Outpatient Appointment Scheduling with Variable Interappointment Times

Abstract

Healthcare currently consumes 17% of the U.S. Gross Domestic Product and is expected to reach 20% within the coming decade. Confronted with such high costs, sharp demand, and limited capacity, many hospitals now are vying for shorter lengths of stay and are transferring services from inpatient to outpatient facilities. This paper seeks to develop a methodology for constructing effective outpatient appointment scheduling systems. The objective of these appointment systems is to minimize the average total cost function describing total costs incurred by patient waiting and by staff idle time and overtime. In the paper, we will establish that the average total cost function exhibits a unimodal curve. The lowest point of the curve essentially means the lowest average total cost. We will next develop a simulation-based heuristic algorithm for finding an outpatient schedule near the lowest point. In the paper, we present numerical examples using the heuristic based upon a set of predetermined unit costs. Specifically, we find the near optimal interappointment times for schedules, where there are two and three patients in each block, respectively. The current work does not consider possible no shows and walk-ins. Future work will undertake these issues.