A characterization of the wald distribution

Suppose X is a random variable having an absolutely continuous distribution function F(x). We assume that F(x) has the Wald distribution. A relation between the probability density function of X⁻¹ with that of X is used to characterize the Wald distribution.     

Country survey: military expenditure and defence policy in Norway 1970–2013

This article examines military expenditure and defence policy in Norway from 1970 to 2013. Until 1990 Norwegian military expenditure remained between 2.5 and 3.0 per cent of Gross Domestic Product (GDP). Despite constant GDP shares, the military expenditure could not sustain a large and properly armed mobilization army. The constant nominal defence budgets of the 1990s accentuated the Norwegian Armed Forces' underlying imbalance between tasks, structure and budget. Around year 2000, large organizational reforms were effectuated, in which costs, the number of man-years, and underlying imbalances between tasks, structure and budget were reduced. Military expenditure increased in nominal terms between 2003 and 2013, while real military expenditure remained practically constant.     

Involving the elephant: technical isolation and the role of India in a possible solution to the Iranian nuclear crisis

Apart from North Korea, no state's nuclear program in the twenty-first century has raised more concern to international security than Iran's. While Iran insists that its nuclear program is strictly for civilian purpose in line with Article IV of non-proliferation treaty, the USA and its allies insist that Iran has military intentions and called for sanctions. The failure of sanctions to deter Iran from its nuclear agenda had made many scholars and policy-makers call for a preemptive attack on Iranian nuclear facilities. Situated within this debate, this paper positions itself as an antagonist to the preemptive airstrike option and argues that involving India in a possible nuclear “iron curtain” against Iran – a move known as technical isolation – remains the best option to the current nuclear crises.     

Models for multi-item continuous review inventory policies subject to constraints

Models are formulated for determining continuous review (Q, r) policies for a multiitem inventory subject to constraints. The objective function is the minimization of total time-weighted shortages. The constraints apply to inventory investment and reorder workload. The formulations are thus independent of the normal ordering, holding, and shortage costs. Two models are presented, each representing a convex programming problem. Lagrangian techniques are employed with the first, simplified model in which only the reorder points are optimized. In the second model both the reorder points and the reorder quantities are optimized utilizing penalty function methods. An example problem is solved for each model. The final section deals with the implementation of these models in very large inventory systems.     

The Hungarian method for the assignment problem

This paper has been presented with the Best Paper Award. It will appear in print in Volume 52, No. 1, February 2005.     

Analysis of a finite‐buffer bulk‐service queue with discrete‐Markovian arrival process: D‐MAP/Ga,b/1/N

Discrete‐time queues with D‐MAP arrival process are more useful in modeling and performance analysis of telecommunication networks based on the ATM environment. This paper analyzes a finite‐buffer discrete‐time queue with general bulk‐service rule, wherein the arrival process is D‐MAP and service times are arbitrarily and independently distributed. The distributions of buffer contents at various epochs (departure, random, and prearrival) have been obtained using imbedded Markov chain and supplementary variable methods. Finally, some performance measures such as loss probability and average delay are discussed. Numerical results are also presented in some cases. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 345–363, 2003.     

Extrapolation of the mean lifetime of a large population from its preliminary survival history

A large population of independent identical units having finite mean lifetime T is observed. From the history A(y) of cumulative arrivals and the history B(y) of cumulative removals in the interval 0 ≦ y ≦ τ one must predict at time τ the desired T . Two lifetime predictors X(τ) and Y(τ) and related simple predictors obtained from A(y) and B(y) are shown to converge to T with a rate of convergence dependent on the structure of the failure rate function of the units. This dependence is studied theoretically and numerically.     

Stochastic control of queueing systems

Suppose that the state of a queueing system is described by a Markov process { Y_t, t ≥ 0}, and the profit from operating it up to a time t is given by the function f(Y_t). We operate the system up to a time T, where the random variable T is a stopping time for the process Yt. Optimal stochastic control is achieved by choosing the stopping time T that maximizes Ef(Y_T) over a given class of stopping times. In this paper a theory of stochastic control is developed for a single server queue with Poisson arrivals and general service times.     

An infiltration game with time dependent payoff

The problem of assigning patrol boats, subject to resource constraints, to capture or delay an infiltrator with perishable contraband attempting escape across a long, narrow strait is formulated as a two-sided time sequential game. Optimal mixed strategies are derived for the situation of one patrol boat against one smuggler. Procedures for obtaining numerical solutions for R > 1 patrol boats are discussed.     

Exponential size neighborhoods for makespan minimization scheduling

We investigate the quality of local search heuristics for the scheduling problem of minimizing the makespan on identical parallel machines. We study exponential size neighborhoods (whose size grows exponentially with the input length) that can be searched in polynomial time, and we derive worst‐case approximation guarantees for the local optima of such neighborhoods. The so‐called split neighborhood splits a feasible schedule into two layers, and then recombines the two layers by finding a perfect matching. We show that the makespan of every local optimum for split is at most a factor of 2 away from the globally optimal makespan. We then combine the split neighborhood with two neighborhoods from the literature. The combination of split with the jump neighborhood only marginally improves the approximation guarantee, whereas the combination with the lexicographic‐jump neighborhood decreases the approximation guarantee from 2 to 3/2. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011