An efficient algorithm for the single machine total tardiness problem
Date
2001Source Title
IIE Transactions (Institute of Industrial Engineers)
Print ISSN
0740-817X
Electronic ISSN
1545-8830
Publisher
Taylor & Francis
Volume
33
Issue
8
Pages
661 - 674
Language
English
Type
ArticleItem Usage Stats
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Abstract
This paper presents an exact algorithm for the single machine total tardiness problem (1// L T;). We present a new synthesis of various results from the literature which leads to a compact and concise representation of job precedences, a simple optimality check, new decomposition theory, a new lower bound, and a check for presolved subproblems. These are integrated through the use of an equivalenceconcept that permits a continuous reformation of the data to permit early detection of optimality at the nodes of an enumeration tree. The overall effect is a significant reduction in the size of the search tree, CPU times, and storage requirements. The algorithm is capable of handling much larger problems (e.g., 500 jobs) than its predecessors in the literature (:s; 150). In addition, a simple modification of the algorithm gives a new heuristic which significantly outperforms the best known heuristics in the literature.
Keywords
AlgorithmsBoundary conditions
C (programming language)
Computational complexity
Computer simulation
Data structures
Dynamic programming
Job analysis
Theorem proving
Search tree
Single machine total tardiness problem
Scheduling