Some renewal theory results with application to fleet warranties

The fleet warranty guarantees the purchaser of a large population of like items that the mean life of the fleet will meet or exceed some negotiated mean μ_L. If the mean life is less than μ_L, compensation may be given in terms of a number of free replacement parts R. The expected number of replacements E[R] is studied based upon how the mean life of items in the field is determined and on whether the sampling window starts at time t = 0 (ordinary renewal process) or at some arbitrarily large time w (equilibrium renewal process). Properties of E[R] are compared and examples are given. © 1994 John Wiley & Sons, Inc.     

Applications of renewal theory in analysis of the free-replacement warranty

Under a free-replacement warranty of duration W, the customer is provided, for an initial cost of C, as many replacement items as needed to provide service for a period W. Payments of C are not made at fixed intervals of length W, but in random cycles of length Y = W + γ(W), where γ(W) is the (random) remaining life-time of the item in service W time units after the beginning of a cycle. The expected number of payments over the life cycle, L, of the item is given by M_Y(L), the renewal function for the random variable Y. We investigate this renewal function analytically and numerically and compare the latter with known asymptotic results. The distribution of Y, and hence the renewal function, depends on the underlying failure distribution of the items. Several choices for this distribution, including the exponential, uniform, gamma and Weibull, are considered.     

D-S 证据理论应用中的一种图解方法

D-S证据理论是对概率论的进一步扩充,在多传感器数据融合中,有着广泛的应用.当利用D-S合成公式进行融合时,由于需计算的项数较多且不易直接判定具体该有哪些项,容易造成漏项或错项,引起计算错误.提出了一种直观、简单的图解法,可使需计算的项一目了然.     

D-S证据理论应用中的一种验证方法

D-S证据理论是一种比概率论确定性弱的不确定性理论,它能将"不知道"和"不确定"两个认知学上的主要概念区别开来,在多传感器数据融合中具有广泛的应用前景.D-S证据理论在实际应用中却存在一个困难,当目标的个数较多时,需要计算的项数太多,容易造成漏项,引起计算错误.提出了一种确定计算项数的算法,作为验证计算结果的必要条件,并通过图解的方法找出需要计算的项.     

Asymptotic results in search theory

This article addresses a basic problem in search theory concerning the future distribution of a target's location. Given an initial distribution of a target's location and a distribution for its constant velocity, what will its future distribution be? Asymptotics are used to obtain closed-form solutions to that question. We also extend and generalize certain results from the classic search theory text by Koopman.     

Expected time delay in multi‐item inventory systems with correlated demands

This paper considers multi‐item inventory systems where a customer order may require several different items (i.e., demands are correlated across items) and customer satisfaction is measured by the time delays seen by the customers. Most inventory models on time delay in the literature assume each demand only requires one item (i.e., demands are not correlated across items or are independent). In this paper, we derive an exact expression for the expected total time delay. We show that when items are actually correlated, assuming items are independent leads to an overestimate of the total time delay. However, (1) it is extremely difficult in practice to obtain the demand information for all demand types (especially in a system with tens of thousands of part numbers), and (2) the problem becomes too complicated to be of practical interest when the correlation is considered. We then explore the possibility of including the demand information partially and develop bounds for the time delays. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 671–688, 1999     

基于模糊证据理论的船舶安全评估

针对船舶安全评估过程中的诸多不确定因素,提出了一种基于模糊证据理论的安全评估方法.将证据体空间中的事件视为模糊子集,并引入模糊概率,更好地描述了专家意见(或知识),给出了质量分配函数的表示.最后,结合某船舶系统,给出了其安全评估的具体实现过程.结果表明,该方法可靠、有效.     

Application of renewal theory to continuous sampling plans

Renewal theory is used to study the effectiveness of a class of continuous sampling plans first introduced by Dodge. This approach provides a simple way of viewing and computing the long-run Average Outgoing Quality (AOQ) and its maximum AOQL. More importantly, it is used to study the average outgoing quality in a short production run through an approximation formula AOQ^*(t). Formulas for AOQ and AOQ^*(t) are provided. By simulation, it is found that AOQ^*(t) is sufficiently accurate in situations corresponding to actual practice.     

