A two-echelon multi-station inventory model for navy applications

The two inventory echelons under consideration are the depot, D, and k tender ships E₁, …, E_k. The tender ships supply the demand for certain parts of operational boats (the customers). The statistical model assumes that the total monthly demands at the k tenders are stationary independent Poisson random variables, with unknown means λ₁, …, λ_k. The stock levels on the tenders, at the heginning of each month, can be adjusted either by ordering more units from the depot, or by shipping bach to the depot an excess stock. There is no traffic of stock between tenders which is not via the depot. The lead time from the depot to the tenders is at most 1 month. The lead time for orders of the depot from the manufacturer is L months. The loss function due to erroneous decision js comprised of linear functions of the extra monthly stocks, and linear functions of shortages at the tenders and at the depot over the N months. A Bayes sequential decision process is set up for the optimal adjustment levels and orders of the two echelons. The Dynamic Programming recursive functions are given for a planning horizon of N months.     

Some approximations in multi-item,multi-echelon inventory systems for recoverable items

The optimization problem as formulated in the METRIC model takes the form of minimizing the expected number of total system backorders in a two-echelon inventory system subject to a budget constraint. The system contains recoverable items – items subject to repair when they fail. To solve this problem, one needs to find the optimal Lagrangian multiplier associated with the given budget constraint. For any large-scale inventory system, this task is computationally not trivial. Fox and Landi proposed one method that was a significant improvement over the original METRIC algorithm. In this report we first develop a method for estimating the value of the optimal Lagrangian multiplier used in the Fox-Landi algorithm, present alternative ways for determining stock levels, and compare these proposed approaches with the Fox-Landi algorithm, using two hypothetical inventory systems – one having 3 bases and 75 items, the other 5 bases and 125 items. The comparison shows that the computational time can be reduced by nearly 50 percent. Another factor that contributes to the higher requirement for computational time in obtaining the solution to two-echelon inventory systems is that it has to allocate stock optimally to the depot as well as to bases for a given total-system stock level. This essentially requires the evaluation of every possible combination of depot and base stock levels – a time-consuming process for many practical inventory problems with a sizable system stock level. This report also suggests a simple approximation method for estimating the optimal depot stock level. When this method was applied to the same two hypotetical inventory systems indicated above, it was found that the estimate of optimal depot stock is quite close to the optimal value in all cases. Furthermore, the increase in expected system backorders using the estimated depot stock levels rather than the optimal levels is generally small.     

Optimal inventory control policy for periodic‐review inventory systems with inventory‐level‐dependent demand

We consider a setting in which inventory plays both promotional and service roles; that is, higher inventories not only improve service levels but also stimulate demand by serving as a promotional tool (e.g., as the result of advertising effect by the enhanced product visibility). Specifically, we study the periodic‐review inventory systems in which the demand in each period is uncertain but increases with the inventory level. We investigate the multiperiod model with normal and expediting orders in each period, that is, any shortage will be met through emergency replenishment. Such a model takes the lost sales model as a special case. For the cases without and with fixed order costs, the optimal inventory replenishment policy is shown to be of the base‐stock type and of the (s,S) type, respectively. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

鱼雷装备备件隶属关系的两级库存系统配置优化研究

备件库存系统配置优化是提高武器装备的战备完好性和降低寿命周期费用的重要途径,但在装备组成结构中,由于部件之间存在一定的隶属关系,并不是所有的项目都能够进行串件。针对现有两级库存系统备件配置优化研究的不完善之处,根据装备结构层次特点,通过分析鱼雷装备LRU和SRU备件两级库存系统,提出了备件初始配置方案下的备件库存缺货数模型,并在此基础上建立了基于备件隶属关系的两级库存系统配置优化模型。该模型以鱼雷装备使用度和库存费用为优化目标,通过优化备件库存配置结构,生成较好的备件库存配置方案,从而节约备件配置费用,避免造成资源浪费。     

