Study on Routing Optimization of Fresh Meat Joint Distribution System

The path optimization problem of fresh meat joint distribution system is a multi-center distribution problem.Based on the shortest distance principle,the service scope and customer group of each distribution center can be determined to convert the multi-center optimization problem into several single-center optimization problems,and the joint distribution scheme can be obtained with genetic algorithm.Taking a fresh meat distribution system in the core area of Chongqing City as an example,this paper compares and analyzes the operation status of the system before and after the implementation of joint distribution.The case analysis shows that carrying out the mode of joint distribution can significantly improve the efficiency of fresh meat distribution.


Introduction
The path optimization problem of the fresh meat joint distribution system is a complex problem with time windows in a multi-center distribution environment. This problem has acquired considerable importance by researchers, and some results have been put forward in mathematical model and algorithm exploration [1][2][3][4][5] ,but the solution process proposed is complicated and lacks technical support, which making it difficult to use in business practice. The important idea from the existing literature is to firstly use a reasonable method to divide the service scope of each distribution center, determine its customer group, convert the multi-center distribution problem into a few single-center problems, then use genetic algorithm to solve them one by one [6][7][8][9][10] ,finally get the optimal route of the multi-center distribution system. Based on the above mentioned literature, the idea of single distribution center problem and genetic algorithm is used to analyze and solve the optimization route problem of the urban fresh meat joint distribution system.

Path optimization of the fresh meat joint distribution system
The fresh meat joint distribution system is a logistics network composed of several distribution companies and many customers. The distribution path optimization is an important issue to improve the efficiency of the system. Assuming that the joint distribution system meets the general conditions of the distribution model. The information of the distribution network node is known, including the coordinates of the customer and the distribution center, the customer demand and time window, and the maximum load of the vehicle, etc. Each vehicle departs from the distribution center, and returns to its original place after completing the delivery based on the time window [ai, bi], where ai is the earliest delivery time allowed by the customer i, and bi is the latest end time. The transportation volume of the vehicle does not exceed its maximum load. It is required to determine the driving path of each vehicle in each 2 distribution center to complete the delivery task in the least time, and the time must within the scope allowed by the time window.

Genetic algorithm design of fresh meat distribution path optimization
The genetic algorithm design of fresh meat distribution path optimization should solve the problems of coding, population, fitness function and genetic operator.

Coding, population and fitness function
(1) Coding.The natural numbers are used to encode the vehicle path. Supposing the total number of customers in the distribution center is n, the customers are coded with natural numbers 1～n. A chromosome of length n can be represented by a continuous number string composed of natural numbers 1～n .This number string represents a distribution plan of the distribution center, including several feasible vehicle routes or delivery routes. Each vehicle path is determined according to the customer's time window and vehicle load constraints.
(2) Population. The population is expressed by the number of chromosomes, which corresponds to the collection of feasible distribution plans for the distribution centers. The large population size is good for finding the optimal solution, but the calculation speed is slow; conversely, the population is small and calculation speed is fast, but easy to fall into the local optimal solution. The population size of the vehicle routing problem should be moderate, generally in the range of 20-200.
(3) Fitness function. The fitness function represents the individual's ability to adapt to the environment. For the vehicle routing problem (VRP), any chromosome fitness refers to the total distance (or total time) of vehicle delivery, which is an important criterion to measure the quality of the delivery plan. The genetic algorithm must calculate the total delivery distance of each chromosome in the population, and select the parents based on the fitness to produce a better offspring population.

Genetic operators
The genetic operators select inheritance method according to the chromosome fitness value, including the following three genetic operators.
(1) Selection operator. The selection operator selects good individuals from the previous generation population to produce the offspring population. The selection methods include roulette law, random selection method and binary tournament selection method. Roulette law can be used for distribution issues.
(2) Crossover and mutation operators. The crossover operator refers to determine randomly the two gene positions p1 and p2 of a parent's chromosome, and perform reverse sorting of the number strings in the p1~p2 region to achieve chromosome crossover and produce new offspring. The mutation operator refers to determine randomly two mutation positions t1 and t2 of a parent's chromosome, and the genes at positions t1 and t2 to realize the chromosome gene mutation, and obtain the genetic mutation individual, that is the new offspring.

An example of fresh meat distribution system
There are three companies in Chongqing city that provide fresh meat delivery services in the urban core area, each company relies on its distribution center to deliver the hot fresh meat to the stores in the early morning, and they must complete the delivers before 5 a.m. in every day, while its customers are mixed in the urban core area of the city in an overlapping form. Each company has a unique distribution center, which are represented by the codes DA, DB, and DC respectively.

Data collection of fresh meat distribution system
The Baidu coordinates of the longitude and latitude of the distribution center DA is (106.607243, 29.650195), the DB is (106.547753, 29.386002), and the DC is (106.44637, 29.620419). The customers of distribution centers DA, DB, and DC are represented respectively by lowercase letters a, b, and c, the number beside the letter represents the customer number.DA has 30 customers (a1~a30), DB has 30 3 customers (b1~b30),DC has 20 customers (c1~c20),a total of 80 customers. The distribution centers use box-type trucks with a carrying capacity of 2.5 tons, and the service time for every customer is 10 minutes, including parking, cargo handover and loading and unloading time. Each truck returns to the original place after delivery. According to the survey data, the coordinates, demand, and time windows of each customer are listed in Table 1.  Table 1, the customer demand selects the customer's daily demand of fresh meat under normal business conditions, in ton (t); the coordinates are Baidu coordinates, in degrees (°); in the time window, bi=inf means that there is no time limit for leaving, and the working time is allowed to be large enough, in minute.

