Linear search with bounded resources

A point is placed at random on the real line according to some known distribution F, and a search is made for this point, beginning at some starting points s on the line, and moving along the line according to some function x(t). The objective of this article is to maximize the probability of finding the point while traveling at most d units. Characterizations of simple optimal searches are found for arbitrary distributions, for continuous distributions with continuous density everywhere (e.g., normal, Cauchy, triangular), and for continuous distributions with density which is continuous on its support (e.g., exponential, uniform). These optimal searches are also shown to be optimal for maximization of the expected number of points found if the points are placed on the line independently from a known distribution F.     

Capacity expansion under a service‐level constraint for uncertain demand with lead times

For a service provider facing stochastic demand growth, expansion lead times and economies of scale complicate the expansion timing and sizing decisions. We formulate a model to minimize the infinite horizon expected discounted expansion cost under a service‐level constraint. The service level is defined as the proportion of demand over an expansion cycle that is satisfied by available capacity. For demand that follows a geometric Brownian motion process, we impose a stationary policy under which expansions are triggered by a fixed ratio of demand to the capacity position, i.e., the capacity that will be available when any current expansion project is completed, and each expansion increases capacity by the same proportion. The risk of capacity shortage during a cycle is estimated analytically using the value of an up‐and‐out partial barrier call option. A cutting plane procedure identifies the optimal values of the two expansion policy parameters simultaneously. Numerical instances illustrate that if demand grows slowly with low volatility and the expansion lead times are short, then it is optimal to delay the start of expansion beyond when demand exceeds the capacity position. Delays in initiating expansions are coupled with larger expansion sizes. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Competitive location and capacity decisions for firms serving time‐sensitive customers

In this article we explore how two competing firms locate and set capacities to serve time‐sensitive customers. Because customers are time‐sensitive, they may decline to place an order from either competitor if their expected waiting time is large. We develop a two‐stage game where firms set capacities and then locations, and show that three types of subgame perfect equilibria are possible: local monopoly (in which each customer is served by a single firm, but some customers may be left unserved), constrained local monopoly (in which firms serve the entire interval of customers but do not compete with each other), and constrained competition (in which firms also serve the entire interval of customers, but now compete for some customers). We perform a comparative statics analysis to illustrate differences in the equilibrium behavior of a duopolist and a coordinated monopolist. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Landmarks in defense literature

Military operations and maritime preponderance by Charles E. Callwell, Edinburgh: William Blackwood & Sons, 1905.     

An Investigation of the Weights of Pattern 1907 Bayonets made in the UK around the First World War Period

The standard issue bayonet of the British Army immediately preceding and during the First World War was the Pattern 1907. This was manufactured at different times and in varying numbers during that period by one official body, the Royal Small Arms Factory at Enfield, and by five private contractors. These bayonets were made according to published official specifications issued by the War Department and based on a ‘pattern example’ provided by the Royal Small Arms Factory. The specifications indicate, inter alia, the quality of metal used in making the bayonets, methods of inspection and proofing, and the required maximum and minimum weight range of the completed bayonet. However, examination of a series of these bayonets in a private collection suggested that their weights varied considerably from the mid-point values of the allowed weight ranges in the original and amended specifications (16.5 oz. and 17 oz., respectively). To establish if this was a common feature among this class of bayonet as opposed to a chance factor, the weights of other surviving Pattern 1907 bayonets were determined and compared to establish the degree of variance from the official specifications as originally set out by the Royal Small Arms Factory. Seventy-six percent of the 142 bayonets surveyed were found to be above the mid-point of the allowed weight range given in the amended manufacturing specifications, with many being at the upper end of the allowed range. This is a statistically unusual result. It is speculated that the target weight may have been deliberately set higher by the individual manufacturers to eliminate the possibility of rejection of any underweight bayonets by the Royal Small Arms Factory inspectors and so a refusal of acceptance and payment for the work.     

The Clausewitzian fallacy of absolute war

Clausewitz was much preoccupied with the apparent contradiction between real and absolute war. Why did war in history so rarely exhibit the extremes of violence and energy implied in the pure concept of war? Clausewitz’s commentators have usually followed him in thinking that this was a genuine problem in need of a solution, but I want to question that view. I will argue that Clausewitz did not have a coherent philosophy of absolute war, and therefore the contradiction he posited between real and absolute war was equally meaningless – as, too, was his effort to resolve it by claiming that some real wars approached or even attained the absolute form of war. The real problem was not the opposition of real and absolute war, but the self-contradictory theory of absolute war.     

An index policy for a stochastic scheduling model with improving/deteriorating jobs

We consider stochastic scheduling models which have the natural character that jobs improve while being processed, but deteriorate (and may possibly leave the system altogether) while processing is diverted elsewhere. Such restless bandit problems are shown to be indexable in the sense of Whittle. A numerical study which elucidates the strong performance of the resulting index policy is complemented by a theoretical study which demonstrates the optimality of the index policy under given conditions and which develops performance guarantees for the index heuristic more generally. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 706–721, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10036