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Zbl 1230.90104
Yang, Shu-Hui; Wang, Ji-Bo
Minimizing total weighted completion time in a two-machine flow shop scheduling under simple linear deterioration. (English)
[J] Appl. Math. Comput. 217, No. 9, 4819-4826 (2011). ISSN 0096-3003

Summary: We address a two-machine flow shop scheduling problem under simple linear deterioration. By a simple linear deterioration function, we mean that the processing time of a job is a simple linear function of its execution start time. The objective is to find a sequence that minimizes total weighted completion time. Optimal schedules are obtained for some special cases. For the general case, several dominance properties and two lower bounds are derived to speed up the elimination process of a branch-and-bound algorithm. A heuristic algorithm is also proposed to overcome the inefficiency of the branch-and-bound algorithm. Computational analysis on randomly generated problems is conducted to evaluate the branch-and-bound algorithm and heuristic algorithm.

MSC 2000:: *90B35 Scheduling theory

Keywords: scheduling; flow shop; simple linear deterioration; total weighted completion time; branch-and-bound algorithm; heuristic algorithm

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