A Lagrangean relaxation based approach for the capacity allocation problem in flexible manufacturing systems

This study considers the operation assignment and capacity allocation problem in flexible manufacturing systems. A set of operations is selected to be processed and assigned to the machines together with their required tools. The purchase or usage of the required tools incurs a cost. The machines have scarce time and tool magazine capacities. The objective is to maximize the total weight of the assigned operations minus the total tooling costs. We use Lagrangean relaxation approach to obtain upper and lower bounds on the optimal objective function values. The computational experiments show that our approach provides near optimal bounds in reasonable solution times.