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Management Science
A survey of algorithms for the single machine total weighted tardiness scheduling problem
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
Minimizing total tardiness on one machine is NP-hard
Mathematics of Operations Research
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Computers and Operations Research - Special issue on genetic algorithms
Computers and Operations Research
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Journal of Heuristics
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Computers and Operations Research
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Proceedings of the 8th annual conference on Genetic and evolutionary computation
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Computers and Operations Research
Computers and Operations Research
Computers and Operations Research
Expert Systems with Applications: An International Journal
Computers and Operations Research
Information Sciences: an International Journal
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Computers and Operations Research
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This paper deals with the single machine scheduling problem to minimize the total weighted tardiness in the presence of sequence dependent setup. Firstly, a mathematical model is given to describe the problem formally. Since the problem is NP-hard, a general variable neighborhood search (GVNS) heuristic is proposed to solve it. Initial solution for the GVNS algorithm is obtained by using a constructive heuristic that is widely used in the literature for the problem. The proposed algorithm is tested on 120 benchmark instances. The results show that 37 out of 120 best known solutions in the literature are improved while 64 instances are solved equally. Next, the GVNS algorithm is applied to single machine scheduling problem with sequence dependent setup times to minimize the total tardiness problem without changing any implementation issues and the parameters of the GVNS algorithm. For this problem, 64 test instances are solved varying from small to large sizes. Among these 64 instances, 35 instances are solved to the optimality, 16 instances' best-known results are improved, and 6 instances are solved equally compared to the best-known results. Hence, it can be concluded that the GVNS algorithm is an effective, efficient and a robust algorithm for minimizing tardiness on a single machine in the presence of setup times.