vehicles in Japan account for 7% of the country’s total, it is a responsibility and obligation to build a micrologistics distribution system, and joint distribution is undoubtedly a very suitable distribution method [13]. The revision of the “Urban Construction Law” requires accelerating the formation of “compact cities” [14]. The Ministry of Land, Infrastructure, Transport and Tourism of Japan revised the “Urban Construction Law,” namely, the “Urban Planning Law,” the “Central Block Activation Law,” and the “Measures for Site Selection of Large-Scale Retail Shopping Malls,” and put forward restrictions on the location selection of large-scale retail stores in the suburbs [15]. In order to restore the prosperity of the central block and strengthen the construction of “compact city,” new requirements are put forward for urban logistics and distribution, and the temporary loading and unloading and parking places of freight vehicles are perfected, and multiparty cooperation is required [16]. The revised “Road Traffic Law” in 2007 put forward new requirements for illegal parking, and the punishment is stronger [17]. Therefore, for urban logistics and distribution, vehicle parking, loading, and unloading problems are very big, and joint distribution can reduce the number of distribution vehicles.


## 2.2. The Distribution Center in the United States Is Developing Rapidly

### 2.2.1. Types of U.S. Distribution Centers

(1) Wholesale distribution center mainly relies on computer management. The business office of the distribution center receives the order information of the retail store through the computer system and immediately informs the manufacturer and freight forwarder. Manufacturers and warehouses issue orders for product assembly and delivery based on order information. (2) In retail distribution center, the distribution centers established by large retail enterprises ensure the timely delivery of their networks. Walmart has established a distribution center, which is a typical retail distribution center in the United States. (3) In storage and distribution center, Fleming distribution center is a typical warehouse distribution center. It accepts orders from the headquarters of the alliance of independent grocery stores in the United States and distributes products to the alliance stores.


### 2.2.2. Reasons for the Development of Distribution Centers in the United States

The improvement of distribution facilities is the key to its success. A flexible and efficient logistics distribution system can achieve the largest sales volume and the lowest cost [18]. The Walmart distribution center is based on more than 100 retail stores and is established in its central location to reduce distribution time and cost [19]. In addition, Walmart’s unique cross-distribution operation mode makes the incoming and outgoing goods basically at the same time, reducing unnecessary processes such as warehousing, storage, and sorting, so as to speed up the circulation of goods. This efficient and flexible operation mode makes it possible. It has more advantages in the competition of the same industry [20]. Powerful logistics information technology is an important guarantee for Walmart’s success. The operation of efficient distribution centers and distribution methods is inseparable from the support of information technology [21, 22]. At the same time, Walmart has also launched its own satellites to provide guarantee for its powerful information system, and advanced technologies such as EDI, EOS, and POS are widely used, which improves the distribution efficiency and enhances the decision-making ability [23]. The tight and smooth operation of the logistics distribution system is also an important factor for Walmart’s success. The purpose of the “seamless point-to-point” logistics system established by Walmart is to make the connection of the entire supply chain smoother, so as to provide services faster [24]. The second is the automatic replenishment delivery system. Every Walmart store has such a system; it can know the inventory quantity of each store’s goods, how many are in transit, and which products are selling fast and can predict the sales situation in the next week or month based on these data. It saves a lot of time and effort for reshipping [25]. The third is the retail link system. Let suppliers come in, let them know how the product is selling, and make updates.


## 2.2.1. Types of U.S. Distribution Centers

(1) Wholesale distribution center mainly relies on computer management. The business office of the distribution center receives the order information of the retail store through the computer system and immediately informs the manufacturer and freight forwarder. Manufacturers and warehouses issue orders for product assembly and delivery based on order information. (2) In retail distribution center, the distribution centers established by large retail enterprises ensure the timely delivery of their networks. Walmart has established a distribution center, which is a typical retail distribution center in the United States. (3) In storage and distribution center, Fleming distribution center is a typical warehouse distribution center. It accepts orders from the headquarters of the alliance of independent grocery stores in the United States and distributes products to the alliance stores.


