Note: Open-shop scheduling with release dates to minimize maximum lateness

We present the first polynomial-time algorithm for an open-shop problem with unit execution times, arbitrary release dates, and due dates. The objective is to minimize maximum lateness. © 1995 John Wiley & Sons, Inc.     

Gittins-index heuristics for research planning

The classical work of Gittins, which resulted in the celebrated index result, had applications to research planning as an important part of its motivation. However, research planning problems often have features that are not accommodated within Gittins's original framework. These include precedence constraints on the task set, influence between tasks, stopping or investment options and routes to success in which some tasks do not feature. We consider three classes of Markovian decision models for research planning, each of which has all of these features. Gittins-index heuristics are proposed and are assessed both analytically and computationally. They perform impressively. © 1995 John Wiley & Sons, Inc.     

Optimal timing schedules in earliness-tardiness single machine sequencing

The article deals with a single machine earliness-tardiness scheduling model where idle times are permitted in job processing. Based on a cluster concept we develop properties of the model that lead to a very fast algorithm to find an optimal timing schedule for a given sequence of jobs. The performance of this algorithm is tested on 480 randomly generated problems involving 100, 200, 400 and 500 jobs. It takes less than two seconds to solve a 500 job problem on a PC. © 1995 John Wiley & Sons, Inc.     

Between a rock and a hard place: Europe in a post-INF world

The end of the 1987 Intermediate-range Nuclear Forces (INF) Treaty has the potential to plunge Europe and NATO into deep crisis. Russia’s continued violation coupled with the Donald J. Trump administration’s desire to balance against Moscow and Beijing could force a new missile debate on Europeans. Even though Washington is trying to assuage its allies, the specter of another round of INF missile deployments to Europe is not unrealistic. Meanwhile, NATO’s European members face a dilemma. Some want NATO to resolutely push back against Russia. Others want to avoid a new deployment debate, at almost all costs. The Kremlin will use these cleavages to weaken NATO. If not carefully handled, NATO’s response to the Russian missile buildup could lead to domestic turmoil in a number of European states and render the alliance ineffective for a prolonged period. Europeans need to act now and voice their preferences in the military and diplomatic domains. A number of different military options are available, below the level of deploying new INF missiles in Europe. However, Europeans need to consider trade-offs regarding crisis and arms-race stability. At the same time, it will be up to European capitals to conceptualize a new arms-control framework for the post-INF world, one that takes into account today’s geopolitical realities and the entanglement of modern conventional and nuclear forces. Given the Trump administration’s loathing of arms control, concepts of mutual restraint may well have to wait for the next US administration. In any case, that should not stop Europeans from taking on more responsibility for their own security.     

Humanitarian response to hurricane disasters: Coordinating flood‐risk mitigation with fundraising and relief operations

To alleviate flooding, caused by hurricanes, governments build structural barriers called levees. In addition, relief providers such as the nongovernmental organizations and charities raise funds, and procure and deliver supplies (food, water, and medicines) for humanitarian relief. The strategy for managing disasters must, therefore, weigh the costs and benefits of building levees as well as procuring and delivering supplies. We use a three‐stage decision making framework to study how the investment in levee capacity can be integrated with supply procurements, fundraising, and rapid response. One of our major findings is that a large fundraising cost discourages postdisaster funding, implying relatively large investments in levee and prepositioned supplies. That notwithstanding, a large social value (of saving life) can tilt the balance in favor of postdisaster funding. If the levee capacity increases, funding for predisaster procurement is reduced without affecting postdisaster funding. For a sufficiently large increase in capacity, however, postdisaster response becomes superfluous. We also find that hurricane uncertainty motivates levees with large capacity. In contrast, levee‐failures motivate levees with small capacity.     

An optimal ordering policy for situations with uncertainty in supply

A one-period inventory model where supply is a random variable with mean proportional to the quantity ordered has been considered. Under new better than used in expectation assumption on the supply variable, a strategy which maximizes a minimum profit has been suggested. An estimate for this maximin order quantity whenever the (customer) demand distribution is unknown has been proposed and almost sure convergence of this estimate to its true value with increasing sample size has been established.     

Asymptotic normality of the estimated optimal order quantity for one-period inventories with supply uncertainty

A one-period inventory situation where the supply is an NBUE random variable with mean proportional to the quantity ordered has been considered. The optimal exponential order quantity, which maximizes the minimum profit obtainable in the NBUE class of supply distributions, is a function of the demand distribution function. Here we show that an estimator of the maximin order quantity, which is already known to converge almost surely to its true value, converges also in distribution to an appropriate normal law with increasing sample size.     

The discrete evasion game with three-move lag

The discrete evasion game with three-move lag, formulated over 30 years ago, was one of the earliest games with time-lag complications. This game remains unsolved even though it is well known that the game has a value. In this article we obtain an upper bound for the value by constructing a strategy which consists of 400 conditional probabilities for the minimizing player. This is believed to be the best upper bound known.     

New purification algorithms for linear programming

Two new algorithms are presented for solving linear programs which employ the opposite-sign property defined for a set of vectors in m space. The first algorithm begins with a strictly positive feasible solution and purifies it to a basic feasible solution having objective function value no less under maximization. If this solution is not optimal, then it is drawn back into the interior with the same objective function value, and a restart begins. The second algorithm can begin with any arbitrary feasible point. If necessary this point is purified to a basic feasible solution by dual-feasibility–seeking directions. Should dual feasibility be attained, then a duality value interval is available for estimating the unknown objective function value. If at this juncture the working basis is not primal feasible, then further purification steps are taken tending to increase the current objective function value, while simultaneously seeking another dual feasible solution. Both algorithms terminate with an optimal basic solution in a finite number of steps.