Bi-level multi-objective mathematical model for job-shop scheduling: the application of Theory of Constraints

This study highlights a different systematic approach to the application of Theory of Constraints (TOC). The work describes the decisions involved in the implementation of TOC in a job-shop environment as a bi-level multi-objective mathematical model. On the first level, the decision is made by minimising idle time on the bottleneck to generate the initial schedule. The second level decision is to improve additional performance measurements by applying the multi-objective technique, while maintaining the bottleneck sequence obtained from the first level decision. Moreover, the concept of transfer lot is also adopted in this model to reduce the waiting time on each machine by allowing overlapped operations. The concept of transfer lot is applied as the constraint on earliest starting time for each job on each machine in the proposed mathematical model. Additionally, the machine set up time and product demands are also adopted to make the model practical to use in the real situation. The numerical examples for both single and multiple bottleneck cases are given to demonstrate how this approach works. The commercially available optimiser, the LINGO 10 software package, is used to solve the examples and the result shows how this approach works in practice.