Abstract    Making decisions about the economic selection of the customers plays a significant role in the sale and logistic management of the companies. Furthermore, another issue affecting the relationship between the suppliers and the customers is the proper and timely distribution of the products as well as the optimum mixing of the distribution routes to reduce transportation costs. In this paper, the issues of the integration of routing, and the economic selection of customers has been explored aiming at minimizing the transportation, maintenance, and discount costs and maximizing the products selling profits. In addition to the amount of customer's purchasing, costumers' collection period is effective to offer them discounts. The economic customers are selected due to three factors: the discount on the price of the product, the marginal profit of the requested products, and the distance from the supplier's warehouse. Games software was used for the exact solution of the model, and Simulated annealing algorithm was used to solve the model in larger dimension. The efficiency and applicability of the proposed model was approved comparing the optimum results with a high preciseness as 98.91 percent. Moreover, in the case study of Kalleh Company, the results revealed 14% increase in pure profits.

Keywords    Vehicle Routing, Economic Selection of the Customers, Discounts, Collection Period, Optimization, Distribution and Sales Planning

چکیده    تصمیم گیری در مورد انتخاب اقتصادی مشتریان نقش قابل توجهی در فروش و مدیریت لجستیک شرکت ها دارد. همچنین، یکی دیگر از موضوعات تاثیرگذار در روابط میان تامین کنندگان و مشتریان، توزیع صحیح و به موقع محصولات و ترکیب بهینه از مسیرهای توزیع جهت کاهش هزینه های حمل و نقل است. در این مقاله به مسئله یکپارچه سازی چند دوره ای، چند محصولی مسیریابی و انتخاب اقتصادی مشتریان با هدف حداقل نمودن هزینه های حمل و نقل، هزینه های نگهداری موجودی در انبار، هزینه های تخفیف و حداکثر نمودن سود حاصل از فروش محصولات، پرداخته شده است. علاوه بر حجم خرید مشتریان، مدت زمان پرداخت مشتریان در میزان ارائه تخفیف به آنها موثر است. مشتریان اقتصادی با توجه به سه عامل تخفیف قیمت کالا، حاشیه سود محصولات درخواستی و فاصله از انبار تامین کننده انتخاب می شوند. برای حل دقیق مدل از نرم افزار گمز و برای حل در ابعاد بزرگتر از الگوریتم شبیه سازی تبرید استفاده شده است. کارایی مدل پیشنهادی با مقایسه جواب های بهینه با دقت بالای 98.91 درصد می باشد. همچنین در مطالعه موردی شرکت کاله شیراز ، نتایج حاصل، کاهش 14 درصدی در هزینه‌های این شرکت را نشان می دهد.

References    1.      Sohrabi, B. and Bassiri, M., "Experiments to determine the simulated annealing parameters case study in vrp", International Journal of Engineering Transactions B,  Vol. 17, No. 1, (2004), 71-80. 2.      Bakal, I. S., Geunes, J. and Romeijn, H. E., "Market selection decisions for inventory models with price-sensitive demand", Journal of Global Optimization,  Vol. 41, No. 4, (2008), 633-657. 3.      Geunes, J., Shen, Z.-J. and Romeijn, H. E., "Economic ordering decisions with market choice flexibility", Naval Research Logistics,  Vol. 51, No. 1, (2004), 117-136. 4.      Rabbani, M., Farshbaf-Geranmayeh, A. and Haghjoo, N., "Vehicle routing problem with considering multi-middle depots for perishable food delivery", Uncertain Supply Chain Management,  Vol. 4, No. 3, (2016), 171-182. 5.      Padasht, S. and Razmi, J., "A location-routing model on relief distribution centers", Uncertain Supply Chain Management,  Vol. 4, No. 4, (2016), 269-276. 6.      Zabihi, A., Gharakhani, M. and Afshinfar, A., "A multi criteria decision-making model for selecting hub port for iranian marine industry", Uncertain Supply Chain Management,  Vol. 4, No. 3, (2016), 195-206. 7.      Geunes, J., Romeijn, H. E. and Taaffe, K., "Requirements planning with pricing and order selection flexibility", Operations Research,  Vol. 54, No. 2, (2006), 394-401. 8.      Lee, T.-R. and Ueng, J.-H., "A study of vehicle routing problems with load-balancing", International Journal of Physical Distribution & Logistics Management,  Vol. 29, No. 10, (1999), 646-657. 9.      Ballou, R. H., "A multiproduct plant/warehouse location model with nonlinear inventory costs", Journal of Operations Management,  Vol. 5, (1975), 75-90. 10.    Apte, U. M. and Viswanathan, S., "Effective cross docking for improving distribution efficiencies", International Journal of Logistics,  Vol. 3, No. 3, (2000), 291-302. 11.    Wang, J.-L., "A supply chain application of fuzzy set theory to inventory control models–drp system analysis", Expert Systems with Applications,  Vol. 36, No. 5, (2009), 9229-9239. 12.    Fakhrzada, M. and Esfahanib, A. S., "Modeling the time windows vehicle routing problem in cross-docking strategy using two meta-heuristic algorithms", International Journal of Engineering-Transactions A: Basics,  Vol. 27, No. 7, (2013), 1113-1126. 13.    Hua, G., Wang, S. and Cheng, T., "Optimal pricing and order quantity for the newsvendor problem with free shipping", International Journal of Production Economics,  Vol. 135, No. 1, (2012), 162-169. 14.    Setak, M., Dastaki, M. S. and Karimi, H., "Investigating zone pricing in a location-routing problem using a variable neighborhood search algorithm", International Journal of Engineering-Transactions B: Applications,  Vol. 28, No. 11, (2015), 1624-1633. 15.    Mirzaei, A. H., Nakhai, K. I. and Zegordi, S. H., "A new algorithm for solving the inventory routing problem with direct shipment", Journal of Production and Operations Management, (2012), 1-28. 16.    Lee, A. H., Kang, H.-Y. and Lai, C.-M., "Solving lot-sizing problem with quantity discount and transportation cost", International Journal of Systems Science,  Vol. 44, No. 4, (2013), 760-774. 17.    Lee, A. H., Kang, H.-Y., Lai, C.-M. and Hong, W.-Y., "An integrated model for lot sizing with supplier selection and quantity discounts", Applied Mathematical Modelling,  Vol. 37, No. 7, (2013), 4733-4746. 18.    Fereiduni, M. and Hamzehee, M., "A p-robust model in humanitarian logistics in a non-neutral political environment", Uncertain Supply Chain Management,  Vol. 4, No. 4, (2016), 249-262. 19.    Potvin, J.-Y. and Rousseau, J.-M., "An exchange heuristic for routeing problems with time windows", Journal of the Operational Research Society,  Vol. 46, No. 12, (1995), 1433-1446. 20.    Tavakkoli-Moghaddam, R., Sayarshadand, H. and ElMekkawy, T., "Solving a new multi-period mathematical model of the rail-car fleet size and car utilization by simulated annealing", International Journal of Engineering, Transactions A: Basics,  Vol. 22, No. 1, (2009), 33-46.