Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems

Authors:
Yasin Unlu;Scott J. Mason
Affiliations:
Department of Industrial Engineering, University of Arkansas, 4207 Bell Engineering Center, Fayetteville, AR 72701, USA;Department of Industrial Engineering, University of Arkansas, 4207 Bell Engineering Center, Fayetteville, AR 72701, USA
Venue:
Computers and Industrial Engineering
Year:
2010

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Abstract

Mixed integer programming (MIP) formulations for scheduling problems can be classified based on the decision variables upon which they rely. In this paper, four different MIP formulations based on four different types of decision variables are presented for various parallel machine scheduling problems. The goal of this research is to identify promising optimization formulation paradigms that can subsequently be used to either (1) solve larger practical scheduling problems of interest to optimality and/or (2) be used to establish tighter lower solution bounds for those under study. We present the computational results and discuss formulation efficacy for total weighted completion time and maximum completion time problems for the identical parallel machine case.