## 2.2.2. Reasons for the Development of Distribution Centers in the United States

The improvement of distribution facilities is the key to its success. A flexible and efficient logistics distribution system can achieve the largest sales volume and the lowest cost [18]. The Walmart distribution center is based on more than 100 retail stores and is established in its central location to reduce distribution time and cost [19]. In addition, Walmart’s unique cross-distribution operation mode makes the incoming and outgoing goods basically at the same time, reducing unnecessary processes such as warehousing, storage, and sorting, so as to speed up the circulation of goods. This efficient and flexible operation mode makes it possible. It has more advantages in the competition of the same industry [20]. Powerful logistics information technology is an important guarantee for Walmart’s success. The operation of efficient distribution centers and distribution methods is inseparable from the support of information technology [21, 22]. At the same time, Walmart has also launched its own satellites to provide guarantee for its powerful information system, and advanced technologies such as EDI, EOS, and POS are widely used, which improves the distribution efficiency and enhances the decision-making ability [23]. The tight and smooth operation of the logistics distribution system is also an important factor for Walmart’s success. The purpose of the “seamless point-to-point” logistics system established by Walmart is to make the connection of the entire supply chain smoother, so as to provide services faster [24]. The second is the automatic replenishment delivery system. Every Walmart store has such a system; it can know the inventory quantity of each store’s goods, how many are in transit, and which products are selling fast and can predict the sales situation in the next week or month based on these data. It saves a lot of time and effort for reshipping [25]. The third is the retail link system. Let suppliers come in, let them know how the product is selling, and make updates.


## 3. Method

In this stage, if the level of logistics information service is low, it will lead to a disconnection between production and sales, and the production volume of consumer electronic products cannot be adjusted in time to meet market demand. At this time, the sales targets are mainly universities, university towns, canteens of enterprises and institutions, and special counters in large supermarkets. The specific distribution mode is shown in Figure1.Figure 1
The first stage distribution mode diagram.The logistics and distribution tasks at this stage are solely responsible for the enterprise, and the distribution methods used are mainly divided into two types, namely, joint distribution and direct delivery from the origin. At this stage, the main customers of enterprises should be large- and medium-sized factories. The consumer electronic products required by the factory do not need to be processed and distributed directly. Therefore, the direct delivery method is adopted, which can not only shorten the delivery time but also greatly maintain the timeliness of consumer electronic products. For customers such as supermarkets and shopping malls, the method of joint distribution is adopted, and the products of different customers are assembled in one vehicle and delivered to the designated delivery location of the customer. This approach reduces the transportation cost of the enterprise and improves the loading rate, and in the long run, it can also reduce the traffic congestion rate and contribute to the construction of a green city, as shown in Figure2.Figure 2
The second stage distribution mode diagram.In logistics and distribution, attention should be paid to adopting appropriate packaging for consumer electronic products to reduce the loss of consumer electronic products in transit. The third stage distribution mode is shown in Figure3. The business process of the consumer electronic product logistics distribution system is shown in Figure 4.Figure 3
The third stage distribution mode diagram.Figure 4
Logistics and distribution system business process.At major consumer electronics retailers, takeaway items (DVDs, supplies, etc.) are stocked in store. Supplies are ordered by customers in stores and other locations and received from distribution centers once a day. The ordering method is as follows: (1) in normal times, the store’s target inventory is set in advance, and as much as it sells, it will be replenished semiautomatically. (2) When demand fluctuates, individual orders are placed based on past performance and workshop know-how. The ordering method is manual entry into the information system. An image of the target supply chain is shown in Figure5.Figure 5
Image of the target supply chain.In order to minimize procurement, delivery, and inventory costs, the problem of determining the quantity of goods to be purchased and delivered is formulated (see Figures6 and 7), and inventory transitions and m delivery points inn periods strictly abide by the planned target noncompliance rate in each period. In formulating the problem, assume the following points.
(1)
The planning cycle is once/week (or once/day), but the plan is made for the next week (or 2-3 days)(2)
The outstanding rate of planned objectives for each distribution point and type can be considered. The open order rate is the ratio of the number of missed deliveries. The unfulfilled planned order rate refers to the unfilled order rate allowed under the standard lead time for each delivery point and variety. A planned target miss rate can be set for each delivery location and variety, so that purchasing and delivery managers can individually control the miss rate for each delivery location and variety(3)
Delivery preparation time for each delivery point can be considered(4)
Assume that the dispensing capacity of each period is limitedFigure 6
Concept map of the problem.Figure 7
Statement of the problem.As shown in Figure7, i is the term (however, i≤n), j is the delivery point (but, j≤m), k is the variety (however, n≤k), xijk is the quantity of the j-th variety purchased at the j-th delivery point, and pi0k is the inventory quantity of the k-th variety per unit factory.rjk is the total delivery volume target, SOa is the percentage of the delivery point that is not realized in the current period, and Qi is the purchasing power of period i.This paper considers the minimization problem with two objectives.(1)Minimizefd=f1d,f2d∈R2(2)subjecttod=d1,⋯,dM∈ZM≡D,whered is the decision variable vector, an integer of dimension M, representing the Dmap in the next chapter. In the actual objective function f:D⟶R2, D and R are called decision variable space and target space, respectively.
(3)f1da<f1db,f2da≤f2db,f1da=f1db,f2da<f2db.


