Effects of a demand-curve’s shape on the optimal solutions of a multi-echelon inventory/pricing model. (English) Zbl 1026.90002

Summary: When a price-demand relationship is needed in inventory/pricing models, very often a convenient (typically linear) function is arbitrarily chosen. The common-wisdom implication is that any downward-sloping demand curve would lead to similar conclusions. This paper applies different demand-curve functions to a simple inventory/pricing model, and shows that while the common-wisdom implication is valid for a single-echelon system, assuming different demand-curve functions can lead to very different results in a multi-echelon system. In some situations, a very small change in the demand-curve appearance leads to very large changes in the model’s optimal solutions. Other significant but counter-intuitive effects of the demand-curve form are also revealed. This paper does not completely resolve the difficulties revealed by the counter-intuitive effects reported here, but establishing the existence of these effects represents a first step towards developing procedures to handle such effects; these procedures will be necessary to ensure the reliability of many multi-echelon models for products having price-sensitive demands.


90B05 Inventory, storage, reservoirs
Full Text: DOI


[1] Arcelus, F. J.; Srinivasan, G., Inventory policies under various optimizing criteria and variable markup rates, Management Science, 33, 6, 756-762 (1987)
[2] Banaszak, S.; Chakravorty, U.; Leung, P. S., Demand for ground transportation fuel and pricing policy in Asian tigers: A comparative study of Korea and Taiwan, The Energy Journal, 20, 2, 145-165 (1999)
[3] Chopra, S.; Meindl, P., Supply Chain Management (2001), Prentice Hall: Prentice Hall New Jersey
[4] Chu, W.; Messinger, P. R., Information and channel profits, Journal of Retailing, 73, 4, 487-499 (1997)
[5] Crouch, G. I., Demand elasticities for short-haul versus long-haul tourism, Journal of Travel Research, 34, 2-7 (1994)
[6] Emmons, H.; Gilbert, S. M., The role of returns policies in pricing and inventory decisions for catalogue goods, Management Science, 44, 276-283 (1998) · Zbl 0989.90043
[7] Jeuland, A. P.; Shugan, S. M., Channel of distribution profits when channel members form conjectures, Marketing Science, 7, 2, 202-210 (1988)
[8] Khouja, M. J., Optimal ordering, discounting, and pricing in the single-period problem, International Journal of Production Economics, 65, 201-216 (2000)
[9] Lau, A. H.L.; Lau, H. S., The newsboy problem with price-dependent demand function, IIE Transactions, 20, 168-175 (1988)
[10] Li, S. X.; Huang, Z. M.; Ashley, A., Inventory, channel coordination and bargaining in a manufacturer-retailer system, The Annals of Operations Research, 68, 47-60 (1996) · Zbl 0867.90064
[11] Parlar, M.; Wang, Q., Discounting decisions in a supplier-buyer relationship with a linear buyer’s demand, IIE Transactions, 26, 2, 34-41 (1994)
[12] Petruzzi, N. C.; Dada, M., Pricing and the newsvendor problem: A review with extensions, Operations Research, 47, 2, 183-194 (1999) · Zbl 1005.90546
[13] Stavins, J., Estimating demand elasticities in a differentiated product industry: The personal computer market, Journal of Economics and Business, 49, 347-367 (1997)
[14] Urban, T. L.; Baker, R. C., Optimal ordering and pricing policies in a single-period environment with multivariate demand and markdowns, European Journal of Operational Research, 103, 573-583 (1997) · Zbl 0921.90065
[15] Ward, M., Product substitutability and competition in long-distance telecommunications, Economic Inquiry, 37, 4, 657-677 (1999)
[16] Weingarten, M.; Stuck, B., It’s a stretch to believe in high price elasticity, Business Communications Review, 31, 1, 33-34 (2001)
[17] Weng, Z. K., Modeling quantity discounts under general price-sensitive demand functions: Optimal policies and relationships, European Journal of Operational Research, 86, 300-314 (1995) · Zbl 0906.90102
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.