Improved dynamic programs for batching problems with maximum lateness criterion
AbstractWe study a class of scheduling problems involving the maximum lateness criterion and an element of batching. For all the problems that we examine, algorithms appear in the literaturewhich consist of a sorting step to determine an optimal job sequence, followed by a dynamic programming step which determines the optimal batches. In each case, the dynamic program is based on a backward recursion of which astraightfoward implementation requires O(n^2) time, where n is the number of jobs. We present improved implementations of these dynamicprograms that are based on monotonicity properties of the objective expressed as a function of the length of the first batch. Theseproperties and the use of efficient data structures enable us to exclude partial schedules that cannot lead to an overall optimumearly on in the enumeration process. The four problems that we consider are solved in O(n log n) time; in two occasions, the batching step is actually performed in linear time and the overallcomplexity is determined by the sorting step.
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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 9857.
Date of creation: 31 Dec 1998
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batching problems; dynamic programs;
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