NEW SOLUTION PROCEDURES FOR THE SINGLE-MACHINE SCHEDULING PROBLEM WITH AN OBJECTIVE OF MINIMIZING WEIGHTED TARDINESS
Abstract
The problem of minimizing the sum of weighted tardiness on a single machine is a difficult problem that has been shown to be NP-complete 16 . A number of curtailed enumeration algorithms (dynamic programming and branch-and-bound) have been proposed 10,15,34,35,36,38,39 , although no algorithm to date is capable of consistently finding solutions in reasonable time for problems containing more than 30 jobs. Due to the difficulty of this problem several heuristics have been proposed 25,32,37 . In this thesis the problem of minimizing weighted tardiness is approached in two ways. The first is to develop heuristics that produce lower cost solutions than previous heuristics. Previous heuristics have concentrated on developing simple constructive ordering procedures that guarantee an optimal solution in special cases. In contrast, the heuristics proposed in this thesis are obtained by relaxing an optimal algorithm. Computational tests show that these relaxations in general produce very close-to-optimal cost solutions. The second solution approach is a hybrid dynamic programming/branch-and-bound algorithm (DPB&B). Computational tests show that the proposed algorithm investigates fewer nodes in finding an optimal solution than does the Potts and Van Wassenhove DPB&B algorithm (PVW) 24 . Several additional results are also contained in this thesis. A pairwise interchange heuristic is proposed which improves the lower bound procedure used in PVW. Also, it is shown that the amount of tardiness inherent in a problem can be a factor in the effectiveness of a solution procedure. It is shown that heuristics which depend heavily on the due dates give closer-to-optimal cost solutions on problems with relatively low tardiness, while heuristics which depend heavily on weighted processing time give closer-to-optimal cost solutions on problems with relatively high tardiness. For optimal algorithms, backward scheduling (recursion) algorithms, which allow the use of Elmaghraby's Lemma 7 , are faster on low tardiness problems, while an adjusted weighted lateness lower bound (used by PVW) is most effective when used in a forward scheduling (recursion) algorithm on high tardiness problems.
Degree
Ph.D.
Subject Area
Management
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