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

Abstract

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.