Learning models for pricing and inventory control under uncertainty
Abstract
Optimal operating policies and corresponding managerial insight are developed for a monopolist that establishes on a periodic basis both a stocking level and a selling price for a single product while exploiting information gathered from ongoing operations. Given management situations in which the demand function depends on selling price and includes an unknown scale parameter, learning occurs as the firm monitors the market's response to its decisions and then updates its characterization of the demand function. Of primary interest is the effect of censored data because, in many practical circumstances, a firm's observations are restricted to sales rather than demand. Mathematical models are formulated and analyzed for several scenarios. For example, consideration is given both to a perishable product case (which corresponds to the situation in which the firm transfers information from period to period, but not inventory) and a durable product case (which corresponds to the situation in which the firm transfers information and inventory from period to period). Also considered are two forms for the price-dependent demand function, differentiated by whether the unknown scale parameter is incorporated as an additive or a multiplicative term. In an extension, the effects of learning and the strategic roles of inventory and pricing are analyzed for a firm operating in a two-market, international setting with only a single opportunity to procure. In general, results indicate that the firm's joint quantity/price problem reduces to a single variable problem in which the firm's principal decision is its safety stock. In particular, the firm's most recent decision for safety stock sufficiently captures past learning, thereby providing all relevant information for revising the characterization of the demand function. And, given the optimal safety stock for a given period, both the optimal stocking quantity and the optimal selling price are established myopically. Further results include an algorithm for computing the optimal safety-stock decisions for a multi-period problem. From a managerial standpoint, evidence is provided to suggest that the firm's first-period optimal decision for selling price increases with the length of the problem horizon, although the same is not necessarily true of the stocking quantity.
Degree
Ph.D.
Advisors
Dada, Purdue University.
Subject Area
Operations research|Management|Economic theory
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