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. The principal incurs all costs for holding inventory and backordering demand. The agent dynamically controls the production rate at the server and incurs a convex production cost. The principal cannot monitor the production rate but can draw inference from increases in the inventory level. Furthermore, by making payments contingent on the inventory level, the principal motivates the agent to control the production rate in a manner that will minimize the principal's own total expected discounted cost. We show that an optimal incentive payment scheme consists of piece rates and inventory penalties that vary dynamically with the inventory level. This scheme coordinates the system if the agent is risk neutral. Otherwise, operational performance is degraded by the conflict in incentives between principal and agent. We identify some drivers of this agency loss: 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.