A Dynamic Inventory Model with Random Replenishment Quantities

A periodic-review, random-demand inventory model is analyzed under the assumption that replenishment quantities are random fractions of the amounts ordered. Results of a previous study of a single-period model are generalized to form an easily computed heuristic adaptation of the (s, S) policy for use in this environment. The heuristic is based on the simple practice of scaling down pipeline inventories to estimate the inventory position, and scaling up the order quantity in anticipation of an average replenishment yield. Simulation experiments are used to estimate the most cost-efficient (s, S) policies and to estimate the performance of heuristic policies in environments where replenishment randomness ranges from mild (0-20% defectives) to moderate (0-50% defectives). The heuristic is shown to perform quite well, with expected total costs typically within a few percent of the best (s, S) costs. The results tend to support common practice in industry which is similar to the approach studied here. Although the heuristic is naive in the sense that it ignores the degree of randomness in the replenishment quantity, the simulation results support the speculation that unless the target service level is extremely high, the replenishment process must be extremely random for its variability to be a significant explicit factor in the selection of a practical, cost-effective policy

A model of JIT make-to-stock inventory with stochastic demand

We consider a firm that manages its internal manufacturing operations according to a just-in-time (JIT) system but maintains an inventory of finished goods as a buffer against random demands from external customers. We formulate a model in which finished goods are replenished by a small fixed quantity each time period. In the interest of schedule stability, the size of the replenishment quantity must remain fixed for a predetermined interval of time periods. We analyse the single-interval problem in depth, showing how to compute a cost-minimising value of the replenishment quantity for a given interval length, and characterising the optimal cost, inventory levels and service as functions of the interval length and initial inventory. The model displays significant cost and service penalties for schedule stability. A dynamic version of the problem is also formulated, and shown to be convex in nature with relatively easily computed optima

A Revision of the Power Approximation for Computing (s,S) Policies

A revision of the Power Approximation for computing (s, S) inventory policies is presented. The revision incorporates modifications which (1) ensure homgeneity in the units chosen to measure demand and (2) ensure the proper limiting behavior of S - s when the variance of demand is extremely small. Computational experience shows that the revision has operating characteristics that are typically within a few percent of optimal, which is nearly as accurate as the original Power Approximation

(s, S) Policies for a Dynamic Inventory Model with Stochastic Lead Times

This study analyzes a stochastic lead time inventory model under the assumptions that (a) replenishment orders do not cross in time and (b) the lead time distribution for a given order is independent of the number and sizes of outstanding orders. The study extends the existing literature on the finite horizon version of the model and yields an intuitively appealing dynamic program that is nearly identical to one that would apply in a transformed model with all lead times fixed at zero. Hence, many results that have been derived for fixed lead time models generalize easily. Conditions for the optimality of myopic base stock policies, and for the optimality of (s, S) policies are established for both finite and infinite planning horizons. The infinite-horizon model analysis is extended by adapting the fixed lead time results for the efficient computation of optimal and approximately optimal (s, S) policies

Finished goods management for JIT production: new models for analysis

A firm is considered that manages its internal manufacturing operations according to a just-in-time system, but maintains an inventory of finished goods as a buffer against random demands from external customers. The finished goods inventory may be analysed by the methods of classical inventory theory in order to characterize the trade-off between inventory costs and schedule stability. A model is formulated in which the supply of finished goods is replenished by a small fixed quantity each time period. The size of the replenishment quantity may be revised only at pre-specified intervals. The single-interval problem is analysed, the cost-minimizing value of the replenishment quantity for a given revision interval length is computed, and the optimal cost is characterized as a function of the revision interval length. The dynamic problem is shown to be convex, with relatively easily computed optima. Finally, alternative formulations of the problem are described and suggestions made for further research

Cost effectiveness of high risk and population approaches for preventing CHD: A comparative study in New Brunswick, Canada.

