تعیین سیاست بهینه سفارش‌دهی در مدل چند دوره‌ای احتمالی با در نظر گرفتن قیمت خرید تصادفی

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد مهندسی صنایع، دانشکده مهندسی، دانشگاه کردستان، سنندج، ایران

2 استادیار گروه مهندسی صنایع، دانشکده مهندسی، دانشگاه کردستان، سنندج، ایران

10.22084/ier.2020.20328.1909

چکیده

در این مقاله مسئله برنامه‌ریزی و کنترل موجودی دو دوره‌ای با تقاضای احتمالی موردبررسی قرار می‌گیرد. در این سیستم فقط در اول دوره امکان سفارش‌دهی وجود دارد. تقاضا در طول دوره اول تصادفی و از توزیع مشخصی پیروی می‌کند و تقاضا برای محصولات باقیمانده در پایان دوره اول، وابسته به قیمت فروش آن در طول دوره دوم است. در این حالت قیمت فروش محصولات پایان دوره اهمیت زیادی پیدا می‌کند به‌گونه‌ای که قیمت کم باعث فروش بیشتر می‌شود. همچنین در مسئله موردبررسی فرض شده است که قیمت خرید محصولات در اول دوره یک فرآیند تصادفی و وابسته به زمان است. برای مسئله بیان شده مدل ریاضی ارائه‌شده است و سپس سعی می‌شود براساس نگرش برنامه‌ریزی پویا احتمالی، مقدار بهینه قیمت فروش پایان دوره، مقدار بهینه سفارش‌دهی و قیمت خرید محصولات به‌منظور ماکزیمم کردن سود سیستم تعیین گردد. در نهایت با بیان مثال عددی به بررسی عملکرد مدل بیان شده و تحلیل حساسیت آن پرداخته می‌شود.

کلیدواژه‌ها


عنوان مقاله [English]

Determining The Optimal Ordering Policy In A Multi-Period Stochastic Model With The Uncertainty Purchase Price

نویسندگان [English]

  • Zahra Rajabi 1
  • Heibatolah Sadeghi 2
  • Anwar Mahmoodi 2
1 Department of industrial of engineering, Faculty of engineering, University of Kurdistan, Sanandaj, Iran
2 Assistant Professor, Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran
چکیده [English]

This paper deals with a two-period inventory planning and control problem with stochastic demand. In this system, a distributor can order the products in a preseason period and sell them in two subsequent selling periods. Demand during the first period is a random variable with a known probability distribution, while the demand for the remaining products at the end of the first period depends on their selling price during the second period. Therefore, the selling price of end-of-period products is very important so that a low price will achieve more sales. It is also assumed that the purchase price of the products in the preseason period is a time-dependent and follows a random process. For the considered problem, a mathematical model is suggested and then using the probabilistic dynamic planning approach, the optimal selling price at the second period, the optimal ordering quantity, and the purchase price of the products are determined to maximize the system profit. Finally, a numerical example is presented to investigate the performance of the model, and the sensitivity analysis of the main parameters.

کلیدواژه‌ها [English]

