قیمت‏ گذاری و کنترل موجودی خرده‏ فروش‏ های رقیب با کمبود جزئی؛ رویکرد نظریه بازی‏ها

نوع مقاله : مقاله پژوهشی

نویسندگان

استادیار مهندسی صنایع، گروه مهندسی صنایع، دانشکده مهندسی، دانشگاه کردستان

چکیده

DOR : 20.1001.1.24766291.1399.5.2.5.8
استراتژی قیمت‏ ‏گذاری و کنترل موجودی در محیط رقابتی، از مهمترین تصمیمات یک واحد خرده‏ فروشی است که بر روی بقا و سوددهی آن به شدت تاثیرگذار است. هنگامی که کالاها فاسدشدنی هستند، اهمیت این تصمیمات دوچندان می ‏شود. در این مقاله، مساله تعیین همزمان قیمت و سیاست ‏موجودی در محیط رقابتی برای کالاهای فاسدشدنی فرموله ‏بندی و حل می ‏شود. بدین منظور تعدادی خرده ‏فروش رقیب در نظر گرفته می ‏شود که یک کالای فاسدشدنی جایگزین را به یک بازار مشترک عرضه می‏ کنند. فرض شده است که کمبود کالا مجاز بوده و به صورت پس افت جزئی است. هر خرده فروش به دنبال تعیین سیاست موجودی و قیمت ‏گذاری خود به منظور بیشینه کردن سود است. در ابتدا توابع سود هر خرده‏ فروش ارائه شده و وجود تعادل نش بین خرده‏ فروش‏ها ثابت می ‏شود. سپس یک روش حل برای تعیین مقادیر تعادلی قیمت و سیاست موجودی خرده‏ فروش‏ها ارائه می ‏شود. در نهایت، یک مثال عددی به منظور شناسایی اثر پارامترهای مختلف بر روی جواب‏های تعادلی ارائه می ‏شود. نتایج عددی نشان می دهد که افزایش شدت رقابت منجر به کاهش مجموع سود خرده ‏فروش‏ها و افزایش مجموع تقاضای برآورد شده توسط آنها می ‏شود. به علاوه، بر خلاف مدل‏های انحصاری، تغییر نرخ فاسد شدن کالا در یک خرده ‏فروش در مدل رقابتی تاثیر زیادی بر روی قیمت خرده‏ فروشی او ندارد.

کلیدواژه‌ها


عنوان مقاله [English]

Pricing and inventory decisions of oligopoly retailers with partial backlogging: a game theoretic approach

نویسندگان [English]

  • Anwar Mahmoodi
  • Heibatolah Sadeghi
Department of industrial of engineering, Faculty of engineering, University of Kurdistan, Sanandaj, Iran
چکیده [English]

Pricing and inventory strategies are two important decisions of a retailer which directly affect her/his profitability. They are even more prominent when the considered product undergoes deterioration. In this paper, the problem of joint pricing and inventory control is investigated in a competitive environment. In particular, we consider a number of competing retailers who sell substitutable deteriorating items to a common market. In addition, shortage is allowed and partially backlogged at the retailers. Each retailer aims to maximize their profit determining their price and inventory policies. At first, the profit function of the retailers is derived. Then, the existence of Nash Equilibrium solution is shown. Next, a solution procedure is developed to obtain the equilibrium quantities of price and replenishment policy. Furthermore, a numerical study is carried out to analyze the effect of the main parameters on the equilibrium solution. Numerical results show that the increase of competition intensity would decrease the summation of the retailers' profits, while it would increase the total satisfied demands. Moreover, in contrast to the monopoly models, changing the deterioration rate at a retailer does not significantly impact his/her selling price.

کلیدواژه‌ها [English]

