A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times
International Journal of Production EconomicsPublished 17 February 2005
Djamel Nait Tahar, Farouk Yalaoui, Chengbin Chu, Lionel Amodeo
Citations107
SJR quartileQ1
SJR score2.83
SNIP2.67
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TL;DR
A heuristic algorithm improving an existing one, using a linear programming modeling with setup times and job splitting considerations is suggested, which is tested on over 6000 instances with different size by comparing it with a lower bound.
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Computer ScienceEngineering
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An underlying theory for the traveling-salesman problem is developed, pathological performance of some existing techniques are predicted, and two algorithms are presented, based upon the theory, with predictable polynomial growth in expected computation time and resistence to pathological problems.
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ACM Transactions on Mathematical SoftwareAlgorithm 548: Solution of the Assignment Problem [H]
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R H U first ( s ) nex t (s) last ( s) as the row ass igned to c o l u m n y ( j -1 ) as the label o f c o L R , = 0, row i is un labe led (i = 1 , . . . , n);
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OmegaScheduling jobs with uncertain setup times and sequence dependency
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Annals of discrete mathematicsComputational Performance of Three Subtour Elimination Algorithms for Solving Asymmetric Traveling Salesman Problems
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