Shortest path interdiction problem with arc improvement recourse: A multiobjective approach

We consider the shortest path interdiction problem involving two agents, a leader and a follower, playing a Stackelberg game. The leader seeks to maximize the follower's minimum costs by interdicting certain arcs, thus increasing the travel time of those arcs. The follower may improve the network after the interdiction by lowering the costs of some arcs, subject to a cardinality budget restriction on arc improvements. The leader and the follower are both aware of all problem data, with the exception that the leader is unaware of the follower's improvement budget. The effectiveness of an interdiction action is given by the length of a shortest path after arc costs are adjusted by both the interdiction and improvement. We propose a multiobjective optimization model for this problem, with each objective corresponding to a different possible improvement budget value. We provide mathematical optimization techniques to generate a complete set of strategies that are Pareto‐optimal. Additionally, for the special case of series‐parallel graphs, we provide a dynamic‐programming algorithm for generating all Pareto‐optimal solutions.     

Optimal arrangement of components via pairwise rearrangements

We introduce the notion of comparison of the criticality of two nodes in a coherent system, and devlop a monotonicity property of the reliability function under component pairwise rearrangement. We use this property to find the optimal component arrangement. Worked examples illustrate the methods proposed.     

International Norms in Ethno-Territorial Disputes: Legitimacy and Efficacy in Outsiders’ Views of Independence and Irredentism

Ethno-national territorial disputes typically involve conflicting homeland claims between states and minority ethnic groups. Where such minority ethnic groups have cross-border ethnic kin who themselves constitute a dominant or influential ethnic group in a neighbouring state, separatist goals may take the form of either irredentism or independence. We conjecture that external sympathy for irredentism and independence may vary significantly, and that this variation may be an important influence in situations where secessionist groups and ethnic kin states have a choice between the two goals. Using a bargaining framework that controls for variation in relative power, status quo conditions and minority-side leadership preferences, we present experimental evidence indicating that external audiences are likely to support more confrontational policies in pursuit of independence than in pursuit of irredentism. Our evidence also indicates that independence attracts greater support largely because outsiders perceive it as a more legitimate goal; and that practical efficacy is not important in stimulating sympathy for either independence or irredentism. These results also support a broader argument in the literature on international norms – that such norms receive support not only because they may justify pre-existing goals or interests, but also because they are perceived as having greater legitimacy per se.     

Note: Dual sourcing with nonidentical suppliers

We analyze a dual-sourcing inventory model with exponential lead times and constant unit demand in which the order quantity is split in some proportion between two sources of supply. Unlike earlier studies, we do not require that the two sources be identical in terms of the lead-time parameters or the supply prices. We compare the expected total annual costs for the two-source and the traditional single-source models over a wide range of parameter values. We confirm the findings of earlier studies that, under stochastic lead times, dual sourcing yields savings in holding and shortage costs that could outweigh the incremental ordering costs. With this more general model, we demonstrate that savings from dual sourcing are possible even where the mean or the variability of the second source is higher. © 1993 John Wiley & Sons, Inc.     

Explicit modeling of detection within a stochastic duel

Many mathematical models have been formulated to describe combat between two weapon systems. However, until recently duel models did not explicitly represent target detection within a duel, leading to the necessity for the development of new model for each tactical situation. An earlier article by two of the authors described a duel between weapons with constant firing times and explicit modeling of detection. This article enhances the study of this form of duel between weapons by introducing a variable parameter for firing times. This enhancement removes the discontinuities evident during parametric analysis of the earlier model and hence provides a more coherent model of this combat situation. © 1993 John Wiley & Sons, Inc.     

Establishing Reliability Goals for Naval Major-Caliber Ammunition

We describe a decision process for establishing the threshold reliabilities for components of naval major-caliber ammunition. We present a measure of reliability performance, called ef*, which relates directly to the weapons system's performance in a naval gunfire support environment. We use a simulation model to establish this relationship, a regression metamodel to estimate its parameters, and a simple decision process to specify component reliability thresholds which ensure that the ammunition is mission effective. We present this article as an example of the integration of discrete event dynamic system analysis within a decision process. © 1992 John Wiley & Sons, Inc.     

Estimating a survival curve when new is better than used with respect to a distinguished set

Hollander, Park, and Proschan define a survival function S of a positive random variable X to be new better than used at age t₀ (NBU-{t₀}) if S satisfies $ \begin{array}{*{20}c} {\frac{{S(x + t_0)}}{{S\left({t_0} \right)}} \le S\left(x \right),} & {{\rm for}\,{\rm all}\,x\, \ge \,0,} \\ \end{array}$ where S(x) = P(X > x). The NBU-{t₀} class is a special case of the NBU-A family of survival distributions, where A is a subset of [0, ∞). These families introduce a variety of modeling possibilities for use in reliability studies. We treat problems of nonparametric estimation of survival functions from these classes by estimators which are themselves members of the classes of interest. For a number of such classes, a recursive estimation technique is shown to produce closed-form estimators which are strongly consistent and converge to the true survival distribution at optimal rates. For other classes, additional assumptions are required to guarantee the consistency of recursive estimators. As an example of the latter case, we demonstrate the consistency of a recursive estimator for S ∈ NBU-[t₀, ∞) based on lifetime data from items surviving a preliminary “burn-in” test. The relative precision of the empirical survival curve and several recursive estimators of S are investigated via simulation; the results provide support for the claim that recursive estimators are superior to the empirical survival curve in restricted nonparametric estimation problems of the type studied here.     

Vector processing approach to constrained network problems

Modification of algorithms designed for scalar computing, to take advantage of vector processing, raises several challenges. This article presents the vectorization of the primal simplex based network algorithm and results in a 50% improvement in computational time. One of the major contributors to this improvement is the matching of the size of the pricing candidate list to the vector register size. The side constraints are relaxed into a single surrogate constraint. The single constraint network algorithm is vectorized and used as the basis for solving large-scale constrained network problems. Computational experiments are presented which illustrate the vectorization of the network code as well as the ability of the surrogate constraint approach to deal with large constrained network problems.     

Timing replacement decisions under discontinuous technological change

We consider the problem of deciding whether to keep a piece of equipment or replace it with a more advanced technology in an environment of technological change. Our model assumes that the costs associated with the presently available technology and future technologies are known, but that the appearance times of future technologies are uncertain. We develop a procedure for computing the optimal keep-or-replace decision that iteratively incorporates a technological forecast. For a certain class of situations, we show that our approach requires the minimum possible amount of forecasted data.     

Estimation of the survival function of a repairable standby series system

This article deals with the statistical analysis of an N-component series system supported by an active standby and one repair facility. Assuming that the life and repair times of the components are independent exponential random variables, the probability distribution of the first passage to the system failure time is shown to be a convolution of two independent exponential distributions. Three observation schemes are considered to obtain the maximum likelihood estimates of the survival function. Information matrices are supplied. Numerical results based on Monte Carlo simulation are presented. It is noted that component level information (failure rate, repair rate) is not necessary for estimating the survival function of the system.