Inventory Timing: How to Serve a Stochastic Season

Abstract

Problem Definition. Firms that sell products over a limited selling season often have only imperfect information about (a) the exact timing of that season, (b) the demand volume to expect, and (c) the temporal distribution of demand over the selling season. Given these uncertainties, firms must determine not only how much inventory to stock but also when to make that inventory available to customers. We ask: What is a firm’s optimal inventory quantity and timing for products sold during a stochastic selling season?

Academic and Practical Relevance. Managers are frequently confronted with challenging inventory timing decisions, especially when the products they manage exhibit high inventory holding costs and substantial uncertainty concerning the pattern of customer demand. Although the newsvendor literature has developed a thorough understanding of the firm’s optimal inventory quantity, it has failed to inform decision makers about choosing the optimal inventory timing.

Methodology. We develop a theoretical model of a firm that sells a product over a stochastic selling season, and we study how this firm should choose its inventory timing and inventory quantity so as to maximize expected profits.

Results. We derive the firm’s optimal inventory policy—which comprises inventory timing and inventory quantity—and discuss the interaction effects between these two decisions. We also identify the effects of optimal inventory timing on a firm’s ability to satisfy customer demand and show how early inventory timing can be detrimental to customer service.

Managerial Implications. Our core insights imply two immediate recommendations for managers. First, optimal inventory timing is an effective weapon for combatting both high inventory holding costs and high levels of uncertainty in the firm’s customer demand pattern. Second, naive decision rules (e.g., “earlier is better”) may reduce not only the firm’s profits but also its capacity to serve customer demand.