Economic screening procedures with multi-decision alternatives in logistic and normal models

For situations where there are several markets with different profit/cost structures, economic screening procedures with dichotomous performance variable T and continuous screening variable X are proposed for determining the market to ship the products to. Logistic and normal models are considered. It is assumed that P[T = 1| X = x] is given by a logistic function in the logistic model and X given T is normally distributed in the normal model. Profit models are constructed which involve three profit/cost components: profit from a conforming item, cost from an accepted nonconforming item, and screening inspection cost. Methods of finding the optimal screening procedures are presented and a numerical example is given.