یک تخفیف کمیت چندهدفه و مدل مشترک بهینه سازی برای هماهنگی زنجیره تأمین با خریدار واحد و فروشندگان متعدد

Supply chain management is concerned with the coordination of different parts of the production system. Companies have realized that they must closely collaborate with the suppliers of their strategic components or products. Recently, developing integrated inventory models for the supplier selection problem has attracted a significant amount of attention amongst researchers. In these models some incentives are required from the vendors to motivate the buyer to change his (her) policies to the policy which is optimal for the entire system. Quantity discount policies are used as common incentives in the literature. However, the literature on this problem does not incorporate quantity discount into the coordination model. This paper develops a multi-objective mixed integer nonlinear programming model to coordinate the system of a single buyer and multiple vendors under an all-unit quantity discount policy for the vendors. Due to the complexity of the problem two well known meta-heuristic algorithms are proposed to solve the problem. An illustrative example is given to show the behavior of the model. Results obtained from solving the sample problems show good performance of the proposed algorithms in finding the optimal solutions.

In the last few years the procurement function has become more critical for companies because of the increase in the level of outsourcing. Companies have realized that to remain in control of their destiny they must focus on closely collaborating with the suppliers of their strategic components or products. In these cases effective strategies are required to coordinate the supply chain. There are many academic and industrial researchers who have contributed to the joint optimization of buyer(s) and supplier(s). They have strived to improve the overall performance of the supply chain by considering the benefits of both parts of the supply chain. Recently the topic of one buyer and multiple suppliers has attracted significant attention among the researchers. In this topic the buyer should consider the benefits of the suppliers in the process of supplier selection and allocates his (her) orders among the suppliers. By optimizing the whole supply chain, the buyer’s total cost increases when compared with independent optimization. In order to overcome this problem, encouraging policies such as discounts and revenue sharing can be used. Quantity discount usually is used as a coordination mechanism to reduce the total system costs or maximize the total system profits. This policy encourages the buyer to order larger quantities and applies a mechanism that leads to a balance between the discounts obtained due to larger purchasing quantities and inventory holding costs. Furthermore it has been shown that when a typical discount policy is used, both the buyer and the supplier can realize higher overall profits [1]. In the supply chain different members have different conflicting objectives. Various criteria have been proposed for evaluating the suppliers [2] and [3]. Some of these criteria such as price/cost, quality and delivery performances are quantitative and some others such as flexibility, background of relationship and reputation are qualitative. Furthermore, some criteria may conflict with each other, such as cost and quality or quality and on time delivery. Hence, it is necessary to make a tradeoff between conflicting quantitative and qualitative criteria to find the best suppliers. This paper proposes a multi-objective supplier selection and order allocation model that tries to optimize the overall performance of a one-buyer and multiple-supplier supply chain by minimizing the total system cost including buyer’s annual cost and vendors’ annual cost, the total number of defective items and the total number of late delivered items. Furthermore, to incorporate the qualitative criteria in the model, maximizing the total purchasing value is also considered as another objective. In this model while the vendors benefit from the coordination by joint optimization, quantity discounts offered by the suppliers can guarantee that a buyer’s total relevant cost of coordination will not increase when compared with independent optimization. The remainder of the paper is organized as follows. Section 2 reviews some previous studies and researches. Section 3 states the problem specifications and presents a mathematical model. Section 4 discusses the procedures to solve the problem. In Section 5, a numerical example is presented to show the behavior of the model. In Section 6, the performance of the proposed algorithms is evaluated by solving some sample problems. Finally Section 7 is devoted to the conclusions achieved from this research.

In order to enhance the overall performance of the supply chain all members should closely collaborate with each other. Over the last few years various buyer–vendor coordination models have been established. The multi-vendor coordinated model creates a significant reduction in the vendors’ cost but the cost to the buyer significantly increases. Hence some incentives are required to motivate the buyer to adopt the coordinated policy. Furthermore in a typical supply chain there are several quantitative and qualitative conflicting criteria that must be considered in the decision making process. In this paper a multi-objective integrated inventory model is introduced in which joint optimization and quantity discount schemes are used to develop coordination between the two parts of the supply chain and to enhance the overall performance of the system. The compromise objective function in terms of sum of the relative deviations from the optimal values of the four objective functions is used to obtain a unique optimal decision for the problem. Since the problem is NP-hard, we proposed two meta-heuristic algorithms, the particle swarm optimization algorithm and scatter search algorithm to solve the problem. Furthermore, LINGO package version 8.0 is used to compute the exact optimal solutions for small problems. Results obtained from solving the sample problems showed that the proposed algorithms are capable of finding high quality solutions.