Capacity commitment and pricing for substitutable products under competition

Abstract

Capacity acquisition and pricing decisions are a company’s long-term strategic decisions. However, demand uncertainty and substitutability of multiple products cause the difficulty to solve capacity and pricing decision problems. In this paper, we address a multiple product pricing and multiple resource capacity acquisition problem with demand uncertainties and competition. The company needs to determine capacity commitment for each resource and product prices before demands are realized so that the total profit is maximized. If the demand exceeds the committed capacity, extra amounts can be purchased from the spot market. Variable unit production costs, capacity acquisition and maintenance costs are considered. We first analyze a single company basic problem and find the optimal solutions on prices and capacity. Based on the single company model, we address the two-product, two-firm capacity commitment and pricing problem considering across product and across company price competition factors. The existence and uniqueness of equilibrium on price and capacity commitment are proved, and then we extended the results to the multiple product, multiple company case.

Keywords

Capacity commitment / multiple product pricing / product substitution / price competition / stochastic demand

References

[1] Ahmet K.H., Ioana P.. Deterministic price-inventory management for substitutable products. Journal of Revenue and Pricing Management, 2006, 4(4): 354-366.

[2] Alptekinôglu A., Corbett C.J.. Mass customization vs. mass production: variety and price competition. Manufacturing & Service Operations Management, 2008, 10(2): 204-217.

[3] Aydin G., Porteus E.L.. Joint inventory and pricingdecisions for an assortment. Operations Research, 2008, 56(5): 1247-1256.

[4] Aydin, G. & Ryan, J.K. (2002). Product line selection and pricing under the multinomial logit choice model. Working Paper, Standford University

[5] Banker R., Hugnes J.S.. Product costing and pricing. The Accounting Review, 1994, 69(3): 479-494.

[6] Banker R., Hwang I., Misha B.K.. Product costing and pricing under long-term capacity commitment. Journal of Management Accounting Research, 2002, 14: 79-97.

[7] Bernstein F., DeCroix G.A.. Decentralized pricingand capacity decisions in a multitier system with modular assembly. Management Science, 2004, 50(9): 1293-1308.

[8] Bernstein F., Federgruen A.. A general equilibrium model for industries with price and service competition. Operations Research, 2004, 52(6): 868-886.

[9] Bertsimas D., de Boer S.. Dynamic pricing and inventory control for multiple products. Journal of Revenue and Pricing Management, 2005, 3(4): 303-319.

[10] Birge J., Drogosz J., Duenyas I.. Setting single-period optimal capacity levels and prices for substitutable products. The International Journal of Flexible Manufacturing Systems, 1998, 10: 407-430.

[11] Bitran, G., Caldentey, R. & Vial, R. (2009). Pricing policiesfor perishable products with demand substitution. Working paper, MIT

[12] Dong L., Kouvelis P., Tian Z.. Dynamic pricing and inventory control of substitute products. Manufacturing & Service Operations Management, 2009, 11(2): 317-339.

[13] Gallego G., Huh W.T., Kang W., Philips R.. Price competition with the attraction demand model: existence of unique equilibrium and its stablity. Manufacturing & Service Operations Management, 2006, 8(4): 359-375.

[14] Kuyumcu H.A., Popescu L.. Deterministic price — inventory management for sub-stitutable products. Journal of Revenue and Pricing Management, 2005, 4(4): 354-366.

[15] Maddah B., Bish E.K.. Joint pricing, assortment, and inventory decisions for a retailer’s product line. Naval Research Logistics, 2007, 54(2): 315-330.

[16] Maglaras C., Meissner J.. Dynamic pricing strategies for multi-product revenue management problems. Manufacturing & Service Operations Management, 2006, 8(2): 136-148.

[17] Netessine S., Rudi N.. Centralized and competitive inventory models with demand substitution. Operations Research, 2003, 51(2): 329-335.

[18] Rajaram K., Tang C.S.. The impact of product substitution on retail merchandising. European Journal of Operations Research, 2001, 135: 582-601.

[19] Song, J.-S. & Xue, Z. (2007). Demand management and inventorycontrol for substitutable products. Working paper, Duke University

[20] Suh, M. & Aydin, G. (2009). Dynamic pricing of substituable products with limited inventories under logit demand. Working paper, University of Michigan

[21] Sundaram R.K.. A First Course in Optimization Theory, 1996, Cambridge, UK: Cambridge University Press.

[22] Tang C.S., Yin R.. Joint ordering and pricing strategies for managing substitutable products. Production and Operations Management, 2007, 16(1): 138-153.

[23] Topkis D.M.. Supermodularity and Complementarity, 1998, New Jersey, US: Princeton University Press

[24] Vives X.. Nash equalibrium with startegic complementarities. Journal of Mathematical Economics, 1990, 19: 305-321.

[25] Vives X.. Oligopoly Pricing: Old Ideas and New Tools, 1999, Cambridge, MA: The MIT Press

[26] Zhu K., Thonemann U.. Coordination of pricing and inventory control across products. Naval Research Logistics, 2009, 56(2): 175-190.