DEA models for two‐stage processes: Game approach and efficiency decomposition

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). This tool has been utilized by a number of authors to examine two‐stage processes, where all the outputs from the first stage are the only inputs to the second stage. The current article examines and extends these models using game theory concepts. The resulting models are linear, and imply an efficiency decomposition where the overall efficiency of the two‐stage process is a product of the efficiencies of the two individual stages. When there is only one intermediate measure connecting the two stages, both the noncooperative and centralized models yield the same results as applying the standard DEA model to the two stages separately. As a result, the efficiency decomposition is unique. While the noncooperative approach yields a unique efficiency decomposition under multiple intermediate measures, the centralized approach is likely to yield multiple decompositions. Models are developed to test whether the efficiency decomposition arising from the centralized approach is unique. The relations among the noncooperative, centralized, and standard DEA approaches are investigated. Two real world data sets and a randomly generated data set are used to demonstrate the models and verify our findings. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

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     

Graveyard of Analogies: The Use and Abuse of History for the War in Afghanistan

Decades of scholarship have warned against using historical analogies for policymaking. But the Taliban insurgency appears, on the surface, to confirm the usefulness of historical analogies to the British and Soviet wars in Afghanistan. I review the use of analogies for the war in Afghanistan and argue the analogies were historically unsound and strategically unhelpful. In fact, their effect on policy helped create the conditions for the very insurgency policymakers most hoped to avoid. The Taliban insurgency did not occur because of the presence of too many foreign troops and aid workers, but because there were too few.     

Optimal weapons allocation against layered defenses

We solve the problem of optimal allocation of weapons to targets in the presence of layered regional defenses. The general solution technique is an integer program transformable to a minimum-cost network flow. This model assumes the defense has perfect weapons. Results of a small sample scenario are included. Additionally, a representative attrition algorithm is described and the two models combined to form a hybrid algorithm. The hybrid algorithm allows for less-than-perfect weapons while maintaining optimality.     

Asymptotically optimal component assembly plans in repairable systems and server allocation in parallel multiserver queues

T identical exponential lifetime components out of which G are initially functioning (and B are not) are to be allocated to N subsystems, which are connected either in parallel or in series. Subsystem i, i = 1,…, N, functions when at least K_i of its components function and the whole system is maintained by a single repairman. Component repair times are identical independent exponentials and repaired components are as good as new. The problem of the determination of the assembly plan that will maximize the system reliability at any (arbitrary) time instant t is solved when the component failure rate is sufficiently small. For the parallel configuration, the optimal assembly plan allocates as many components as possible to the subsystem with the smallest K_i and allocates functioning components to subsystems in increasing order of the K_i's. For the series configuration, the optimal assembly plan allocates both the surplus and the functioning components equally to all subsystems whenever possible, and when not possible it favors subsystems in decreasing order of the K_i's. The solution is interpreted in the context of the optimal allocation of processors and an initial number of jobs in a problem of routing time consuming jobs to parallel multiprocessor queues. © John Wiley & Sons, Inc. Naval Research Logistics 48: 732–746, 2001     

Moral Aspects of “Moral Injury”: Analyzing Conceptualizations on the Role of Morality in Military Trauma

In clinical circles, the concept of “moral injury” has rapidly gained traction. Yet, from a moral philosophical point of view the concept is less clear than is suggested. That is, in current conceptualizations of moral injury, trauma’s moral dimension seems to be understood in a rather mechanistic and individualized manner. This article makes a start in developing an adequately founded conceptualization of the role of morality in deployment-related distress. It does so by reviewing and synthesizing insights from different disciplines into morality and trauma. This discussion will lead to three positions: (1) values and norms are by definition characterized by conflict, (2) moral conflict may entail important social dimensions, and (3) moral conflict may lead to altered beliefs about previously held values. These insights provide important steps in further developing conceptions of the role of morality in deployment-related suffering.     

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     

A nonidentical parallel processor scheduling problem

The problem considered in this article is a generalization of the familiar makespan problem, in which n jobs are allocated among m parallel processors, so as to minimize the maximum time (or cost) on any processor. Our problem is more general, in that we allow the processors to have (a) different initial costs, (b) different utilization levels before new costs are incurred, and (c) different rates of cost increase. A heuristic adapted from the bin-packing problem is shown to provide solutions which are close to optimal as the number of iterations is allowed to increase. Computational testing, over a large number of randomly generated problem instances, suggests that heuristic errors are, on average, very small.