ارائه مدل کنترل موجودی برای اقلام منسوخ شدنی با لحاظ نمودن تخفیف کلی و قیمت وابسته به مقدار سفارش

نوع مقاله: مقاله پژوهشی

نویسندگان

1 عضو هیات علمی/دانشکده مهندسی صنایع، دانشگاه علم و صنعت ایران

2 دانشجوی دکتری، دانشکده مهندسی صنایع، دانشگاه علم و صنعت ایران

چکیده

در این مطالعه‌، مدل کنترل موجودی منسوخ شدنی کالاهایی که خرده‌فروشی می‌شود و با وجود تخفیف کلی در سفارش بررسی‌ شده است. خرده‌فروش‌ها کالاهای منسوخ شدنی را بر اساس قیمت خریدی که وابسته به مقدار سفارش است، خریداری می‌کنند. فرضیه این مقاله این است که بین تصمیم‌های مختلف، مقدار سفارش با توجه به احتمال منسوخ شدن کالا در هر لحظه و قیمت خرید کالا با توجه به استفاده از تخفیف وابستگی دارد، در نظر گرفتن این وابستگی‌‌‌ها در مدلی هماهنگ، باعث بهبود عملکرد خرده فروش‌ها می‌‌‌شود. هدف مدل، کم کردن هزینه موجودی خرده‌فروش‌ها ، از راه پیدا کردن مقدار بهینه قیمت خرید و مقدار سفارش­دهی می‌‌‌باشد. هرچند مدل‌‌‌های تخفیف برای کالاهای فسادپذیر که کالا با قیمتی ثابت یا تغییرپذیر است و در حال نابودی هستند، توضیح داده‌شده‌اند؛ اما به‌کار‌گیری این مدل‌ها، برای کالاهای منسوخ شده‌ای که بر اساس توزیعی احتمالی در آینده دچار کاهش تقاضا می‌‌‌شود، بررسی نشده است. درحالی‌ که این شرایط واقعی و بسیاری از خرده‌فروش‌ها با آن رو‌به‌رو می‌شوند و در چنین شرایطی خرده‌فروش‌ها نیاز دارند که مشتری‌ها را به خرید بیشتر تشویق کنند. در این مدل، طول زمان منسوخ شدن کالا، توزیع نمایی دارد و نوع منسوخ شدن کالا ناگهانی است. مدل به‌صورت ریاضی توسعه داده شده و جواب بهینه و تحدّب آن به‌وسیله مشتقات اول و دوم به‌دست آمده است. در انتها برای شفاف سازی مدل پیشنهادی، مثالی عددی ارائه شده و بررسی حساسیتی بر روی عامل‌های اصلی مدل انجام شده است.

کلیدواژه‌ها


عنوان مقاله [English]

An inventory control model for obsolete items with consideration of all unit quantity discount and price-dependent on order quantity

نویسندگان [English]

  • Mohammad Reza Gholamian 1
  • Hasan Zamani Bajegani 2
1 Faculty Member/ School of Industrial Engineering, Iran University of Science and Technology (IUST), Tehran, Iran
2 Ph.D. Candidate, School of Industrial Engineering, Iran University of Science and Technology (IUST), Tehran, Iran
چکیده [English]

In this study, a single-item obsolescence inventory model with one retailer and with all-unit quantity discounts has been investigated. The retailer purchases items with a possibility of future obsolescence based on the purchase price which is dependent into the order quantity. It is assumed in this paper that there are dependencies between different decisions on the amount of order quantity, considering the probability of obsolescence at any given moment and the purchase price of items by taking into account the use of discount. The aim of the model is to minimize the retailer’s inventory cost through the finding optimal purchase price and order replenishment. Although discount models have been developed for deteriorating items with a constant or varying rate of deterioration, but the use of these models, for obsolete items, in which the demand of item falls suddenly in the future based on a probability distribution, has not been so far investigated. While, these are the real conditions that many retailers are facing and in such situations the retailers need to encourage the customers to buy more. In this model, the length of obsolescence time is considered as exponential function and the obsolescence is occurred suddenly. The model has been developed mathematically and then the optimal solution and convexity are resulted from the first and second derivatives of objective function respectively. Finally, for the sake of clarity of the proposed model, a numerical example is presented and sensitivity analyses are performed on critical parameters of the model.

کلیدواژه‌ها [English]

  • Inventory Control
  • All-unit Quantity Discount
  • Obsolescence
  • Price-Dependent on Order Quantity
[1] Y.J.Lin, and C.H. Chia-Huei Ho, “Integrated inventory model with quantity discount and price-sensitive demand”, TOP, vol. 19, pp. 177–188, 2011.

[2] Y. Duan, J. Luo, and J. Huo, “Buyer–vendor inventory coordination with quantity discount incentive for fixed lifetime product, international journal Production Economics”, vol. 128,  pp. 351–357, 2010.

[3] H.N. Nguyen, C.E. Rainwater, S.J. Mason, and E.A. Pohl, ‘Quantity discount with freight consolidation”, Transportation Research Part E., vol. 66, pp. 66–82, 2014.

