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On the unimodality of the manufacturer’s objective function in the newsvendor model. (English) Zbl 1080.90004

Summary: We derive new sufficient conditions for the manufacturer’s profit function to be unimodal. We show that if the demand density function is unimodal and right-skewed, then the profit function is quasi-concave over the support of the distribution. We also report some counterintuitive properties of the profit function.

MSC:

90B05 Inventory, storage, reservoirs
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References:

[1] G. Cachon, The allocation of inventory risk and advanced purchase discounts in a supply chain, Handbooks in Operations Research and Management Science, vol. 11, Supply Chain Management, North-Holland, New York, 2003.; G. Cachon, The allocation of inventory risk and advanced purchase discounts in a supply chain, Handbooks in Operations Research and Management Science, vol. 11, Supply Chain Management, North-Holland, New York, 2003.
[2] M. Lariviere, Supply chain contracting and coordination with stochastic demand, Quantitative Models for Supply Chain Management, Kluwer, Boston, 1999, pp. 233-268.; M. Lariviere, Supply chain contracting and coordination with stochastic demand, Quantitative Models for Supply Chain Management, Kluwer, Boston, 1999, pp. 233-268. · Zbl 1052.90511
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[4] Lariviere, M.; Porteus, E., Selling to the newsvendoran analysis of price-only contracts, Manuf. Service Oper. Manag., 3, 4, 293-305 (2001)
[5] Ziya, S.; Ayhan, H.; Foley, R. D., Relationships among three assumptions in revenue management, Oper. Res., 52, 5, 804-809 (2003) · Zbl 1165.90445
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