Securing a border under asymmetric information

We study a stochastic interdiction model of Morton et al. IIE Transactions, 39 (2007):3–14 that locates radiation sensors at border crossings to detect and prevent the smuggling of nuclear material. In this model, an interdictor places sensors at customs checkpoints to minimize a potential smuggler's maximum probability of crossing a border undetected. We focus on a model variant in which the interdictor has different, and likely more accurate, perceptions of the system's parameters than the smuggler does. We introduce a model that is tighter and uses fewer constraints than that of Morton et al. We also develop a class of valid inequalities along with a corresponding separation procedure that can be used within a cutting‐plane approach to reduce computational effort. Computational results demonstrate the effectiveness of our approach.Copyright © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 91–100, 2014     

A stochastic network formulation for complex sequential processes

A network model incorporating stochastic features is considered. The model represents a complex sequential process where an object or system moves through a succession of states (nodes) and operating modes (classes) in the course of carrying out its function (fulfilling its purpose). Transitions between states and operating modes occur in a possibly random manner and require (consume) some resource in randomly varying amounts. We discuss the routing behavior and resource requirements of a typical object as it moves through (and eventually out of) the network. We then shift our focus from a single object and its odyssey to the network as a whole, where time is the resource and many objects are entering the network according to a possibly nonhomogeneous Poisson pattern; in this vein, we discuss the evolution of the network over time. Finally, we consider some applications of the formulation, and results.     

On estimating population characteristics from record-breaking observations. i. parametric results

Consider an experiment in which only record-breaking values (e.g., values smaller than all previous ones) are observed. The data available may be represented as X₁,K₁,X₂,K₂, …, where X₁,X₂, … are successive minima and K₁,K₂, … are the numbers of trials needed to obtain new records. We treat the problem of estimating the mean of an underlying exponential distribution, and we consider both fixed sample size problems and inverse sampling schemes. Under inverse sampling, we demonstrate certain global optimality properties of an estimator based on the “total time on test” statistic. Under random sampling, it is shown than an analogous estimator is consistent, but can be improved for any fixed sample size.     

Hybrid heuristics for minimum cardinality set covering problems

Minimum cardinality set covering problems (MCSCP) tend to be more difficult to solve than weighted set covering problems because the cost or weight associated with each variable is the same. Since MCSCP is NP-complete, large problem instances are commonly solved using some form of a greedy heuristic. In this paper hybrid algorithms are developed and tested against two common forms of the greedy heuristic. Although all the algorithms tested have the same worst case bounds provided by Ho [7], empirical results for 60 large randomly generated problems indicate that one algorithm performed better than the others.