Approximation algorithms for minimizing total weighted completion time of orders on identical machines in parallel

We consider the problem of scheduling orders on identical machines in parallel. Each order consists of one or more individual jobs. A job that belongs to an order can be processed by any one of the machines. Multiple machines can process the jobs of an order concurrently. No setup is required if a machine switches over from one job to another. Each order is released at time zero and has a positive weight. Preemptions are not allowed. The completion time of an order is the time at which all jobs of that order have been completed. The objective is to minimize the total weighted completion time of the orders. The problem is NP‐hard for any fixed number (≥2) of machines. Because of this, we focus our attention on two classes of heuristics, which we refer to as sequential two‐phase heuristics and dynamic two‐phase heuristics. We perform a worst case analysis as well as an empirical analysis of nine heuristics. Our analyses enable us to rank these heuristics according to their effectiveness, taking solution quality as well as running time into account. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Maximizing project cash availability

Consider a project during the life cycle of which there are cash payouts and in‐flows. To better meet his financial commitments, the project owner would like to meet all deadlines without running out of cash. We show that the cash availability objective is similar to the total weighted flowtime used to measure work‐in‐progress performance in the scheduling and inventory control literatures. In this article we provide several specialized solution methods for the problem of minimizing total weighted flowtime in an arbitrary acyclic project network, subject to activity release times and due dates, where the activity weights may be positive or negative and represent cash in‐ and out‐flows. We describe the structure of an optimal solution and provide several efficient algorithms and their complexity based on mincost and maxflow formulations. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Transient analysis of Markov models of fault‐tolerant systems with deferred repair using split regenerative randomization

The (standard) randomization method is an attractive alternative for the transient analysis of continuous time Markov models. The main advantages of the method are numerical stability, well‐controlled computation error, and ability to specify the computation error in advance. However, the fact that the method can be computationally very expensive limits its applicability. In this paper, we develop a new method called split regenerative randomization, which, having the same good properties as standard randomization, can be significantly more efficient. The method covers reliability‐like models with a particular but quite general structure and requires the selection of a subset of states and a regenerative state satisfying some conditions. For a class of continuous time Markov models, model class C₂, including typical failure/repair reliability‐like models with exponential failure and repair time distributions and deferred repair, natural selections are available for both the subset of states and the regenerative state and, for those natural selections, theoretical results are available assessing the efficiency of the method in terms of “visible” model characteristics. Those results can be used to anticipate when the method can be expected to be competitive. We illustrate the application of the method using a large class C₂ model and show that for models in that class the method can indeed be significantly more efficient than previously available randomization‐based methods. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

WHO IS THE ENEMY?

We examine who benefits when there is a strong leader in place, and who benefits when a situation lacks a proper leader. There are fractious terrorist groups who seek to serve the same people in common cause against a common enemy. The groups compete for rents obtained from the public by engaging in actions against the common enemy. We determine the leadership structure under which each group is better off, as well as the circumstance that the common enemy prefers. We are able to state simple and general conditions for each group and the common enemy to benefit.     

DESIGNING A VIABLE PREDICTION MARKET TO FORECAST DEFENSE ACQUISITION COST AND SCHEDULE OUTCOMES

This paper is the first to demonstrate a viable prediction market that successfully forecasts defense acquisition cost and schedule outcomes, and to provide insights for defense executive decision‐making. Already used in private industry, prediction markets can also accurately forecast outcomes and their associated risks for government programs. Using virtual money, prediction markets allow traders to ‘bet’ on some future outcome. This market mechanism turns out to be a relatively simple and accurate way to discover, aggregate, and communicate to a defense executive the collective market’s beliefs about the likelihood of an eventual outcome of an acquisition program of interest.     

Property distribution and configurations of sovereign states: A rational economic model

A nation's wealth is both an object of conquest to covetous aggressors and a resource to its owners for self defense. To maintain autonomy every country must mount a defense which either makes its capture (1) more expensive than any aggressor can afford, or (2) more expensive than it is worth to aggressors. Whether this condition can be satisfied for all countries simultaneously depends as shown in this paper on relative efficacy of military offense versus defense, the aggregate of wealth among nations and its distribution, and the benefits a conqueror may obtain from conquest, including the duration of these benefits. The paper shows how these factors fit together to determine the sustainability and stability of the international distribution of property as embodied in the configuration of sovereign states.     

ECONOMIC GROWTH AND VIOLENT INTERNATIONAL CONFLICT: 1875–1999

This paper extends the joint product model of military alliances to apply to the new strategic doctrine adopted by NATO in the 1990s. In particular, a choice must be made between protecting one's own territory and pooling forces for an alliancewide rapid reaction force. This new model accounts for a host of externalities and their implications for burden sharing, full financing, and allocative efficiency. The Pigouvian taxes that adjust for force thinning and attack deflection are shown to finance optimal border‐protecting forces under a variety of circumstances. Second‐best considerations arise owing to the pure publicness of rapid reaction forces. The ideal toll arrangement does not currently characterize NATO financing, nor is it likely to do so.     

RETROSPECT AND PROSPECT: TRENDS IN COST AND THEIR IMPLICATIONS FOR UK AEROSPACE

This paper, intended to stimulate debate, suggests that we are at a turning point in the history of the UK military aerospace industry. It argues that there is urgent need for a fresh vision as to how the UK military aerospace industry can both prosper and make its maximum contribution to the defence of Britain. Further, the resulting plans and policies must emphasise the robustness of defence capabilities in a future in which the only thing we can be certain is that it will be very different from the present – especially whenever defence most matters.     

NEGOTIATING NONPROLIFERATION: Scholarship,Pedagogy, and Nuclear Weapons Policy

In nuclear nonproliferation negotiations, many governments pursue multiple objectives, and changes in policy can occur rapidly—and often unexpectedly. For these reasons, understanding nonproliferation requires empathy and imagination rather than just historical fact. This article considers one teaching tool to encourage such insight—simulations—and demonstrates how teaching and scholarship can interact to improve our understanding of the complex decisions and negotiations involved in nuclear nonproliferation. The article consists of five parts: first, it explains the benefits of simulations as both a policy development tool in Washington and as a teaching tool in universities; second, it describes the pedagogical strategy of the Stanford University simulation program; third, it shows how the simulations have identified and highlighted theoretical and substantive insights that are often neglected in scholarly studies of nonproliferation; and fourth, it describes how students are tested to enhance the learning experience from the simulation. Fifth and finally, the article provides concluding observations about how using simulations in the classroom can help scholars develop insights that improve their understanding of real-world nuclear negotiation dynamics and outcomes.     

INTEGRATING NUCLEAR WEAPONS STOCKPILE MANAGEMENT AND NUCLEAR ARMS CONTROL OBJECTIVES TO ENABLE SIGNIFICANT STOCKPILE REDUCTIONS

In his 2009 Prague speech and the 2010 Nuclear Posture Review, President Barack Obama committed the United States to take concrete steps toward nuclear disarmament while maintaining a safe, secure, and effective nuclear deterrent. There is an inherent tension between these two goals that is best addressed through improved integration of nuclear weapons objectives with nuclear arms control objectives. This article reviews historical examples of the interaction between the two sets of objectives, develops a framework for analyzing opportunities for future integration, and suggests specific ideas that could benefit the nuclear weapons enterprise as it undergoes transformation and that could make the future enterprise compatible with a variety of arms control futures.