Batch scheduling in a multi-purpose system with machine downtime and a multi-skilled workforce

The paper presents a discrete-time mixed-integer linear programming (MILP) model for a generalised flexible job-shop scheduling problem as represented by a state-task network. The problem is characterised by reentrant flow, sequence-dependent changeover time, machine downtime, and skilled labour requirements. Two preprocessing procedures are proposed to reduce the size of the MILP model, and represent a major contribution of the research. The procedures reduce the number of assignment variables by exploiting job precedence and workforce qualifications. Machine availability for each task is determined as a function of possible start and end times, given duration, and maintenance schedule. The overall objective is to maximise the number of scheduled tasks while minimising their total finish time. Computational experiments are conducted with real and randomly generated instances. The results show that optimal solutions can be obtained for medium-size problems within a reasonable amount of time, primarily due to the use of the preprocessing procedures.