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.     

A note on explicit solution in linear fractional programming

In this note we analyze the fractional interval programming problem (FIP) and find, explicitly, all its optimal solutions. Though our results are essentially the same as those in Charnes and Cooper [4], the proofs and analysis we provide here are considerably simpler.     

A note on testing for exponentiality

In this note some extensions are made to previous work by a number of authors on the development of tests for exponentiality. The most recent example is due to Fercho and Ringer in which they compare the small sample powers of a few well-known test statistics for the hypothesis of a constant failure rate. It is the primary intent of this current work to extend Gnedenko's F test to situations with hypercensoring and to provide guidance for its use, particularly when a log-normal distribution is the alternative.     

Redundant spares allocation to reduce reliability costs

The problem considered here is the optimal selection of the inventory of spares for a system built from two kinds of modules, the larger of which can be connected so it performs the role of the smaller one. The optimal inventory is the least costly one which achieves a specified probability that the spares will not be exhausted over the design lifetime. For some costs and failure rates it is most economical to use the larger module for both roles, due to the resulting increase in flexibility in the deployment of a single type of spare module. Both analytical and simulation methods have been used to study this problem.     

Flowshop sequencing problem with ordered processing time matrices: A general case

The ordered matrix flow shop problem with no passing of jobs is considered. In an earlier paper, the authors have considered a special case of the problem and have proposed a simple and efficient algorithm that finds a sequence with minimum makespan for a special problem. This paper considers a more general case. This technique is shown to be considerably more efficient than are existing methods for the conventional flow shop problems.     

An algorithm for solving general fractional interval programming problems

A Linear Fractional Interval Programming problem (FIP) is the problem of extremizing a linear fractional function subject to two-sided linear inequality constraints. In this paper we develop an algorithm for solving (FIP) problems. We first apply the Charnes and Cooper transformation on (FIP) and then, by exploiting the special structure of the pair of (LP) problems derived, the algorithm produces an optimal solution to (FIP) in a finite number of iterations.     

The long shadow of colonial cartography: Britain and the Sino-Indian war of 1962

ABSTRACT

This article examines British responses to the Sino-Indian border war of 1962. It illustrates how, in the years leading up to the war, Britain’s colonial legacy in the Indian subcontinent saw it drawn reluctantly into a territorial dispute between Asia’s two largest and most powerful nations. It analyses disagreements in Whitehall between the Foreign Office and Commonwealth Relations Office over the relative strength of India and China’s border claims, and assesses how these debates reshaped British regional policy. It argues that the border war was instrumental in transforming Britain’s post-colonial relationship with South Asia. Continuing to filter relations with India through an imperial prism proved unsatisfactory, what followed was a more pragmatic Indo-British association.     

Slow failure: Understanding America’s quagmire in Afghanistan

ABSTRACT

The United States government has no organised way of thinking about war termination other than seeking decisive military victory. This implicit assumption is inducing three major errors. First, the United States tends to select military-centric strategies that have low probabilities of success. Second, the United States is slow to modify losing or ineffective strategies due to cognitive obstacles, internal frictions, and patron-client challenges with the host nation government. Finally, as the U.S. government tires of the war and elects to withdraw, bargaining asymmetries prevent successful transitions (building the host nation to win on its own) or negotiations.     

Scheduling workers in a constricted area

A generalization of the equi-partitioning problem, termed the 2D-Partition Problem, is formulated. The motivation is an aircraft maintenance scheduling problem with the following characteristics. The complete maintenance overhaul of a single aircraft requires the completion of some 350 tasks. These tasks require a varying number of technicians working at the same time. For large subsets of these 350 tasks, the constraining resource is physical space—tasks must be completed in a physical space of limited size such as the cockpit. Furthermore, there is no precedence relationship among the tasks. For each subset, the problem is to schedule the tasks to minimize makespan. Let m denote the maximum number of technicians that can work at the same time in the physical area under consideration. We present optimization algorithms for m = 2 and 3. © 1996 John Wiley & Sons, Inc.     

A lost sales (S — 1, S) perishable inventory system with renewal demand

This article analyzes a one-to-one ordering perishable inventory model with renewal demands and exponential lifetimes. The leadtimes are independently and exponentially distributed and the demands that occur during stock out periods are lost. Although the items are assumed to decay at a constant rate, the output process is not renewal and the Markov renewal techniques are successfully employed to obtain the operating characteristics. The problem of minimizing the long run expected cost rate is discussed and numerical values of optimal stock level are also provided. © 1996 John Wiley & Sons, Inc.