Rescheduling to minimize makespan on a changing number of identical processors

We consider the problem of rescheduling n jobs to minimize the makespan on m parallel identical processors when m changes value. We show this problem to be NP-hard in general. Call a list schedule totally optimal if it is optimal for all m = 1, …,n. When n is less than 6, there always exists a totally optimal schedule, but for n ≥ 6 this can fail. We show that an exact solution is less robust than the largest processing time first (LPT) heuristic and discuss implications for polynomial approximation schemes and hierarchical planning models.     

Optimal replacement for fault-tolerant systems

We consider the optimal replacement problem for a fault tolerant system comprised of N components. The components are distingushable, and the state of the system is given by knowing exactly which components are operationl and which have failed. The individual component failure rates depend on the state of the entire system. We assume that the rate at which the system produces income decreases as the system deteriorates and the system replacement cost rises. Individual components cannot be replaced. We give a greedy-type algorithm that produces the replacement policy that maximizes the long-run net system income per unit time.     

Optimal refueling sequence for a mixed fleet with limited refuelings

Consider a fleet of vehicles comprised of K₁ identical tankers and K₂ identical nontankers (small aircraft). Tankers are capable of refueling other tankers as well as nontankers. The problem is to find that refueling sequence of the tankers that maximizes the range simultaneously attainable by all K₂ nontankers. A recent paper established that the “unit refueling sequence,” comprised of one tanker refueling at each of K₁ refueling operations, is optimal. The same paper also proffered the following conjecture for the case that the number of refueling operations is constrained to be less than the number of tankers: A nonincreasing refueling sequence is optimal. This article proves the conjecture.     

INTRODUCTION: THE DYNAMICS OF NUCLEAR DISARMAMENT

Decisionmaking processes leading to the acquisition of nuclear weapons by democratic states have served as the basis for theories about nuclear proliferation. In contrast, less is known about how a totalitarian regime responds to immense external pressure to abolish unconventional weapons it considers crucial for its security and survival. This article will analyze how we can explain Iraq's behavior after the passing of Resolution 1441 and during the United Nations inspections in 2002–2003.     

THE FUTURE OF BIOLOGICAL DISARMAMENT

The Sixth Review Conference of the Biological Weapons Convention (BWC) gave the future of biological disarmament new hope. It brought the BWC back closer to the core of multilateral efforts to combat the weaponization of disease, agreed to an intersessional work program for 2007–2010, created an implementation support unit, and revived the interrupted process of BWC evolution through extended understandings agreed at review conferences. However, its aims were deliberately modest. Having set their sights realistically low, delegations did not have to lower them much further. What was most important was to prevent U.S.-Iranian acrimony from paralyzing the conference. With deadlock once again narrowly averted, the conference had to clear away the debris left from past dissensions in order to open the way to constructive evolution for the treaty. In particular the conference avoided contentious subjects such as permanent organization and verification measures for the BWC; its institutional deficit and compliance problems remain. Successes and limitations of the conference are analyzed, as is its equivocal outcome on confidence-building measures. Developing on the endogenous principle, the BWC will continue to need constant attention. At the center of a complex edifice, the BWC must be kept sound, strong, and solid.     

STRENGTHENING THE SECOND LINE OF DEFENSE

On Nuclear Terrorism, by Michael Levi. Harvard University Press, 2007. 210 pages, $24.95.