A vertex-closing approach to the p-center problem

This article uses a vertex-closing approach to investigate the p-center problem. The optimal set of vertices to close are found in imbedded subgraphs of the original graph. Properties of these subgraphs are presented and then used to characterize the optimal solution, to establish a priori upper and lower bounds, to establish refined lower bounds, and to verify the optimality of solutions. These subgraphs form the foundation of two polynomial algorithms of complexity O(|E| log |E|) and O(|E|²). The algorithms are proven to converge to an optimum for special cases, and computational evidence is provided which suggests that they produce very good solutions more generally. Both algorithms perform very well on problems where p is large relative to the number of vertices n, specifically, when p/n ≥ 0.30. One of the algorithms is especially efficient for solving a sequence of problems on the same graph.     

Stochastic linear fractional programming with the ratio of independent Cauchy variates

In this article is studied a stochastic linear fractional programming problem, in which the parameters of both the numerator and the denominator are assumed to be mutually independent Cauchy variates. The deterministic equivalent of the problem is obtained and is shown to be a linear fractional program. A numerical example is also added for illustration.     

Robust preallocated preferential defense

The problem is to protect a set of T identical targets that may come under attack by A identical weapons. The targets are to be defended by D identical interceptors, which must be preallocated to defend selected targets. The attacker is aware of the number of interceptors, but is ignorant of their allocation. The size of the attack is chosen by the attacker from within a specified range. The robust strategies developed in this article do not require the defender to assume an attack size. Rather, the defender chooses a strategy which is good over a wide range of attack sizes, though not necessarily best for any particular attack size. The attacker, knowing that the defender is adopting a robust strategy, chooses the optimal attack strategy for the number of weapons he chooses to expend. The expected number of survivors is a function of the robust defense strategy and optimal attack strategy against this robust defense.     

Democracy for the rescue—of dictators? The role of regime type in civil war interventions

Intrastate conflicts, long eclipsing interstate conflicts, are often internationalized. This paper examines internationalized intrastate conflicts through the types of both the intervening and the embattled regimes. Do democracies, more or less than autocracies, support autocratic governments in their fights against rebels? This paper tests three hypotheses: (1) democracies support autocrats fighting rebels less than autocracies do. (2) Democracies support democratic governments fighting against rebels more than autocracies do. (3) The more democratic two states are, the higher the probability one would support the other’s fight against rebels. Covering all documented external support in intrastate wars (1975–2000), our findings support hypothesis one and two only partly and confirm hypothesis three. However, comparing the two major accounts of the Democratic Peace theory (DPT)—the normative and the structural—our findings corroborate only the former robustly. The paper thus helps enriching the insights of the DPT beyond interstate conflicts.     

Optimal resource allocation and redistribution strategy in military conflicts with Lanchester square law attrition

We address the problem of optimal decision‐making in conflicts based on Lanchester square law attrition model where a defending force needs to be partitioned optimally, and allocated to two different attacking forces of differing strengths and capabilities. We consider a resource allocation scheme called the Time Zero Allocation with Redistribution (TZAR) strategy, where allocation is followed by redistribution of defending forces, on the occurrence of certain decisive events. Unlike previous work on Lanchester attrition model based tactical decision‐making, which propose time sequential tactics through an optimal control approach, the present article focuses on obtaining simpler resource allocation tactics based on a static optimization framework, and demonstrates that the results obtained are similar to those obtained by the more complex dynamic optimal control solution. Complete solution for this strategy is obtained for optimal partitioning of resources of the defending forces. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Scheduling multiple products on parallel machines with setup costs

We consider a class of production scheduling models with m identical machines in parallel and k different product types. It takes a time p_i to produce one unit of product type i on any one of the machines. There is a demand stream for product type i consisting of n_i units with each unit having a given due date. Before a machine starts with the production of a batch of products of type i a setup cost c is incurred. We consider several different objective functions. Each one of the objective functions has three components, namely a total setup cost, a total earliness cost, and a total tardiness cost. In our class of problems we find a relatively large number of problems that can be solved either in polynomial time or in pseudo‐polynomial time. The polynomiality or pseudo‐polynomiality is achieved under certain special conditions that may be of practical interest; for example, a regularity pattern in the string of due dates combined with earliness and tardiness costs that are similar for different types of products. The class of models we consider includes as special cases discrete counterparts of a number of inventory models that have been considered in the literature before, e.g., Wagner and Whitin (Manage Sci 5 (1958), 89–96) and Zangwill (Oper Res 14 (1966), 486–507; Manage Sci 15 (1969), 506–527). © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Scheduling parallel machines with inclusive processing set restrictions

We consider the problem of assigning a set of jobs to different parallel machines of the same processing speed, where each job is compatible to only a subset of those machines. The machines can be linearly ordered such that a higher‐indexed machine can process all those jobs that a lower‐indexed machine can process. The objective is to minimize the makespan of the schedule. This problem is motivated by industrial applications such as cargo handling by cranes with nonidentical weight capacities, computer processor scheduling with memory constraints, and grades of service provision by parallel servers. We develop an efficient algorithm for this problem with a worst‐case performance ratio of + ε, where ε is a positive constant which may be set arbitrarily close to zero. We also present a polynomial time approximation scheme for this problem, which answers an open question in the literature. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Factors that affect the optimal amount of central control in complex systems

Whereas much of the previous research in complex systems has focused on emergent properties resulting from self‐organization of the individual agents that make up the system, this article studies one vital role of central organization. In particular, four factors are conjectured to be key in determining the optimal amount of central control. To validate this hypothesis, these factors are represented as controllable parameters in a mathematical model. For different combinations of parameter values, the optimal amount of central control is found, either analytically or by computer simulation. The model is shown to provide results that match well with the level of control found across a broad spectrum of specific complex systems. This model also provides general guidelines as to how combinations of these factors affect the desirable level of control and specific guidelines for selecting and evaluating leaders. These results indicate that all of these factors, though not exhaustive, should be considered carefully when attempting to determine the amount of control that is best for a system. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Signature based analysis of m‐Consecutive‐k‐out‐of‐n: F systems with exchangeable components

In this article, we study reliability properties of m‐consecutive‐k‐out‐of‐n: F systems with exchangeable components. We deduce exact formulae and recurrence relations for the signature of the system. Closed form expressions for the survival function and the lifetime distribution as a mixture of the distribution of order statistics are established as well. These representations facilitate the computation of several reliability characteristics of the system for a given exchangeable joint distribution or survival function. Finally, we provide signature‐based stochastic ordering results for the system's lifetime and investigate the IFR preservation property under the formulation of m‐consecutive‐k‐out‐of‐n: F systems. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Do Distinct (National) Operational Styles of Conflict Resolution Exist?

This article contains a reply to a previously published paper on the use and abuse of the so-called Dutch approach to counterinsurgency. In addition to commenting on this paper, the article constitutes an argument to initiate more comparative studies in the field of military and strategic studies. Only comparative studies will help to better understand the effectiveness of military force in preventing, containing and solving violent conflicts.