Dynamic hoist scheduling problem with multi-capacity reentrant machines: A mixed integer programming approach

• We show that the solution obtained by an existing model is not necessarily optimal.
• New formulation is developed to handle the multi-capacity reentrant machine.
• Our model can guarantee the optimality of its obtained solution.
• Computational results indicate the effectiveness of the proposed model.

This paper deals with the dynamic hoist scheduling problem with multi-capacity reentrant machines, where some reentrant machines have parallel processing units and can process multiple jobs at the same time. The system is served by a hoist for transporting jobs among machines. Jobs to be processed randomly arrive at the input station. When new jobs come, the system should be rescheduled so as to minimize the makespan. A mixed integer programming (MIP) model is developed to generate an optimal reschedule, which improves an existing model in the literature from several dimensions. The proposed model is solved by commercial software CPLEX. Computational results are reported to evaluate the proposed MIP model.