An Adaptive SPT Rule for Scheduling and Testing Heterogeneous Jobs

Motivated by common practices in maintenance and healthcare operations, in which diagnostic activities precede service, we study the problem of scheduling jobs with random processing times on a server that can test jobs (i.e., perform a diagnostic procedure) prior to serving them in order to observe their durations. On one hand, testing utilizes the server and increases service delays, but on the other hand, testing reduces uncertainty and informs future scheduling decisions, which contributes to reducing overall delays. We consider two cases in which tests are either optional or mandatory prerequisites for processing heterogeneous jobs whose random processing times (and in some cases weights) are statistically different. For several interesting cases of optional testing problems, we develop an adaptive shortest processing time (SPT) rule, which characterizes the optimal policy using intuitive testing thresholds given by closed-formulas. We then show that a generalization of these thresholds forms an optimal index policy for mandatory testing problems.Our work provides tools for analyzing similar problems, as well as practical insights on how to prioritize uncertainty reduction efforts, in order to reduce delays in service systems