A markov chain version of the secretary problem

This paper deals with the Secretary Problem where n secretaries are interviewed sequentially and the best k must be hired. The values of the secretaries are observed as they are interviewed, but beforehand only the distributions of these values are known. Furthermore, the distributions of two successive secretaries' values are governed by a Markov chain. Optimal hiring policies for finite n and limiting optimal policies as k and n approach infinity are obtained.     

Strategy,theory, and history: Operation Husky 1943

In his 1987 work Strategy: The Logic of War and Peace (Harvard University Press, Cambridge, MA, 1987), Edward Luttwak described strategy as a field of activity characterised not only by an innately complex relationship between designs, actions and outcomes, but so too by the frequent disparity between its theory and praxis. Similar observations on this subject have since been made by Richard K. Betts, Lawrence Freedman and Antulio Echevarria II. This article will use the Allied invasion of Sicily in July–August 1943 as a vehicle through which to test these theories against a signal event in the European theatre of the Second World War. It will illustrate how Operation Husky and its aftermath are a paradigm of the confusing and often illogical course of events associated with the process of formulating strategy and waging war. In so doing it demonstrates the benefits of using strategic theory to illuminate events and so move beyond the often insular focus of campaign histories, and simultaneously reinforces the importance of military history in informing a theoretical understanding of strategy.     

Introduction

ABSTRACT

The new nuclear history can make a critical contribution by forcing us to reconsider or reframe the theoretical premises of the concepts we apply to our understanding of the present – and with which we try to navigate the future. It bears on fundamental questions, such as: How should the US manage its alliances? Should it establish a multilateral nuclear policy dialogue in Asia? In what depth should it discuss issues of doctrine and targeting with its Asian allies? What capabilities might reassure European allies in light of current Russian revisionism? Could nuclear war be limited and controlled in an East Asian maritime arena? Do nuclear weapons strengthen an alliance, or do they introduce a divisive bone of contention? Is extended nuclear deterrence (END) stabilizing or is it on the contrary pushing the allies to ask for more? What is the relationship between nuclear and conventional forces in END credibility? How do nuclear alliances contribute to international security and international order? The lessons and insights from these papers, which look at five historical cases of US extended deterrence during the Cold War, should help us think about crucial current issues, and be of use both to historians who want to have a better understanding of the Cold War past and to policymakers who are currently grappling with these issues.     

Steady-state approximation of a multiechelon multi-indentured repairable-item inventory system with a single repair facility

We model a two-echelon multi-indentured repairable-item inventory system where each “base” has a maximum number of identical online machines, and each machine consists of several module types. Machine failures are due to module failures and occur according to an exponential distribution. When a machine fails, the failed module is replaced by an identical spare module if one is available. Otherwise, the module is backordered. All failed modules go to a single “depot” repair facility which consists of a finite number of identical repairmen who are able to repair any module type in an exponentially distributed time, although the repair rates for different module types may differ. The principal contribution of this article is an approximation algorithm for calculating the steady-state characteristics of the system. In comparison with simulation results, the algorithm is quite accurate and computationally efficient. © 1993 John Wiley & Sons, Inc.     

The British Army, ‘Understanding’, and the Illusion of Control

Over the past decade, Western military doctrines concerned with matters of irregular warfare and counterinsurgency have emphasised the requirement for properly ‘understanding’ the social, political and cultural environments in which those militaries may operate; the so-called human and socio-political ‘terrain’. This has led to a number of advancements and initiatives designed to facilitate the way that militaries may enhance that understanding. One of those initiatives has been the emergence from within the British military of a doctrine – JDP 04 ‘Understanding’ – designed for that purpose. Using that doctrine and other subsequent publications as a template, this article will examine the utility of ‘understanding’ for those commanders seeking to match military activities with political ends. It proposes that while any advances in understanding the operating environment are to be applauded, the ‘understanding’ of greatest importance is that relating to the feasibility of the strategic objectives at hand. If those objectives lack inherent feasibility, then the development of subordinate forms of understanding, particularly in relation to the socio-political dynamics of target societies, will likely only serve to slow the process of failure.     

Thinking Globally and Acting Locally: Counterinsurgency Lessons from Modern Wars – A Reply to Jones and Smith

In light of present day calls for increased levels of cultural understanding on the part of Western forces engaged in conflict, this article assesses the utility of such knowledge in light of the British experience of the North-West Frontier of India 1901–1945. By using the British concept of the Political Officer as an example, it proposes that while cultural understanding is of genuine importance when operating in such a challenging environment, possession of it does not necessarily aid either the design or implementation of successful policy. As the British experience on the Frontier during this period illustrates, cultural awareness and understanding may be possessed in abundance, and the mechanisms for achieving such a state of understanding may be advanced, but traditional factors such as a cultural bias on the part of policy-makers, conservatism, underfunding, local resistance to unfamiliar concepts and a fractured civil-military relationship will dominate such awareness and overshadow the benefits that it may provide.     

Grand Strategy and the Graveyard of Assumptions: Britain and Afghanistan, 1839–1919

This article comprises a reply to those who seek to use the British historical experience in Afghanistan in order to draw parallels with current operations in that country. It argues that, while the conceptual and physical response to the issue of Afghanistan on the part of Empire policy-makers during the period 1839–1919 was characterised by periods of indecision and mistaken assumptions, their grasp of strategic principles allowed the formulation of a series of Afghan policies that would serve to protect and indeed enhance British interests in the region for over a century and which stand in stark contrast to the seemingly incoherent Afghan strategy articulated by the current British government.     

Real-time task scheduling with overheads considered

n periodic tasks are to be processed by a single machine, where each task i has a maximum request rate or periodicity F_i, a processing time E_i, a deadline D_i, relative to each request of task i, a task-request interrupt overhead I_i, and a task-independent scheduling overhead S. Two scheduling strategies are considered for sequencing the execution of an arbitrary arrangement of task requests in time: the preemptive and the nonpreemptive earliest-deadline algorithms. Necessary and sufficient conditions are derived for establishing whether a given set of tasks can be scheduled by each scheduling strategy. The conditions are given in the form of limited simulations of a small number of well-defined task-request arrangements. If all simulations succeed, the schedule is feasible for the given set of tasks. If any simulation fails, the schedule is infeasible. While interrupt handling and scheduling overheads can be handled by such simulations, context switching overhead resulting from preemption cannot. A counterexample illustrates how the simulations fail to uncover unschedulable task sets when context switching overhead is considered.     

Optimal maintenance-repair policies for the machine repair problem

We consider a model with M + N identical machines. As many as N of these can be working at any given time and the others act as standby spares. Working machines fail at exponential rate λ, spares fail at exponential rale γ, and failed machines are repaired at exponential rate μ. The control variables are λ. μ, and the number of removable repairman, S, to be operated at any given time. Using the criterion of total expected discounted cost, we show that λ, S, and μ are monotonic functions of the number of failed machines M, N, the discount factor, and for the finite time horizon model, the amount of time remaining.