Optimal joint set-up and calibration policy with unequal revenue from oversized and undersized items

The algorithm in this paper jointly determines the optimal level to which the mean of a critical variable should be set up, and the optimal number of repetitions until recalibration, for the case where the variable is distributed normally, the mean changes linearly with the number of repetitions, and the revenue per oversized and undersized item is unequal. The paper proves that the optimal set-up level should be below the mid-point between the specification limits by a distance which depends on the slope of change of the mean, on the recalibration cycle, and on a function of the per unit revenues, in such a manner that just prior to the recalibration the mean reaches a different distance above the mid-point. It outlines a method for the numerical evaluation of the optimal number of cycle repetitions, and derives a general approximation formula which allows its closed loop determination. It provides a numerical example and sensitivity analysis.