Joint production control and inspection schedule for imperfect production processes

In this thesis, we have address two different production control problems with imperfect production processes. In both problems, (s, S) control policies are used for the production process. In addition, the demand rate, production rate, and repair period are assumed to be constant. We first addressed a single-product, single-machine production control problem with uncertain machine breakdowns. The production capacity of the machine is uncertain due to unexpected failures. Shortages may be experienced and the unmet demand is assumed to be lost. The optimality of the (s, S) production control policy is established as well as the expressions for finding the total expected cost for given values of s and S. We develop an algorithm to find the optimal control policy. In addition, we also provide computational results to investigate the effect of the various problem parameters on the optimal control policy. In the second problem, also we consider a single machine producing a single product. The machine can go out-of-control while producing items. Once out of control, a certain portion of items produced is defective until the out-of-control state of the machine is discovered through an actual inspection. Periodic inspection is used to detect the machine failure. Upon detection of failure, the machine is stopped and under repair. Two types of (s, S) control policies are considered. We develop an algorithm to find the optimized (s, S) control policy. In addition, we also provide computational results to investigate the effect of the various cost parameters and the failure rates on the optimized (s, S) control policy