Approximately optimal control of fluid networks
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Mathematics of Operations Research
Multiproduct Systems with Both Setup Times and Costs: Fluid Bounds and Schedules
Operations Research
A fluid approach to large volume job shop scheduling
Journal of Scheduling
Asymptotically optimal schedules for single-server flow shop problems with setup costs and times
Operations Research Letters
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We design an algorithm for the high-multiplicity 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 with 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 grow linearly withN, then the algorithm is within an additive factorO( N) from the optimal (which scales asO( N2)); thus, it is asymptotically optimal. We report computational results on benchmark instances chosen from the OR library comparing the performance of the proposed algorithm and several commonly used heuristic methods. These results suggest that for problems of moderate to high multiplicity, the proposed algorithm outperforms these methods, and for very high multiplicity the overperformance is dramatic. For problems of low to moderate multiplicity, however, the relative errors of the heuristic methods are comparable to those of the proposed algorithm, and the best of these methods performs better overall than the proposed method.