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Minimizing maximum lateness under linear deterioration. (English) Zbl 0976.90039
Summary: The paper deals with a single machine scheduling problem, where job processing time is given as a start time dependent linear function. The objective is to find such a schedule (processing order) which minimizes the maximum lateness criterion. We show that the problem is NP-complete and present two heuristic algorithms. An experimental analysis of the proposed algorithms is also given.

90B35Scheduling theory, deterministic
90C60Abstract computational complexity for mathematical programming problems
Full Text: DOI
[1] A. Bachman, A. Janiak, Scheduling jobs with special type of start time dependent processing times, Report No 34/97, Institute of Engineering Cybernetics, Wroclaw University of Technology, Wroclaw, 1997 · Zbl 1095.90033
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[3] Garey, M. R.; Johnson, D. S.: Computers and intractability: A guide to the theory of NP-completeness. (1979) · Zbl 0411.68039
[4] S. Gawiejnowicz, L. Pankowska, Scheduling jobs with time-dependent processing times, Report 027/1995, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznan, 1995 · Zbl 0875.68421
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[6] Kunnathur, A. S.; Gupta, S. K.: Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem. European journal of operational research 47, 56-64 (1990) · Zbl 0717.90034
[7] Mosheiov, G.: Scheduling jobs under simple linear deterioration. Computers and operations research 21, No. 3, 653-659 (1994) · Zbl 0810.90074
[8] Sundararaghavan, P. S.; Kunnathur, A. S.: Single machine scheduling with start time dependent processing times: some solvable cases. European journal of operational research 78, 394-403 (1994) · Zbl 0816.90088