This paper uses management science methodology to compare the cost-effectiveness of two different approaches to preventing coronary heart disease in the province of New Brunswick, Canada. The general model utilized included realistic assumptions about implementation costs, effectiveness levels, budget constraints and implementation strategies. Integer linear programming methods were then used to examine the cost-effectiveness of the two approaches, as well as to compare them with a third "integrated" approach which combined elements of both approaches. The study concludes that under ideal circumstances, a population approach has greater potential to prevent CHD, and when costs were considered from a societal perspective, it is also the more cost-effective option. However, under more realistic outcome conditions we found that a high risk approach may be more effective, and when costs were considered from the perspective of the publicly funded health care system we found that there are conditions under which the high risk approach is more cost-effective. Our final conclusion is that an integ

An inventory model with random replenishment quantities.

A single-period random demand inventory model is analysed under the assumption that the replenishment quantity is a random function of the amount ordered. The structure of optimal policies is characterized for linear ordering cost functions, both with and without a setup cost. Generalizations of base-stock policies and (s, S) policies are shown to be optimal. Closed form analytic expressions for optimal policies are obtained for the special ease of linear ordering cost and uniformly distributed demand. Optimal policies are compared with two heuristics in a more general demand environment. It is shown that a very simple heuristic policy performs quite well

Die Brüder Grimm. Pioniere deutscher Sprachkultur des 21. Jahrhunderts

Die bekanntesten Märchenerzähler der Deutschen - und doch reicht die Wirkung der weltberühmten Brüder viel weiter: Tatsächlich zählen Jacob und Wilhelm Grimm zu den produktivsten Sprachforschern ihres Jahrhunderts. Sie kamen der Entstehung der germanischen Sprachen auf die Spur, und sie schufen mit dem »Deutschen Wörterbuch« das umfangreichste Nachschlagewerk zur deutschen Sprache überhaupt. Wissenschaft verstanden sie dabei als Dienst an der Gesellschaft: In all ihren Arbeiten war immer auch der Gedanke an Aufklärung, Sprachkultur und Volksbildung lebendig. Die Brüder Grimm - Pioniere deutscher Sprachkultur des 21. Jahrhunderts gibt einen aufschlussreichen Überblick über das Wirken der Grimms, vermittelt Einblicke in zwei außergewöhnliche Forscherleben und zeigt, wie ihre Ideen und Konzepte bis heute aktuell geblieben sind

Multidisciplinary Baseline Assessment of Homosexual Men with and without Human Immunodeficiency Virus Infection. Iii. Neurologic and Neuropsychological Findings

We explored the possibility that neurologic and neuropsychological changes constitute the earliest detectable manifestations of human immunodeficiency virus (HIV) infection. Without knowledge of HIV status, we assessed neurologic signs and symptoms and administered a battery of neuropsychological tests to 208 homosexual men, of whom 84 were HIV negative, 49 were HIV positive and asymptomatic, 29 were mildly symptomatic, and 46 had significant medical symptoms but not the acquired immunodeficiency syndrome. There was no difference between the HIV-negative and HIV-positive men in the frequency of neurologic signs or of defective or borderline performance on any neuropsychological test. However, HIV-positive men performed slightly but significantly worse than HIV-negative men on tests of verbal memory, executive function, and language. Similar results were obtained when comparisons were limited to HIV-positive medically asymptomatic and HIV-negative men. There was no degradation of neurologic status or neuropsychological performance across stages of HIV severity, but neurologic and neuropsychological summary scores correlated with CD4/CD8 ratios in the HIV-positive group. Ratings of neurologic signs and symptoms correlated with neuropsychological summary scores in the HIV-positive group only. Cognitive complaints were more frequent in the HIV-positive men; they correlated with actual test performance in the HIV-positive but not HIV-negative men. The constellation of subjective and objective neuropsychological and neurologic findings suggests the possibility of a definable syndrome associated with HIV infection in asymptomatic individuals