System analysis before the implementation of joint distribution system
Before the implementation of joint distribution system, the three distribution companies work independently and only provide distribution services to their own customers. There is no cooperation between the distribution companies, and each company pursues its own lowest cost.

Determine the distance between nodes
Firstly, the Baidu coordinates of the aforementioned distribution center and customers are converted into the international standard coordinates WGS84, and the angle between nodes (unit: °) is calculated out by using the distance function of Matlab software and inputting the WGS84 latitude and longitude coordinates of the node. Secondly, using the conversion formula of degrees and radian: degrees/360=radian/2π, combined with the radius of the earth (average radius of 6371km), the arc distance between nodes can be obtained, which is equal to angle between nodes×π/180×6371km, instead of actual distance. Finally, using distance and meshgrid functions, the distance between the service network nodes of each distribution center can be calculated out.

The path optimization of the Distribution system
Assuming that the delivery vehicle's speed of traveling normally on urban roads is 50 kilometers per hour. Based on this, the distance between nodes can be converted into the travel time of the delivery vehicle, and the data of the vehicle travel time between nodes can be obtained. Using natural numbers to represent customers. For example,1 represents customer a1, and using a string of numbers represent the customers the distribution center serve for. Taking the minimum delivery time as the goal, considering the customer time window and the maximum load limit of the vehicle, the genetic algorithm program for the vehicle routing problem can be designed. For distribution centers DA, DB, and DC, the total chromosome length set to 30,30, and 20 respectively according to the total number of customers; The initial group size N set to 60;Setting the simulation termination condition as "the fitness value of the offspring after the calculation reaches 500 generations or the calculation reaches 200 generations is not significantly improved", once the simulation process meets one of the conditions, the operation will be stopped, and the simulation result of the genetic algorithm will be given. Substituting the distance value between nodes, customer demand and time window data in Table 1 into the genetic algorithm program and running it repeatedly, the optimal distribution plan and operation information of each distribution center can be obtained, as shown in Table 3.

Optimization of the fresh meat joint distribution system
After the implementation of the joint distribution system model, the ownership relationship between the customer and the distribution center will be reorganized. The customer group served by the distribution center is divided according to the principle of proximity to obtain a reorganization plan: distribution center DA serves 19 customers, DC serves 28 customers, and DB serves 33 customers. According to the requirements of genetic algorithm, after renumbering the customers in the distribution center DA, we get the number 1-19, the DB customer number 1-33, and the DC customer number 1-28.
Using Table 1 customer coordinates and distribution center coordinates, the distance between the network nodes is respectively calculated; Using an average speed of 50 kilometers per hour, the distance between the nodes is converted into the travel time of the delivery vehicle to obtain the data of the vehicle travel time between the nodes. Substituting the customer data of the distribution center DA,DB,DC into the genetic algorithm program, respectively, simulation calculations are performed one by one to obtain the optimal distribution plan and operation information of each distribution center, as shown in Table 2.  From Table 2, it can be seen that the running time of the distribution center DA is 311.627 minutes, and the delivery volume is 8.2 tons; The DB running time is 632.23 minutes, and the delivery volume is 12.7 tons; The DC running time is 491.119 minutes, and the delivery volume is 10.7 tons. The simulation information when the distribution system reaches its optimum is shown in Figure 1, Figure 2 and    Table 3 shows the operation data of the fresh meat distribution system in the urban core area before and after the implementation of joint distribution model.

Conclusion
The main conclusions of this study are as follows: (1) The fresh meat distribution center in the urban core area matches more reasonably with customers, and the space utilization is better. The service scope of the distribution center is divided according to the spatial distance factor. Due to the disadvantaged position of the distribution center DA, the number of its customers has been greatly reduced from the original 30 to 19, and the freight volume has been reduced from 11.7 tons to 8.2 tons. The distribution center DA no longer has a strong position, while the number of DB and DC customers has been enhanced, DB has increased by 3 customers, and DC has increased by 8 customers. DC's freight volume has increased from 7.6 tons to 10.7 tons, and DC's geographical advantages are outstanding.
(2) Before the implementation of joint distribution, the distribution system used a total of 25 vehicles for delivery, with a total running time of 1,880.169 minutes. After the implementation of joint distribution, only 23 vehicles are needed for delivery, the number of vehicles used is reduced by 8%; the delivery running time is 1434.976 minutes, and the distribution running time is reduced by 445.193 minutes, which is a reduction of 23.68% compared to before the implementation. Since the total number of customers and customer service time are fixed, the reduced time is mainly the traveling time of the vehicle, the savings amount of the delivery vehicle traveling is (445.193/60)×50=371 kilometers. It can be seen that after the implementation of joint distribution, the number of vehicles and running time have been significantly reduced, and the operating efficiency of the fresh meat distribution system in the core area has been significantly improved.