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A capacity allocation problem in flexible manufacturing systems

Bilgin, Selin
In this study, we consider a capacity allocation problem in flexible manufacturing systems. We assume time and tool magazine capacities on the Numerical Controlled (NC) machines and limited number of available tools. Our problem is to allocate the available capacity of the NC machines to the required demand of the operations, so as to maximize the total weight of operation assignments. We formulate the problem as a Mixed Integer Linear Program and show that it is NP-hard in the strong sense. We solve the moderate-sized problems optimally by the available Integer Programming software. We also develop Lagrangean relaxation based upper bounds and several heuristic procedures. Our computational results have revealed that the Lagrangean upper bounds are very close to optimal solutions and the heuristic procedures produce near optimal solutions in very small solution times even when the problem sizes are large.