Immune co-evolutionary algorithm based partition balancing optimization for tobacco distribution system

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Abstract

In China, the tobacco distribution is organized by fixed districts and routes with low efficiency and high distribution cost due to its unbalanced workload. And, though the dynamic method adopting vehicle routing algorithms produces optimal routes, the unstable routes increase the delivery time and managerial cost. So it is urgent and feasible to break the fixed districts to provide periodic balanced partitions for tobacco distribution. In this paper, a multi-criteria balanced partition model is built, whose minimal objectives including total number of tours in all districts, the travel distance and time of all tours, and the balance objectives include number of tours, total demand, traveling distance and time of each district are considered. An immune co-evolutionary algorithm with two stages is designed to search the optimal balanced partitions. In the first stage, the initial balanced partitions are produced. In the second stage, the clonal selection procedure, with partition proliferation, selection and elimination, and cooperative searching among districts, is adopted to achieve balanced partition. The experiments on Lenfen city in China as a practical application reveal the efficiency of the proposed model and algorithm. First, the searching processes are analyzed by exploring the partitions and Pareto partitions. Second, the evolutionary process of the algorithm is shown by the varying of the multiple objectives. Finally, three methods including fixed districts and routes, dynamic VRP scheduling and periodic balanced partition are compared to show the value of the study.

Introduction

In China, most of the cities still adopt fixed districts and routes to organize the tobacco distribution. The tobacco distribution is organized by the city tobacco companies. The distribution cycle is commonly five workdays in a week. The region of city is correspondingly divided into five districts. Every workday the distribution center deals with one region. Although the old method which adopts fixed districts is convenient and simple, the efficiency is low and the distribution cost is high because of its unbalanced workload. It is urgent and feasible to break the fixed districts by optimized partitioning methods.

In logistics system, partitioning is also a technique for vehicle routing problem (VRP) to choose targets for a single tour. A lot of attention is given to the problem of determining efficient routes within a given district. However, more significant long-term savings can be achieved if the borders of the districts are optimally determined. Though VRP is widely studied, in most case the studies are limited to the theoretical routing under the parameters and the objectives. In particular, it is assumed that all parameters are given and the feasibility of the model and algorithm in fact depends on the objectives, such as the total cost. And the VRP scheduling methods produce different routes passing though different customers set for every execution. The “dynamic” scheduling is difficult for operations which increases the cost to organize the transportation and delivery process. Therefore, a periodic balanced partition should be a better choice for Chinese tobacco companies. The balanced partition is based on the average demands from all detailers. For each district, delivery vehicles, distance and time are minimized and balanced to achieve a balanced workload. And, the district should be in a better geographical shape without overlap each other.

In this paper, the partition balancing problem in Chinese tobacco distribution is studied. The tobacco distribution problem with Chinese specific characters is seldom studied before. The problem of partition balancing, especially in the context of Chinese tobacco market, is hardly addressed in the existing literatures. Here, we build a multi-criteria model and propose an immune co-evolutionary algorithm to search the optimal partitions for tobacco distribution in China.

The remaining sections are organized as follows. In Section 2, the background knowledge is introduced including partitioning optimization models, vehicle routing problem, immune algorithm, co-evolutionary algorithm and multi-objective optimization. In Section 3, we describe the problem of partition balance of tobacco distribution in China. In Section 4, the problem is modelled as a multi-objective optimization problem on the graph, and related concepts, optimal objectives and constraints of which are defined and analyzed. Then, an immune co-evolutionary algorithm is designed to solve the problem. In Section 5, the partition balancing for tobacco distribution in Linfen city as a demonstration case is studied. Finally, conclusions and future researches follow in Section 6.

Section snippets

Partitioning optimization

Partitioning involves dividing a large geographical region into districts or assigning the detailers to different clusters according to the criteria to achieve minimal/maximal objectives and to balance the workload. The partitioning or districting problems have many practical applications. Over the last four decades, some researchers from different fields have developed models, algorithms and applications concerning the techniques to group the elementary units of territory into large districts

The current situations

In China, the sales and distribution of tobacco are commonly organized in the unit of city and by city tobacco companies. The cycle of sales and distribution are commonly five workdays. Then, it is naturally that the whole city area is divided into five districts and each district contains a set of routes, therefore every driver takes charge five routes. The existing partition criterion is the political district. The districts and routes are commonly fixed in a long run. This condition has

The multiple criteria partition balance model

Because the map data in China does not support geo-encoding for the street numbers, and the road map does not contains the detailed road segments to every detailer, the detailers in the residential area are associated to the road crossing points. The road map of the city can be modeled as a graph from the GIS based system. The partition problem can be regarded as grouping road nodes into clusters, with each cluster corresponding to a district. The elementary unit is the vertex of the graph,

Description of the real problem

As a demonstration of the study, eight political districts of Linfen city in Shanxi Province, China, distributed from the center depot are divided into five districts. Each district consists of one or several political districts. The tobacco distribution center owns 30 vehicles (150 tours for five workdays) with the capacity of 4500 to delivery about 500,000 tobaccos to more than 10,000 detailers through the fixed districts and routes every week. However, the load ratio of the vehicles is lower

Conclusion

In this paper, we study the partition balance problem of tobacco distribution in China. First, the problem is carefully defined including some guidelines and balance criteria. Second, the problem is modelled as a multi-criteria optimization problem on the graph, and correlated concepts, optimal objectives and constraints of which are defined and analyzed. Third, based on the large scale of the problem and inspired by the cooperative searching ability of immune system, an immune co-evolutionary

Acknowledgement

This work was supported in part by the Key Project of the National Nature Science Foundation of China (No. 60534020), the National Nature Science Foundation of China (No. 60775052, 70701009), the Cultivation Fund of the Key Scientific and Technical Innovation Project from Ministry of Education of China (No. 706024), International Science Cooperation Foundation of Shanghai (No. 061307041), Shanghai Talent Developing Foundation, and Specialized Foundation for Excellent Talent from Shanghai.

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