شبیه‌سازی مسئله کنترل موجودی محصولات فسادپذیر با هزینه سفارش‎دهی متغیر به کمک پویایی‎های سیستم

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکترا مهندسی صنایع، دانشگاه صنعتی خواجه نصیرالدین

2 مدیر گروه صنایع

3 عضو هیات علمی / دانشگاه خواجه نصیرالدین طوسی

چکیده

وابستگی هزینه‎ی سفارش‎دهی محصول به اندازه سفارش یکی از فرضیات کاربردی و کمتر مورد بررسی قرار گرفته در ادبیات مربوط به مدل مقدار سفارش اقتصادی است. این فرض باعث غیرمحدب شدن تابع هدف و پیچیدگی مدل مسئله می‎شود. همچنین کنترل موجودی محصولاتی که در طی زمان امکان از مد افتادن یا فاسد شدن آن‌ها وجود دارد، بسیار مهم است. در این راستا، شبیه‌سازی مسئله‎ی کنترل موجودی محصولات فسادپذیر با تقاضای تصادفی و وابسته به زمان و قیمت فروش محصول، در نظر گرفته شده است. همچنین وابستگی هزینه سفارش‎دهی به اندازه سفارش و وابستگی هزینه نگهداری به سطح موجودی که از فرضیات کاربردی و عملیاتی در دنیای تجارت هستند نیز در نظر گرفته شده‎اند که مجموعاً باعث می‌شوند از روش‌های معمول ریاضیاتی قادر به حل مسئله نباشیم. برای مدل‌سازی و حل مسئله از روش پویایی‎های سیستم به عنوان یک روش قدرتمند، انعطاف‎پذیر و کاربردی استفاده شده است. یک مثال عددی نیز برای درک بهتر نحوه عملکرد شبیه‌سازی مدل، ارائه شده است و به کمک بهینه‎سازی مقادیر ورودی (نقطه سفارش مجدد و مقدار سفارش)، مقادیر بهینه تابع هدف (میانگین خالص هزینه‎ها) به دست آمده است. نتایج نشان می‌دهند که خط‌مشی پرکردن موجودی پیشنهادی می‌تواند در تصمیم‌گیری‌های لازم برای مدیریت و کنترل موجودی محصولات فسادپذیر مفید واقع شود.

کلیدواژه‌ها


عنوان مقاله [English]

Simulation of Perishable Products Inventory Management Problem with Varying Order Cost by System Dynamics

نویسندگان [English]

  • Abdollah Sharifi 1
  • Abdollah Aghaei 2
  • Donya Rahmani 3
1 Industrial Engineering Doctoral Student, K. N. Toosi University of Technology
2 Industrial Engineering Professor, K. N. Toosi University of Technology
3 Industrial Engineering Associate Professor, K. N. Toosi University of Technology
چکیده [English]

Dependence of a product order cost to the order quantity is one of the practical and less surveyed assumptions of the literature of economic order quantity model. This assumptions will cause the goal function to be non-convex and increases the complexity of the problem model. Furthermore, inventory management of the products which are likely to be out of fashion or perished over time, has a great importance. In this regard, simulation of the inventory control model of perishable products has been considered in the present study via the stochastic demand of the product which depends on the time and price of the product. In addition, the dependence of the order cost to the order quantity and dependence of holding cost to the inventory level which are among the practical assumptions of the business world have been considered. These factors cause the usual mathematical solutions not to be able to solve the problem. Therefore, system dynamics have been used as a powerful, flexible, and practical solution to model and solve the problem. A numerical example is also presented to provide a better understanding of the simulation operation; and with the assistance of the optimization of the input variables (ReOrder Point, Order Quantity) the optimal amount of the objective function (Gross Cost Average) is reached. The results showed that the proposed replenishment policy can benefit the necessary decisions regarding inventory management and control of the perishable products.

