Appointment Scheduling with Limited Distributional Information

41 Pages Posted: 29 Aug 2013

See all articles by Ho-Yin Mak

Ho-Yin Mak

University of Oxford - Said Business School

Ying Rong

Shanghai Jiao Tong University (SJTU) - Antai College of Economics and Management

Jiawei Zhang

New York University (NYU) - Department of Information, Operations, and Management Sciences

Date Written: August 28, 2013

Abstract

In this paper, we develop distribution-free models that solve the appointment sequencing and scheduling problems by assuming only moments information of job durations. We show that our min-max appointment scheduling models, which minimize the worst-case expected waiting and overtime costs out of all probability distributions with the given marginal moments, can be exactly formulated as tractable conic programs. These formulations are obtained by exploiting hidden convexity of the problem. In the special case where only the first two marginal moments are given, the problem can be reformulated as a second-order cone program. Based on the structural properties of this formulation, under a mild condition, we derive the optimal time allowances in closed form and prove that it is optimal to sequence jobs in increasing order of job duration variance. We also prove similar results regarding the optimal time allowances and sequence for the case where only means and supports of job durations are known.

Suggested Citation

Mak, Ho-Yin and Rong, Ying and Zhang, Jiawei, Appointment Scheduling with Limited Distributional Information (August 28, 2013). Available at SSRN: https://ssrn.com/abstract=2317332 or http://dx.doi.org/10.2139/ssrn.2317332

Ho-Yin Mak

University of Oxford - Said Business School ( email )

Park End Street
Oxford, OX1 1HP
Great Britain

Ying Rong

Shanghai Jiao Tong University (SJTU) - Antai College of Economics and Management ( email )

No.535 Fahuazhen Road
Shanghai Jiao Tong University
Shanghai, Shanghai 200052
China

Jiawei Zhang (Contact Author)

New York University (NYU) - Department of Information, Operations, and Management Sciences ( email )

44 West Fourth Street
New York, NY 10012
United States

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