We design an algorithm for the job shop scheduling problem with the objective of minimizing the total holding cost by appropriately rounding an optimal solution to a fluid relaxation in which we replace discrete jobs witht the flow of a continuous fluid. The algorithm solves the fluid relaxation optimally and then aims to keep the schedule in the discrete network close to the schedule given by the fluid relaxation. If the number of jobs from each type grows linearly with N, then the algorithm is within an additive factor O(N) from the optimal (which scales as )(N2)), thus it is asymptotically optimal in N. We report computational results based on benchmark instances chosen from the OR library that suggest that the algorithm is a practical and attractive alternative for solving job shop scheduling problems of even moderate multiplicity.
By: Dimitris Bertsimas, David Gamarnik, Jay Sethuraman
Published in: RC21919 in 2000
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