A new mathematical model for the closed-loop supply chains considering pricing for product, a fleet of heterogeneous vehicles, and inventory costs

Journal of Optimization in Industrial Engineering

مقاله 4، دوره 10، شماره 21، خرداد 2017، صفحه 29-40   

نوع مقاله: Original Manuscript

شناسه دیجیتال (DOI): 10.22094/joie.2016.258

نویسندگان

Isa Nakhai Kamalabadi^{* 1}؛ mohammad mohammadnejad²؛ Ramin sadeghian³؛ Fardin ahmadizar⁴

¹Professor of Industrial Engineering at University of Kurdistan, Sanandaj, Iran

²Department of Industrial Engineering, Payame Noor University , Tehran ,Iran.

³Assistant Professor at Department of Industrial Engineering, Payame Noor University, Tehran, Iran

⁴Associate Professor at Department of Industrial Engineering, kordstan University, Sanandaj, Iran

چکیده

Mathematical models have been used in many areas of supply chain management. In this paper, we present a mixed-integer non-linear programing (MINLP) model to solve a multi-period, closed-loop supply chains (CLSCs) with two echelons consist of producers and customers. In order to satisfy the demands, the producers are be able to order for materials in the beginning of each period for one or more periods. A fleet of heterogeneous vehicles are routed to deliver the products from producers to customers and to pick up defective products from the customers and move them to the collection-repair center. Also, it is assumed that the rate of defective products is related to the price. In the other words, the more expensive product, the less rate of defect. The objective function maximize the profit which comes from total cost which is subtracted from income. The income is divided two part, selling products and wastes, and total cost consists of several part such as, costs of defective products, ordering cost, cost of holding in producers and collection-repair center, transportation costs, and the cost of assigning place for collection-repair center. Finally, computational results are discussed and analyzed for a numerical example in order to demonstrate the effectiveness of the proposed model.

کلیدواژه‌ها

Closed-loop supply chain؛ Mathematical Modeling؛ Heterogeneous vehicles routing؛ Inventory؛ Pricing