Three-Stage Assembly Flow Shop Scheduling Problem with a Fixed Maintenance Period

Abstract

This paper investigates the three-stage assembly flow shop scheduling problem, provided that there is a fixed maintenance period (MP) imposed on one of the machines in the first stage, the objective is to minimize the makespan. The starting time and duration of MP are known in advance, during MP no job can be processed on the corresponding machine. Only the non-resumable scenario is considered, i.e., if a job fails to finish before MP, it must restart from the beginning after the machine becomes available again, rather than continuing its processing. The problem generalizes the three-stage assembly flow shop scheduling problem without MPs and is therefore strongly NP-hard. To the best of our knowledge, the problem has not been explored so far. We propose three approximation algorithms for the problem.