Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case
Name
IMST005.pdf
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160.9 KB
Format
Adobe PDF
Checksum (MD5)
457cafaa8cc344db24b79ff6978466f0
Author(s)
Chen, Xin
Simchi-Levi, David
Date Issued
January 2005
Series/Report no.
Innovation in Manufacturing Systems and Technology (IMST);
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.
Subjects
Inventory/production
uncertainty
stochastic
planning horizons
operating characteristics
marketing
pricing
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