On the (S − 1, S) lost sales inventory model with priority demand classes

In this paper an inventory model with several demand classes, prioritised according to importance, is analysed. We consider a lot‐for‐lot or (S ? 1, S) inventory model with lost sales. For each demand class there is a critical stock level at and below which demand from that class is not satisfied from stock on hand. In this way stock is retained to meet demand from higher priority demand classes. A set of such critical levels determines the stocking policy. For Poisson demand and a generally distributed lead time, we derive expressions for the service levels for each demand class and the average total cost per unit time. Efficient solution methods for obtaining optimal policies, with and without service level constraints, are presented. Numerical experiments in which the solution methods are tested demonstrate that significant cost reductions can be achieved by distinguishing between demand classes. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 593–610, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10032     

Queueing models for spares provisioning

A population of items which break down at random times and require repair is studied (the classic “machine repair problem with spares”). It is desired to determine the number of repair channels and spares required over a multiyear planning horizon in which population size and component reliability varies, and a service level constraint is imposed. When an item fails, a spare (if available) is immediately dispatched to replace the failed item. The failed item is removed, transported to the repair depot, repaired, and then placed in the spares pool (which is constrained to be empty not more than 10% of the time) unless there is a backlog of requests for spares, in which case it is dispatched immediately. The first model considered treats removal, transportation, and repair as one service operation. The second model is a series queue which allows for the separate treatment of removal, transportation, and repair. Breakdowns are assumed Poisson and repair times exponential.     

In Defense of Mercy

ABSTRACT

Though it is legally permissible to kill combatants in war, unless they are rendered hors de combat, the existence of “Naked Soldiers” raises an important moral question: should combatants kill vulnerable enemy combatants or show mercy towards them? Most philosophers who address this question argue that it is morally permissible to kill the Naked Soldier given the extended notion of self-defense during war. They ground their arguments in a form of collectivism. In this article, I use Larry May’s argument. He offers an approach that extends the principle of discrimination that would apply also to combatants. Instead of assuming all combatants are de facto dangerous, this approach would allow for nuance in targeting the enemy and showing mercy when enemy combatants clearly pose no danger, in other words, when they are Naked Soldiers. I defend this view against two criticisms: Noam Zohar’s view of armies as complex collectives and Stephen Deakin’s view that a policy that spares Naked Soldiers would be open to abuse. I argue that it is not only morally suspect to kill Naked Soldiers, but also it is within the spirit of both international laws governing war and the just war tradition to offer mercy whenever possible.     

Optimal maintenance-repair policies for the machine repair problem

We consider a model with M + N identical machines. As many as N of these can be working at any given time and the others act as standby spares. Working machines fail at exponential rate λ, spares fail at exponential rale γ, and failed machines are repaired at exponential rate μ. The control variables are λ. μ, and the number of removable repairman, S, to be operated at any given time. Using the criterion of total expected discounted cost, we show that λ, S, and μ are monotonic functions of the number of failed machines M, N, the discount factor, and for the finite time horizon model, the amount of time remaining.     

Optimal control of a production‐inventory system with both backorders and lost sales

We consider the optimal control of a production inventory‐system with a single product and two customer classes where items are produced one unit at a time. Upon arrival, customer orders can be fulfilled from existing inventory, if there is any, backordered, or rejected. The two classes are differentiated by their backorder and lost sales costs. At each decision epoch, we must determine whether or not to produce an item and if so, whether to use this item to increase inventory or to reduce backlog. At each decision epoch, we must also determine whether or not to satisfy demand from a particular class (should one arise), backorder it, or reject it. In doing so, we must balance inventory holding costs against the costs of backordering and lost sales. We formulate the problem as a Markov decision process and use it to characterize the structure of the optimal policy. We show that the optimal policy can be described by three state‐dependent thresholds: a production base‐stock level and two order‐admission levels, one for each class. The production base‐stock level determines when production takes place and how to allocate items that are produced. This base‐stock level also determines when orders from the class with the lower shortage costs (Class 2) are backordered and not fulfilled from inventory. The order‐admission levels determine when orders should be rejected. We show that the threshold levels are monotonic (either nonincreasing or nondecreasing) in the backorder level of Class 2. We also characterize analytically the sensitivity of these thresholds to the various cost parameters. Using numerical results, we compare the performance of the optimal policy against several heuristics and show that those that do not allow for the possibility of both backordering and rejecting orders can perform poorly.© 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010     

