Inventory systems with imperfect demand information

An inventory system is described in which demand information may be incorrectly transmitted from the field to the stocking point. The stocking point employs a forwarding policy which attempts to send out to the field a quantity which, in general, is some function of the observed demand. The optimal ordering rules for the general n-period problem and the steady state case are derived. In addition orderings of the actual reorder points as functions of the errors are presented, as well as some useful economic interpretations and numerical illustrations.     

Suboptimal ordering policies under the full cost criterion

This note extends some previous work in dependent inventory models previously studied by the author. A comparison is given between optimal policies under the shortage probability criterion and a class of suboptimal policies using the usual cost minimization criterion.     

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.     

A new bivariate negative binomial distribution

A new bivariate negative binomial distribution is derived by convoluting an existing bivariate geometric distribution; the probability function has six parameters and admits of positive or negative correlations and linear or nonlinear regressions. Given are the moments to order two and, for special cases, the regression function and a recursive formula for the probabilities. Purely numerical procedures are utilized in obtaining maximum likelihood estimates of the parameters. A data set with a nonlinear empirical regression function and another with negative sample correlation coefficient are discussed.     

A note on integer solutions to linear fractional interval programming problems by a branch & bound technique

This paper provides a method for solving linear fractional interval programming problems in integers with the help of a branch and bound technique.     

A procedure for generating time-dependent arrivals for queueing simulations

This paper presents a method for modeling cyclic inputs to a congested system in a discrete event digital simulation. Specifically, we express the mean of the interarrival time conditional on the last arrival as a linear combination of harmonic components whose coefficients can be determined by stepwise regression. We also assume that the conditional interarrival time normalized by its corresponding mean follows a distribution that is independent of time. The result can, in turn, be used to generate the desired input for a simulation, An example based on a set of actual data is used to illustrate the process of parameter estimation for the model.     

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.