A branch-and-bound algorithm for solving a two-machine flow shop problem with deteriorating jobs

Authors:
C. T. Ng;J. -B. Wang;T. C. E. Cheng;L. L. Liu
Affiliations:
Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, People's Republic of China;Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, People's Republic of China and Department of Science, Shenyang Institute of Ae ...;Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, People's Republic of China;Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, People's Republic of China and School of Science, Shanghai Second Polytechnic ...
Venue:
Computers and Operations Research
Year:
2010

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Abstract

In this paper we consider a two-machine flow shop scheduling problem with deteriorating jobs. By a deteriorating job we mean that the job's processing time is an increasing function of its starting time. We model job deterioration as a function that is proportional to a linear function of time. The objective is to find a sequence that minimizes the total completion time of the jobs. For the general case, we derive several dominance properties, some lower bounds, and an initial upper bound by using a heuristic algorithm, and apply them to speed up the elimination process of a branch-and-bound algorithm developed to solve the problem.