Browsing by Subject "Single machine total tardiness problem"

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Open Access
An efficient algorithm for the single machine total tardiness problem
(Taylor & Francis, 2001) Tansel, B. Ç.; Kara, B. Y.; Sabuncuoğlu İ.
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.
Open Access
New insights on the single machine total tardiness problem
(Palgrave Macmillan, 1997) Tansel, B. C.; Sabuncuoğlu, İ.
Virtually all algorithmic studies on the single machine total tardiness problem use Emmons' theorems that establish precedence relations between job pairs. In this paper, we investigate these theorems with a geometric viewpoint. This approach provides a compact way of representing Emmons' theorems and promotes better insights into dominance properties. We use these insights to differentiate between certain classes of easy and hard instances.