Political Scientists and Historians in Search of the Bomb

Britain's failure to cut military commitments in spite of escalating defence costs was not the result of blocking policies by disgruntled services. Rather, there was no determination among Whitehall's political departments to cut commitments even before the service departments could obstruct a decision on force levels. The Conservative governments under Macmillan and Douglas‐Home showed a propensity for substantial force reductions in Europe rather than in out‐of NATO areas. This remained London's long‐term aim even after it had been accepted to build up British troops in Europe to agreed force levels. During Alec Douglas‐Home's premiership Britain's global military role, especially east of Suez, gained a greater significance. An Anglo‐American military axis operating in the Far East and the Indian Ocean became a prominent feature. Ultimately, Anglo‐American military interdependence outside NATO was to ensure that Britain would be able to pursue a policy with more room for independent action.     

Analysis of algorithms for two‐stage flowshops with multi‐processor task flexibility

In this article we introduce a 2‐machine flowshop with processing flexibility. Two processing modes are available for each task: namely, processing by the designated processor, and processing simultaneously by both processors. The objective studied is makespan minimization. This production environment is encountered in repetitive manufacturing shops equipped with processors that have the flexibility to execute orders either individually or in coordination. In the latter case, the product designer exploits processing synergies between two processors so as to execute a particular task much faster than a dedicated processor. This type of flowshop environment is also encountered in labor‐intensive assembly lines where products moving downstream can be processed either in the designated assembly stations or by pulling together the work teams of adjacent stations. This scheduling problem requires determining the mode of operation of each task, and the subsequent scheduling that preserves the flowshop constraints. We show that the problem is ordinary NP‐complete and obtain an optimal solution using a dynamic programming algorithm with considerable computational requirements for medium and large problems. Then, we present a number of dynamic programming relaxations and analyze their worst‐case error performance. Finally, we present a polynomial time heuristic with worst‐case error performance comparable to that of the dynamic programming relaxations. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Dual criteria preemptive open-shop problems with minimum makespan

In this article we present an algorithm for the minimum makespan preemptive open shop, which is superior to existing algorithms in both space and time requirements. We define the more complex generalized open shop and flexible open shop and address the minimum makespan problem on these shops. We show how we can use the algorithm for the minimum makespan open shop to achieve load balancing in simple and generalized open shops without increasing the complexity of the algorithm. Load balancing dictates that the number of busy machines in each period is as even as possible. We also consider preventive maintenance issues in the open shop, and makespan retains its minimum value. In particular we consider the scenario where a machine can be maintained during any period that it happens to be idle. Also we consider the case that a maintenance schedule is prespecified. We show that this problem can be solved via a linear programming formulation that can also take into account release times for the jobs and ready times for the machines. Faster algorithms are presented for open shops with three machines or less. © 1995 John Wiley & Sons, Inc.     

Primal dual algorithms for the vehicle refueling problem

Mehrez, Stern, and Ronen have defined a vehicle refueling problem in which a fleet of vehicles travels on a round-trip, self-contained mission from a common origin, with the objective of maximizing the operational range of the fleet. They have defined a “pure refueling chain” strategy for transferring fuel between vehicles in the fleet, and have solved the problem in the special cases when all vehicles have the same fuel capacity or consumption rate. In this article we present algorithms for the general case, where vehicles have different capacities and consumption rates. Our approach is based on a new primal dual formulation of the problem. The exact algorithm was effective to find the optimal solution for a fleet size n ⩽13. For larger fleets, we present an approximation version of it, which very quickly found a solution within 1% of the maximum possible range for arbitrarily large (up to n = 200) fleets. We also show that a small number of the best vehicles can always reach almost the same range as a large fleet. © 1992 John Wiley & Sons, Inc.     

Rank‐Cluster‐and‐Prune: An algorithm for generating clusters in complex set partitioning problems

Clustering problems are often difficult to solve due to nonlinear cost functions and complicating constraints. Set partitioning formulations can help overcome these challenges, but at the cost of a very large number of variables. Therefore, techniques such as delayed column generation must be used to solve these large integer programs. The underlying pricing problem can suffer from the same challenges (non‐linear cost, complicating constraints) as the original problem, however, making a mathematical programming approach intractable. Motivated by a real‐world problem in printed circuit board (PCB) manufacturing, we develop a search‐based algorithm (Rank‐Cluster‐and‐Prune) as an alternative, present computational results for the PCB problem to demonstrate the tractability of our approach, and identify a broader class of clustering problems for which this approach can be used. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Minimax and maximin facility location problems on a sphere

The problem dealt with in this article is as follows. There are n “demand points” on a sphere. Each demand point has a weight which is a positive constant. A facility must be located so that the maximum of the weighted distances (distances are the shortest arcs on the surface of the sphere) is minimized; this is called the minimax problem. Alternatively, in the maximin problem, the minimum weighted distance is maximized. A setup cost associated with each demand point may be added for generality. It is shown that any maximin problem can be reparametrized into a minimax problem. A method for finding local minimax points is described and conditions under which these are global are derived. Finally, an efficient algorithm for finding the global minimax point is constructed.