In this thesis the service tim e control problem for the multistage manufacturing systems was solved. We covered the multistage flow shop manufacturing environment where each stage is modeled as a single-server queue. We also considered simple assembly systems, analyzed them and presented a solution for their service time control problem as well.

Necessary optim ality conditions were obtained for the above mentioned manufacturing systems. The framework was that of hybrid systems and the associated formulation and solution of the related optim al control problem. The optim al control problem we dealt with was by its nature non-differentiable and nonconvex. The necessary optimality conditions were derived by exploiting the special structure of the problem and by the use of one-sided derivatives of the associated cost function.

Three algorithms were devised for computing the optimal service controls, two for the multistage tandem system and one for the assembly system. The considered performance metric constituted measures of deviations of completion times from a given schedule of due dates, as well as a measure of quality of the finished product at each stage of the manufacturing system.

The algorithms in this thesis present basic tools that can be used to optim ally time the processing of distinct products given the schedule of their arrival and their operational sequence as well as their required due dates.