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A note on “resource flexibility with responsive pricing”

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  • Ebru K. Bish
  • Juqi Liu
  • Douglas R. Bish

Abstract

We revisit the capacity investment decision problem studied in the article “Resource Flexibility with Responsive Pricing” by Chod and Rudi [Operations Research 53, (2005) 532–548]. A monopolist firm producing two dependent (substitutable or complementary) products needs to determine the capacity of one flexible resource under demand risk so as to maximize its expected profit. Product demands are linear functions of the prices of both products, and the market potentials are random and correlated. We perform a comparative statics analysis on how demand variability and correlation impact the optimal capacity and the resulting expected profit. In particular, C&R study this problem under the following assumptions/approximations: (i) demand intercepts follow a bivariate Normal distribution; (ii) demand uncertainty is of an additive form; (iii) and under approximate expressions for the optimal capacity and optimal expected profit. We revisit Propositions 2, 3, 4, 5, and 10 of C&R without these assumptions and approximations, and show that these results continue to hold (i) for the exact expressions for the optimal expected profit and optimal capacity, and (ii) under any arbitrary continuous distribution of demand intercepts. However, we also show that the additive demand uncertainty is a critical assumption for the C&R results to hold. In particular, we provide a case of multiplicative uncertainty under which the C&R results (Propositions 2 and 3) fail. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010

Suggested Citation

  • Ebru K. Bish & Juqi Liu & Douglas R. Bish, 2010. "A note on “resource flexibility with responsive pricing”," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(2), pages 119-126, March.
    • Handle: RePEc:wly:navres:v:57:y:2010:i:2:p:119-126
    DOI: 10.1002/nav.20389
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    References listed on IDEAS

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    1. Nicholas C. Petruzzi & Maqbool Dada, 1999. "Pricing and the Newsvendor Problem: A Review with Extensions," Operations Research, INFORMS, vol. 47(2), pages 183-194, April.
    2. Marco Scarsini, 1998. "Multivariate convex orderings, dependence, and stochastic equality," Post-Print hal-00541775, HAL.
    3. Simon GB Cowan & Simon Cowan, 2004. "Demand shifts and imperfect competition," Economics Series Working Papers 188, University of Oxford, Department of Economics.
    4. Jiri Chod & Nils Rudi, 2005. "Resource Flexibility with Responsive Pricing," Operations Research, INFORMS, vol. 53(3), pages 532-548, June.
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