Multi-period job selection: planning work loads to maximize profit

We examine the profitability of job selection decisions over a number of periods when current orders exceed capacity with the objective of maximizing profit (per-job revenue net of processing costs, minus weighted lateness costs), and when rejecting a job will result in no future jobs from that customer. First we present an optimal dynamic programming algorithm, taking advantage of the structure of the problem to reduce the computational burden. Next we develop a number of myopic heuristics and run computational tests using the DP as benchmark for small problems and the best heuristic as benchmark for larger problems. We find one heuristic that produces near-optimal results for small problems, is tractable for larger problems, and requires the same information as the dynamic program (current and future orders), and another that produces good results using historical information. Our results have implications for when it is more or less worthwhile to expend resources to maintain past records and obtain future information about orders.