Solving the scheduling problem of machines with auxiliary tools

Most existing studies on production scheduling considered only one resource type, usually the machines. But in certain actual manufacturing environments, other resources, such as tools, operators, and so on, may become a scare resource for the short term production scheduling. Therefore, this study investigates the scheduling problem that simultaneously considers machines and their auxiliary tools. Both of these two resources are limited and their eligibility to processing various jobs are considered. Also, the initial work-in-process (WIP) job for each machine and for each auxiliary tool is an initial parameter for a problem instance. A mixed integer programming (MIP) model with the objective of minimizing makespan is proposed. Several tested problems are solved to validate the MIP model.