A generalization of the entropy model for brand purchase behavior

Hemiter's entropy model for brand purchase behavior has been generalized for Renyi's measure of entropy which is a more general concept than Shannon's measure of entropy used by Herniter and which includes Shannon's measure as a limiting case. The generalized model considered here is more flexible than Herniter's model since it can give different marketing statistics for different products and it can give these statistics even when only some of the brands are considered.     

Optimal control for multi-servers queueing systems under periodic review

This paper deals with the problem of finding the optimal dynamic operating policy for an M/M/S queue. The system is observed periodically, and at the beginning of each period the system controller selects the number of service units to be kept open during that period. The optimality criterion used is the total discounted cost over a finite horizon.     

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.     

Optimal policies for a multi-echelon inventory system with demand forecasts

Consider an inventory system consisting of two installations, the stocking point and the field. Each period two decisions must be made: how much to order from outside the system and how much to ship to the field. The first decision is made based on the total amounts of stock then at the two installations. Next a forecast of the demand in the current period is sent from the field to the stocking point. Based upon a knowledge of the joint distribution of the forecast and the true demand, and the amounts of stock at the two installations, a decision to ship a certain amount of stock to the field is taken. The goal is to make these two decisions so as to minimize the total n-period cost for the system. Following the factorization idea of Clark and Scarf (1960), the optimal n period ordering and shipping policy, taking into account the accuracy of the demand forecasts, can be derived so as to make the calculation comparable to those required by two single installations.     

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.     

More ado about economic order quantities (EOQ)

This paper is concerned with the determination of explicit expressions for economic order quantities and reorder levels, such that the cost of ordering and holding inventory is minimized for specific backorder constraints. Holding costs are applied either to inventory position or on-hand inventory, and the backorder constraint is considered in terms of the total number of backorders per year or the average number of backorders at any point in time. Through the substitution of a new probability density function in place of the normal p.d.f., explicit expressions are determined for the economic order quantities and the reorder points. The resulting economic order quantities are independent of all backorder constraints. It is also concluded that under certain conditions, the minimization of ordering costs and inventory holding costs (applied to inventory position), subject to a backorder constraint, is equivalent in terms of reorder levels to minimization of the safety level dollar investment subject to the same backorder constraint.     

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.     

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.