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The impact of product substitution on retail merchandising. (English) Zbl 0989.90050

Summary: We analyze the impact of product substitution on two key aspects of retail merchandising: order quantities and expected profits. To perform this analysis, we extend the basic news-vendor model to include the possibility that a product with surplus inventory can be used as a substitute for out of stock products. This extension requires a definition and an approximation for the resulting effective demand under substitution. A service rate heuristic is developed to solve the extended problem. The performance of this heuristic is evaluated using an upper bound generated by solving the associated Lagrangian dual problem. Our analysis suggests that this heuristic provides a tractable and accurate method to determine order quantities and expected profits under substitution. We apply this heuristic to examine how the level of demand uncertainty and correlation, and the degree of substitution between products affect order quantities and expected profits under substitutable demand. In addition, we use the heuristic to better understand the mechanism by which substitution improves expected profits.

MSC:

90B30 Production models
90C59 Approximation methods and heuristics in mathematical programming
49M30 Other numerical methods in calculus of variations (MSC2010)

Software:

Matlab
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Full Text: DOI

References:

[1] Anupindi, R.; Dada, M.; Gupta, S., Estimation of consumer demand with stock-out based substitution: An application to vending machine products, Marketing Science, 17, 4, 406-423 (1998)
[2] Bassok, Y., Anupindi, R., Akella, R., 1997. Single period multi-product inventory models with substitution. Operations Research, to appear; Bassok, Y., Anupindi, R., Akella, R., 1997. Single period multi-product inventory models with substitution. Operations Research, to appear · Zbl 0979.90005
[3] Bitran, G.; Dasu, S., Ordering policies in an environment of stochastic yields and substitutable demand, Operations Research, 50, 999-1017 (1992) · Zbl 0775.90139
[4] Ermoliv, Y.; Wetts, R. J.B., Numerical Techniques for Stochastic Optimization (1998), Springer: Springer New York
[5] Fisher, M.L., Raman, A., 1998. Survey results reported at the Harvard/Wharton Merchandising Effectiveness Project. May, 1998; Fisher, M.L., Raman, A., 1998. Survey results reported at the Harvard/Wharton Merchandising Effectiveness Project. May, 1998
[6] Frazier, R.M., 1986. Quick response in soft lines. Discount Merchandiser, January 1986, pp. 42-56; Frazier, R.M., 1986. Quick response in soft lines. Discount Merchandiser, January 1986, pp. 42-56
[7] Garg, A., Lee, H.L., 1999. Managing product variety: An operations perspective. In: Quantitative Models for Supply Chain Management. Kluwer Academic Publishers, Dordrecht, pp. 467-490; Garg, A., Lee, H.L., 1999. Managing product variety: An operations perspective. In: Quantitative Models for Supply Chain Management. Kluwer Academic Publishers, Dordrecht, pp. 467-490 · Zbl 1052.90508
[8] Ho, T.; Tang, C., Research Advances in Product Variety Management (1998), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht
[9] Hooper, L., Yamada, K., 1992. IBM signals delay affecting low-cost line. Wall Street Journal; Hooper, L., Yamada, K., 1992. IBM signals delay affecting low-cost line. Wall Street Journal
[10] Hsu, A., Bassok, Y., 1994. Multi-product inventory problem with substitution and random yield. Operations Research, to appear; Hsu, A., Bassok, Y., 1994. Multi-product inventory problem with substitution and random yield. Operations Research, to appear
[11] JCrew web page, 2000. http://www.Jcrew.com; JCrew web page, 2000. http://www.Jcrew.com
[12] Lee, H.L., Nahamias, S., 1993. Single product and single-location models. In: Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, P. (Eds.), Handbooks in Operations Research and Management Science-Logistics of Production and Inventory, Vol. 4. Elsevier, Amsterdam, The Netherlands, pp. 3-55 (Chapter 1); Lee, H.L., Nahamias, S., 1993. Single product and single-location models. In: Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, P. (Eds.), Handbooks in Operations Research and Management Science-Logistics of Production and Inventory, Vol. 4. Elsevier, Amsterdam, The Netherlands, pp. 3-55 (Chapter 1) · Zbl 0798.90028
[13] Math Works Inc. 1998. The Matlab Curriculum Series. Users Guide; Math Works Inc. 1998. The Matlab Curriculum Series. Users Guide
[14] Mahajan, S., van Ryzin, G., 1998. Stocking retail assortments under dynamic consumer substitution. Operations Research, forthcoming; Mahajan, S., van Ryzin, G., 1998. Stocking retail assortments under dynamic consumer substitution. Operations Research, forthcoming · Zbl 1163.90339
[15] McGillivray, A.; Silver, E., Some concepts for inventory control under substitutable demand, INFOR, 16, 47-63 (1978) · Zbl 0384.90037
[16] New York Times, 2 June 1994; New York Times, 2 June 1994
[17] Pashigan, P. B., Demand uncertainty and sales: a study of fashion and markdown pricing, American Economic Review, 78, 936-953 (1988)
[18] Parlar, M.; Goyal, S., Optimal ordering decisions for two substitutable products with stochastic demand, OPSEARCH, 21, 1-15 (1984) · Zbl 0545.90030
[19] Pasternack, B.; Drezner, Z., Optimal inventory policies for two substitutable commodities with stochastic demand, Naval Research Logistics, 38, 221-240 (1991) · Zbl 0737.90019
[20] Pentico, D., The assortment problem with stochastic demand, Management Science, 21, 268-290 (1974) · Zbl 0304.90040
[21] Rao, U., Swaminathan, J., Zhang, J., 1998. Managing multi-product inventory systems with setup costs using downward conversion. Working paper, University of California Press, Berkeley, CA; Rao, U., Swaminathan, J., Zhang, J., 1998. Managing multi-product inventory systems with setup costs using downward conversion. Working paper, University of California Press, Berkeley, CA
[22] Rudi, N., Netessine, S., 1999. Demand substitution in retail: Centralization and competition. Working paper, Simon School of Business Administration, University of Rochester; Rudi, N., Netessine, S., 1999. Demand substitution in retail: Centralization and competition. Working paper, Simon School of Business Administration, University of Rochester
[23] Smith, S. A.; Aggrawal, N., Management of multi-item retail inventory systems with demand substitution, Operations Research, 48, 1, 50-64 (2000) · Zbl 1106.90306
[24] Stewart, T.A., 1992. Brace for Japan’s hot new strategy. Fortune 21 September 1992; Stewart, T.A., 1992. Brace for Japan’s hot new strategy. Fortune 21 September 1992
[25] White, J.B., 1992. Hughes charge gives GM net loss of 357 million. Wall Street Journal; White, J.B., 1992. Hughes charge gives GM net loss of 357 million. Wall Street Journal
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