In this thesis, we consider a capacity allocation problem in flexible manufacturing systems. We assume limited time and tool magazine capacities on the Computer Numerically Controlled (CNC) machines. We have a set of operations that have to be assigned to the machines and each operation requires a set of tools to be processed. Our problem is to allocate the available capacity of the CNC machines to operations and their required tools. We consider two problems in this study: maximizing the total weight of operations where there are a limited number of tools of each type available and maximizing total weight minus total tooling cost where the tools can be used or purchased at a cost. We model the problems as Integer Linear Programs and show that they are NP-hard in the strong sense. For the total weight problem, we propose upper bounds, branch and bound algorithm for exact solutions and several heuristics for approximate solutions. For the bicriteria problem, we use Lagrangean relaxation technique to obtain lower and upper bounds. Our computational results have revealed that all solution approaches give satisfactory results in reasonable times.

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