  • Multi period news vendor
  • Pricing
  • Random process
  • Probabilistic dynamic programming
[1] Khouja, M. (1999). “The single-period (news-vendor) problem: literature review and suggestions for future research”, omega, 27(5): 537-553.
[2] Mitra, S. (2018). “Newsvendor problem with clearance pricing”, European Journal of Operational Research, 268(1): 193-202.
[3] Hu, X., Su, P. (2018). “The newsvendor's joint procurement and pricing problem under price-sensitive stochastic demand and purchase price uncertainty”, Omega, 79: 81-90.
[4] Taleizadeh, A.A., Niaki, S.T.A., Hosseini, V. (2008). “The multi-product multi-constraint newsboy problem with incremental discount and batch order”, Asian Journal of Applied Sciences, 1: 110-122.
[5] Taleizadeh, A.A., Akhavan Niaki, S.T. (2010). “A hybrid meta-heuristic method to optimize bi-objective single period newsboy problem with fuzzy cost and incremental discount”, Journal of Optimization in Industrial Engineering, (3): 1-13.
[6] Zhang, B., Hua, Z. (2010). “A portfolio approach to multi-product newsboy problem with budget constraint”, Computers & Industrial Engineering, 58(4): 759-765.
[7] Bashiri, M., Badri, H.,  Talebi, J. (2012). “A new approach to tactical and strategic planning in production–distribution networks”, Applied Mathematical Modelling, 36(4): 1703-1717.
[8] Sajadi, S., Arianezhad, M.G., Sadeghi, H.A. (2009). An Improved WAGNER-WHITIN Algorithm.
[9] Sadeghi, H. (2020). “Building to forecast system by considering product reliability, POQ policy, and periodic demand”, Journal of Quality Engineering and Production Optimization, Articles in Press, Accepted Manuscript, Available Online.
[10] Pal, B., Sana, S.S., Chaudhuri, K. A. (2015). “distribution-free newsvendor problem with nonlinear holding cost”, International Journal of Systems Science, 46(7): 1269-1277.
[11] Pasandideh, S.H.R., Niaki, S.T.A., Keshavarzi, A. (2017). “A two-echelon single-period inventory control problem with market strategies and customer satisfaction”, Journal of Uncertain Systems, 11(1): 18-34.
[12] Keramatpour, M., Niaki, S.T.A., Pasandideh, S.H.R. (2018). “A bi-objective two-level newsvendor problem with discount policies and budget constraint”, Computers & Industrial Engineering, 120: 192-205.
[13] ابراهیمی نسب، حمیدرضا.، حیدری، جعفر، طالعی‌زاده، عطاالله. (1395). "هماهنگ‌سازی سیاست‌های سفارش دهی و تولید در مدل روزنامه‌فروش دوسطحی تحت قرارداد انعطاف مقداری"، نشریهپژوهش‌های مهندسی صنایع در سیستم‌های تولید، 4(8): 119-131.
[14] Mitra, S., Chatterjee, A. K. (2018). “Single-period newsvendor problem under random end-of-season demand”, Journal of the Operational Research Society, 69(7): 1046-1060.
[15] Petruzzi, N. C., Dada, M. (1999). “Pricing and the newsvendor problem: A review with extensions”, Operations research, 147(2): 183-194.
[16] Petruzzi, N.C., Dada, M. (2001). “Information and inventory recourse for a two-market, price-setting retailer”, Manufacturing & Service Operations Management, 3(3): 242-263.
[17] Tang, O., Musa, S.N., Li, J. (2012). “Dynamic pricing in the newsvendor problem with yield risks”, International Journal of Production Economics, 139(1): 127-134.
[18] Hua, G., Wang, S., Cheng, T. (2012). “Optimal pricing and order quantity for the newsvendor problem with free shipping”, International Journal of Production Economics, 135(1): 162-169.
[19] Monahan, G.E., Petruzzi, N.C., Zhao, W. (2004). “The dynamic pricing problem from a newsvendor's perspective”, Manufacturing & Service Operations Management, 6(1): 73-91.
[20] Soon, W. (2011). “A review of multi-product pricing models”, Applied mathematics and computation, 217(21): 8149-8165.
[21] Murray, C.C., Gosavi, A., Talukdar, D. (2012). “The multi-product price-setting newsvendor with resource capacity constraints”, International Journal of Production Economics, 138(1): 148-158.
[22] Shi, J., Zhang, G., Sha, J. (2011). “Jointly pricing and ordering for a multi-product multi-constraint newsvendor problem with supplier quantity discounts”, Applied Mathematical Modelling, 35(6): 3001-3011.
[23] Ma, S. et al. (2017). Analysis of the Newsboy Problem subject to price dependent demand and multiple discounts.
[24] Arrow, K.J., Harris, T., Marschak, J. (1951). “Optimal inventory policy. Econometrica”, Journal of the Econometric Society, 19(3): 250–272‍.
[25] Alfares, H.K., Elmorra, H.H. (2005). “The distribution-free newsboy problem: Extensions to the shortage penalty case”, International Journal of Production Economics, 93: 465-477.
[26] Kim, G., Wu, K., Huang, E. (2015). “Optimal inventory control in a multi-period newsvendor problem with non-stationary demand”, Advanced Engineering Informatics, 29(1): 139-145.
[27] Azad Gholami, R., Sandal, L.K., Uboe, J. (2016). “Channel Coordination in a Multi-period Newsvendor Model with Dynamic, Price-dependent Stochastic Demand”, NHH Dept. of Business and Management Science Discussion Paper, (2016/6).
[28] Zhang, Y. et al. (2019). “A two-product, multi-period nonstationary newsvendor problem with budget constraint”, Soft Computing, 23(12): 4277-4287.
[29] Ullah, M., Khan, I., Sarkar, B. (2019). “Dynamic Pricing in a Multi-Period Newsvendor Under Stochastic Price-Dependent Demand”, Mathematics, 7(6): 1-15.
[30] نخعی, عیسی، رسولی، نادیا، محمدی­پور، هیرش. (2013). "قیمت‎گذاری و کنترل موجودی توأم برای کالاهای فصلی و جایگزین"، نشریه پژوهش‌های مهندسی صنایع در سیستم‌های تولید، 1(2): 85-95.
[31] Mun, J. (2002). “Real options analysis: Tools and techniques for valuing strategic investments and decisions”, John Wiley & Sons, Vol. 137.
[32] Black, F. and Scholes, M. (1973). “The pricing of options and corporate liabilities”. Journal of political economy, 81(3): 637-654.
[33] Cox, J. C., Ross, S. A., Rubinstein, M. (1979). “Option pricing: A simplified approach”, Journal of financial Economics, 7(3): 229-263.