ترکیبی از الگوریتم ژنتیک و بهینه سازی ازدحام ذرات برای حل مسئله برنامه ریزی خطی سطح دوطرفه- یک مطالعه موردی در مدل زنجیره تامین

The main goal of supply chain management is to coordinate and collaborate the supply chain partners seamlessly. On the other hand, bi-level linear programming is a technique for modeling decentralized decision. It consists of the upper level and lower level objectives. Thus, this paper intends to apply bi-level linear programming to supply chain distribution problem and develop an efficient method based on hybrid of genetic algorithm (GA) and particle swarm optimization (PSO). The performance of the proposed method is ascertained by comparing the results with GA and PSO using four problems in the literature and a supply chain distribution model.

Bi-level linear programming problem (BLPP) has the hierarchical relationship between upper and lower levels. It is developed for decentralized planning systems in which the upper level is termed as the leader and the lower level pertains to the objective of the follower. Thus, many researches applied it to make the best decision with the upper-and-lower hierarchical relationships in the organizations. Thus, the first effort of this study is made to use collaboration function of supply chain systems to obtain the best resources distribution. This can result in reducing production, inventory and distribution costs and increasing the efficiency and the coordination of supply chain partners. On the other hand, metaheuristics, like genetic algorithm (GA) and particle swarm optimization (PSO), are the generic computational technique espoused from the progression of biological life in the natural humanity [1]. GA is a global optimization algorithm by simulating heredity and process of evolution in environment. It uses three operating process that are selection, crossover and mutation to be survival of the fittest. Additionally, PSO can mimic cooperation between individuals in the same group by using swarm intelligence and exchange experiences from generation to generation [2]. There are some advantages to exploit and explore the hyperspace global optimum with PSO method, especially the fast convergence. Because of the characteristics of GA and PSO, it is feasible to make use of the crossover and mutation of algorithm process into PSO. Moreover, it can effectively integrate the characteristic of global search in GA and the capability of local search in PSO to avoid converging ahead of time and to raise the accuracy of problem solving. Therefore, the second effort of this study is to develop three hybrids of GA and PSO (HGAPSO) for solving BLPP and apply them to the area of supply chain management with pattern of hierarchy. Four problems adopted from the literature are employed to validate the proposed methods’ feasibility. The results demonstrate that the proposed three hybrid methods are able to provide better performance than GA and PSO. Additionally, this study also employs the three proposed hybrid methods to solve the BLPP for the supply chain. The main purpose is to collaboratively arrange the inventory between distribution centers and manufacturers. The experimental results show that the proposed methods also have better performance than GA and PSO. The rest of this paper is organized as follows. Section 2 describes basic concept of supply chain management, BLPP, GA and PSO, while the proposed hybrid methods for solving BLPP are explained in Section 3. Sections 4 and 5 make a thorough discussion on computational experiences for four problems from literature and supply chain distribution model, respectively. Finally, the concluding remarks are made in Section 6.

This study has demonstrated a supply chain model can be formulated by using BLPP. The proposed supply chain model is able to deal with the relationship between distribution center and manufacturer. We can find out that the proposed model is more suitable for the practical applications, especially in supply chain. Three hybrid methods though integrating GA and PSO have been validated using four examples adopted from the literature. The experimental results indicate that hybrid methods are always better than only using only one algorithm. Among three hybrid methods, we can find out that the third method, HGAPSO-3, is superior to other two hybrid methods. It is recommended for the further application. Also, HGAPSO-3 has smaller standard deviation. This implies that HGAPSO-3 has better stability compared to GA and PSO and other two hybrid methods. However, the current method is only suitable for BLPP. It is promising to extend the proposed method for multi-level linear programming problem in the future. Definitely, other metaheuristics, like artificial immune system, can also be employed for the current application.