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The two-machine total completion time flow shop problem
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DOI：10.1016/0377-2217(95)00351-7.png)
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Abstract
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In this paper we study the NP-hard scheduling problem of minimizing total completion time in a two-machine now shop. Five known lower bounds are discussed and two new ones are presented. A new dominance criterion is also proposed. Several versions of a branch and bound method are derived by applying, both individually and combined, these lower bounds. A heuristic procedure is also presented that uses a constructive O(n(2)) time method, which computes a good starting solution, together with a neighborhood search based on pairwise interchanges. Computational results show that the exact method can handle problems of up to 30 jobs in size within a reasonable amount of time and that the heuristic procedure has an average error of less than 0.5% from the optimal value and less than 2.7% from the lower bound.
Keywords:
flow shop scheduling
branch and bound
neighborhood search
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