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Minimizing the number of workers for one cycle of a paced production line

机译：在有节奏的生产线的一个周期中减少工人数量

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摘要

We consider a paced line that produces various products and consists of several assembly stations. Each product or semi-product requires a specific set of operations to be performed by identical workers. The assignment of operations to the stations and precedence relations between the operations are known. Operations assigned to different stations are performed simultaneously and those assigned to the same station are performed sequentially. No worker can perform more than one operation at a time. The processing time of an operation depends on the number of identical workers performing this operation. If a worker is assigned to an operation, he is busy with this task from its start till completion. The problem is to find a schedule, which specifies operation start times and assignment of workers to the operations, such that the line cycle time constraint and the number of workers box constraints for each operation are satisfied. We prove that the problem is NP-hard in the strong sense, suggest conventional and randomized heuristics, describe a reduction to a series of feasibility problems, show relation of the feasibility problem to multi-mode project scheduling and multiprocessor scheduling, and introduce a MILP model for the feasibility problem.
机译：我们考虑一条生产各种产品并由几个装配工位组成的有节奏的生产线。每个产品或半产品都需要由相同的工人执行的一组特定操作。已知对站的操作分配和操作之间的优先级关系。分配给不同工作站的操作是同时执行的，分配给同一工作站的操作是依次执行的。没有工人可以一次执行多个操作。一项操作的处理时间取决于执行此操作的相同工人的数量。如果将工人分配给某项操作，则他将从开始到完成都在忙于此任务。问题是要找到一个时间表，该时间表指定操作开始时间和为该操作分配工作人员，以便满足每个操作的生产线周期时间约束和工作人员箱约束数量。我们从强烈的意义上证明了该问题是NP难的，提出了常规的和随机的启发式方法，描述了一系列可行性问题的简化，展示了可行性问题与多模式项目计划和多处理器计划的关系，并介绍了MILP可行性问题的模型。

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