A mathematical model for workload distribution and balancing with setup times under finite capacity constraints

Production planning is a challenging problem for enterprises especially in the high-mix and low-volume production environment. Finite capacity scheduling tries to allocate resources over time to perform a set of tasks such that precedence constraints and resource capacity constraints are not violated, and overall deadline goals are met to the best extent possible. A novel mathematical model for workload distribution and balance with setup times under finite capacity constraints is present. This model considers setup times and alternate resources, which makes it more comprehensive than others. The objective is to minimize the delay time, early time and cycle time. This model is solved by an optimization software called Xpress-MP. An example is given to illustrate its practicability.