Improved dynamic programs for some batching problems involving the maximum lateness criterion

Improved dynamic programs for some batching problems involving the maximum lateness criterion

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Article ID: iaor200698
Country: Netherlands
Volume: 27
Issue: 3
Start Page Number: 109
End Page Number: 118
Publication Date: Oct 2000
Journal: Operations Research Letters
Authors: ,
Keywords: combinatorial analysis, programming: dynamic
Abstract:

We study four scheduling problems involving the maximum lateness criterion and an element of batching. For all the problems that we examine, algorithms appear in the literature that consist of a sorting step to determine an optimal job sequence, followed by a dynamic programming step that determines the optimal batches. In each case, the dynamic program is based on a backward recursion of which a straightforward implementation requires O(n2) time, where n is the number of jobs. We present improved implementations of these dynamic programs that are based on monotonicity properties of the objective expressed as a function of the total processing time of the first batch. These properties and the use of efficient data structures enable optimal solutions to be found for each of the four problems in O(n log n) time; in two cases, the batching step is actually performed in linear time and the overall complexity is determined by the sorting step.

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