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- W2083187712 abstract "We consider the single-machine problem of scheduling n jobs to minimize the sum of the deviations of the job completion times from a given small common due date. For this NP-hard problem, we develop a branch-and-bound algorithm based on Lagrangian lower and upper bounds that are found in O(n log n) time. We identify conditions under which the bounds concur; these conditions can be expected to be satisfied by many instances with n not too small. In our experiments with processing times drawn from a uniform distribution, the bounds concur for n ≥ 40. For the case where the bounds do not concur, we present a refined lower bound that is obtained by solving a subset-sum problem of small dimension to optimality. We further develop a 4/3-approximation algorithm based upon the Lagrangian upper bound." @default.
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- W2083187712 date "1994-02-01" @default.
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- W2083187712 title "New Lower and Upper Bounds for Scheduling Around a Small Common Due Date" @default.
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- W2083187712 doi "https://doi.org/10.1287/opre.42.1.102" @default.
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