Template-Type: ReDIF-Paper 1.0
Author-Name: Wagelmans, A.P.M.
Author-Name-Last: Wagelmans
Author-Name-First: Albert
Author-Name: Gerodimos, A.E.
Author-Name-Last: Gerodimos
Title: Improved dynamic programs for batching problems with maximum lateness criterion
Abstract: We 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 literature
 which 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 a
 straightfoward implementation requires O(n^2) 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 length of the first batch. These
 properties and the use of efficient data structures enable us to exclude partial schedules that cannot lead to an overall optimum
 early 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 overall
 complexity is determined by the sorting step.
Creation-Date: 1998-12-31
File-URL: https://repub.eur.nl/pub/1521/1_feweco19990330090244.pdf
File-Format: application/pdf
Series: RePEc:ems:eureir
Number: EI 9857
Keywords: batching problems, dynamic programs
Handle: RePEc:ems:eureir:1521