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Flow-shop scheduling with a learning effect. (English) Zbl 1082.90041
Summary: The paper is devoted to some flow-shop scheduling problems with a learning effect. The objective is to minimize one of the two regular performance criteria, namely, makespan and total flowtime. A heuristic algorithm with worst-case bound \(m\) for each criteria is given, where \(m\) is the number of machines. Furthermore, a polynomial algorithm is proposed for both of the special cases: identical processing time on each machine and an increasing series of dominating machines. An example is also constructed to show that the classical Johnson’s rule is not the optimal solution for the two-machine flow-shop scheduling to minimize makespan with a learning effect. Some extensions of the problem are also shown.

90B35 Deterministic scheduling theory in operations research
90C59 Approximation methods and heuristics in mathematical programming
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