کلیدواژه‌ها [English]

  • Inventory Control Simulation
  • Perishable
  • System Dynamics
  • Varying Order Cost
  • Non-convex
[1]   Harris, F. W. (1913). How many parts to make at once. Factory, The Magazine of Management, 10: 135-136.
[2]   Abuo-El-Ata, M., Fergany, H. A. and El-Wakeel, M. F. (2003). Probabilistic multi-item inventory model with varying order cost under two restrictions: a geometric programming approach. International Journal of Production Economics, 83: 223-231.
[3]   Hariri, A. and Abou-El-Ata, M. (1997). Multi-item production lot-size inventory model with varying order cost under a restriction: a geometric programming approach. Production Planning & Control, 8: 179-182.
[4]   Kotb, K. and Fergany, H. A. (2011). Multi-item EOQ model with varying holding cost: a geometric programming approach. International Mathematical Forum. 1135-1144.
[5]   El-Wakeel, M. F. (2012). Constrained backorders inventory system with varying order cost: Lead time demand uniformly distributed. Journal of King Saud University-Science, 24: 285-288.
[6]   Fergany, A. and El-Wakeel, M. F. (2006). Constrained probabilistic lost sales inventory system with normal distribution and varying order cost. Journal of Mathematics and Statistics, 2: 363-366.
[7]   Fergany, A. and El-Wakeel, M. F. (2006). Constrained probabilistic lost sales inventory system with continuous distributions and varying order cost. Journal of Association for the Advancement of Modeling & Simulation Techniques in Enterprises, 27: 3-4.
[8]   Choi, T. M. (2014). Handbook of EOQ Inventory Problems: Stochastic and Deterministic Models and Applications, Springer US.
[9]   Mendoza, A. and Ventura, J. A. (2010). A serial inventory system with supplier selection and order quantity allocation. European Journal of Operational Research, 207: 1304-1315.
[10] Matsuyama, K. (2001). The EOQ-Models modified by introducing discount of purchase price or increase of setup cost. International Journal of Production Economics, 73: 83-99.
[11] Ting, P. S., Hou, K. L. and Chung, K. J. (2009). An accurate and reliable solution algorithm for the (Q, r) inventory system with a fixed shortage cost. Mathematical and Computer Modelling, 49: 128-135.
[12] Chung, K. J., Lin, S. D. and Srivastava, H. M. (2012). The complete solution procedures for the mathematical analysis of some families of optimal inventory models with order-size dependent trade credit and deterministic and constant demand. Applied Mathematics and Computation, 219: 142-157.
[13] Lagodimos, A., Skouri, K., Christou, I. and Chountalas, P. (2018). The discrete-time EOQ model: Solution and implications. European Journal of Operational Research, 266: 112-121.
[14] Saavedra-Nieves, A., García-Jurado, I. and Fiestras-Janeiro, M. G. (2018). On coalition formation in a non-convex multi-agent inventory problem. Annals of Operations Research, 261: 255-273.
[15] Mendoza, A. and Ventura, J. A. (2005). An Inventory Model with Incremental Quantity Discounts and Transshipment Costs. IIE Annual Conference. Proceedings. Institute of Industrial and Systems Engineers (IISE), 1.
[16] Tabatabaei, S. R. M., Sadjadi, S. J. and Makui, A. (2017). Optimal pricing and marketing planning for deteriorating items. PloS one, 12: e0172758.
[17] Nghia, N. D. and Toan, N. T. (1997). On a Non-convex Optimization Problem in the Inventory Control System. Vietnam Journal of Mathematics, 25: 203-209.
[18] Azizan, N., Su, Y., Dvijotham, K. and Wierman, A. (2018). Optimal Pricing in Markets with Non-Convex Costs. Operations Research (OR).
[19] Nahmias, S. (2011). Perishable inventory systems, Springer Science & Business Media.
[20] Abramovitz, M. (1954). Whitin's Inventory Theoty. Kyklos, 7: 287-289.
[21] Ghare, P. (1963). A model for an exponentially decaying inventory. J. ind. Engng, 14: 238-243.
[22] Feng, L., Chan, Y. L. and Cárdenas-Barrón, L. E. (2017). Pricing and lot-sizing polices for perishable goods when the demand depends on selling price, displayed stocks, and expiration date. International Journal of Production Economics, 185: 11-20.
[23] Van Donselaar, K., Van Woensel, T., Broekmeulen, R. and Fransoo, J. (2006). Inventory control of perishables in supermarkets. International Journal of Production Economics, 104: 462-472.
[24] Duan, Q. and Liao, T. W. (2013). A new age-based replenishment policy for supply chain inventory optimization of highly perishable products. International Journal of Production Economics, 145: 658-671.
