1990
DOI: 10.1287/moor.15.3.483
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Abstract: The problem of minimizing the total tardiness for a set of independent jobs on one machine is considered. Lawler has given a pseudo-polynomial-time algorithm to solve this problem. In spite of extensive research efforts for more than a decade, the question of whether it can be solved in polynomial time or it is NP-hard (in the ordinary sense) remained open. In this paper the problem is shown to be NP-hard (in the ordinary sense).

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Cited by 632 publications
(220 citation statements)
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“…This problem, which we call PFSP-WT , is N P-hard in the strong sense even for a single machine [3]. Let π i denote the job in the i-th position of a permutation π.…”
Section: Permutation Flowshop Schedulingmentioning
confidence: 99%
“…This problem, which we call PFSP-WT , is N P-hard in the strong sense even for a single machine [3]. Let π i denote the job in the i-th position of a permutation π.…”
Section: Permutation Flowshop Schedulingmentioning
confidence: 99%
“…Both of them have been proven to be N P -hard [9,7]. In addition, all the FSP instances used in this paper are taken from Taillard benchmark instances and extended into biobjective case [17] 2 .…”
Section: Bi-objective Flow Shop Problemmentioning
confidence: 99%
“…Du and Leung [8] have shown that the total tardiness problem, 1j j j , is NP-hard in the ordinary sense, whereas unequal release dates problem, 1jr j j j is strongly NP-hard because the alternatives of inserting machine idle times need to be considered as stated by Lawler et al [11]. Although customer orders may not arrive simultaneously in real-life problems, to our knowledge, there is only one exact approach in the literature to solve the 1jr j j j problem by Chu [5].…”
Section: Scheduling the Brokendown Machinementioning
confidence: 99%