Cumulative search-evasion games

Cumulative search-evasion games (CSEGs) are two-person zero-sum search-evasion games where play proceeds throughout some specified period without interim feedback to either of the two players. Each player moves according to a preselected plan. If (X_t, Y_t,) are the positions of the two players at time t, then the game's payoff is the sum over t from 1 to T of A(X_t, Y_t, t). Additionally, all paths must be “connected.” That is, the finite set of positions available for a player in any time period depends on the position selected by that player in the previous time period. One player attempts to select a mixed strategy over the feasible T-time period paths to maximize the expected payoff. The other minimizes. Two solution procedures are given. One uses the Brown-Robinson method of fictitious play and the other linear programming. An example problem is solved using both procedures.     

Simulation of stochastic activity networks using path control variates

This article details several procedures for using path control variates to improve the accuracy of simulation-based point and confidence-interval estimators of the mean completion time of a stochastic activity network (SAN). Because each path control variate is the duration of the corresponding directed path in the network from the source to the sink, the vector of selected path controls has both a known mean and a known covariance matrix. This information is incorporated into estimation procedures for both normal and nonnormal responses. To evaluate the performance of these procedures experimentally, we examine the bias, variance, and mean square error of the controlled point estimators as well as the average half-length and coverage probability of the corresponding confidence-interval estimators for a set of SANs in which the following characteristics are systematically varied: (a) the size of the network (number of nodes and arcs); (b) the topology of the network; (c) the percentage of activities with exponentially distributed durations; and (d) the relative dominance of the critical path. The experimental results show that although large improvements in accuracy can be achieved with some of these procedures, the confidence-interval estimators for normal responses may suffer serious loss of coverage probability in some applications.     

The rise of targeted killing

Targeted killings have become a central tactic in the United States' campaigns against militant and terrorist groups in the Middle East, Asia, and Africa. Both ‘demand’ and ‘supply’ factors explain the rise of targeted killings. Demand for targeted killings increased as the United States faced new threats from militant groups that could not be effectively countered with conventional military force. Concerns about the political consequences of long-term military involvement overseas and American casualties led political leaders to supply more targeted killings. The conclusion discusses how this tactic may have unintended consequences as other states follow the United States use of targeted killings.     

Target selection in Lanchester combat: Linear-law attrition process

We develop the solution to a simple problem of target selection in Lanchester combat against two enemy force types each of which undergoes a “linear-law” attrition process. In addition to the Pontryagin maximum principle, the theory of singular extremals is required to solve this problem. Our major contribution is to show how to synthesize the optimal target selection policies from the basic optimality conditions. This solution synthesis methodology is applicable to more general dynamic (tactical) allocation problems. For constant attrition-rate coefficients we show that whether or not changes can occur in target priorities depends solely on how survivors are valued and is independent of the type of attrition process.     

Project scheduling: The effects of problem structure on heuristic performance

Individual characteristics of multiple-constrained resource, project scheduling problems are examined in an attempt to predict the solution obtainable with heuristic methods. Difficulties encountered in performing this type of research are described, and several multiple regression models are developed for predicting heuristic performance. Both single and multiple project data are examined, and results reported demonstrate the efficacy of determining beforehand the method used for problem solution.     

The simplex method for integral multicommodity networks

The simplex method is interpreted as a labeling procedure for certain classes of multicommodity flow problems in a manner similar to that for single commodity networks. As opposed to general multicommodity algorithms, no explicit matrix inversion is required; all simplex operations are performed graph-theoretically.     

Differential-game examination of optimal time-sequential fire-support strategies

Optimal time-sequential fire-support strategies are studied through a two-person zero-sum deterministic differential game with closed-loop (or feedback) strategies. Lanchester-type equations of warfare are used in this work. In addition to the max-min principle, the theory of singular extremals is required to solve this prescribed-duration combat problem. The combat is between two heterogeneous forces, each composed of infantry and a supporting weapon system (artillery). In contrast to previous work reported in the literature, the attrition structure of the problem at hand leads to force-level-dependent optimal fire-support strategies with the attacker's optimal fire-support strategy requiring him to sometimes split his artillery fire between enemy infantry and artillery (counterbattery fire). A solution phenomnon not previously encountered in Lanchester-type differential games is that the adjoint variables may be discontinuous across a manifold of discontinuity for both players' strategies. This makes the synthesis of optimal strategies particularly difficult. Numerical examples are given.