Incentive Efficient Control of a Make-to-Stock Production System

This paper considers a principal-agent variant of the classical make-to-stock single server queueing system. A principal (whom we call “her”) has a primary stake in the performance of the system, incurs linear holding and backorder inventory costs, and delegates production control to an agent. Production is modeled by a single server queue with exponential service times, flexible production rates, and convex production cost. The production rates are chosen by the agent and are unobservable by the principal. The principal pays the agent according to observed inventory levels and job completions, and strives to induce action that would minimize her expected total discounted cost. Using the dynamic principal-agent framework of Plambeck and Zenios (2000), we show that the principal’s optimal incentive payment scheme consists of a differential piece rate and a delay penalty. Furthermore, this scheme fails to induce the first-best production rates that are optimal in centralized system. The main frictional forces contributing to this “loss of efficiency” are also identified: In addition to discounting and risk aversion in the agent’s preferences, which are standard causes of friction in dynamic agency models, an increasing marginal cost of production and slack in the agent’s capacity are also found to be lead contributors, Heavy traffic analysis supports these findings through closed form expressions for the performance of the system under the optimal incentive scheme.