Filter-and-fan approaches for scheduling flexible job shops under workforce constraints

This paper addresses a flexible job shop scheduling problem that takes account of workforce constraints and aims to minimise the makespan. The former constraints ensure that eligible workers that operate the machines and may be heterogeneously qualified, are assigned to the machines during the processing of operations. We develop different variants of filter-and-fan (F&F) based heuristic solution approaches that combine a local search procedure with a tree search procedure. The former procedure is used to obtain local optima, while the latter procedure generates compound transitions in order to explore larger neighbourhoods. In order to be able to adapt neighbourhood structures that have formerly shown to perform well when workforce restrictions are not considered, we decompose the problem into two components for decisions on machine allocation and sequencing and decisions on worker assignment, respectively. Based on this idea, we develop multiple definitions of neighbourhoods that are successively locked and unlocked during runtime of the F&F heuristics. In a computational study, we show that our solution approaches are competitive when compared with the use of a standard constraint programming solver and that they outperform state-of-the-art heuristic approaches on average.