Single-period inventory models with demand uncertainty and quantity discounts: Behavioral implications and a new solution procedure

Quantity discounts are considered in the context of the single-period inventory model known as “the newsboy problem.” It is argued that the behavioral implications of the all-units discount schedule are more complex and interesting than the literature has suggested. Consideration of this behavior and the use of marginal analysis lead to a new method for solving this problem that is both conceptually simpler and more efficient than the traditional approach. This marginal-cost solution procedure is described graphically, an algorithm is presented, and an example is used to demonstrate that this solution procedure can be extended easily to handle complex discount schedules, such as some combined (simultaneously applied) purchasing and transportation cost discount schedules.     

Application of perturbation analysis to a class of periodic review (s,S) inventory systems

In this article we apply perturbation analysis (PA), combined with conditional Monte Carlo, to obtain derivative estimators of the expected cost per period with respect to s and S, for a class of periodic review (s, S) inventory systems with full backlogging, linear holding and shortage costs, and where the arrivals of demands follow a renewal process. We first develop the general form of four different estimators of the gradient for the finite-horizon case, and prove that they are unbiased. We next consider the problem of implementing our estimators, and develop efficient methodologies for the infinite-horizon case. For the case of exponentially distributed demand interarrival times, we implement our estimators using a single sample path. Generally distributed interarrival times are modeled as phase-type distributions, and the implementation of this more general case requires a number of additional off-line simulations. The resulting estimators are still efficient and practical, provided that the number of phases is not too large. We conclude by reporting the results of simulation experiments. The results provide further validity of our methodology and also indicate that our estimators have very low variance. © 1994 John Wiley & Sons, Inc.     

Optimal control policies for a periodic review inventory system with emergency orders

We describe a periodic review inventory system where emergency orders, which have a shorter supply lead time but are subject to higher ordering cost compared to regular orders, can be placed on a continuous basis. We consider the periodic review system in which the order cycles are relatively long so that they are possibly larger than the supply lead times. Study of such systems is important since they are often found in practice. We assume that the difference between the regular and emergency supply lead times is less than the order-cycle length. We develop a dynamic programming model and derive a stopping rule to end the computation and obtain optimal operation parameters. Computational results are included that support the contention that easily implemented policies can be computed with reasonable effort. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 187–204, 1998     

An optimal structured policy for maintenance of partially observable aircraft engine components

This paper considers the maintenance of aircraft engine components that are subject to stress. We model the deterioration process by means of the cumulative jump process representation of crack growth. However, because in many cases cracks are not easily observable, maintenance decisions must be made on the basis of other information. We incorporate stress information collected via sensors into the scheduling decision process by means of a partially observable Markov decision process model. Using this model, we demonstrate the optimality of structured maintenance policies, which support practical maintenance schedules. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 335–352, 1998     

The validity of assumptions underlying current uses of Lanchester attrition rates

This study examines critically the various assumptions, results, and concepts that exist to date in the literature and scientific community concerning the relationships among the Lanchester, stochastic Lanchester, and the general renewal models of combat. Many of the prevailing understandings are shown to be erroneous.     

Variance of the number of units produced on a transfer line with buffer inventories during a period of length T

The transfer-line models in the literature are planning models rather than operational models. That is, they are very useful for planning or designing the transfer line, but are less useful for controlling the daily operation of the line. The performance measure used in these models is the efficiency of the line A. The expected number of units produced during a period of length T cycles is AT. In this article a procedure is presented for calculating the variance of the number of units produced by the transfer line during a period of length T cycles. These two performance measures can be used to construct an interval estimate for, say, the number of units produced during a shift. This interval estimate is an operational guide for the production manager.