Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The finite horizon case

Xin Chen, David Simchi-Levi

Research output: Contribution to journalArticlepeer-review

Abstract

We analyze a finite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon. We show that when the demand model is additive, the profit-to-go functions are k-concave and hence an (s, S, p) policy is optimal. In such a policy, the period inventory is managed based on the classical (s, S) policy and price is determined based on the inventory position at the beginning of each period. For more general demand functions, i.e., multiplicative plus additive functions, we demonstrate that the profit-to-go function is not necessarily k-concave and an (s, S, p) policy is not necessarily optimal. We introduce a new concept, the symmetric k-concave functions, and apply it to provide a characterization of the optimal policy.

Original languageEnglish (US)
Pages (from-to)887-896
Number of pages10
JournalOperations Research
Volume52
Issue number6
DOIs
StatePublished - Nov 2004

Keywords

  • Inventory/production: uncertainty, stochastic
  • Marketing: pricing
  • Operating characteristics
  • Planning horizons

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research

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