Title: The multi-product competitive price-setting newsvendor problem

Authors: Soulaymane Kachani, Kyrylo Shmatov

Addresses: Department of Industrial Engineering and Operations Research, Columbia University, Mudd Bldg., 500 W120th St., #334, New York, NY 10027, USA. ' Department of Applied Physics and Applied Mathematics, Columbia University, Mudd Bldg., 500 W120th St., #200, New York, NY 10027, USA

Abstract: We consider the problem where a number of firms simultaneously compete in price and inventory level decisions. Each firm offers a line of several products, both complementary products and substitutes, the product line demand is also sensitive to prices of outside competitors| products. We also consider the case of excess demand, where the firm faces part of the demand its competitors could not satisfy because of stock-out, and an application of the proposed approach to the serial inventory problem. Although in most practical settings, multi-product dynamic pricing problems are approximately solved by decoupling across products and solving a large number of single-product problems. In this paper, we propose an iterative relaxation algorithm that solves the multi-product problem, and we prove sufficient conditions for convergence of the algorithm. Finally, we present extensive computational examples and a real-world case study derived from the successful testing and implementation of our models and algorithms in several industries.

Keywords: serial inventories; pricing policies; marketing policies; non-linear algorithms; newsvendor problem; competitive price-setting; competitiveness; multi-products; multiple products; inventory levels; competition; complementary products; product substitutes; product line demand; price sensitivity; competitors; excess demand; demand satisfaction; stock-out; dynamic pricing; decoupling; single-products; iterative relaxation algorithms; production planning; consumer perishables; revenue management.

DOI: 10.1504/IJRM.2011.038617

International Journal of Revenue Management, 2011 Vol.5 No.1, pp.16 - 41

Available online: 15 Feb 2011 *

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