[4] B. Sarkar, B. Mandal, and S. Sarkar, “Quality improvement and backorder price discount under controllable lead time in an inventory model”, Journal of Manufacturing Systems., vol. 35, pp. 26–36, 2015.

[5] D. Zissis, G. Ioannou, and A. Burnetas, “Supply chain coordination under discrete information asymmetries and quantity discounts”, Omega, vol. 53, pp.  21–29, 2015.

[6] H. Azizi, and R. Jahed, Supplier Selection in Volume Discount Environments in the Presence of Both Cardinal and Ordinal Data: A New Approach Based On Double Frontiers DEA, Management Research in Iran, vol. 19, no. 3, pp. 185-210, 2015. (In Persian).

[7] J.K. Alfares, and A.M. Ghaithan, “Inventory and Pricing Model with Price-Dependent Demand, Time-Varying Holding Cost, and Quantity Discounts”, Computers & Industrial Engineering., vol. 94, pp. 170-177, 2016.

[8] F. Manoouri, T. Abbasnejad and H.R. Askarpour, “Designing an agile supply chain network in terms of demand dependence on price”, Modern Research in Decision Making., vol. 2, no. 3, pp. 50-75, 2017. (In Persian)

[9] O. Jadidi, M.T. Jaber, and S. Zolfaghari, “Joint pricing and inventory problem with price dependent stochastic demand and price discounts”, Computers & Industrial Engineering., vol. 114, pp. 45-53, 2017.

[10] B.B. Venegas, and J.A. Ventura, “A Two-Stage Supply Chain Coordination Mechanism considering Price Sensitive Demand and Quantity Discounts”, European Journal of Operational Research., vol. 264, pp. 524-533, 2018.

[11] H. Wang,  Y. Yu, W. Zhang, and Z.H. Hua, “Procurement Strategies for Lost-Sales Inventory Systems with All-Units Discounts”, European Journal of Operational Research., vol. 272, pp. 539-548, 2019.

[12] H.M. Wee, “Deteriorating inventory model with quantity discount, pricing and partial backordering”, international journal Production Economics., and vol. 59, pp. 511-518, 1999.

[13] S. Banerjee, and S. Agrawal, “Inventory Model for Deteriorating Items with Freshness and Price Dependent Demand: Optimal Discounting and Ordering Policies”, Applied Mathematical Modelling, vol. 52, pp. 53-64, 2017.

[14] J. Xu, Q. Qi, and Q. Bai, “Coordinating a dual-channel supply chain with price discount contracts under carbon emission capacity regulation”, Applied Mathematical Modelling., vol. 56, pp. 449–468, 2018.

[15] A. Mohammdi, and A., Rajabi, “Application of Markov Chain Model to Provide the Appropriate Model of Tax Discount with Dynamic Programming Approach”, Management Research in Iran, vol. 16, no. 1, pp. 107-129, 2012. (In Persian).

[16] S.H. Tamjidzad, and S.H. Mirmohammadi, “An optimal (r,Q) policy in a stochastic inventory system with all-units quantity discount and limited sharable resource”, European Journal of Operational Research., vol. 247, pp. 93–100, 2015.

[17] R. Mohammadi-vojdan, and J. Geunes, “The newsvendor problem with capacitated suppliers and quantity discounts”, European Journal of Operational Research., vol. 271, pp. 1–11, 2018.

[18] S.P. Chen, and Y.H. Ho, “Optimal inventory policy for the fuzzy newsboy problem with quantity discounts”, Information Sciences., vol. 228, pp. 75–89, 2013.

[19] J.Sadeghi, S,M. Mousavi, and S.T. Akhavan Niaki, “Optimizing an Inventory Model with Fuzzy Demand, Backordering, and Discount Using a Hybrid Imperialist Competitive Algorithm”, Applied Mathematical Modelling., vol. 40, pp. 7318-7335, 2016.

[20] A. Kundu, P. Guchhait, P. Pramanik, M.K. Maiti, and M.A. Maiti, “production inventory model with price discounted fuzzy demand using an interval compared hybrid algorithm”, Swarm and Evolutionary Computation., vol. 34, pp. 1-17, 2017.

[21] J. Behnamian, and M.M. Bashar, “Multi-stage modeling for non-cooperative multi-echelon supply chain management problem with discount under uncertainty”, Modern Research in Decision Making., vol. 2, no. 3, pp. 50-75, 2017.(In Persian)

[22] S.H. Tamjidzad, and S.H. Mirmohammadi, Optimal (r, Q) policy in a stochastic inventory system with limited resource under incremental quantity discount, Computers & Industrial Engineering., vol. 103, pp. 59-69, 2017.

[23] S.H. Tamjidzad, and S.H. Mirmohammadi,  “A two-stage heuristic approach for a multi-item inventory system with limited budgetary resource and all-units discount”, Computers & Industrial Engineering., vol. 124, pp. 293-303, 2018.

[24] C.V. Delft, and J.P. Vial, Discounted costs, “obsolescence and planned stock outs with the EOQ formula”. International Journal of Production Economics, vol. 44, pp. 255-265, 1996.

[25] P. Joglekar, P. Lee, A profit-maximization model for a retailer's stocking decisions on products subject to sudden obsolescence. Production and Operations Management vol. 5, no. 3, pp. 288-294, 1996.