0-1 Quadratic programming approach for optimum solutions of two scheduling problems |
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Authors: | BAHRAM ALIDAEE GARY A. KOCHENBERGER AHMAD AHMADIAN |
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Affiliation: | 1. Mathematics and Physical Sciences Department , West Texas State University , Canyon, TX, 79016, U.S.A.;2. College of Business Administration , University of Colorado at Denver , Denver, CO, 80217-3364, U.S.A.;3. Management Department , University of Southern Colorado , Pueblo, CO, 81001-4901, U.S.A. |
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Abstract: | Two scheduling problems are considered: (1) scheduling n jobs non-preemptively on a single machine to minimize total weighted earliness and tardiness (WET); (2) scheduling n jobs non-preemptively on two parallel identical processors to minimize weighted mean flow time. In the second problem, a pre-ordering of the jobs is assumed that must be satisfied for any set of jobs scheduled on each specific machine. Both problems are known to be NP-complete. A 0-1 quadratic assignment formulation of the problems is presented. An equivalent 0-1 mixed integer linear programming approach for the problems are considered and a numerical example is given. The formulations presented enable one to use optimal and heuristic available algorithms of 0-1 quadratic assignment for the problems considered here. |
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