Optimal shift scheduling: A branch‐and‐price approach

We present a branch‐and‐price technique for optimal staff scheduling with multiple rest breaks, meal break, and break windows. We devise and implement specialized branching rules suitable for solving the set covering type formulation implicitly, using column generation. Our methodology is more widely applicable and computationally superior to the alternative methods in the literature. We tested our methodology on 365 test problems involving between 1728 and 86400 shift variations, and 20 demand patterns. In a direct comparison with an alternative method, our approach yields significant improvements both in cpu time and in the number of problem instances solved to optimality. The improvements were particularly marked for problems involving larger numbers of feasible shifts. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 185–200, 2000     

Bayesian inference for a Lanchester type combat model

We undertake inference for a stochastic form of the Lanchester combat model. In particular, given battle data, we assess the type of battle that occurred and whether or not it makes any difference to the number of casualties if an army is attacking or defending. Our approach is Bayesian and we use modern computational techniques to fit the model. We illustrate our method using data from the Ardennes campaign. We compare our results with previous analyses of these data by Bracken and Fricker. Our conclusions are somewhat different to those of Bracken. Where he suggests that a linear law is appropriate, we show that the logarithmic or linear‐logarithmic laws fit better. We note however that the basic Lanchester modeling assumptions do not hold for the Ardennes data. Using Fricker's modified data, we show that although his “super‐logarithmic” law fits best, the linear, linear‐logarithmic, and logarithmic laws cannot be ruled out. We suggest that Bayesian methods can be used to make inference for battles in progress. We point out a number of advantages: Prior information from experts or previous battles can be incorporated; predictions of future casualties are easily made; more complex models can be analysed using stochastic simulation techniques. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 541–558, 2000     

Exploiting self‐canceling demand point aggregation error for some planar rectilinear median location problems

When solving location problems in practice it is quite common to aggregate demand points into centroids. Solving a location problem with aggregated demand data is computationally easier, but the aggregation process introduces error. We develop theory and algorithms for certain types of centroid aggregations for rectilinear 1‐median problems. The objective is to construct an aggregation that minimizes the maximum aggregation error. We focus on row‐column aggregations, and make use of aggregation results for 1‐median problems on the line to do aggregation for 1‐median problems in the plane. The aggregations developed for the 1‐median problem are then used to construct approximate n‐median problems. We test the theory computationally on n‐median problems (n ≥ 1) using both randomly generated, as well as real, data. Every error measure we consider can be well approximated by some power function in the number of aggregate demand points. Each such function exhibits decreasing returns to scale. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 614–637, 2003.     

Military Ethics and the Situationist Critique

Many contributors to military ethics from diverse locations and philosophical perspectives maintain that virtues are central to martial theory and practice. Yet several contemporary philosophers and psychologists have recently challenged the empirical adequacy of this perspective. Their challenge is known as the situationist critique, a version of which asserts that: (a) situational features rather than character traits such as virtues cause and explain human behavior, and (b) ethical theories and development programs are empirically inadequate to the extent that they incorporate virtues. In this paper, I assess the merit of this critique and consider some implications of my assessment for military practitioners and theorists.