Optimal control of entry to an M/Ek/1 queue serving several classes of customers

The individual and social optimum control policies for entry to an M/M//1 queue serving several classes of customers have been shown to be control-limit policies. The technique of policy iteration provides the social optimum policy for such a queue in a straightforward manner. In this article, the problem of finding the optimal control policy for the M/E_k/1 system is solved, thereby expanding the potential applicability of the solutions developed. The Markovian nature of the queueing system is preserved by considering the service as having k sequential phases, each with independent, identically distributed, exponential service times, through which a customer must pass to be serviced. The optimal policy derived by policy iteration for such a system is likely to be difficult to use because it requires knowledge of the number of phases rather than customers in the system when an arrival occurs. To circumvent this difficulty, a heuristic is used to find a good usable (implementable) solution. In addition, a mixed-integer program is developed which yields the optimal implementable solution when solved.     

Book reviews

Military Helicopters. By E. J. Everett‐Heath, G. M. Moss, A. W. Mowat and K. E. Reid. Brassey's, London (1990), ISBN 0–08–037341–0 (hardcover), ISBN 0–08–036716‐X (flexicover), £22.50 (hardcover), £12.95 (flexicover)

The Killing Ground: the British Army, the Western Front and the Emergence of Modern Warfare 1900–1918. By Tim Travers. Unwin‐Hyman, London (1990), ISBN 0–04–4457367, £11.95

The Influence of S. L. A. Marshall on the United States Army. By Major F. D. G. Williams. TRADOC Historical Monograph Series, Fort Monroe, VA (1990)     

Optimal timing of switches between product sales for sports and entertainment tickets

Like airlines and hotels, sports teams and entertainment venues can benefit from revenue management efforts for their ticket sales. Teams and entertainment venues usually offer bundles of tickets early in their selling horizon and put single‐event tickets on sale at a later date; these organizations must determine the best time to offer individual tickets because both types of ticket sales consume the same fixed inventory. We model the optimal a priori timing decision for a seller with a fixed number of identical tickets to switch from selling the tickets as fixed bundles to individual tickets to maximize the revenue realized before the start of the performance season. We assume that bundle and single‐ticket customers each arrive according to independent, nonhomogeneous Markovian death processes with a linear death rate that can vary over time and that the benefit from selling a ticket in a package is higher than from selling the ticket individually. We characterize the circumstances in which it is optimal for the seller to practice mixed bundling and when the seller should only sell bundles or individual tickets, and we establish comparative statics for the optimal timing decision for the special case of constant customer arrival rates. We extend our analytical results to find the optimal time for offering two groups of tickets with high and low demand. Finally, we apply the timing model to a data set obtained from the sports industry. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

International Involvement in Restructuring and Creating Security Forces: The Case of Haiti

The controversy over banning landmines in the past decade has removed matters of military technical expertise to the purview of civilian interest groups. According to a Huntingtonian perspective, this could be an indicator of unhealthy civil-military relations. Evidence of this includes political leaders' disregard of senior military advice and the initiation of a program to develop landmine alternatives after having already committed to banning them. The desire to ban landmines may represent a pragmatic revision of pacifist attempts to ban warfare altogether. Because of the development of self-destructing or deactivating mines, the landmine ban movement intrudes on technical military matters without redeeming humanitarian value. This intrusion may have further ramifications for civil-military relations.     

The Renaissance of Pre-First World War Naval History

In the 1990s no-fly zones were introduced as a new way to utilize airpower in the context of Peace Support Operations (PSOs). During that time, they were put to use over Iraq and over Bosnia. However, it is unclear to what extent the no-fly zones were successful in those two instances. This article examines the capabilities of no-fly zones and analyzes the Iraq and Bosnia cases of enforcement. It concludes that no-fly zones can be very effective if properly implemented and offers guidance for policy-makers on how to achieve maximum efficacy.     

A view from Berlin: Colonel Frederick trench and the development of British perceptions of German aggressive intent, 1906–1910

This essay traces the image of Germany that emerges from the reports of Colonel Frederick Trench (1857–1942), British military attache in Berlin from 1906 to 1910. At this time, the British Army possessed only the most limited intelligence‐gathering apparatus and had to rely heavily on the reports of military attaches for information about their continental rivals. Trench, who believed that Germany planned to wage war against Britain and said so categorically in his reports, was the main source of data on the German Army. From the limited surviving records of who read these reports and how they responded to them, this essay posits that Trench's views contributed to the growing British perception of a German threat, a perception that did much to influence British strategic planning in this period.     

NUCLEAR BOMB SQUAD

Defusing Armageddon: Inside NEST, America's Secret Nuclear Bomb Squad, by Jeffrey T. Richelson. W.W. Norton & Company, 2009. 318 pages, $27.95.     

Building Stability Overseas: Three case studies in British defence diplomacy – Uganda,Rhodesia–Zimbabwe,and Sierra Leone

In 2011, the Department for International Development, the Foreign & Commonwealth Office, and the Ministry of Defence launched the Building Stability Overseas Strategy (BSOS). This document sought to integrate cross-government activity as it related to conflict and security so as to ‘take fast, appropriate and effective action to prevent a crisis or stop it escalating and spreading’. At the heart of the strategy was the recognition that addressing instability and conflict overseas was morally right and in the UK's national interests. This confluence of foreign policy realism and ethical outlook most clearly found harmony in the acknowledgement that it was cheaper for the international community to avoid conflict than it was to try to manage it. Through an examination of three historical case studies (Uganda 1964–1972, Rhodesia–Zimbabwe 1979–1981, and Sierra Leone 2000–2007), this article seeks to demonstrate just how difficult this seemingly sensible strategic outlook is. In particular, the article shows there are historical parallels in British postcolonial history that very closely resemble contemporary policy choices; that these can be used to define what is different about past and present practice; and, which in turn, can be used to – at least tentatively – mark out the potential strengths and weaknesses in BSOS.     

Strategic capacity decision‐making in a stochastic manufacturing environment using real‐time approximate dynamic programming

In this study, we illustrate a real‐time approximate dynamic programming (RTADP) method for solving multistage capacity decision problems in a stochastic manufacturing environment, by using an exemplary three‐stage manufacturing system with recycle. The system is a moderate size queuing network, which experiences stochastic variations in demand and product yield. The dynamic capacity decision problem is formulated as a Markov decision process (MDP). The proposed RTADP method starts with a set of heuristics and learns a superior quality solution by interacting with the stochastic system via simulation. The curse‐of‐dimensionality associated with DP methods is alleviated by the adoption of several notions including “evolving set of relevant states,” for which the value function table is built and updated, “adaptive action set” for keeping track of attractive action candidates, and “nonparametric k nearest neighbor averager” for value function approximation. The performance of the learned solution is evaluated against (1) an “ideal” solution derived using a mixed integer programming (MIP) formulation, which assumes full knowledge of future realized values of the stochastic variables (2) a myopic heuristic solution, and (3) a sample path based rolling horizon MIP solution. The policy learned through the RTADP method turned out to be superior to polices of 2 and 3. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010