An algorithm for single machine sequencing with deadlines to minimize total weighted completion time |
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Authors: | CN Potts LN Van Wassenhove |
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Institution: | University of Keele, Department of Mathematics, Keele, Straffordshire, ST5 5BG, United Kingdom;Katholieke Universiteit Leuven, Afdeling Industrieel Beleid, 3030 Leuven (Heverlee), Belgium |
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Abstract: | Each of n jobs is to be processed without interruption on a single machine. Each job becomes available for processing at time zero, has a deadline by which it must be completed and has a positive weight. The objective is to find a processing order of the jobs which minimizes the sum of weighted completion times. In this paper a branch and bound algorithm for the problem is presented which incorporates lower bounds that are obtained using a new technique called the multiplier adjustment method. Firstly several dominance conditions are derived. Then a heuristic is described and sufficient conditions for its optimality are given. The lower bound is obtained by performing a Lagrangean relaxation of the deadline constraints; the Lagrange multipliers are chosen so that the sequence generated by the heuristic is an optimal solution of the relaxed problem, thus yielding a lower bound. The algorithm is tested on problems with up to fifty jobs. |
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