  • Inventory Control
  • Pricing
  • Game Theory
  • Nash Equilibrium
  • Partial Backlogging
[1]       A. Mahmoodi, Stackelberg-Equilibrium of Pricing and Inventory Decisions in a Supply Chain, in:  2019 15th Iran International Industrial Engineering Conference (IIIEC), IEEE, 2019, pp. 14-17.
[2]      M.A. Cohen, Joint pricing and ordering policy for exponentially decaying inventory with known demand, Naval Research Logistics, 24 (1977) 257-268.
[3]      C.-Y. Dye, Joint pricing and ordering policy for a deteriorating inventory with partial backlogging, Omega, 35 (2007) 184-189.
[4]      Z. Chen, Joint decision of inventory and pricing for deteriorating items with partial backlogging and multi-constraint, International Journal of Modelling in Operations Management, 3 (2013) 184-205.
[5]      S. Panda, S. Saha, M. Basu, Optimal pricing and lot-sizing for perishable inventory with price and time dependent ramp-type demand, International Journal of Systems Science, 44 (2013) 127-138.
[6]      P. Chintapalli, Simultaneous pricing and inventory management of deteriorating perishable products, Annals of Operations Research, 229 (2015) 287-301.
[7]      M.R. Gholamian, H. Zamani Bajegani, An inventory control model for obsolete items with consideration of all unit quantity discount and price-dependent on order quantity, Modern Research in Decision Making, 4 (2019) 127-146. (in persian)
[8]      L. Feng, J. Zhang, W. Tang, Optimal inventory control and pricing of perishable items without shortages, IEEE Transactions on Automation Science and Engineering, 13 (2016) 918-931.
[9]      G.A. Chua, R. Mokhlesi, A. Sainathan, Optimal discounting and replenishment policies for perishable products, International Journal of Production Economics, 186 (2017) 8-20.
[10]  F. Lu, H. Xu, P. Chen, S.X. Zhu, Joint pricing and production decisions with yield uncertainty and downconversion, International Journal of Production Economics, 197 (2018) 52-62.
[11]  S. Tiwari, C.K. Jaggi, M. Gupta, L.E. Cárdenas-Barrón, Optimal pricing and lot-sizing policy for supply chain system with deteriorating items under limited storage capacity, International Journal of Production Economics, 200 (2018)278-290.
[12]  C.N. Rapolu, D.H. Kandpal, Joint pricing, advertisement, preservation technology investment and inventory policies for non-instantaneous deteriorating items under trade credit, OPSEARCH, (2019) 1-27.
[13]  M.A. Agi, H.N. Soni, Joint pricing and inventory decisions for perishable products with age-, stock-, and price-dependent demand rate, Journal of the Operational Research Society, 71 (2020) 85-99.
[14]  F. Bernstein, A. Federgruen, Dynamic inventory and pricing models for competing retailers, Naval Research Logistics (NRL), 51 (2004) 258-274.
[15]  F. Bernstein, A. Federgruen, Decentralized supply chains with competing retailers under demand uncertainty, Management Science, 51 (2005) 18-29.
[16]  E. Adida, G. Perakis, Dynamic pricing and inventory control: Uncertainty and competition, Operations Research, 58 (2010) 289-302.
[17]  K. Chen, T. Xiao, Pricing and replenishment policies in a supply chain with competing retailers under different retail behaviors, Computers & Industrial Engineering, 103 (2017) 145-157.
[18]  Y. He, H. Huang, D. Li, Inventory and pricing decisions for a dual-channel supply chain with deteriorating products, Operational Research, (2018) 1-43.
[19]  M. Malekitabar, S. Yaghoubi, A two-stage pricing and inventory optimization model for both ameliorating and deteriorating items in a competing environment, Journal of Industrial and Systems Engineering, 10 (2017) 50-71.
[20]  A. Mahmoodi, Joint pricing and inventory control of duopoly retailers with deteriorating items and linear demand, Computers & Industrial Engineering, 132 (2019) 36-46.
[21]  A. Mahmoodi, Stackelberg–Nash equilibrium of pricing and inventory decisions in duopoly supply chains using a nested evolutionary algorithm, Applied Soft Computing, 86 (2020) 105922.
[22]  H.R. Akbarfakhrabadi, J. Gheidar-Kheljani, S.H. Ghodsypour, Competition modeling in coordinating a three level supply chain, Modern Research in Decision Making, 1 (2016) 1-22. (in persian)
[23]  J. Behnamian, M.M. Bashar, Multi-stage modeling for non-cooperative multi-echelon supply chain management problem with discount under uncertainty, Modern Research in Decision Making, 2 (2017) 49-75. (in persian)
[24]  E.J. Anderson, Y. Bao, Price competition with integrated and decentralized supply chains, European Journal of Operational Research, 200 (2010) 227-234.
[25]  A. Mahmoodi, K. Eshghi, Price competition in duopoly supply chains with stochastic demand, Journal of Manufacturing Systems, 33 (2014) 604-612.
[26]  H. Nikaidô, K. Isoda, Note on non-cooperative convex games, Pacific Journal of Mathematics, 5 (1955) 807-815.
[27] A. Matsumoto, F. Szidarovszky, Game theory and its applications, Springer, 2016.