Determining input parameters under process uncertainties

In many industrial operations, certain proportions for the output quantities or dimensions have to be maintained. Due to process uncertainties, the resulting output proportions deviate from the desired target levels. In this paper, a model for selecting the levels of input parameters (dimensions or quantities) which minimize the economic consequences of deviations from the target levels is developed. Two different objective functions are considered. When the expected costs of deviations are minimized, the optimizing condition is similar to that of the classical newsboy problem. For the quadratic loss function the optimal input proportions are explicitly determined. This model can be used in a variety of ways: while specifying dimensions for parts, at the materials planning stage and for process control as well.