Optimal Capacities of Production Facilities

This paper presents a general cost model and the methods of solution for determining the optimum combination of capacities of the production facilities of a steady-state production system. The model is applied to the practical problem of finding the optimum combination of capacities of the production facilities of an oxygen production and inventory system. Because the cost equations involved are quite complex, the objective function of the formulated model is a very complex non-linear function of two decision variables: the oxygen production rate and the oxygen storage pressure. A computerized gradient method is used to find the optimum values of the two decision variables using parameter values that have been determined empirically. The paper finally studies the effect of variations in some of the parameter values on the optimum values of the decision variables.