Optimal division of inventory between depot and bases

We consider a problem of optimal division of stock between a logistic depot and several geographically dispersed bases, in a two‐echelon supply chain. The objective is to minimize the total cost of inventory shipment, taking into account direct shipments between the depot and the bases, and lateral transshipments between bases. We prove the convexity of the objective function and suggest a procedure for identifying the optimal solution. Small‐dimensional cases, as well as a limit case in which the number of bases tends to infinity, are solved analytically for arbitrary distributions of demand. For a general case, an approximation is suggested. We show that, in many practical cases, partial pooling is the best strategy, and large proportions of the inventory should be kept at the bases rather than at the depot. The analytical and numerical examples show that complete pooling is obtained only as a limit case in which the transshipment cost tends to infinity. © 2017 Wiley Periodicals, Inc. Naval Research Logistics, 64: 3–18, 2017     

A stock redistribution model

Multi-depot supply systems are subject to stock distribution imbalances; i. e., the fraction of total system stock located at a depot may be too small to support the fraction of system demand expected to be placed on it. In the supply system of concern, a cutomer is always satisfied if there is stock anywhere in the system. Stock redistributions to correct imbalances may reduce both transportation costs and customer waiting times. A model for determining optimum redistribution quantities is formulated, and a practical method of solution for the two depot case is described. Selected numerical illustrations are given.     

备件供应系统及其保证度模型研究

本文针对备件供应决策问题,提出了备件保证度的概念,阐述了保证度与使用可用度的关系,认为影响保证度的主要因素是:备件修复时间、备件获取时间、库存水平、设备数量及复杂程度和备件需求率,分析了二级供应系统的普遍性和代表性,并应用概率论的原理,建立了备件保证度模型。     

Why Culture Matters: Revisiting the Sino-Indian Border War of 1962

This article examines the nuclear command and control (C²) system implemented in Pakistan since 1998, and discusses its potential consequences for the risk of inadvertent or unauthorised use of nuclear weapons. I argue that troubled civil-military relations and Pakistan's doctrine of ‘asymmetric escalation’ account for the creation of a command and control system with different characteristics during peacetime and military crises. Although the key characteristics of Pakistan's nuclear C² system allow relatively safe nuclear operations during peacetime, operational deployment of nuclear weapons during military standoffs is likely to include only rudimentary protections against inadvertent or unauthorised nuclear release. The implication of this study is that any shift from peacetime to wartime command and control procedures is likely to further destabilise Indo-Pakistani relations during the early stages of a diplomatic or military standoff, and introduce a non-trivial risk of accidental escalation to the nuclear level.     

Optimal policy for a dynamic multi-echelon inventory model

A general multiperiod multi-echelon supply system consisting of n facilities each stocking a single product is studied. At the beginning of a period each facility may order stock from an exogenous source with no delivery lag and proportional ordering costs. During the period the (random) demands at the facilities are satisfied according to a given supply policy that determines to what extent stock may be redistributed from facilities with excess stock to those experiencing shortages. There are storage, shortage, and transportation costs. An ordering policy that minimizes expected costs is sought. If the initial stock is sufficiently small and certain other conditions are fulfilled, it is optimal to order up to a certain base stock level at each facility. The special supply policy in which each facility except facility 1 passes its shortages on to a given lower numbered facility called its direct supplier is examined in some detail. Bounds on the base stock levels are obtained. It is also shown that if the demand distribution at facility j is stochastically smaller (“spread” less) than that at another facility k having the same direct supplier and if certain other conditions are fulfilled, then the optimal base stock level (“virtual” stock out probability) at j is less than (greater than) or equal to that at facility k.     

A three-echelon,multi-item model for recoverable items

The main objective of this paper is to develop a mathematical model for a particular type of three-echelon inventory system. The proposed model is being used by the Air Force to evaluate inventory investment requirements for alternative logistic structures. The system we will model consists of a group of locations, called bases, and a central depot. The items of concern in our analysis are called recoverable items, that is, items that can be repaired when they fail. Furthermore, each item has a modular or hierarchical design. Briefly, the model is used to determine the stock levels at each location for each item so as to achieve optimum inventory-system performance for a given level of investment. An algorithm for the computation of stock levels for each item and location is developed and illustrated. Some of the ways the model can be used are illustrated with Air Force data.     

