Approximations for the consolidation of multiechelon repair facilities

This paper develops and illustrates an approximate approach for analytically assessing the impacts on both costs and service of consolidation of repair facilities. The repair facilities are two echelon generalizations of the classical repairmen problem in which two types of failures, say major and minor, can occur, each type requiring repair at a different echelon: The questions addressed are the reductions possible in spares, repairmen, and service rates due to the consolidated system's increased efficiency, as well as the physical separation between the users and the consolidated repair facility that is economical. The method of analysis is based upon asymptotic approximations developed for the repairmen problem, valid when the number of operational equipments is large (greater than 50); it is helpful since it provides a tractable means for predicting the steady-state performance of the decentralized and consolidated installations as a function of the many parameters involved without having to resort to an exhaustive computation of all the exact steady-state probabilities.     

An analysis of the long range operating characteristics of the MIL-STD-105D sampling scheme and some suggested modifications

An integral part of the MIL–STD–105D scheme for sampling inspection by attributes is the transfer from normal inspection to reduced or tightened inspection when the historical record of inspected lots suggests unusually good or bad quality. The switching rules in MIL–STD–105D have been criticized, especially by Japanese manufacturers, as being too severe when what is defined as acceptable quality material is submitted. This paper examines the long range fraction of lots rejected for several MIL–STD–105D sampling plans by using the MIL–STD–105D switching rules, using a modification suggested by the Japanese Standards Association, and by using a second modification developed by the authors. The Japanese Standards Association switching rules are more complex than those in MIL–STD–105D. It is demonstrated that they lead to improved long–range properties for Normal–Tightened–Reduced schemes, but to poorer properties for Normal–Tightened schemes. A simplified set of switching rules is suggested, wherein the “limit numbers” in MIL–STD–105D are eliminated. In comparison to MIL–STD–105D, the simpler rules lead to a lower probability of rejection for good lots and a comparable probability of rejection for bad lots.     

Product moments of order statistics from the doubly truncated exponential distribution

Recurrence relations for the product moments of order statistics from a doubly truncated exponential distribution are obtained. These relations allow us to evaluate the product moments for all sample sizes.     

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.