Finite Markov chain models skip-free in one direction

Finite Markov processes are considered, with bidimensional state space, such that transitions from state (n, i) to state (m, j) are possible only if m ≤ n + 1. The analysis leads to efficient computational algorithms, to determine the stationary probability distribution, and moments of first passage times.     

Book reviews

British Naval Policy and Norwegian Security: Maritime Power in Transition, 1951-60.. By Mats Berdal. Forsvarsstudier No. 2/92, Institutt For Forsvarsstudier (IFS) Oslo, Norway, 1992, ISSN 0333-3981.

The European Security Order Recast: Scenarios for the Post-Cold War Era.. By Barry Buzan, Morten Kelstrup, Pierre Lemaitre, Elzbieta Tromer and OLE Waever. Pinter, London (1990), ISBN 086187143X, £30.00.

Mates and Muchachos: Unit Cohesion in the Falklands War.. By Nora Kinzer Stewart. Brassey's (US), Washington DC (1991), ISBN 008-037-4395, $20.

The Declining Hegemon: The United States and European Defense, 1960-1990.. By Joseph Lepgold. Praeger, New York (1990), ISBN 0-275-93657-0, $15.95 pb.

Inventing Accuracy: A Historical Sociology of Nuclear Missile Guidance.. By Donald Mackenzie. MIT Press, Cambridge MA, and London, England (1990), ISBN 262-132-583, £19.95.     

Application of level crossing analysis to discrete state processes in queueing systems

In this paper we introduce a discrete state level crossing analysis and present some basic results and a key theorem of level crossings. We illustrate the fertility of the discrete state level crossing analysis by applying it to queueing systems with (i) bulk arrival, (ii) instantaneous feedback, (iii) limited waiting space, and (iv) to machine interference problems.     

A Lanchester-type aggregated-force model of conventional ground combat

This article develops a Lanchester-type model of large-scale conventional ground combat between two opposing forces in a “sector”. It is shown that nonlinear Helmbold-type equations of warfare with operational losses may be used to represent the loss-rate curves that have been used in many aggregated-force models. These nonlinear differential equations are used to model the attrition of combat capability (as quantified by a so-called firepower index) in conjunction with a rate-of-advance equation that relates motion of the contact zone (or FEBA) between the opposing forces to the force ratio and tactical decisions of the combatants. This simplified auxiliary model is then used to develop some important insights into the dynamics of FEBA movement used in large-scale aggregated-force models. Different types of behavior for FEBA movement over time are shown to correspond to different ranges of values for the initial force ratio, for example, an attack will “stall out” for a range of initial force ratios above a specific threshold value, but it will “break out” for force ratios above a second specific threshold value. Such FEBA-movement predictions are essentially based on being able to forecast changes over time in the force ratio.     

A branch-and-bound algorithm for solving fixed charge problems

Numerous procedures have been suggested for solving fixed charge problems. Among these are branch-and-bound methods, cutting plane methods, and vertex ranking methods. In all of these previous approaches, the procedure depends heavily on the continuous costs to terminate the search for the optimal solution. In this paper, we present a new branch-and-bound algorithm that calculates bounds separately on the sum of fixed costs and on the continuous objective value. Computational experience is shown for various standard test problems as well as for randomly generated problems. These test results are compared to previous procedures as well as to a mixed integer code. These comparisons appear promising.     

Scheduling with earliest start and due date constraints on multiple machines

We consider the scheduling of n jobs on m identical machines when the jobs become available for processing at ready times a_i, a_i, ? 0, require d_i time units for processing and must be completed by times b_i for i = 1, 2, … n. The objective chosen is that of minimizing the total elapsed time to complete all jobs subject to the ready time and due date constraints, preemption is not allowed. We present a multi-stage solution algorithm for this problem that is based on an implicit enumeration procedure and also uses the labelling type algorithm which solves the problem when preemption is allowed.     

The economic effects of inspector error on attribute sampling plans

In this paper the effects of inspector error on a cost-based quality control system are investigated. The system examined is of a single sampling plan design involving several cost components. Both type I and type II inspector errors are considered. The model employs a process distribution, thus assuming that a stochastic process of some kind governs the quality of incoming lots. Optimal plan design is investigated under both error-free and error-prone inspection procedures and some comparisons are made.