A particle swarm optimization algorithm for flexible job shop scheduling problem

The classical job shop scheduling problem (JSP) is the most popular machine scheduling model in practice and is well known as NP-hard. The formulation of the JSP is based on the assumption that for each part type or job there is only one process plan that prescribes the sequence of operations and the machine on which each operation has to be performed. Flexible job shop scheduling problem (FJSP) is an extension of the JSP, which allows an operation to be processed by any machine from a given set. Since FJSP requires an additional decision of machine allocation during scheduling, therefore it is much more complex problem than JSP. To solve such NP-hard problems, heuristic approaches are commonly preferred over the traditional mathematical techniques. This paper proposes a particle swarm optimization (PSO) based heuristic for solving the FJSP for minimum makespan time criterion. The performance of the proposed PSO is evaluated by comparing its results with the results obtained using ILOG Solver, a constraint-programming tool. The comparison of the results proves the effectiveness of the proposed PSO for solving FJSP instances.