Entropy-based selection with multiple objectives

In this article we present an approach to determine the initially unspecified weights in an additive measurable multiattribute value function. We formulate and solve a series of nonlinear programming problems which (1) incorporate whatever partial information concerning the attribute weights or overall relative value of alternatives the decision maker chooses to provide, yet (2) yield a specific set of weights as a result. Although each formulation is rather easily solved using the nonlinear programming software GINO (general interactive optimizer), solutions in closed form dependent on a single parameter are also provided for a number of these problems.     

Nonpreemptive scheduling of independent tasks with prespecified processor allocations

In this article we study the problem of scheduling independent tasks, each of which requires the simultaneous availability of a set of prespecified processors, with the objective of minimizing the maximum completion time. We propose a graph-theoretical approach and identify a class of polynomial instances, corresponding to comparability graphs. We show that the scheduling problem is polynomially equivalent to the problem of extending a graph to a comparability graph whose maximum weighted clique has minimum weight. Using this formulation we show that in some cases it is possible to decompose the problem according to the canonical decomposition of the graph. Finally, a general solution procedure is given that includes a branch-and-bound algorithm for the solution of subproblems which can be neither decomposed nor solved in polynomial time. Some examples and computational results are presented. © 1994 John Wiley & Sons, Inc.     

Bounds for circular error probabilities

Bounds for P(X + X ⩽ k²σ) are given where X₁ and X₂ are independent normal variables having zero means and variances σ, σ, respectively. This is generalized when X₁ and X₂ are dependent variables with known covariance matrix.     

Optimal sequential replenishment of ships during combat

A carrier battle group is operating in an area where it is subject to attack by enemy aircraft. It is anticipated that air raids will occur in large waves. The uncertain time between raids is available for the replenishment of supplies. We consider the problem of how best to schedule ammunition replenishment during this period. The theory of Gittins indices provides the technical background to the development of a range of models which yield a hierarchy of index-based heuristics for replenishment. One such heuristic is assessed computationally in a more realistic scenario than is explicitly allowed for by the models.     

An inventory model of incentives for on-time delivery in just-in-time purchasing contracts

This article formulates an analytic model of just-in-time purchasing contracts and compares the minimum cost solution with the cost attainable through vertical integration. The models use standard inventory theory cost parameters and decision variables. The results quantify the increase in cost of buying an item rather than making it. Optimal incentives are characterized when JIT purchasing contracts are used. When JIT purchasing is implemented, buffer inventories are typically reduced. This inventory reduction makes on-time delivery critical to the buyer; yet timeliness is controlled by the supplier. As an incentive to provide on-time delivery, the buyer offers the supplier a bonus for on-time delivery. The supplier chooses a flow time allowance based upon the bonus offered. First- and second-order conditions are characterized in general, and examples are provided for exponentially and uniformly distributed flow times. The delivery timeliness obtainable in a vertically integrated firm is determined and compared with timeliness obtainable between separate firms. This comparison indicates that buyers who choose to purchase materials from a separate firm are more likely to experience late deliveries. The relationship between the value of the bonus and the proportion of on-time deliveries is also considered. The bonus required to achieve the same probability of on-time delivery as under vertical integration is also determined. © 1993 John Wiley & Sons, Inc.     

A generalized model for the economic design of x̄control charts for production systems with increasing failure rate and early replacement

This article generalizes the model for the economic design of x̄-control charts of Duncan [4], starting from the more recent papers of Lorenzen and Vance [8] and Banerjee and Rahim [3]. The classical model of Duncan [4] and its several extensions including the unified model of Lorenzen and Vance [8] assumed exponentially distributed in-control periods and provided uniform sampling schemes. Banerjee and Rahim [3], however, assumed a Weibull-distributed in-control period having an increasing failure rate and used variable sampling intervals. The present article is an extension of the work of Banerjee and Rahim [3], where a general distribution of in-control periods having an increasing failure rate is assumed and the possibility of age-dependent repair before failure is considered. Several different truncated and nontruncated probability models are chosen. It is proposed that economic benefits can be achieved by adopting a nonuniform inspection scheme and by truncating a production cycle when it attains a certain age. Numerical examples are presented to support this proposition. Finally, the effect of model specification in the choice of failure mechanism is investigated. © 1993 John Wiley & Sons, Inc.     

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     

An Unlikely Alliance: Portuguese and South African Airpower in Angola, 1968–1974

The war that Portugal was obliged to fight in Africa began in 1961 and immediately stretched the resources of its armed forces. Nowhere was this thinness more apparent than in policing the vast territory of Angola. The east and southeast of Angola were particularly vulnerable, as the area was a vast, sparsely populated region characterised by enormous featureless plains or chanas covered in tall grass and broken by an extensive river system and mountainous forests. The only military solution to policing these immense spaces was aviation and specifically the helicopter that could carry troops into battle, protect them with a gunship and bring them home when the operation was concluded. The immediate problem for the Portuguese Air Force (Força Aérea Portuguesa or FAP) in Angola and elsewhere was a scarcity of helicopters. The solution was an alliance with South Africa, which had a strong inventory of Alouette IIIs, to help in policing the east. This move was likewise in the interest of South Africa, as its threat came from Zambia through south-eastern Angola. This article examines the strategic and tactical development of this unusual, cross-cultural alliance and the symbiotic relationship that resulted in destruction of the enemies of both in Angola.     

MODELS OF MILITARY EXPENDITURE AND GROWTH: A CRITICAL REVIEW

This paper reviews some of the theoretical and econometric issues involved in estimating growth models that include military spending. While the mainstream growth literature has not found military expenditure to be a significant determinant of growth, much of the defence economics literature has found significant effects. The paper argues that this is largely the product of the particular specification, the Feder–Ram model, that has been used in the defence economics literature but not in the mainstream literature. The paper critically evaluates this model, detailing its problems and limitations and suggests that it should be avoided. It also critically evaluates two alternative theoretical approaches, the Augmented Solow and the Barro models, suggesting that they provide a more promising avenue for future research. It concludes with some general comments about modelling the links between military expenditure and growth.