### 3.1. Raising the Question

(4)∑k=1K∑i=1npi0kxi0k+∑k=1K∑j=1m∑i=1ntijkxijk+hijksijk,(5)S0jk+∑i=1ixt−L,jkk−∑t=1id¯ijk≥0∀i∀j∀k,(6)S0,k−∑t=1id¯ik≥0∀i∀j∀k,(7)xi0k−∑j=1mxijk=0∀i∀k,(8)∑i=1nxijk=rjk∀j∀k,(9)SOjk≤βjk∀j∀k,(10)∑j,kxijk≤Qi∀i,(11)xijk≥0∀i∀j∀k,(12)xi0k≥0∀i∀k.Equation (4) represents the minimization of the expectation of the sum of delivery cost and inventory cost. Equations (5) and (6) represent the minimum initial inventory constraints to meet demand expectations when no delivery is received, and (7) and (8), respectively, indicate that the inventory matches the total quantity at the delivery location, respectively. Equation (8) is the constraint on the total purchase amount, and Equation (9) is the percentage of each variety that does not meet the planned target by delivery location. Equation (10) expresses the constraints of the phase-by-period scheduling capability. The needs of the above problem, a random procurement and inventory problem, is a promising problem of this type, but it is difficult to apply when there are many on-time and by-delivery-location constraints on procurement and delivery.Consider the problem of Equation (4) without Equation (11), that is, the multisite, multiproduct delivery P problem. This is a linear programming problem for which there is a simple solution. By eliminating S, the objective function equation is also simplified.


#### 3.1.1. The Problem of Multisite and Multivariety Distribution

(13)minimize∑k=1K∑j=1mhjk∑t=1nn−t+1xt−L,jks.t.S0jk+∑t=1ixt−Lj,jk−∑i=1id¯tjk≥0∀i∀j∀kS0jk−∑i=1id¯tk≥0∀i∀j∀kxi0k−∑j=1mxijk=0∀i∀k∑i=1nxijk=rjk∀j∀k∑j,kxijk≤Qi∀ixijk≥0∀i∀j∀kxi0k≥0∀i∀k.x1jko,x2jko,⋯,xnjko is the optimal solution to the multisite, multiproduct delivery P problem; if this satisfies Equation (5), then x1jko,x2jko,⋯,xnjko is the overall optimal solution.


