Lanchester-type models of warfare and optimal control

The optimization of the dynamics of combat (optimal distribution of fire over enemy target types) is studied through a sequence of idealized models by use of the mathematical theory of optimal control. The models are for combat over a period of time described by Lanchester-type equations with a choice of tactics available to one side and subject to change with time. The structure of optimal fire distribution policies is discussed with reference to the influence of combatant objectives, termination conditions of the conflict, type of attrition process, and variable attrition-rate coefficients. Implications for intelligence, command and control systems, and human decision making are pointed out. The use of such optimal control models for guiding extensions to differential games is discussed.     

An experimental comparison of solution algorithms for the single-machine tardiness problem

A basic problem in scheduling involves the sequencing of a set of independent tasks at a single facility with the objective of minimizing mean tardiness. Although the problem is relatively simple, the determination of an optimal sequence remains a challenging combinatorial problem. A number of algorithms have been developed for finding solutions, and this paper reports a comparative evaluation of these procedures. Computer programs for five separate algorithms were written and all were run on a data base designed to highlight computational differences. Optimizing algorithms developed by Emmons and by Srinivasan appeared to be particularly efficient in the comparative study.     

A computation procedure for the exact solution of location-allocation problems with rectangular distances

A method is presented to locate and allocate p new facilities in relation to n existing facilities. Each of the n existing facilities has a requirement flow which must be supplied by the new facilities. Rectangular distances are assumed to exist between all facilities. The algorithm proceeds in two stages. In the first stage a set of all possible optimal new facility locations is determined by a set reduction algorithm. The resultant problem is shown to be equivalent to finding the p-median of a weighted connected graph. In the second stage the optimal locations and allocations are obtained by using a technique for solving the p-median problem.     

Transportation problems with some xij negative and transshipment problems

The general solution process of the Hitchcock transportation problem resulting from the application of the method of reduced matrices may give solutions with some negative x_ij values. This paper is devoted to a review of the reduced matrices method, an examination of suitable interpretation of sets of x_ij which include some negative values, and ways of interpreting these values in useful modifications of the Hitchcock problem. Such modifications include a) the reshipment problem, b) the overshipment problem, and c) the transshipment problem. Techniques are developed for determining and eliminating c_ij which are not optimal. These techniques and results are useful in solving the problems indicated above. The natural applicability of the simple and general method of reduced matrices is emphasized.     

On the treatment of force-level constraints in times-equential combat problems

The treatment of force-level constraints in time-sequential combat optimization problems is illustrated by further studying the fire-programming problem of Isbell and Marlow. By using the theory of state variable inequality constraints from modern optimal control theory, sharper results are obtained on necessary conditions of optimality for an optimal fire-distribution policy (in several cases justifying conjectures made in previous analysis). This leads to simplification of the determination of the domains of controllability for extremals leading to the various terminal states of combat. (Additionally, some new results for the determination of boundary conditions for the adjoint variables in optimal control problems with state variable inequality constraints have arisen from this work.) Some further extensions of previous analysis of the fire-programming problem are also given. These clarify some key points in the solution synthesis. Some important military principles for target selection and the valuation of combat resources are deduced from the solution. As a result of this work, more general time-sequential combat optimization problems can be handled, and a more systematic solution procedure is developed.     

Reassessing Military Assistance to the Civil Powers: Are Traditional British Anti-Terrorist Responses Still Effective?

The provision of Military Assistance to the Civil Powers (MACP) encapsulates the traditional approach towards countering terrorism on the British mainland, which emphasises minimum force, proportionality, police primacy and the rule of law, with the military retained as a supporting instrument, being employed only as a measure of last resort. Recent terrorist incidents in major urban centres do, however, question the effectiveness of these established methods. This analysis initially codifies the conceptual issues that underscore the tensions between civil policing and military anti-terrorist approaches in the UK, and proceeds to evaluate and compare a number of operations that indicate the nature of the challenges facing the MACP apparatus. In particular, potential shortcomings in the MACP provisions are identified in the form of threat perception and deployment and enforcement gaps. The assessment finds that there are facets of MACP that are of enduring relevance in the current era, yet a continuing need persists to reconcile police and military imperatives toward serious civil disorder contingencies and conditions of emergency.     

Civil wars and economic growth: A regional comparison

The paper examines the impact of civil wars on income per-capita growth at home and in neighbors for four regional groupings of countries: Africa, Asia, Latin America, and a pooled Asian and Latin American sample. Both macroeconomic and civil-war influences on growth differ by region. With the use of a distance measure, we demonstrate that the spatial reach from the negative consequences of a civil war are region and time period specific. Generally, there was less dispersion in Africa than in Asia and Latin America. Moreover, Africa demonstrates a greater ability to recover from the adverse effects of civil wars than the other regions tested.