Manufacturing managers have the option of improving their operations through practices such as setup time reduction or quaiity improvement. Making improvements requires the investment of resources. For the purpose of determining the level of investments in each practice, projects are normally assumed to be independent, and are justified on the basis of the expected retuni;​ from the improvements. This research investigates the effects of this implicit assumption of independence between improvement practices on optimal investment decisions. To answer the question of whether improvement practices interact with each other, and if so, whether the effect of the interaction is significant to the investment decision, a model of a manufacturing system was developed. in the modei, the independent variables are the levels of investment in each of two improvernent practices and the performance rneasure of the system is relevant expected operating costs. For the purpases of this study, the two improvement practices implemented in the model are setup time reduction and quality irnprovement.

The model developed here draws primarily upon two previous models. The first, by Porteus [1985], adapted an Economic Order Quantity model to include investments in setup reduction, and was later extended [Porteus, 19861 to include investments in quaiity improvement. In these models. when the EOQ for a system was caiculated, cotai costs were rninimized as a function of order quantity, investment in setup reduction and investment in quaiity improvement. A limitation of Porteus' EOQ-based model is that it neglected WIP holding costs, which can be substantial in manufacturing systems. Karmarkar [1987] developed a mode1 based on the M/M/1 queuing system which predicted WIP levels in a system, and with this model was able to calculate an order quantity which minimizes total costs of the system, although no work has been found on reducing setup tines or improving quaiity with this type of model. In this research an M/G/1 queuing model was used to represent a manufacturing cell and estimate WIP levek. Stochastic service times include setup time and time for rework of defective units in each batch processed, with these quantities king the independent variabIes of the model. By linking the levels of the independent variables to IeveIs of investment necessary to achieve those values, a total expected relevant cost for the system can be estimated, and used as an objective function to optimize setup times and defect rates.

This model has been used to detennine optimum investrnent strategies for cases where batch size is fixed or variable, and where the investment-improvement function for each decision variable is Iinear or strictly convex. Analytic and numerical results have been obtained.

By comparing optimal levels of the decision variables when each practice is explicitly assumed independent of the other to when the optimization is performed simultaneously, the question of whether interactions between practices can be answered. The research question has been answered in the affirmative:​ each case of this mode1 shows that interactions between the improvement practices exist, and if ignored, these interactions can lead to significant levels of over-investment. The most significant factor in determining the potential levels of over-investment has been found to be the form of the investment-improvement function, which is also one of the empincalIy lest understood elements of this model.