#### 3.1.2. The MP Problem of Multisite Multiproduct Delivery

(14)minimize∑k=1K∑j=1mhjk∑t=1nn−t+1xt−Lj,jk(15)s.t.S0jk+∑t=1ixt−Lj,jk−∑t=1id¯tjk≥0∀i∀j∀k(16)S0jk−∑t=1id¯tk≥0∀i∀j∀k(17)xi0k−∑j=1mxijk=0∀i∀k(18)S0jk+∑t=1ixt−Lj,jk−∑t=1id¯tjk≥Kijk∀∀i,j,k∈Bjk(19)∑i=1nxijk=rjk∀j∀k(20)∑j,kxijk≤Qi∀i(21)xi0k≥0∀i∀j∀k.The following is the multivariety and multisite distribution planning system for uncertain demand (multivariety MCPS-D):(22)xi0k≥0∀i∀k.Compared with the multisite multiproduct distribution MP problem and the multisite multiproduct distribution P problem, Equation (14) is added. The process of solving this problem is shown in Figure 8.
(23)βijk=∫−∞yjk12πσijke−Sijk−mijk2/2σijk2dSijk,Kijk=mijk−yjk.Figure 8
Basic framework of the solution.To be less than or equal to the outstanding rate/franchise of each period, as long asβijk is met, the expected value of the inventory in period i is Sijk.For the first delivery point and the first variety, letTjk be the index set for the period and βijk the index set for the period, where the percentage of underperformance in each period is less than or equal to Bjk.
(24)βijk2=βijk1−sgnβijk1−βijk·βijk1−βijkINC,ijk2=argmaxi≤nβijk2,βijk2=∫−∞yjk212πσijke−Sjjk−mjjk2/2σjjkdSijk,Kijk2=mijk−yjk2.Equation (2) is applied to Kijk2,ijk2∈Bjk; we can construct a multisite, multiproduct delivery MP problem, that is, the j-th delivery point; the k-th item inventory Sijk is less than or equal to the planned target miss rate βijk2 when stretched. And INC=2.


### 3.2. Improved Genetic Algorithms

The next step is to consider how to find a facility arrangement that minimizes the objective function. A simple way is to check all the combinations, calculate the evaluation value, and take the smallest one. However, in many cases, it is difficult to do this in a realistic time. According to the previous discussion, thek elements selected from the N elements in the set J represent a solution.Here, we mention such a method, the genetic algorithm (GA), which is a search algorithm based on the principle of biological evolution, which can derive an approximate solution to Equation (10). An approximate solution is not strictly an optimal solution, but a good solution to some extent. To understand how GA finds this solution, some terms (individual, genetic, viability, selection, hierarchical strategy, uniform mating, etc.) are used.A person represents a solution, where a solution is a set of facility location patterns that satisfy constraints. If the number of facilities to be installed isk, then the length of the solution is 2k (since the coordinates of a facility require two numbers, longitude, and latitude), and the latitude and longitude of the two locations are j1,λ1 and j3,λ3, so the sequence j1,λ1,j3,λ3 is an individual and a solution, and each element is a gene.Viability refers to the assessed value that an individual possesses. According to Equation (10), it is obtained by computing the inner part of the minimum operation of the objective function. In the current situation, the lower the evaluation value, the better, so when it is such a state, we express the survivability as high. The operation of selecting two individuals from several individuals according to some criterion is called selection. For example, if there are five individuals, when they are arranged in order of viability, the selection probabilities α1 are 40%, 30%, 20%, 10%, and 0. The operation of selecting two individuals based on these probabilities is a hierarchical policy. If the same person is selected again, a reselection occurs.After the hierarchical strategy, the process usually proceeds to the unified intersection described below. However, based on mutation probabilityα2, the process mutates, rather than uniformly mating. α2 is usually set to a small value but can be increased if the diversity of solutions is expected to be low, for example, if the variability in the viability of individuals in the current generation is small. This process is called a big mutation.First, the handling when choosing uniform mating rather than mutation is mentioned. In uniform crossover, for two individuals selected by the rank strategy, each of their genes is exchanged according to probability: when two individuals exchange genes with each other, two new individuals are generated. For example, if two individualsj1,λ1,j2,λ2 and j3,λ3,j1,λ1 are selected by the rank strategy, and the first and fourth genes are to be exchanged, and then, the two newly generated individuals are j3,λ1,j2,λ1 and j1,λ3,j1,λ2. The two individuals before the exchange are called the current generation individuals, and the two individuals generated after the exchange are called the next-generation individuals. The exchange probability α3 determines whether each gene is exchanged. In other words, there is no limit to the number of genes to be exchanged. However, it should be noted that if none or all genes are exchanged, the current and next-generation individuals will be the same.The next section describes the process when selecting mutations rather than uniform crossovers. Mutation refers to the process of replacing the only gene in the first individual selected by the rank strategy with a random number. The number of genes that are replaced is random, and in general, random rewriting of genes is likely to result in low survival rates. However, in rare cases, highly viable individuals that cannot be produced through mating may be produced. The range of replacing genes with random numbers must be the region to be analyzed, so the maximum and minimum latitude and longitude values of the region to be analyzed must be obtained in advance, and random numbers within this range must be used.The specific improved GA procedure is as shown in Table1.


