IJE TRANSACTIONS C: Aspects Vol. 27, No. 9 (September 2014) 1385-1394    Article Under Proof

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N. Rasouli and I. Nakhai Kamalabadi
( Received: January 14, 2014 – Accepted: May 22, 2014 )

Abstract    Nowadays many well-known firms may produce similar products at different prices in order to remain in the competitive environment. The price differences may cause substitution condition which motivates the customers to substitute the similar cheaper product with an expensive one leading to an environment which is known as “customer-based price driven substitution”. This research proposes a new mathematical model towards a joint pricing and inventory control for seasonal and substitutable goods in a competitive market over a finite time planning horizon. It is assumed that the two substitute goods belong to two different rival firms. The objective is to determine the optimal price, order quantity and the number of periods for one product in the presence of symmetrical and asymmetrical substitutions such that the total profit of the related firm is maximized. Firs tit is showed that total profit is a concave function of price which leads us to a unique optimal solution. To provide the optimal solution a simple algorithm is developed. Finally, in order to evaluate the performance of proposed algorithm a numerical example is presented.


Keywords    pricing, inventory control, seasonal and substitutable goods, symmetrical and asymmetrical substitution


چکیده    امروزه بسیاری از بنگاههای شناخته شده محصولات مشابه را با قیمتهای مختلف تولید می­کنند. گاهی اختلاف قیمتی سبب می­شود تا مشتریان کالای مشابه ارزانتر را جایگزین کالای گرانتر کنند که این جایگزینی بر مبنای مشتری و بر اساس تفاوت قیمتی نام دارد. در این تحقیق مدل ریاضی قیمت­گذاری پویا و کنترل موجودی برای کالاهای فصلی و جایگزین در بازار رقابتی توسعه داده شده است. فرض بر این است که دو کالای جایگزین مربوط به دو بنگاه رقیب هستند. مدل ریاضی به دنبال تعیین همزمان قیمت دوره­ای، تعداد بهینه دوره و میزان سفارش یک بنگاه با هدف افزایش سود آن بنگاه است. جایگزینی در این تحقیق بر مبنای مشتری و بر اساس تفاوت قیمتی در نظر گرفته شده و در دو حالت متقارن و نامتقارن بررسی می­شود. بعد از ارائه مدل اثبات می‌شود که تابع هدف، تابعی مقعرنسبت به قیمت است، سپس الگوریتم حل مساله ارائه شده و در نهایت مثال عددی به منظور بررسی کارایی مدل و الگوریتم بحث می­شود.



1.     Abad, P.L., "Optimal price and lot size when the supplier offers a temporary price reduction over an interval", Computers & Operations Research,  Vol. 30, No. 1, (2003), 63-74.

2.     Boyacı, T. and Gallego, G., "Coordinating pricing and inventory replenishment policies for one wholesaler and one or more geographically dispersed retailers", International Journal of Production Economics,  Vol. 77, No. 2, (2002), 95-111.

3.     Huang, Y., Huang, G.Q. and Newman, S.T., "Coordinating pricing and inventory decisions in a multi-level supply chain: A game-theoretic approach", Transportation Research Part E: Logistics and Transportation Review,  Vol. 47, No. 2, (2011), 115-129.

4.     Kim, D. and Lee, W.J., "Optimal joint pricing and lot sizing with fixed and variable capacity", European Journal of Operational Research,  Vol. 109, No. 1, (1998), 212-227.

5.     Maihami, R. and Nakhai Kamalabadi, I., "Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand", International Journal of Production Economics,  Vol. 136, No. 1, (2012), 116-122.

6.     Mahmoudi, M. and Tofigh, A.A., "Application of game theory in dynamic competitive pricing leader and n dependent followers", International Journal of Engineering,  Vol. 25, No., (2012), 35-43.

7.     Jain, M., Sharma, G. and Rathore, S., "Economic production quantity models with shortage, price and stock-dependent demand for deteriorating items", International Journal of Engineering Transactions A Basics,  Vol. 20, No. 2, (2007), 159.

8.     Heng, J., "Price and quantity setting for seasonal retail goods with stochastic demands", Senior Thesis, (1995).

9.     Aviv, Y. and Pazgal, A., "Optimal pricing of seasonal products in the presence of forward-looking consumers and prospects", Journal of Manufacturing and Service Operations Management,,  Vol. 10, No., (2008), 339-359.

10.   You, P.-S. and Chen, T.C., "Dynamic pricing of seasonal goods with spot and forward purchase demands", Computers & Mathematics with Applications,  Vol. 54, No. 4, (2007), 490-498.

11.   Soysal, G.P. and Krishnamurthi, L., "Demand dynamics in the seasonal goods industry: An empirical analysis", Marketing Science,  Vol. 31, No. 2, (2012), 293-316.

12.   Chopra, S. and Meindl, P., "Supply chain management. Strategy, planning & operation, Springer,  (2007).

13.   Kim, S.-W. and Bell, P.C., "Optimal pricing and production decisions in the presence of symmetrical and asymmetrical substitution", Omega,  Vol. 39, No. 5, (2011), 528-538.

14.   Karakul, M. and Chan, L.M.A., "Joint pricing and procurement of substitutable products with random demands–a technical note", European Journal of Operational Research,  Vol. 201, No. 1, (2010), 324-328.

15.   Bitran, G., Caldentey, R. and Vial, R., "Pricing policies for perishable products with demand substitution", City,  (2006).

16.   Burkart, W.R., Klein, R. and Mayer, S., "Product line pricing for services with capacity constraints and dynamic substitution", European Journal of Operational Research,  Vol. 219, No. 2, (2012), 347-359.

17.   Dong, L., Kouvelis, P. and Tian, Z., "Dynamic pricing and inventory control of substitute products", Manufacturing & Service Operations Management,  Vol. 11, No. 2, (2009), 317-339.

18.   Bish, E.K. and Suwandechochai, R., "Optimal capacity for substitutable products under operational postponement", European Journal of Operational Research,  Vol. 207, No. 2, (2010), 775-783.

19.   Stavrulaki, E., "Inventory decisions for substitutable products with stock-dependent demand", International Journal of Production Economics,  Vol. 129, No. 1, (2011), 65-78.

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