[25] Akbari, M., Imani, D. M. and Mahmoodjanloo, M. (2017). Optimizing a vendor managed inventory (VMI) supply chain for perishable products by considering discount: Two calibrated meta-heuristic algorithms. Computers & Industrial Engineering, 103: 227-241.
[26] Sarker, B. R., Jamal, A. M. M. and Wang, S. (2000). Supply chain models for perishable products under inflation and permissible delay in payment. Computers & Operations Research, 27: 59-75.
[27] Chen, X., Pang, Z. and Pan, L. (2014). Coordinating Inventory Control and Pricing Strategies for Perishable Products. Operations Research, 62: 284-300.
[28] Chen, W., Li, J. and Jin, X. (2016). The replenishment policy of agri-products with stochastic demand in integrated agricultural supply chains. Expert Systems with Applications, 48: 55-66.
[29] Sana, S. S. (2010). An EOQ Model for Perishable Item with Stock Dependent Demand and Price Discount Rate. American Journal of Mathematical and Management Sciences, 30: 299-316.
[30] Shen, D., Lai, K. K., Leung, S. C. H. and Liang, L. (2011). Modelling and analysis of inventory replenishment for perishable agricultural products with buyer–seller collaboration. International Journal of Systems Science, 42: 1207-1217.
[31] Dobson, G., Pinker, E. J. and Yildiz, O. (2017). An EOQ model for perishable goods with age-dependent demand rate. European Journal of Operational Research, 257: 84-88.
[32] Avinadav, T., Herbon, A. and Spiegel, U. (2013). Optimal inventory policy for a perishable item with demand function sensitive to price and time. International Journal of Production Economics, 144: 497-506.
[33] Kouki, C., Jemaï, Z. and Minner, S. (2015). A lost sales (r, Q) inventory control model for perishables with fixed lifetime and lead time. International Journal of Production Economics, 168: 143-157.
[34] Chiu, H. N. (1995). An approximation to the continuous review inventory model with perishable items and lead times. European Journal of Operational Research, 87: 93-108.
[35] Chiu, H. N. (1995). A heuristic (R, T) periodic review perishable inventory model with lead times. International Journal of Production Economics, 42: 1-15.
[36] Chen, J. M. and Chen, L. T. (2004). Pricing and lot-sizing for a deteriorating item in a periodic review inventory system with shortages. Journal of the Operational Research Society, 55: 892-901.
[37] Chaudhary, V., Kulshrestha, R. and Routroy, S. (2018). State-of-the-art literature review on inventory models for perishable products. Journal of Advances in Management Research, 15: 306-346.
[39] Langroodi, R. R. P. and Amiri, M. (2016). A system dynamics modeling approach for a multi-level, multi-product, multi-region supply chain under demand uncertainty. Expert Systems with Applications, 51: 231-244.
[40] Piewthongngam, K., Vijitnopparat, P., Pathumnakul, S., Chumpatong, S. and Duangjinda, M. (2014). System dynamics modelling of an integrated pig production supply chain. Biosystems Engineering, 127: 24-40.
[41] Kumar, S. and Nigmatullin, A. (2011). A system dynamics analysis of food supply chains – Case study with non-perishable products. Simulation Modelling Practice and Theory, 19: 2151-2168.
[42] Minegishi, S. and Thiel, D. (2000). System dynamics modeling and simulation of a particular food supply chain. Simulation Practice and Theory, 8: 321-339.
[43] Lee, C. F. and Chung, C. P. (2012). An Inventory Model for Deteriorating Items in a Supply Chain with System Dynamics Analysis. Procedia-Social and Behavioral Sciences, 40: 41-51.
[44] Poles, R. (2013). System Dynamics modelling of a production and inventory system for remanufacturing to evaluate system improvement strategies. International Journal of Production Economics, 144: 189-199.
[45] Liu, L. and Yang, T. (1999). An (s, S) random lifetime inventory model with a positive lead time. European Journal of Operational Research, 113: 52-63.
[46] Kalpakam, S. and Shanthi, S. (2006). A continuous review perishable system with renewal demands. Annals of Operations Research, 143: 211-225.
[47] Olsson, F. and Tydesjö, P. (2010). Inventory problems with perishable items: Fixed lifetimes and backlogging. European Journal of Operational Research, 202: 131-137.
[48] Abad, P. L. and Jaggi, C. K. (2003). A joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive. International Journal of Production Economics, 83: 115-122.
]38[ طالعی‎زاده، عطاالله، صالحی، علی، (1394). "مدل کنترل موجودی با طول دوره بازپرسازی تصادفی و پرداخت معوقه برای کالاهای فسادپذیر". نشریه پژوهش‎های مهندسی صنایع در سیستم‎های تولید، 5: 13-25.