## 3.1. Raising the Question

(4)∑k=1K∑i=1npi0kxi0k+∑k=1K∑j=1m∑i=1ntijkxijk+hijksijk,(5)S0jk+∑i=1ixt−L,jkk−∑t=1id¯ijk≥0∀i∀j∀k,(6)S0,k−∑t=1id¯ik≥0∀i∀j∀k,(7)xi0k−∑j=1mxijk=0∀i∀k,(8)∑i=1nxijk=rjk∀j∀k,(9)SOjk≤βjk∀j∀k,(10)∑j,kxijk≤Qi∀i,(11)xijk≥0∀i∀j∀k,(12)xi0k≥0∀i∀k.Equation (4) represents the minimization of the expectation of the sum of delivery cost and inventory cost. Equations (5) and (6) represent the minimum initial inventory constraints to meet demand expectations when no delivery is received, and (7) and (8), respectively, indicate that the inventory matches the total quantity at the delivery location, respectively. Equation (8) is the constraint on the total purchase amount, and Equation (9) is the percentage of each variety that does not meet the planned target by delivery location. Equation (10) expresses the constraints of the phase-by-period scheduling capability. The needs of the above problem, a random procurement and inventory problem, is a promising problem of this type, but it is difficult to apply when there are many on-time and by-delivery-location constraints on procurement and delivery.Consider the problem of Equation (4) without Equation (11), that is, the multisite, multiproduct delivery P problem. This is a linear programming problem for which there is a simple solution. By eliminating S, the objective function equation is also simplified.


### 3.1.1. The Problem of Multisite and Multivariety Distribution

(13)minimize∑k=1K∑j=1mhjk∑t=1nn−t+1xt−L,jks.t.S0jk+∑t=1ixt−Lj,jk−∑i=1id¯tjk≥0∀i∀j∀kS0jk−∑i=1id¯tk≥0∀i∀j∀kxi0k−∑j=1mxijk=0∀i∀k∑i=1nxijk=rjk∀j∀k∑j,kxijk≤Qi∀ixijk≥0∀i∀j∀kxi0k≥0∀i∀k.x1jko,x2jko,⋯,xnjko is the optimal solution to the multisite, multiproduct delivery P problem; if this satisfies Equation (5), then x1jko,x2jko,⋯,xnjko is the overall optimal solution.


