Optimal strategies for problems of simultaneous attack against an area defense with impact-point prediction

An area to be defended consists of separated point targets. These targets are subject to an attack in which the offensive weapons are assumed to arrive simultaneously. The defense has area defenders, each of which is capable of intercepting any attacker'. Furthermore, the defense has impact-point prediction, i.e., it has knowledge of each attacker's intended target prior to allocation of the area interceptors. For a given attack, the defense wishes to allocate its interceptors against attackers so as to maximize the expected total survival value of the targets. In its first move, the offense seeks an attack allocation which will minimize expected total surviving value against best defense. We develop an algorithm to determine optimal attack and defense strategies and the optimal value of this sequential min-max problem. Branch-and-bound techniques are used to obtain integer solutions, and illustrative computational results are provided.     

“simple-approximate” battle-outcome-prediction conditions for variable-coefficient lanchester-type equations of modern warfare

This article considers combat between two homogeneous forces modeled by variable- coefficient Lanchester-type equations of modern warfare and develops new “simple-approximate” battle-outcome-prediction conditions for military engagements terminated by two different types of prescribed conditions being met (fixed-force-level-breakpoint battles and fixed-force-ratio-breakpoint battles). These battle-outcome-prediction conditions are sufficient (but not necessary) to determine the outcome of battle without having to explicitly compute the force-level trajectories, and they are characterized by their simplicity, requiring no advanced mathematical knowledge or tabulations of “special functions” for their application. Integrability properties of the Lanchester attrition-rate coefficients figure prominently in their results, and involved in their development is a generalization of Lanchester's famous square law to variable-coefficient Lanchester-type combat and several other novel mathematical developments for the analysis of ordinary differential equations. Examples are given, with the attack of a mobile force against a static defensive position (both sides armed with weapons whose firepower is range dependent) being examined in detail.     

Cultural Conflict within Civil-Military Cooperation: A Case Study in Bosnia

In peace-support operations, employees of international humanitarian organisations often clash with those of the military. A lack of familiarity with each other's practices and values, embedded in their respective organisational cultures, is often seen as the culprit. This article presents and illustrates a road map to manage such cultural differences between cooperating organisations. We found that the military culture, in our Bosnian case study, was seen to operate as a hierarchical culture (characterised by formalisation, stability, predictability and efficiency). The culture of international humanitarian organisations, on the other hand, was depicted as clan-type (characterised by teamwork, participation and consensus). To facilitate the creation of cultural awareness as well as respect for, and reconciliation of, cultural differences we recommend several concrete actions that could improve civil-military cooperation.     

Optimal cutoff strategies in capacity expansion problems

Capacity expansion refers to the process of adding facilities or manpower to meet increasing demand. Typical capacity expansion decisions are characterized by uncertain demand forecasts and uncertainty in the eventual cost of expansion projects. This article models capacity expansion within the framework of piecewise deterministic Markov processes and investigates the problem of controlling investment in a succession of same type projects in order to meet increasing demand with minimum cost. In particular, we investigate the optimality of a class of investment strategies called cutoff strategies. These strategies have the property that there exists some undercapacity level M such that the strategy invests at the maximum available rate at all levels above M and does not invest at any level below M. Cutoff strategies are appealing because they are straightforward to implement. We determine conditions on the undercapacity penalty function that ensure the existence of optimal cutoff strategies when the cost of completing a project is exponentially distributed. A by-product of the proof is an algorithm for determining the optimal strategy and its cost. © 1995 John Wiley & Sons, Inc.     

Continuous sampling plans for markov-dependent production processes

This article discusses the behavior of three continuous sampling plans: continuous sampling plan 1 (CSP 1) and continuous sampling plan 2 (CSP 2) developed by Dodge [5] and Dodge and Torrey [7], and multilevel continuous sampling plan 2 (MLP 2) developed by Lieberman and Solomon [11], when the quality of successive units in a continuous production process follows a two-state time-homogeneous Markov chain. We first derive the average outgoing quality (AOQ) expressions of these plans. Exact procedures for determining the average outgoing quality limit (AOQL) can be obtained only for CSP 1. For CSP 2 and MLP 2 plans, iterative procedures have been used to obtain the AOQL contours. For these plans, it is assumed that the serial correlation coefficient between the two consecutive random variables of the Markov chain is known. In addition, estimation procedures for the coefficient are given. We show that if the serial correlation coefficient of the Markov chain is positive (negative), the AOQL is increased (decreased) as compared to the case when the successive units in the production process follows a Bernoulli pattern. Let r denote the number of production units examined in succession which are found to be of good quality and k denote the inverse of the sampling fraction employed when quality is good. Then if r and k are sufficiently small, it is observed from the graph that, for small departures of the serial correlation coefficient from zero, the AOQL values do not differ significantly for each of the three plans; whereas for sufficiently large values of r and k, the AOQL values differ significantly. Various aspects of these plans, such as their operating characteristics 2 (OC 2) and the serial correlation coefficient, are discussed.