Myopic Policies for Non-Preemptive Scheduling of Jobs with Decaying Value

TL;DR

This paper studies non-preemptive scheduling of jobs with decaying value, analyzing heuristic policies' performance and providing bounds and practical insights for applications like healthcare and inventory management.

Contribution

It introduces and evaluates three intuitive heuristics for scheduling jobs with decaying value, offering performance guarantees and practical guidelines.

Findings

Performance bounds are established for all three heuristics.

Numerical experiments compare heuristic effectiveness across scenarios.

Rules-of-thumb are derived for applying heuristics in real-world settings.

Abstract

In many scheduling applications, minimizing delays is of high importance. One adverse effect of such delays is that the reward for completion of a job may decay over time. Indeed in healthcare settings, delays in access to care can result in worse outcomes, such as an increase in mortality risk. Motivated by managing hospital operations in disaster scenarios, as well as other applications in perishable inventory control and information services, we consider non-preemptive scheduling of jobs whose internal value decays over time. Because solving for the optimal scheduling policy is computationally intractable, we focus our attention on the performance of three intuitive heuristics: (1) a policy which maximizes the expected immediate reward, (2) a policy which maximizes the expected immediate reward rate, and (3) a policy which prioritizes jobs with imminent deadlines. We provide performance guarantees for all three policies and show that many of these performance bounds are tight. In addition, we provide numerical experiments and simulations to compare how the policies perform in a variety of scenarios. Our theoretical and numerical results allow us to establish rules-of-thumb for applying these heuristics in a variety of situations, including patient scheduling scenarios.