### 3.1.2. The MP Problem of Multisite Multiproduct Delivery

(14)minimize∑k=1K∑j=1mhjk∑t=1nn−t+1xt−Lj,jk(15)s.t.S0jk+∑t=1ixt−Lj,jk−∑t=1id¯tjk≥0∀i∀j∀k(16)S0jk−∑t=1id¯tk≥0∀i∀j∀k(17)xi0k−∑j=1mxijk=0∀i∀k(18)S0jk+∑t=1ixt−Lj,jk−∑t=1id¯tjk≥Kijk∀∀i,j,k∈Bjk(19)∑i=1nxijk=rjk∀j∀k(20)∑j,kxijk≤Qi∀i(21)xi0k≥0∀i∀j∀k.The following is the multivariety and multisite distribution planning system for uncertain demand (multivariety MCPS-D):(22)xi0k≥0∀i∀k.Compared with the multisite multiproduct distribution MP problem and the multisite multiproduct distribution P problem, Equation (14) is added. The process of solving this problem is shown in Figure 8.
(23)βijk=∫−∞yjk12πσijke−Sijk−mijk2/2σijk2dSijk,Kijk=mijk−yjk.Figure 8
Basic framework of the solution.To be less than or equal to the outstanding rate/franchise of each period, as long asβijk is met, the expected value of the inventory in period i is Sijk.For the first delivery point and the first variety, letTjk be the index set for the period and βijk the index set for the period, where the percentage of underperformance in each period is less than or equal to Bjk.
(24)βijk2=βijk1−sgnβijk1−βijk·βijk1−βijkINC,ijk2=argmaxi≤nβijk2,βijk2=∫−∞yjk212πσijke−Sjjk−mjjk2/2σjjkdSijk,Kijk2=mijk−yjk2.Equation (2) is applied to Kijk2,ijk2∈Bjk; we can construct a multisite, multiproduct delivery MP problem, that is, the j-th delivery point; the k-th item inventory Sijk is less than or equal to the planned target miss rate βijk2 when stretched. And INC=2.


## 3.1.1. The Problem of Multisite and Multivariety Distribution

(13)minimize∑k=1K∑j=1mhjk∑t=1nn−t+1xt−L,jks.t.S0jk+∑t=1ixt−Lj,jk−∑i=1id¯tjk≥0∀i∀j∀kS0jk−∑i=1id¯tk≥0∀i∀j∀kxi0k−∑j=1mxijk=0∀i∀k∑i=1nxijk=rjk∀j∀k∑j,kxijk≤Qi∀ixijk≥0∀i∀j∀kxi0k≥0∀i∀k.x1jko,x2jko,⋯,xnjko is the optimal solution to the multisite, multiproduct delivery P problem; if this satisfies Equation (5), then x1jko,x2jko,⋯,xnjko is the overall optimal solution.


## 3.1.2. The MP Problem of Multisite Multiproduct Delivery

(14)minimize∑k=1K∑j=1mhjk∑t=1nn−t+1xt−Lj,jk(15)s.t.S0jk+∑t=1ixt−Lj,jk−∑t=1id¯tjk≥0∀i∀j∀k(16)S0jk−∑t=1id¯tk≥0∀i∀j∀k(17)xi0k−∑j=1mxijk=0∀i∀k(18)S0jk+∑t=1ixt−Lj,jk−∑t=1id¯tjk≥Kijk∀∀i,j,k∈Bjk(19)∑i=1nxijk=rjk∀j∀k(20)∑j,kxijk≤Qi∀i(21)xi0k≥0∀i∀j∀k.The following is the multivariety and multisite distribution planning system for uncertain demand (multivariety MCPS-D):(22)xi0k≥0∀i∀k.Compared with the multisite multiproduct distribution MP problem and the multisite multiproduct distribution P problem, Equation (14) is added. The process of solving this problem is shown in Figure 8.
(23)βijk=∫−∞yjk12πσijke−Sijk−mijk2/2σijk2dSijk,Kijk=mijk−yjk.Figure 8
Basic framework of the solution.To be less than or equal to the outstanding rate/franchise of each period, as long asβijk is met, the expected value of the inventory in period i is Sijk.For the first delivery point and the first variety, letTjk be the index set for the period and βijk the index set for the period, where the percentage of underperformance in each period is less than or equal to Bjk.
(24)βijk2=βijk1−sgnβijk1−βijk·βijk1−βijkINC,ijk2=argmaxi≤nβijk2,βijk2=∫−∞yjk212πσijke−Sjjk−mjjk2/2σjjkdSijk,Kijk2=mijk−yjk2.Equation (2) is applied to Kijk2,ijk2∈Bjk; we can construct a multisite, multiproduct delivery MP problem, that is, the j-th delivery point; the k-th item inventory Sijk is less than or equal to the planned target miss rate βijk2 when stretched. And INC=2.


