On the busy period of the M/G/1 retrial queue

The M/G/1 queue with repeated attempts is considered. A customer who finds the server busy, leaves the service area and joins a pool of unsatisfied customers. Each customer in the pool repeats his demand after a random amount of time until he finds the server free. We focus on the busy period L of the M/G/1$ retrial queue. The structure of the busy period and its analysis in terms of Laplace transforms have been discussed by several authors. However, this solution has serious limitations in practice. For instance, we cannot compute the first moments of L by direct differentiation. This paper complements the existing work and provides a direct method of calculation for the second moment of L. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 115–127, 2000     

Makespan minimization in the two‐machine flowshop batch scheduling problem

In this paper we consider a practical scheduling problem commonly arising from batch production in a flexible manufacturing environment. Different part‐types are to be produced in a flexible manufacturing cell organized into a two‐stage production line. The jobs are processed in batches on the first machine, and the completion time of a job is defined as the completion time of the batch containing it. When processing of all jobs in a batch is completed on the first machine, the whole batch of jobs is transferred intact to the second machine. A constant setup time is incurred whenever a batch is formed on any machine. The tradeoff between the setup times and batch processing times gives rise to the batch composition decision. The problem is to find the optimal batch composition and the optimal schedule of the batches so that the makespan is minimized. The problem is shown to be strongly NP‐hard. We identify some special cases by introducing their corresponding solution methods. Heuristic algorithms are also proposed to derive approximate solutions. We conduct computational experiments to study the effectiveness of the proposed heuristics. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 128–144, 2000     

Air Power in the Six-Day War

In the aftermath of Israel's stunning victory over Egyptian, Jordanian and Syrian forces during the 1967 Six-Day War, accolades for the victory were often showered upon the Israeli Air Force (IAF). Indeed, many believed that it had been Israeli air power that had been the decisive element in the war by first eliminating the Arab air forces and then obliterating the Arab armies in turn. While the IAF did play an extremely important role in the fighting, it was not the decisive element of Israeli victory, and its impact was felt in very different ways from the common perception. Indeed, an appreciation of the true role of Israeli air power in the war reinforces both the importance of psychological factors in combat, and the ability of air forces to have a psychological impact disproportionate to their physical impact.     

Characterizations of the exponential distribution by higher-order gap

Suppose X₁,X₂, ?,X_n is a random sample of size n from a continuous distribution function F(x) and let X_1,n, ≦ X_2,n ≦ ? ≦ X_n,n be the corresponding order statistics. We define the jth-order gap g_i,j as g_i,j = X_i+j,n ? X_i,n, 1 ≦ i < n, 1 ≦ j ≦ n ? i. In this article characterizations of the exponential distribution are given by considering the distributional properties of g_k,n-k, 1 ≦ k ≦ n.     

Lesotho’s 2015 elections in the context of an ongoing security vacuum

After inconclusive elections in 2012, Lesotho had a coalition government for the first time, made up of three political parties that had a narrow majority in parliament. The new government, however, faced several challenges, some of which were of its own making. The agreement among the three parties was to literally divide the government into three parts, leading to a continuous stalemate in its operation; the most serious consequence was the prorogation of parliament and the resultant attempted coup. The flight of the prime minister to South Africa and his return under a Southern African Development Community (SADC) security detail provided a short-term solution to Lesotho's security crisis. Under Cyril Ramaphosa's mediation, the prorogued parliament was conditionally opened and the election date set for 28 February 2015. However, the security dilemma – whereby the prime minister, who is also minister of defence, has no control over the military – remains. When elections are held, there does not seem to be a guarantee that they will be held in peace; moreover, there are now fears that the losers will not accept the results of the elections because of the security vacuum in Lesotho. This article argues that peace can only be salvaged by enhanced SADC security before, during and after the elections. It argues that the SADC mission should remain beyond the elections to oversee the constitutional changes that are necessary for ensuring long-term stability. On their own, Lesotho politicians are unlikely to be able to work together in order to move the country forward.     

Rectangles algorithm for generating normal variates

We propose an algorithm for generating normal random variates that is based on the acceptance–rejection method and uses a piecewise majorizing function. The piecewise function has 2048 equal‐area pieces, 2046 of which are constant, and the two extreme pieces are curves that majorize the tails. The proposed algorithm has not only good performance from correlation induction perspective, but also works well from a speed perspective. It is faster than the inversion method by Odeh and Evans and most other methods. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Note: The economic manufacturing lot-sizing problem with imperfect production processes: Bounds and optimal solutions

In this paper, we consider the economic production quantity problem in the presence of imperfect processes. In the literature, the time to shift from the in-control state to the out-of-control state is assumed to be exponentially distributed. In this study, we consider general time to shift distributions and provide distribution-based and distribution-free bounds on the optimal cost. For the exponential case, we compare the optimal solutions to approximate solutions proposed in the literature. A numerical example is used to illustrate the analysis presented and to conduct a sensitivity analysis in order to see the effect of the input parameters on the various solutions to the problem. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 423–433, 1998     

The Banzhaf value and communication situations

Myerson 3 and 4 proposed and characterized a modification of the Shapley value in the context of communication situations. In this paper we propose several characterizations of the extension of the Banzhaf value proposed by Owen 7 to communication situations. In particular we characterize this value with the properties of fairness, isolation, and pairwise merging. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006