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Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem. (English) Zbl 0717.90034

The authors consider single machine sequencing problems in which processing time of a job is assumed to be split in a fixed and a variable part. For each job j, the variable part is sequence dependent in the sense that it is given by max{0,v j (S j -d j )} where v j and d j are given and S j is the starting time of job j in the sequence under consideration. The objective is to minimize makespan.

A dynamic programming, a branch-and-bound and five heuristic algorithms are proposed. Computational experience with solving randomly generated problems with up to 15 jobs is reported. The paper suffers from such annoying phenomena as unstated assumptions and ambiguous formulations.

Reviewer: M.Vlach
MSC:
90B35Scheduling theory, deterministic
90C39Dynamic programming
90-08Computational methods (optimization)