Static and Dynamic Pricing of Excess Capacity in a Make-to-Order Environment

Abstract

Recent years have seen advances in research and management practice in the area of pricing, and particularly in dynamic pricing and revenue management. At the same time, researchers and managers have made dramatic improvements in production and supply chain management. The interactions between pricing and production/supply chain performance, however, are not as well understood. Can a firm benefit from knowing the status of the supply chain or production facility when making pricing decisions? How much can be gained if pricing decisions explicitly and optimally account for this status? This paper addresses these questions by examining a make-to-order manufacturer that serves two customer classes - core customers who pay a fixed negotiated price and are guaranteed job acceptance, and "fill-in" customers who make job submittal decisions based on the instantaneous price set by the firm for such orders. We examine four pricing policies that span a range of complexity and required knowledge about the status of the production system at the manufacturer, including the optimal policy of setting a different price for each possible state of the queue. We demonstrate properties of the optimal policy, and we illustrate numerically the financial gains a firm can achieve by following this policy vs. simpler pricing policies. The four policies we consider are (1) state-independent (static) pricing, (2) allowing fill-in orders only when the system is idle, (3) setting a uniform price up to a cut-off state, and (4) general state-dependent pricing. Although general state-dependent pricing is optimal in this setting, we find that charging a uniform price up to a cut-off state performs quite well in many settings and presents an attractive trade-off between ease of implementation and profitability. Thus, a fairly simple heuristic policy may actually out-perform the optimal policy when costs of design and implementation are taken into account.

Keywords: Capacity, Pricing, Queueing, Heuristics