The simple multiserver loss system with time-varying intensities

For the loss system with time-varying intensities and a finite number of identical servers we derive formulas for the expected number of refused customers in a given time interval and for the expected number of servers busy at a given time instant. © 1994 John Wiley & Sons, Inc.     

A model for critical crack size estimation in fatigue failure of gun barrels

With repeated firing, fatigue cracks are produced in a gun barrel, and the barrel is no longer useful when a crack reaches a critical size. The initial crack size and the critical crack size, as well as the number of firings producing the critical crack size, may be considered as random variables. Assuming a proportional damage model for crack growth, a method for estimating the critical crack size distribution is presented. From these results, an estimate of the barrel life, or the residual barrel life once a crack of a given size is measured, can be obtained.     

Modeling the performance of a scanning radio communications sensor

A model which allows the prediction of long-term average report rates against an array of radio emitters by a scanning sensor is presented. The model is based on Markov renewal theory.     

Probability inequalities via negative dependence for random variables conditioned on order statistics

Distributions are studied which arise by considering independent and identically distributed random variables conditioned on events involving order statistics. It is shown that these distributions are negatively dependent in a very strong sense. Furthermore, bounds are found on the distribution functions. The conditioning events considered occur naturally in reliability theory as the time to system failure for k-out-of-n systems. An application to systems formed with “second-hand” components is given.     

Optimizing the US Navy's combat logistics force

We study how changes to the composition and employment of the US Navy combat logistic force (CLF) influence our ability to supply our navy worldwide. The CLF consists of about 30 special transport ships that carry ship and aircraft fuel, ordnance, dry stores, and food, and deliver these to client combatant ships underway, making it possible for our naval forces to operate at sea for extended periods. We have modeled CLF operations to evaluate a number of transforming initiatives that simplify its operation while supporting an even larger number of client ships for a greater variety of missions. Our input is an employment schedule for navy battle groups of ships operating worldwide, extending over a planning horizon of 90–180 days. We show how we use optimization to advise how to sustain these ships. We have used this model to evaluate new CLF ship designs, advise what number of ships in a new ship class would be needed, test concepts for forward at‐sea logistics bases in lieu of conventional ports, demonstrate the effects of changes to operating policy, and generally try to show whether and how the CLF can support planned naval operations. Published 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008     

An optimal critical level policy for inventory systems with two demand classes

Traditional inventory systems treat all demands of a given item equally. This approach is optimal if the penalty costs of all customers are the same, but it is not optimal if the penalty costs are different for different customer classes. Then, demands of customers with high penalty costs must be filled before demands of customers with low penalty costs. A commonly used inventory policy for dealing with demands with different penalty costs is the critical level inventory policy. Under this policy demands with low penalty costs are filled as long as inventory is above a certain critical level. If the inventory reaches the critical level, only demands with high penalty costs are filled and demands with low penalty costs are backordered. In this article, we consider a critical level policy for a periodic review inventory system with two demand classes. Because traditional approaches cannot be used to find the optimal parameters of the policy, we use a multidimensional Markov chain to model the inventory system. We use a sample path approach to prove several properties of this inventory system. Although the cost function is not convex, we can build on these properties to develop an optimization approach that finds the optimal solution. We also present some numerical results. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Northern Ireland and minimum force: the refutation of a concept?

The debate over whether there exists a British counter-insurgency tradition of minimum force is one that has been thoroughly discussed. Is there anything left to say? This study suggests there is further insight to be attained if one explicitly evaluates the concept of minimum force in relation to the conduct of the security forces in the years of the Northern Ireland conflict. Through an examination of three key periods in the conflict, it will be shown that while there was invariably an awareness of the need to act with restraint among senior officers at the strategic level, this was often difficult to apply at the tactical level in the heat of confrontation. The argument demonstrates that the British Army, and other instruments of the state, rarely acted in a manner that could be described as ‘minimal’. Instead, it was the broader liberal values of the British state that explains largely the degrees of restraint exhibited by the government and security forces.     

On the use of lexicographic min cost flows in evacuation modeling

Building evacuation problems can be represented as dynamic network-flow problems [3]. The underlying network structure of a building evolves through time yielding a time-expanded network (a dynamic network). Usually in such evacuation problems involving time, more than one objective function is appropriate. For example, minimizing the total evacuation time and evacuating a portion of the building as early as possible are two such objectives. In this article we show that lexicographical optimization is applicable in handling such multiple objectives. Minimizing the total evacuation time while avoiding cyclic movements in a building and “priority evacuation” are treated as lexicographical min cost flow problems.     

Capacity improvement,penalties, and the fixed charge transportation problem

Capacity improvement and conditional penalties are two computational aides for fathoming subproblems in a branch‐and‐bound procedure. In this paper, we apply these techniques to the fixed charge transportation problem (FCTP) and show how relaxations of the FCTP subproblems can be posed as concave minimization problems (rather than LP relaxations). Using the concave relaxations, we propose a new conditional penalty and three new types of capacity improvement techniques for the FCTP. Based on computational experiments using a standard set of FCTP test problems, the new capacity improvement and penalty techniques are responsible for a three‐fold reduction in the CPU time for the branch‐and‐bound algorithm and nearly a tenfold reduction in the number of subproblems that need to be evaluated in the branch‐and‐bound enumeration tree. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 341–355, 1999