Mixed integer linear programming approach for solving assembly scheduling problems

In this research, the problem of scheduling operations in manufacturing facilities with multiple machines that produce complex multi-level assemblies is considered. The problem is modeled with precedence relationships between operations. It has been formulated as a Mixed Integer Linear Program and is modeled as a flow-like problem. The objective of the problem is to reduce the total makespan (cumulative lead time) of production of final product. In addition to that, move sizes and batch sizes of operations are taken into consideration to see their impact on total makespan. Predetermined move size is used which facilitates batch overlapping, which in turn helps reduce the makespan. Column generation method has been used to solve the problem. Subproblem generates solution sets and the master problem selects from the set of generated solutions by the subproblem. Randomly generated problems with up to 100 assembly operations, 100 batch size, and 20 workcenters are used to test the formulations. Results show that makespan increases with increase in move size. This shows that batch overlapping increases the effectiveness of a schedule