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A branch-and-bound algorithm for solving a two-machine flow shop problem with deteriorating jobs. (English) Zbl 1171.90404

Summary: 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.

MSC:

90B35 Deterministic scheduling theory in operations research
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
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[1] Alidaee, B.; Womer, N. K., Scheduling with time dependent processing times: review and extensions, Journal of the Operational Research Society, 50, 711-720 (1999) · Zbl 1054.90542
[2] Cheng, T. C.E.; Ding, Q.; Lin, B. M.T., A concise survey of scheduling with time-dependent processing times, European Journal of Operational Research, 152, 1-13 (2004) · Zbl 1030.90023
[3] Garey, M. R.; Johnson, D. S.; Sethi, R., The complexity of flowshop and jobshop scheduling, Mathematics of Operations Research, 1, 117-129 (1976) · Zbl 0396.90041
[4] Hardy, G. H.; Littlewood, J. E.; Polya, G., Inequalities (1964), Cambridge University Press: Cambridge University Press Cambridge, p. 261 · Zbl 0634.26008
[5] Ignall, E.; Schrage, L. E., Application of the branch and bound technique to some flowshop scheduling problems, Operations Research, 13, 400-412 (1965)
[6] Kononov, A.; Gawiejnowicz, S., NP-hard cases in scheduling deteriorating jobs on dedicated machines, Journal of the Operational Research Society, 52, 708-717 (2001) · Zbl 1181.90120
[7] Lee, W.-C.; Wu, C.-C., Minimizing total completion time in a two-machine flowshop with a learning effect, International Journal of Production Economics, 88, 85-93 (2004)
[8] Mosheiov, G., Complexity analysis of job-shop scheduling with deteriorating jobs, Discrete Applied Mathematics, 117, 195-209 (2002) · Zbl 1004.68031
[9] Wang, C.; Chu, C.; Proth, J. M., Efficient heuristic and optimal approaches for \(n / 2 / F / \sum C_i\) scheduling problems, International Journal of Production Economics, 44, 225-237 (1996)
[10] Wang, J.-B.; Ng, C. T.; Cheng, T. C.E.; Liu, L. L., Minimizing total completion time in a two-machine flow shop with deteriorating jobs, Applied Mathematics and Computation, 180, 185-193 (2006) · Zbl 1104.90023
[11] Wang, J.-B.; Xia, Z.-Q., Flow shop scheduling problems with deteriorating jobs under dominating machines, Journal of the Operational Research Society, 57, 220-226 (2006) · Zbl 1090.90095
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