Multi-class inventory models with demand a function of inventory level

This paper considers the problem of maintaining an inventory of an item which can deteriorate and become useless. A periodic review procedure is used and new items ordered may experience a time lag in delivery. Items are considered to deteriorate through one or two states before becoming useless. Thus the deterioration process in each period plays the role of the usual demand process and is a function of the inventory level at the beginning of each period. For the case of no time lag in delivery, one stage deterioration, and either binomial or uniform deterioration, optimal ordering policies are obtained for the n-period dynamic model with the standard cost structure. (For the shortage probability criterion see the other paper by Iglehart and Jaquette, in this issue.) These policies are of the single critical number type. For more complicated models suboptimal policies of this same type are found.     

Optimal policies under the shortage probability criterion for an inventory model with unknown dependent demands

The principal innovation in this paper is the consideration of a new objective function for inventory models which we call the shortage probability criterion. Under this criterion we seek to minimize the total expected discounted cost of ordering subject to the probability that the stock level at the end of the period being less than some fixed quantity not exceed some prescribed number. For three different models we show that the minimum order policy is optimal. This result is then applied to a particular inventory model in which the demand distribution is not completely known. A Bayesian procedure is discussed for obtaining optimal policies.     

Discounted production scheduling and employment smoothing

We consider the problem of minimizing the sum of production, employment smoothing, and inventory costs over a finite number of time periods where demands are known. The fundamental difference between our model and that treated in [1] is that here we permit the smoothing cost to be nonstationary, thereby admitting a model with discounting. We show that the values of the instrumental variables are nondecreasing in time when demands are nondecreasing. We also derive some asymptotic properties of optimal policies.     

On maximization of the integral of a bell-shaped function over a symmetric set

Given a target T in Euclidean n-space Rⁿ and a point bomb whose point of impact in Rⁿ is governed by a probability distribution about the aim point a, what choice of a maximizes the probability of a hit v_a(T)? Of course, only in special cases is an exact solution of this problem obtainable. This paper treats targets T which are symmetric about the origin o and demonstrates conditions on the extent of T and the impact density f, a density with respect to Lebesgue measure, sufficient for v_a(T) to be monotone in the distance from a to o and maximized at a = o. The results are applied to various tactical situations.     

The machine sequencing problem – review and extensions

The deterministic sequencing problem is reviewed from the points of view of variety, models, context, methodology, and current state of the art. The relationship between the theory of sequencing and other areas of control is illustrated with the relationship of sequencing to inventory. The “cyclical EMQ (Economical Manufacturing Quantities)” problem is discussed and new formulations are presented which promise a computationally feasible resolution of this outstanding problem.     

Selecting among weibull,lognormal and gamma distributions using complete and censored smaples

In a recent paper, Kent and Quesenberry [19] considered using certain optimal invariant statistics to select the best fitting member of a collection of probability distributions using complete samples of life data. In the present work extensions of this approach in two directions are given. First, selection for complete samples based on scale and shape invariant statistics is considered. Next, the selection problem for type I censored samples is considered, and both scale invariant and maximum likelihood selection procedures are studied. The two-parameter (scale and shape) Weibull, lognormal, and gamma distributions are considered and applications to real data are given. Results from a (small) comparative simulation study are presented.