Abstract

http://ssrn.com/abstract=2317332
 
 

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Appointment Scheduling with Limited Distributional Information


Ho-Yin Mak


Hong Kong University of Science & Technology

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

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.

Number of Pages in PDF File: 41

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Date posted: August 29, 2013  

Suggested Citation

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

Contact Information

Ho-Yin Mak
Hong Kong University of Science & Technology ( email )
Clearwater Bay
Kowloon
Hong Kong
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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