Estimates of circular error probabilities

The general problem we are concerned with here is the estimation of P_θ(C) where C is some fixed event and P_θ is unknown in some class. The various available estimation procedures seem to involve the choice of some random probability measure. In particular we consider this problem when C is a disk in R² centered at o and P_θ is restricted to be bivariate normal. Details concerning the implementation of the estimation procedures and a Monte Carlo study are discussed for this case. This particular problem arises when we are concerned with assessing the accuracy of a targeting procedure.     

Robustness of preallocated preferential defense with assumed attack size and perfect attacking and defending weapons

The problem is to protect a set of t targets by n perfect interceptors against an attack by m perfect weapons. If the defender solves for an optimal preallocated preferential defense and associated game value assuming m₁ attackers, and the attacker knows the assumption of the defender and utilizes m₂ attackers, he may be able to achieve significantly more damage than had the defender assumed that there would be m₂ attackers. The article treats the robustness of preallocated preferential defense to assumptions about the size of the attack and presents results of an alternative approach.     

Applying Order-of-Battle to Al Qaeda Operations

Since the global war on terror began, the pursuit of Al Qaeda is widely considered as warfare and not the pursuit of criminals. In light of counter-terrorism being redefined as war, the criteria applied for tracking militaries of conventional enemies may also be applicable to Al Qaeda. Intelligence analysts have long used the nine order-of-battle (OB) criteria as part of the estimative process for conventional, or nation-state, enemies. Applying OB criteria to Al Qaeda may assist intelligence analysts in knowing the enemy and identifying changes that will allow for predictive analysis. Many elements of Al Qaeda's OB prior to the events of 11 September were viewed as clutter and not significant changes that might have otherwise alerted intelligence analysts to the impending attack. This essay suggests how one might go about applying the nine OB criteria to analysis of Al Qaeda. Although more difficult and requiring modification, using an analytical procedure that has been tested successfully over many years is a logical step in the war on Al Qaeda. If all OB changes are tracked and analyzed using a systematic approach as outlined in this essay, Al Qaeda attacks may be predicted and/or curtailed in the future.     

A linear-programming-based method for determining whether or not n demand points are on a hemisphere

Whenever n demand points are located on a hemisphere, spherical location problems can be solved easily using geometrical methods or mathematical programming. A method based on a linear programming formulation with four constraints is presented to determine whether n demand points are on a hemisphere. The formulation is derived from a modified minimax spherical location problem whose Karush-Kuhn-Tucker conditions are the constraints of the linear program. © 1993 John Wiley & Sons, Inc.     

On estimating survival for reliability models based on age-related stochastic comparisons

A new class of nonparametric reliability models is introduced and studied. A distribution is said to be better at age s than at age t (sBt) if the residual lifetime at age s is stochastically greater than or equal to the residual lifetime at age t. Applications to various forms of replacement policies, including the cannibalization of failed systems, are noted. For fixed s < t, the problem of estimating a survival curve assumed to belong to the sBt class is addressed using recursive methods. An sBt estimator is derived in closed form, and its uniform strong consistency at an optimal rate of convergence is demonstrated. A simulation study strongly supports the claim that the sBt estimator tends to outperform the empirical survivor function in small- and moderate-size samples. © 1993 John Wiley & Sons, Inc.     

Solving time/cost trade-off problems with discounted cash flows using generalized benders decomposition

In this article we consider a project scheduling problem where there are cash flows throughout the life of the project and where shorter activity durations can be attained by incurring greater direct costs. In particular, the objective of this problem is to determine the activity durations and a schedule of activity start times so that the net present value of cash flows is maximized. We formulate this problem as a mixed-integer nonlinear program which is amenable to solution using the generalized Benders decomposition technique developed by Geoffrion. We test the algorithm on 140 project scheduling problems, the largest of which contains 30 nodes and 64 activities. Our computational results are quite encouraging inasmuch as 123 of the 140 problems require less than 1 CPU second of solution time. © 1993 John Wiley & Sons, Inc.     

A multi-run interactive method for bicriterion optimization problems

This article introduces a new conceptual and methodological framework for the use of decision makers and their interactions with the computer in bicriterion decision making. The new method, called the multirun interactive method, attempts to estimate the prior of the decision maker on his uncertain preference nature using the minimum cross-entropy principle. A computational study is performed with four hypothesized prior distributions under various interaction conditions. Other important aspects related to the method, such as implementation of the method, decision making under certainty, decision making with multiple decision makers, and bicriterion integer programming, are also discussed.     

Optimal resource extraction with uncertain reserves

We consider the problem of finding a plan that maximizes the expected discounted return when extracting a nonrenewable resource having uncertain reserves. An extraction plan specifies the rate at which the resource is extracted as a function of time until the resource is exhausted or the time horizon is reached. The return per unit of resource extracted may depend on the rate of extraction, time, and the amount of resource previously extracted. We apply a new method called the generalized search optimization technique to find qualitative features of optimal plans and to devise algorithms for the numerical calculation of optimal plans.     

Scheduling workers in a constricted area

A generalization of the equi-partitioning problem, termed the 2D-Partition Problem, is formulated. The motivation is an aircraft maintenance scheduling problem with the following characteristics. The complete maintenance overhaul of a single aircraft requires the completion of some 350 tasks. These tasks require a varying number of technicians working at the same time. For large subsets of these 350 tasks, the constraining resource is physical space—tasks must be completed in a physical space of limited size such as the cockpit. Furthermore, there is no precedence relationship among the tasks. For each subset, the problem is to schedule the tasks to minimize makespan. Let m denote the maximum number of technicians that can work at the same time in the physical area under consideration. We present optimization algorithms for m = 2 and 3. © 1996 John Wiley & Sons, Inc.