New results on a stochastic duel game with each force consisting of heterogeneous units

Two forces engage in a duel, with each force initially consisting of several heterogeneous units. Each unit can be assigned to fire at any opposing unit, but the kill rate depends on the assignment. As the duel proceeds, each force—knowing which units are still alive in real time—decides dynamically how to assign its fire, in order to maximize the probability of wiping out the opposing force before getting wiped out. It has been shown in the literature that an optimal pure strategy exists for this two‐person zero‐sum game, but computing the optimal strategy remained cumbersome because of the game's huge payoff matrix. This article gives an iterative algorithm to compute the optimal strategy without having to enumerate the entire payoff matrix, and offers some insights into the special case, where one force has only one unit. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 56–65, 2014     

Development programs for one‐shot systems using multiple‐state design reliability models

Design reliability at the beginning of a product development program is typically low, and development costs can account for a large proportion of total product cost. We consider how to conduct development programs (series of tests and redesigns) for one‐shot systems (which are destroyed at first use or during testing). In rough terms, our aim is to both achieve high final design reliability and spend as little of a fixed budget as possible on development. We employ multiple‐state reliability models. Dynamic programming is used to identify a best test‐and‐redesign strategy and is shown to be presently computationally feasible for at least 5‐state models. Our analysis is flexible enough to allow for the accelerated stress testing needed in the case of ultra‐high reliability requirements, where testing otherwise provides little information on design reliability change. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Properties of some stochastic orders: A unified study

The notions of the likelihood ratio order of degree s (s ≥ 0) are introduced for both continuous and discrete integer‐valued random variables. The new orders for s = 0, 1, and 2 correspond to the likelihood ratio, hazard rate, and mean residual life orders. We obtain some basic properties of the new orders and their up shifted stochastic orders, and derive some closure properties of them. Such a study is meaningful because it throws an important light on the understanding of the properties of the likelihood ratio, hazard rate, and mean residual life orders. On the other hand, the properties of the new orders have potential applications. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Double Mover–Stayer model on customer switching in telecommunications industry

Customer acquisition and customer retention are the most important challenges in the increasingly competitive telecommunications industry. Traditional studies of customer switching always assume that customers are homogeneous, and thus that model customer switching behavior follows a Markov formulation. However, this postulation is obviously inappropriate in most instances. Blumen et al. (Cornell Studies of Industrial and Labor Relations, Cornell University Press, Ithaca, NY, 1955) developed the Mover–Stayer (MS) model, a generalization of the Markov chain model, to relax the requirement of homogeneity and allow the presence of heterogeneity with two different types of individuals—“stayers,” who purchase the same kinds of products or services throughout the entire observation period; and “movers,” who look for variety in products or services over time. There are two purpose of this article. First, we extend the MS model to a Double Mover‐Stayer (DMS) model by assuming the existence of three types of individuals in the market: (1) stable and loyal customers, who have stable usage within the same company; (2) instable but loyal customers, whose usage varies within the same company over time; and (3) disloyal customers, who switch from one company to another to seek for new experiences or/and benefits. We also propose an estimation method for the DMS model. Second, we apply the DMS model to telecommunications data and demonstrate how it can be used for pattern identification, hidden knowledge discovery, and decision making. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Stein–Chen approximation and error bounds for order fill rates in assemble‐to‐order systems

Assemble‐to‐order (ATO) is an important operational strategy for manufacturing firms to achieve quick response to customer orders while keeping low finished good inventories. This strategy has been successfully used not only by manufacturers (e.g., Dell, IBM) but also by retailers (e.g., Amazon.com). The evaluation of order‐based performance is known to be an important but difficult task, and the existing literature has been mainly focused on stochastic comparison to obtain performance bounds. In this article, we develop an extremely simple Stein–Chen approximation as well as its error‐bound for order‐based fill rate for a multiproduct multicomponent ATO system with random leadtimes to replenish components. This approximation gives an expression for order‐based fill rate in terms of component‐based fill rates. The approximation has the property that the higher the component replenishment leadtime variability, the smaller the error bound. The result allows an operations manager to analyze the improvement in order‐based fill rates when the base‐stock level for any component changes. Numerical studies demonstrate that the approximation performs well, especially when the demand processes of different components are highly correlated; when the components have high base‐stock levels; or when the component replenishment leadtimes have high variability. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

灰色神经网络的鱼雷经济寿命预测

为减少军费开支、降低鱼雷全寿命费用,从经济性角度提出了鱼雷最佳服役年限模型。利用灰色等维新息GM(1,1)模型对鱼雷年度使用维修费用进行预测;采用分组的思想将原始数据分为多组,采用神经网络对灰色模型的预测残差进行修正,以提高预测精度。通过实际算例预测了鱼雷经济寿命,从而证明了模型的实际应用价值。     

Modeling multiple stage manufacturing systems with generalized costs and capacity issues

This study introduces one modeling methodology that describes a broad range of multiple stage production planning issues, including multiple limited resources with setup times and joint fixed cost relationships. An existing production system is modeled in this fashion, creating a new set of 1350 highly generalized benchmark problems. A computational study is conducted with the 1350 benchmark problems introduced in this paper and 2100 benchmark problems, with more restrictive assumptions, from the existing literature. The relative merits of a decomposition‐based algorithm and a neighborhood search technique known as NIPPA, or the Non‐sequential Incremental Part Period Algorithm, are assessed. NIPPA is generally the more successful of the two techniques, although there are specific instances in which the decomposition‐based algorithm displayed a distinct advantage. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

A multi‐objective model for bank ATM networks

In this paper we present an application of the core solution concepts for multi‐objective games to a bank ATM network model. In these games, the worth of a coalition is given by a subset of vectors of the k‐dimensional space rather than by a scalar. The paper investigates how an ATM network model based on multi‐objective cooperative game theory could be used as an alternative way of setting interchange fees paid by the customer's bank to the one that owns the ATM. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

A robust policy for serial agile production systems

One of the major problems in modeling production systems is how to treat the job arrival process. Restrictive assumptions such as Markovian arrivals do not represent real world systems, especially if the arrival process is generated by job departures from upstream workstations. Under these circumstances, cost‐effective policies that are robust with respect to the nature of the arrival process become of interest. In this paper, we focus on minimizing the expected total holding and setup costs in a two‐stage produce‐to‐order production system operated by a cross‐trained worker. We will show that if setup times are insignificant in comparison with processing times, then near‐optimal policies can be generated with very robust performances with respect to the arrival process. We also present conditions under which these near‐optimal policies can be obtained by using only the arrival and service rates. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Evaluating methods for the reliability of a large 2‐dimensional rectangular k‐within‐consecutive‐(r,s)‐out‐of‐(m,n):F system

A 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system consists of m × n components, and fails if and only if k or more components fail in an r × s submatrix. This system can be treated as a reliability model for TFT liquid crystal displays, wireless communication networks, etc. Although an effective method has been developed for evaluating the exact system reliability of small or medium‐sized systems, that method needs extremely high computing time and memory capacity when applied to larger systems. Therefore, developing upper and lower bounds and accurate approximations for system reliability is useful for large systems. In this paper, first, we propose new upper and lower bounds for the reliability of a 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system. Secondly, we propose two limit theorems for that system. With these theorems we can obtain accurate approximations for system reliabilities when the system is large and component reliabilities are close to one. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005