Improved approaches to the exact solution of the machine covering problem |
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Authors: | Rico Walter Martin Wirth Alexander Lawrinenko |
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Affiliation: | 1.Department of Optimization,Fraunhofer Institute for Industrial Mathematics ITWM,Kaiserslautern,Germany;2.Fachgebiet Management Science & Operations Research,Technische Universit?t Darmstadt,Darmstadt,Germany;3.Lehrstuhl für ABWL/Management Science,Friedrich-Schiller-Universit?t Jena,Jena,Germany |
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Abstract: | For the basic problem of scheduling a set of n independent jobs on a set of m identical parallel machines with the objective of maximizing the minimum machine completion time—also referred to as machine covering—we propose a new exact branch-and-bound algorithm. Its most distinctive components are a different symmetry-breaking solution representation, enhanced lower and upper bounds, and effective novel dominance criteria derived from structural patterns of optimal schedules. Results of a comprehensive computational study conducted on benchmark instances attest to the effectiveness of our approach, particularly for small ratios of n to m. |
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