An infiltration game on k arcs

An infiltrator, starting at a safe base, tries to pass, undetected by a guard and within a time limit, along one of k nonintersecting arcs to a safe destination. Optimal strategies and the value are obtained for this discrete zero-sum search-evasion game.     

When is greedy module assembly optimal?

Many coherent systems are configurations of identically structured modules, each consisting of a number of different components. The objective is to assemble the modules out of a collection of available components, and to install the modules in the system in a way that maximizes reliability. The greedy assembly rule builds one module out of the best available components, another out of the best remaining components, and so on. This article shows that greedy assembly is optimal whenever the modules have a series structure, no matter what the structure of the system in which the modules will be used might be, provided that the modules, once assembled, are installed in the system in an optimal way. The article also demonstrates that series modules are unique in this regard.     

An algorithm and new penalties for concave integer minimization over a polyhedron

We present a branch-and-bound algorithm for globally minimizing a concave function over linear constraints and integer variables. Concave cost functions and integer variables arise in many applications, such as production planning, engineering design, and capacity expansion. To reduce the number of subproblems solved during the branch-and-bound search, we also develop a framework for computing new and existing penalties. Computational testing indicates that penalties based on the Tuy cutting plane provide large decreases in solution time for some problems. A combination of Driebeek-Tomlin and Tuy penalties can provide further decreases in solution time. © 1994 John Wiley & Sons, Inc.     

The survival probability function of a target moving along a straight line in a random field of obscuring elements

A target is moving along a straight-line path. Random portions of the path might be invisible to the hunter (in shadow). Shooting trials are conducted only along the visible segments of the path. An algorithm for the numerical determination of the survival probability of the target is developed. This algorithm is based on the distribution of shadow length, which is also developed. © 1994 John Wiley & Sons, Inc.     

Stochastic comparisons for single-server queues

We consider single-server queueing systems with the queue discipline “first come, first served,” interarrival times {u_k, k ≥ l}, and service times {u_k, k ≥ l}, where the {u_k} and {u_k} are independent sequences of non-negative random variables that are independently but not necessarily identically distributed. Let X_k = u_k − u_k (k ≥ 1), S₀ 0, S_n = X₁ + X₂ … + X_n(n≥1). It is known that the (possibly nonhomogeneous) random walk {S_n} determines the behavior of the system. In this paper we make stochastic comparisons of two such systems σ₁,σ₂ whose basic random variables X and X are stochastically ordered. The corresponding random walks are also similarly ordered, and this leads to stochastic comparisons of idle times, duration of busy period and busy cycles, number of customers served during a busy period, and output from the system. In the classical case of identical distributions of {u_k} and {u_k} we obtain further comparisons. Our results are for the transient behavior of the systems, not merely for steady state.     

An extremal problem in subconnectivity

The connectivity of a subgraph of a graph can exceed the connectivity of the graph. We call the largest of the connectivities of all subgraphs the subconnectivity. We then give the exact solution to the extremal problem of determining the maximum number of lines in a p-point graph of subconnectivity two.     

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     

A specially structured nonlinear integer resource allocation problem

We present an algorithm for solving a specially structured nonlinear integer resource allocation problem. This problem was motivated by a capacity planning study done at a large Health Maintenance Organization in Texas. Specifically, we focus on a class of nonlinear resource allocation problems that involve the minimization of a convex function over one general convex constraint, a set of block diagonal convex constraints, and bounds on the integer variables. The continuous variable problem is also considered. The continuous problem is solved by taking advantage of the structure of the Karush‐Kuhn‐Tucker (KKT) conditions. This method for solving the continuous problem is then incorporated in a branch and bound algorithm to solve the integer problem. Various reoptimization results, multiplier bounding results, and heuristics are used to improve the efficiency of the algorithms. We show how the algorithms can be extended to obtain a globally optimal solution to the nonconvex version of the problem. We further show that the methods can be applied to problems in production planning and financial optimization. Extensive computational testing of the algorithms is reported for a variety of applications on continuous problems with up to 1,000,000 variables and integer problems with up to 1000 variables. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 770–792, 2003.     

Lesotho’s 2015 elections in the context of an ongoing security vacuum

After inconclusive elections in 2012, Lesotho had a coalition government for the first time, made up of three political parties that had a narrow majority in parliament. The new government, however, faced several challenges, some of which were of its own making. The agreement among the three parties was to literally divide the government into three parts, leading to a continuous stalemate in its operation; the most serious consequence was the prorogation of parliament and the resultant attempted coup. The flight of the prime minister to South Africa and his return under a Southern African Development Community (SADC) security detail provided a short-term solution to Lesotho's security crisis. Under Cyril Ramaphosa's mediation, the prorogued parliament was conditionally opened and the election date set for 28 February 2015. However, the security dilemma – whereby the prime minister, who is also minister of defence, has no control over the military – remains. When elections are held, there does not seem to be a guarantee that they will be held in peace; moreover, there are now fears that the losers will not accept the results of the elections because of the security vacuum in Lesotho. This article argues that peace can only be salvaged by enhanced SADC security before, during and after the elections. It argues that the SADC mission should remain beyond the elections to oversee the constitutional changes that are necessary for ensuring long-term stability. On their own, Lesotho politicians are unlikely to be able to work together in order to move the country forward.     

Unmasking silence and impunity: the Zimbabwe Peace Project’s e-activism in a polarised political dispensation

This study is an exploration of the use of technology-mediated interventions by the Zimbabwe Peace Project (ZPP) in checkmating the country’s insidious culture of political violence and impunity. It disentangles the ZPP’s strategies and the composite reactions they triggered from state functionaries and the aligned security apparatus. The ZPP exploited and deployed an Internet-circulated monthly newsletter, bulk short message service (SMS) alerts, smartphones, radio and Facebook to shine a spotlight on injustice. It is argued that the ZPP’s whistle-blowing strategies used against human rights violators were not necessarily intended to secure immediate perpetrator conviction; rather, they were a partial but exigent attempt at using perpetrator exposure to reveal extralegal activities and checkmate the country’s culture of impunity. The ZPP’s cybernetic naming and shaming strategies embarrassed some offenders, as evidenced by the intelligence operatives and the police’s constant harassment and arrests of ZPP-affiliated activists. The state-controlled media compounded this pressure by casting aspersions on the ZPP’s bona fides, labelling it a foreign-funded organisation that was attempting to destabilise the country. Finally, this study is informed by a broad evidentiary base that includes ZPP reports on its e-archive, oral interviews, policy documents and newspaper accounts.