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.     

Production-location problems

The joint problems of determining the optimal plant location and optimal input mix and plant size are addressed. The interrelationship between input substitutability and plant location is stressed. Conditions under which the location problem can be separated from the determination of the optimal input mix are developed for a number of problem variations. The stability of the optimal location in the face of changes in problem parameters is also discussed. It is demonstrated that consideration of input substitutability often makes the resulting problem no more difficult to solve than problem formulations in which the inherent input substitutability is ignored.     

A time series analysis of some interrelated logistics performance variables

This paper is a case study. We show how the powerful methods of time series analysis can be used to investigate the interrelationships between Alert Availability, a logistics performance variable, and Flying Hours, an operational requirement, in the presence of a major change in operating procedures and using contaminated data. The system considered is the fleet of C-141 aircraft of the U.S. Air Force. The major change in operating procedures was brought about by what is known as Reliability Centered Maintenance, and the contaminated data were due to anomalies in reporting procedures. The technique used is a combination of transfer function modeling and intervention analysis.     

On nonpreemptive strategies in stochastic scheduling

It is shown that there is an optimal strategy for a class of stochastic scheduling problems which is nonpreemptive. The results which yield this conclusion are generalizations of previous ones due to Glazebrook and Gittins. These new results also lead to an evaluation of the performance of nonpreemptive strategies in a large class of problems of practical interest.     

Selection of the optimal setup policy

A model is developed taking into consideration all the costs (namely cost of sampling, cost of not detecting a change in the process, cost of a false indication of change, and the cost of readjusting detected changes) incurred when a production process, using an unscheduled setup policy, utilizes fraction-defective control charts to control current production. The model is based on the concept of the expected time between detection of changes calling for setups. It is shown that the combination of unscheduled setups and control charts can be utilized in an optimal way if those combinations of sample size, sampling interval, and extent of control limits from process average are used that provide the minimum expected total cost per unit of time. The costs of a production process that uses unscheduled setups in conjunction with the appropriate optimal control charts are compared to the costs of a production process that uses scheduled setups at optimum intervals in conjunction with its appropriate control charts. This comparison indicates the criteria for selecting production processes with scheduled setups using optimal setup intervals over unscheduled setups. Suggestions are made to evaluate the optimal process setup strategy and the accompanying optimal decision parameters, for any specific cost data, by use of computer enumeration. A numerical example for assumed cost and process data is provided.     

Incremental approximation of optimal allocations

This paper concerns the approximation of optimal allocations by δ allocations. δ allocations are obtained by fixing an increment δ of effort and deciding at each step upon a single cell in which to allocate the entire increment. It is shown that δ allocations may be used as a simple method of approximating optimal allocations of effort resulting from constrained separable optimization problems involving a finite number of cells. The results are applied to find δ allocations (called δ plans) which approximate optimal search plans. δ plans have the property that as δ → 0, the mean time to find the target using a δ plan approaches the mean time when using the optimal plan. δ plans have the advantage that. they are easily computed and more easily realized in practice than optimal plans which tend to be difficult to calculate and to call for spreading impractically small amounts of effort over large areas.     

A defense allocation problem with development costs

In this paper, the mathematical model for the allocation of resources among a general mix of percentage vulnerable and of numerically vulnerable weapon systems is presented and solved. Percentage vulnerable systems consist of mobile weapons which are difficult to locate, but relatively easy to destroy once located; numerically vulnerable systems comprise easily located fixed base weapons which are difficult to destroy. The distinguishing feature of this analysis is the inclusion of development costs. The theory of max-min is extended as necessary to solve this problem. References are provided to a sequence of earlier versions of this problem.