Optimal Policy for a Stochastic Scheduling Problem with Applications to Surgical Scheduling

Abstract

W e consider the stochastic, single-machine earliness/tardiness problem (SET), with the sequence of processing of the jobs and their due-dates as decisions and the objective of minimizing the sum of the expected earliness and tardiness costs over all the jobs. In a recent paper, Baker (2014) shows the optimality of the Shortest-Variance-First (SVF) rule under the following two assumptions: (a) The processing duration of each job follows a normal distribution. (b) The earliness and tardiness cost parameters are the same for all the jobs. In this study, we consider problem SET under assumption (b). We generalize Baker's result by establishing the optimality of the SVF rule for more general distributions of the processing durations and a more general objective function. Specifically, we show that the SVF rule is optimal under the assumption of dilation ordering of the processing durations. Since convex ordering implies dilation ordering (under finite means), the SVF sequence is also optimal under convex ordering of the processing durations. We also study the effect of variability of the processing durations of the jobs on the optimal cost. An application of problem SET in surgical scheduling is discussed.

Performance of the Smallest-Variance-First Rule in Appointment Sequencing

“…It is shown that the svf rule is optimal, under a specific assumption on the service times of the jobs. It should be noted, though, that in the model considered in Guda et al [13] all jobs are present from the start, implying that there is no idle time. Compared to our model, this greatly simplifies the evaluation of the cost function, thus facilitating finding an optimal solution.…”

“…The machine scheduling problem that is most closely related to the setup that we consider, can be found in Guda et al [13]. In the problem considered there, the due dates and sequence of jobs are to be decided, in order to minimize a weighted average of expected earliness and tardiness around the due dates.…”

Operational and strategic decision making in the perioperative setting: Meeting budgetary challenges and quality of care goals

“…Many other approaches show promising results in theory. Among these are stochastic models [64,65], exact algorithms (column generation, dynamic programming, branch and bound, branch and cut, branch and price), heuristic algorithms, and simulation-based studies (the Monte Carlo method, discrete-event simulation, and the Markov decision process) [64]. Gul et al proposed Multi-criteria models and compared a dozen heuristics of sequencing and patient appointment time setting, and showed that a bi-criteria genetic algorithm could be effective in balancing OR overtime against patient waiting time [66].…”

Dynamic multi-priority, multi-class patient scheduling with stochastic service times

“…For a higher number of patients, the problem seems to be open and it is very unlikely that a universal optimal sequencing rule could be found unless some restrictions on the service time distributions and costs are imposed. For example, a recent paper by Guda et al (2016) demonstrated that the shortest-variance-first rule is optimal for the single-machine earliness/tardiness problem if the earliness and tardiness cost parameters are the same for all the jobs and there is a dilation ordering of the processing times. The authors discuss the application of this rule to the appointment scheduling problem with sequencing in the case where idling is not allowed.…”