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Two parallel machines scheduling with two-vehicle job delivery to minimize makespan. (English) Zbl 1435.90063

Summary: A problem of parallel machine scheduling with coordinated job deliveries is handled to minimize the makespan. Different jobs call for dissimilar sizes of storing space in the process of transportation. A range of jobs of one customer in the problem have priority to be processed on two identical parallel machines without preemption and then delivered to the customer by two vehicles in batches. For this NP-hard problem, we first prove that it is impossible to have a polynomial heuristic with a worst-case performance ratio bound less than 2 unless P = NP. Thereafter, we develop a polynomial heuristic for this problem, the worst-case ratio of which is bounded by 2.

MSC:

90B35 Deterministic scheduling theory in operations research
90C59 Approximation methods and heuristics in mathematical programming
90C60 Abstract computational complexity for mathematical programming problems
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