Mapping Out a Counterinsurgency Campaign Plan: Critical Considerations in Counterinsurgency Campaigning1

This paper argues on the basis of a series of historical examples that include the Philippines, Vietnam, Malaya and Northern Ireland, that there is no perfect counterinsurgency model and that each counterinsurgency campaign is different. Counterinsurgents need to have a series of basic tenets to wage successful war against guerrillas and insurgents. These include: a clear political policy from the government under insurgent attack, a strategy to keep the population safe, successful intelligence gathering, a recognition that successful counterinsurgency is manpower intensive and a high priority on the destruction of the insurgent infrastructure. This paper urges that in period of peacetime it is essential that militaries develop a Standing Counterinsurgency Concepts Unit that can conceptualise past and present insurgent patterns and build this into military and strategic planning.     

Right Intention and the Ends of War

The jus ad bellum criterion of right intention (CRI) is a central guiding principle of just war theory. It asserts that a country’s resort to war is just only if that country resorts to war for the right reasons. However, there is significant confusion, and little consensus, about how to specify the CRI. We seek to clear up this confusion by evaluating several distinct ways of understanding the criterion. On one understanding, a state’s resort to war is just only if it plans to adhere to the principles of just war while achieving its just cause. We argue that the first understanding makes the CRI superfluous, because it can be subsumed under the probability of success criterion. On a second understanding, a resort to war is just only if a state’s motives, which explain its resort to war, are of the right kind. We argue that this second understanding of the CRI makes it a significant further obstacle to justifying war. However, this second understanding faces a possible infinite regress problem, which, left unresolved, leaves us without a plausible interpretation of the CRI. This constitutes a significant and novel reason for leaving the CRI out of the international law of armed conflict (LOAC).     

Institutions,information, and commitment: the role of democracy in conflict

This paper explores the hypothesis that both the preexisting quality of democracy in a polity at the onset of conflict and the quality of democracy expected to emerge in the aftermath influence the likelihood of civil war. An empirical investigation of the hypothesis presents a challenge due to concerns of endogeneity and selection: the post-conflict level of democracy is endogenous to the pre-conflict level. Further, for a given time period, either a number of countries have not experienced civil war; or if they did, did not resolve the conflict. We overcome this selection bias by implementing a three-step extension to the Heckman procedure using an unbalanced cross-country panel of 77 countries over the period 1971–2005. Consistent with our hypothesis, we find that a standard deviation improvement in the existing level of democracy reduces the probability of civil war by approximately 9 percentage points and a corresponding improvement in expected post-conflict democratization increases the probability of conflict by approximately 48 percentage points.     

Optimal design of a multi-item,multi-location,multi-repair type repair and supply system

The design of a system with many locations, each with many items which may fail while in use, is considered. When items fail, they require repair; the particular type of repair being governed by a probability distribution. As repairs may be lengthy, spares are kept on hand to replace failed items. System ineffectiveness is measured by expected weighted shortages over all items and locations, in steady state. This can be reduced by either having more spares or shorter expected repair times. Design consists of a provisioning of the number of spares for each item, by location; and specifying the expected repair times for each type of repair, by item and location. The optimal design minimizes expected shortages within a budget constraint, which covers both (i) procurement of spares and (ii) procurement of equipment and manning levels for the repair facilities. All costs are assumed to be separable so that a Lagrangian approach is fruitful, yielding an implementable algorithm with outputs useful for sensitivity analysis. A numerical example is presented.     

Spares stocking policies for repairable items with dependent repair times

This paper analyzes the problem of determining desirable spares inventory levels for repairable items with dependent repair times. The problem is important for repairable products such as aircraft engines which can have very large investment in spares inventory levels. While existing models can be used to determine optimal inventory spares levels when repair times are independent, the practical considerations of limited repair shop capacity and prioritized shop dispatching rules combine to make repair times not independent of one another. In this research a simulation model of a limited capacity repair facility with prioritized scheduling is used to explore a variety of heuristic approaches to the spares stocking decision. The heuristics are also compared with use of a model requiring independent repair times (even though that assumption is not valid here). The results show that even when repair time dependencies are present, the performance of a model which assumes independent repair times is quite good.