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.     

语用预设与图式理论

本文将语用预设与图式理论作对比性介绍与分析,探讨了它们在话语分析中的作用,通过明示的语项,激活相关的图式。经过演绎推理过程从百科图式知识中选择、获取最佳假设,从而恢复或再现语用预设含义,推导说话者真正的意图,达到对话语或语篇的理解。两个理论在语言学话语分析中的运用直接回答了“为什么有些事实在话语中被省略而可以被理解,并可以再现”的问题。     

Multiple subset sum with inclusive assignment set restrictions

In a traditional multiple subset sum problem (MSSP), there is a given set of items and a given set of bins (or knapsacks) with identical capacities. The objective is to select a subset of the items and pack them into the bins such that the total weight of the selected items is maximized. However, in many applications of the MSSP, the bins have assignment restrictions. In this article, we study the subset sum problem with inclusive assignment set restrictions, in which the assignment set of one item (i.e., the set of bins that the item may be assigned to) must be either a subset or a superset of the assignment set of another item. We develop an efficient 0.6492‐approximation algorithm and test its effectiveness via computational experiments. We also develop a polynomial time approximation scheme for this problem. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

泛系相对论与供求因缘悖憾(一)——悖论的泛系研究

泛系理论是一种侧重泛系或者广泛联系的一种多层网络型的跨学科新研究 ,探索数理·逻辑·科学思维、系统思维、哲理·辩证思维、美学·诗化思维的某些结合 (联四维 )。泛系理论专门开发了网联不同领域多种专题的泛系相对论、供求因缘悖感分析与泛系悖论。本文论述有关的理法与释例 ,包括数理工医文社史哲许多相对性、悖论与供求因缘悖憾的泛系理悟 ,可以简化强化为 :“泛系悖论 =泛系相对论 +泛系供求论”。具体内容涉及 :泛系理论框架 784e ,泛系相对论·泛系辩证·泛系悖论的 8题 16模式百例 2 9说。     

A two-echelon inventory model with purchases,dispositions, shipments,returns and transshipments

This paper presents a one-period two-echelon inventory model with one warehouse in the first echelon and n warehouses in the second echelon. At the beginning of the period the stock levels at all facilities are adjusted by purchasing or disposing of items at the first echelon, returning or shipping items between the echelons and transshipping items within the second echelon. During the period, demands (which may be negative) are placed on all warehouses in the second echelon and an attempt is made to satisfy shortages either by an expedited shipment from the first echelon to the second echelon or an expedited transshipment within the second echelon. The decision problem is to choose an initial stock level at the first echelon (by a purchase or a disposition) and an initial allocation so as to minimize the initial stock movement costs during the period plus inventory carrying costs and system shortage costs at the end of the period. It is shown that the objective function takes on one of four forms, depending on the relative magnitudes of the various shipping costs. All four forms of the objective function are derived and proven to be convex. Several applications of this general model are considered. We also consider multi-period extensions of the general model and an important special case is solved explicitly.     

An operator theory of parametric programming for the generalized transportation problem: I. Basic theory

This paper gives a new organization of the theoretical results of the Generalized Transportation Problem with capacity constraints. A graph-theoretic approach is utilized to define the basis as a one-forest consisting of one-trees (a tree with an extra edge). Algorithmic development of the pivot-step is presented by the representation of a two-tree (a tree with two extra edges). Constructive procedures and proofs leading to an efficient computer code are provided. The basic definition of an operator theory which leads to the discussion of various operators is also given. In later papers we will present additional results on the operator theory for the generalized transportation problem based on the results in the present paper.     

