A Model for Make-To-Order Revenue Management1

Abstract Seeking to help practitioners establish quantitative guidelines for negotiating make-to-order contracts along the dimensions of price, quantity and lead-time, we investigate the dynamic admission control of jobs with hard deadlines into a single machine queue with preemptive scheduling. Using the concept of minimum workload function, we establish that earliest due-date scheduling can be assumed at no cost to optimality, and propose a discrete-time formulation for the problem of maximizing long-run expected profit. We establish some properties and a characterization of the optimal policy, which we exploit to derive two heuristic policies (fluid and lookahead) relying on different approximations for the opportunity cost of accepting a job. Numerical experiments under various load, stretch and granularity parameters suggest that they always perform better than common simple static policies. Limited experiments also suggest that the optimal static policy may perform nearly as well as our two dynamic heuristics. While that policy is simple to implement however, it seems challenging to derive using known methods. Overall, our fluid heuristic stands out for its robust performance at a relatively low computational cost, and its possible extensions in practice to non-stationary demand and orders with staggered deliveries.