An optimal production run time with imperfect production processes and allowable shortages

A model to determine an optimal run time for a deteriorating production system under allowable shortage is developed and it is shown that there exists a unique optimal production run time to minimize the total relevant cost function.

Abstract

This paper develops a model to determine an optimal run time for a deteriorating production system under allowable shortage. It is assumed that the elapsed time until the production process shift is arbitrarily distributed. We show that there exists a unique optimal production run time to minimize the total relevant cost function. Finally, bounds for the optimal production run time are provided to develop the solution procedure. Rosenblatt and Lee [IIE Trans. 18 (1986) 48] study the effects of an imperfect production process on the optimal production run time assuming that an elapsed time until shift is exponentially distributed. Furthermore, Kim and Hong [Int. J. Prod. Econ. 58 (1999) 183] extend the problem of Rosenblatt and Lee by assuming that elapsed time until the process shift is arbitrarily distributed. Basically, their models do not allow for shortage. Consequently, the main purpose of this paper is to generalize Kim and Hong to assume that the shortage is allowed.