A cooperative game in search theory

Search theory originates from the military research efforts of WWII. Most researchers of that period modeled their search games in noncooperative games, where players are enemies or compete against each other. In this article, we deal with a cooperative search game, where multiple searchers behave cooperatively. First we describe several search problems and discuss the possibility of a coalition or cooperation among searchers. For the cooperative search game, we define a function named quasi‐characteristic function, which gives us a criterion similar to the so‐called characteristic function in the general coalition game with transferable utility. The search operation includes a kind of randomness with respect to whether the searchers can detect a target and get the value of the target. We also propose a methodology to divide the obtained target value among members of the coalition taking account of the randomness. As a concrete problem of the cooperative search game, we take the so‐called search allocation game, where searchers distribute their searching resources to detect a target in a cooperative way and the target moves in a search space to evade the searchers. Lastly, we discuss the core of the cooperative search allocation game. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

基于模糊集理论和D-S证据推理的空袭目标识别

目标识别是防空作战指挥过程中信息处理的一个重要环节。在基于模糊理论目标识别基础上,引入D-S证据理论,通过对模糊隶属度进行重新分配,较好地克服了随机因素的影响,可望进一步提高对空中目标的正确识别率。     

Assemble to order and assemble in advance in a single-period stochastic environment

Faced with stochastic demand, a firm may decide to assemble its products in advance or assemble them once actual demand is realized. In general, the production cost for items assembled in advance (AIA) is lower than for items assembled to order (ATO), because there is no need to expedite, and the production process can be planned and executed well in advance. On the other hand, items assembled in advance (AIA) for which there is no demand incur excessive and unnecessary assembly costs. The two policies, AIA and ATO, as well as a composite one, are compared and analyzed in light of these trade-offs. The composite model, which is shown as the dominating policy, is also extended to deal with the following two scenarios. The first assumes a loss of a fraction of the demand when demand cannot be satisfied from the shelf but rather through ATO. The second considers the effects of budget constraints on the total inventory cost. © 1995 John Wiley & Sons, Inc.     

A theory of war economies

This article presents a proposed theory of how war economies are formed and maintained, as well as an integrated policy framework to guide the dismantling of war economies emanating from the proposed theory. Additionally, six potential areas for future research pertaining to the dismantling of war economies are also presented.     

Prospect theory and foreign policy decision-making: Underexposed issues,advancements, and ways forward

How much mileage can we get out of prospect theory to explain foreign policy decision-making? To answer this question, we first argue that risk as outcome uncertainty is the appropriate definition in prospect-theoretical applications. Then, we indicate that probability weighting—a crucial component of prospect theory—is typically ignored in such applications. We argue why this is problematic and suggest how to move forward. Next, we discuss how to establish the reference point in the face of outcomes in multiple dimensions, as is typically the case in foreign policy decision-making. Finally, we discuss what we have learnt regarding prospect theory’s scope conditions and the differences across individuals in the theory’s applicability. Overall, our contribution lies in identifying several underexposed or neglected issues (e.g., the definition of risk and probability weighting), in examining the advancements regarding prospect theory’s scope conditions, and in discussing avenues for further research.     

Group testing procedures with quantitative features and incomplete identification

We present a group testing model for items characterized by marker random variables. An item is defined to be good (defective) if its marker is below (above) a given threshold. The items can be tested in groups; the goal is to obtain a prespecified number of good items by testing them in optimally sized groups. Besides this group size, the controller has to select a threshold value for the group marker sums, and the target number of groups which by the tests are classified to consist only of good items. These decision variables have to be chosen so as to minimize a cost function, which is a linear combination of the expected number of group tests and an expected penalty for missing the desired number of good items, subject to constraints on the probabilities of misclassifications. We treat two models of this kind: the first one is based on an infinite population size, whereas the second one deals with the case of a finite number of available items. All performance measures are derived in closed form; approximations are also given. Furthermore, we prove monotonicity properties of the components of the objective function and of the constraints. In several examples, we study (i) the dependence of the cost function on the decision variables and (ii) the dependence of the optimal values of the decision variables (group size, group marker threshold, and stopping rule for groups classified as clean) and of the target functionals (optimal expected number of tests, optimal expected penalty, and minimal expected cost) on the system parameters.© 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011