## 3.2. Improved Genetic Algorithms

The next step is to consider how to find a facility arrangement that minimizes the objective function. A simple way is to check all the combinations, calculate the evaluation value, and take the smallest one. However, in many cases, it is difficult to do this in a realistic time. According to the previous discussion, thek elements selected from the N elements in the set J represent a solution.Here, we mention such a method, the genetic algorithm (GA), which is a search algorithm based on the principle of biological evolution, which can derive an approximate solution to Equation (10). An approximate solution is not strictly an optimal solution, but a good solution to some extent. To understand how GA finds this solution, some terms (individual, genetic, viability, selection, hierarchical strategy, uniform mating, etc.) are used.A person represents a solution, where a solution is a set of facility location patterns that satisfy constraints. If the number of facilities to be installed isk, then the length of the solution is 2k (since the coordinates of a facility require two numbers, longitude, and latitude), and the latitude and longitude of the two locations are j1,λ1 and j3,λ3, so the sequence j1,λ1,j3,λ3 is an individual and a solution, and each element is a gene.Viability refers to the assessed value that an individual possesses. According to Equation (10), it is obtained by computing the inner part of the minimum operation of the objective function. In the current situation, the lower the evaluation value, the better, so when it is such a state, we express the survivability as high. The operation of selecting two individuals from several individuals according to some criterion is called selection. For example, if there are five individuals, when they are arranged in order of viability, the selection probabilities α1 are 40%, 30%, 20%, 10%, and 0. The operation of selecting two individuals based on these probabilities is a hierarchical policy. If the same person is selected again, a reselection occurs.After the hierarchical strategy, the process usually proceeds to the unified intersection described below. However, based on mutation probabilityα2, the process mutates, rather than uniformly mating. α2 is usually set to a small value but can be increased if the diversity of solutions is expected to be low, for example, if the variability in the viability of individuals in the current generation is small. This process is called a big mutation.First, the handling when choosing uniform mating rather than mutation is mentioned. In uniform crossover, for two individuals selected by the rank strategy, each of their genes is exchanged according to probability: when two individuals exchange genes with each other, two new individuals are generated. For example, if two individualsj1,λ1,j2,λ2 and j3,λ3,j1,λ1 are selected by the rank strategy, and the first and fourth genes are to be exchanged, and then, the two newly generated individuals are j3,λ1,j2,λ1 and j1,λ3,j1,λ2. The two individuals before the exchange are called the current generation individuals, and the two individuals generated after the exchange are called the next-generation individuals. The exchange probability α3 determines whether each gene is exchanged. In other words, there is no limit to the number of genes to be exchanged. However, it should be noted that if none or all genes are exchanged, the current and next-generation individuals will be the same.The next section describes the process when selecting mutations rather than uniform crossovers. Mutation refers to the process of replacing the only gene in the first individual selected by the rank strategy with a random number. The number of genes that are replaced is random, and in general, random rewriting of genes is likely to result in low survival rates. However, in rare cases, highly viable individuals that cannot be produced through mating may be produced. The range of replacing genes with random numbers must be the region to be analyzed, so the maximum and minimum latitude and longitude values of the region to be analyzed must be obtained in advance, and random numbers within this range must be used.The specific improved GA procedure is as shown in Table1.


