Minimization of a General Quantile Function for Appointment Scheduling

• Activity Number: 186
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Statistics in Business Schools Interest Group
• Author(s): Peijun Sang*
• Companies: Simon Fraser University
• Keywords: appointment scheduling ; optimization ; median computation

Abstract

Appointment scheduling of jobs whose durations are random is commonly encountered in surgery scheduling and in appointment scheduling of oncologist consultations and radiation therapy treatment for cancer patients. Traditional methods focus on how to minimize the expected overall cost via carefully scheduling appointment time for each job. They pay little attention to other objective functions rather than the expected overall cost in addressing appointment scheduling problems. In many situations, median might provide a better description of a population's center compared with expectation. When extreme large or small overall cost is to our interest, the corresponding quantiles of the overall cost may be more worth investigating. We propose an algorithm for multiple appointment scheduling where the distribution of durations is known or unknown. Simulation studies show that when sample size is sufficiently large, the performance of sample-based optimal appointment time (pretending the distribution of durations is unknown) is comparable with that obtained from minimizing the real median of overall costs.