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Centralized and competitive inventory models with demand substitution. (English) Zbl 1163.90344

Summary: A standard problem in operations literature is optimal stocking of substitutable products. We consider a consumer-driven substitution problem with an arbitrary number of products under both centralized inventory management and competition. Substitution is modeled by letting the unsatisfied demand for a product flow to other products in deterministic proportions. We obtain analytically tractable solutions that facilitate comparisons between centralized and competitive inventory management under substitution. For the centralized problem we show that, when demand is multivariate normal, the total profit is decreasing in demand correlation.

MSC:

90B05 Inventory, storage, reservoirs
90B50 Management decision making, including multiple objectives
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