## 4. Experiments

We analyze the logistics distribution in a region of Japan. The center is Kitahiroshima, the delivery base (1) is Kanto, the delivery base (2) is Osaka, and the delivery base (3) is Kyushu. In addition, in this simulation, numerical calculation was carried out by setting the delivery sites and the planned target noncompliance rateβjk of different products, and the planned target noncompliance rates βjk of each delivery site and different products were all below 5%. Or in the case of βjkl+1−βjkl<0.0001, it is judged that further improvement cannot be expected, and the numerical calculation is terminated.In the model, the indicated totals from phase 1 to phase 5 are randomly set to 150 in Kanto, 120 in Kansai, and 90 in Kyushu. The prerequisites are shown in Table2.Table 1Procedure 1Determine the number of facilitiesk to be deployed, the number of individuals to be generated b, the maximum number of updates T, the selection probability α1, the mutation probability α2, and the replacement probability α3, and set the update counter t=0.Procedure 2Obtains the maximum and minimum values of the longitude and latitude of the target area and randomly generatesb individuals within the range.Procedure 3Theb individuals generated by procedure 3 are the individuals of the current generation.Procedure 4Calculates the viability ofb individuals and obtains its standard deviation.Procedure 5If the standard deviation of viability is extremely low, increase the mutation probabilityα2 (large mutation).Procedure 6Retrieves two individuals through a ranking strategy based on the selection probabilityα1.Procedure 7According to mutation probabilityα2, two next-generation individuals are generated by uniform crossover based on crossover probability α3, or one next-generation individual is generated by mutation.Procedure 8If the number of generated next-generation individuals is less thanb, go to procedure 6; if it is greater than b, go to procedure 9.Procedure 9Since two individuals are produced by uniform mating, the number of individuals may exceedb. In this case, the next generation of individuals is deleted, bringing the number of individuals to b.Procedure 10Update countert is incremented.Procedure 11Ift is less than T, proceed to procedure 3 using the generated b next-generation individuals. If t is T, proceed to procedure 12.Procedure 12Among the generatedb next-generation individuals, the individual with the highest survivability is taken as an approximate solution.Table 2
Base prerequisites.
(a)
Preconditions (Kanto variety 1)
Period12345Indication2430283830Initial inventory130Total delivery limit of five80Variations0.35Planned target5%(b)
Prerequisites (Kanto variety 2)
Period12345Indication2428333035Initial inventory130Total delivery limit of five80Variations0.35Planned target5%(c)
Prerequisites (Osaka variety 1)
Period12345Indication2024182830Initial inventory90Total delivery limit of five80Variations0.35Planned target5%(d)
Prerequisites (Osaka variety 2)
Period12345Indication2225183025Initial inventory90Total delivery limit of five80Variations0.35Planned target5%(e)
Prerequisites (Kyushu variety 1)
Period12345Indication1520181522Initial inventory50Total delivery limit of five80Variations0.35Planned target5%(f)
Prerequisites (Kyushu variety 1)
Period12345Indication1820152314Initial inventory50Total delivery limit of five80Variations0.35Planned target5%(g)
Prerequisites
Factory productivity in each period130Cost of production1Inventory cost1Delivery cost1An image of the operation of the proposed multiproduct, multisite delivery planning model is shown in Figure9.Figure 9
Operation of multibase multiagent distribution planning model.Figure10 shows the mean median of the residuals in the initial learning phase for 100 modeling trials.Figure 10
Modeling results (average of median residuals).Figure11 shows the results of investigating how the worst-case accuracy of each method varies across 100 modeling trials.Figure 11
Modeling results (worst-case residual median).Through the results of Figures9 and 10, we can see that the method proposed in this paper is very effective in optimizing the multiobjective problem, and its performance is superior to traditional GA and DNN and has obvious advantages.We further analyzed customers’ satisfaction with our distribution plan. The specific statistical results are shown in Figure12. The vast majority of customers agree with our plan, and most of them are aged between 35 and 39.Figure 12
Customers’ views on our logistics distribution.


## 5. Conclusion

In today’s society, logistics is called “the third source of profit for enterprises.” Logistics enterprises can adjust investment and development strategies according to the inverse relationship between logistics distribution cost and distribution time reliability and optimize the logistics distribution process. At the same time, the reliability of logistics delivery time can be used as a criterion for judging the quality of logistics services. To reduce the total cost of consumer electronics distribution, reduce carbon emissions, and improve customer satisfaction in view of the rapid growth in demand for consumer electronic products, the increasing importance of customer satisfaction, and the increasing awareness of green environmental protection in society, this paper establishes a multimodel model that considers customer satisfaction. The optimization model of low-carbon consumer electronics distribution route is proposed, and the model established by the improved hybrid genetic algorithm is proposed.



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