On excess-, current-, and total-life distributions of phase-type renewal processes

Consider a renewal process whose interrenewal-time distribution is phase type with representation (α, T). We show that the (time-dependent) excess-life distribution is phase type with representation (α′, T), where α′ is an appropriately modified initial probability vector. Using this result, we derive the (time-dependent) distributions for the current life and the total life of the phase-type renewal process. They in turn enable us to obtain the equilibrium distributions for the three random variables. These results simplify the computation of the respective distribution functions and consequently enhance the potential use of renewal theory in stochastic modeling—particularly in inventory, queueing, and reliability applications. © 1992 John Wiley & Sons, Inc.     

Safety stock reduction by order splitting

In this article we consider an item for which a continuous review, reorder point, order quantity inventory control system is used. The amount of safety stock required depends upon, among other factors, the average value and variability of the length of the replenishment lead time. One way to reduce these quantities is to split orders among two or more vendors. In this article the random lead times are assumed to have Weibull distributions. This permits the development of analytic expressions for the reduction in the expected value and variability of total demand until the critical first (earliest) delivery received from a vendor. An expression is also obtained for the reorder point that provides a given probability of no stockout prior to the first delivery. Lower bounds are given on the order quantity so as to ensure that the probability of a stockout before any one of the later (second, third, etc.) deliveries is sufficiently small to be considered negligible. The analytic and tabular results can be used to estimate the benefits (reduced carrying costs and/or increased service level) of order splitting.     

Gas and the North‐West Frontier

John Terraine, Business in Great Waters: The U Boat Wars 1916 ‐1945. London: Leo Cooper, 1989. Pp.xx + 841; £19.50.

Peter Simkins, Kitchener's Armies: The Raising of the New Armies, 1914–16. Manchester: Manchester University Press, 1988. Pp.xvi + 359; index; illustrations. £37.50 (hardback).

Keith Grieves, Sir Eric Geddes: Business and Government in War and Peace. Manchester and New York: Manchester University Press, 1989. Pp.xiv + 188; £35.

Jeffrey Grey, The Commonwealth Armies and the Korean War: An Alliance Study. Manchester: Manchester University Press, 1988. Pp.xii + 244; £12.95.

Rajan Menon and Daniel N. Nelson (eds.), Limits to Soviet Power. Lexington, MA/Toronto: Lexington Books, 1989. Pp.vii + 231; $35.

Michael Leifer, ASEAN and the Security of South‐East Asia. London and New York: Routledge, 1989. Pp.x + 198; £30.

Grant Wardlaw, Political Terrorism: Theory, Tactics and Counter‐measures. Cambridge: Cambridge University Press, second edn. 1989. Pp.xv + 248; £27.50 (hardback); £10.95 (paperback).

John F. Murphy, Punishing International Terrorists: The Legal Framework for Policy Initiatives. Totowa, NJ: Rowman &; Allanheld 1985. Pp.x + 142; $25.95.

Hanns Maull and Otto Pick (eds.), The Gulf War. London: Pinter Publishers, 1989. Pp.193; £30.

Royal United Services Institute for Defence Studies and Brassey's Defence Yearbook 1989. London: Brassey's Defence Publishers, 1989. Pp.xxviii + 361; £35.

Virginia Gamba‐Stonehouse, Strategy in the Southern Oceans: A South American View. London: Pinter Publishers, 1989. Pp.xiii + 155; £30.

Ola Tunander, Cold Water Politics: The Maritime Strategy and Geopolitics of the Northern Front. London: Sage Publications for the International Peace Research Institute, Oslo, 1989. Pp.194; £25.

Richard Fieldhouse and Shunji Taoka, Superpowers at Sea: An Assessment of the Naval Arms Race. Oxford: Oxford University Press for SIPRI, 1989. Pp.183; £19.50.

Kenneth E. Boulding, Conflict and Defense: A General Theory. University Press of America, 1988. Pp.xiv + 347; $16.75 (paperback). (First Published, 1962).     

Ho Chi Minh and the origins of the Vietnamese doctrine of guerrilla tactics

In a very important sense, the Vietnamese military history of the communist era began in 1941, when Ho Chi Minh prepared ‘Guerrilla Tactics’ (Cach Danh Du Kich).1 ?1. Ministry of Defense Center for the Military Encyclopedia Ministry of Defense Center for the Military Encyclopedia. 1996. Tu Dien Bach Hoa Quan Su Vietnam, Hanoi: People's Army Publishing Company.  [Google Scholar], Tu Dien Bach Hoa Quan Su Vietnam, 69. The publication of this essay, which was a manual on the tactics, techniques, and procedures of guerrilla warfare, preceded the founding of the first armed propaganda unit (Tuyen Truyen Doi Vo Trang) on 22 December 1944, which later became the People's Army of Vietnam (PAVN, Quan Doi Nhan Dan); as well as the revolutionary writings of Truong Chinh (1946–1947) and Vo Nguyen Giap (1959). The fact that ‘Tactics’ was published by the Viet Minh reinforces the claim made by the PAVN that it was the first authoritative Vietnamese writing on this important subject.     

Using real options analysis to value reoptimization options in the shifting bottleneck heuristic

The reoptimization procedure within the shifting bottleneck (SB) involves reevaluation of all previously scheduled toolgroup subproblems at each iteration of the SB heuristic. A real options analysis (ROA) model is developed to value the option to reoptimize in the SB heuristic, such that reoptimization only occurs when it is most likely to lead to a schedule with a lower objective function. To date, all ROA models have sought to value options financially (i.e., in terms of monetary value). The ROA model developed in this paper is completely original in that it has absolutely no monetary basis. The ROA methodologies presented are shown to greatly outperform both full and no reoptimization approaches with respect to both computation time and total weighted tardiness. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Warranty analysis and renewal function estimation

Estimation of the expected cost of a warranty for a stochastically failing unit is closely tied to estimation of the renewal function. The renewal function is a basic tool also used in probabilistic models arising in other areas such as reliability theory, inventory theory, and continuous sampling plans. In these other areas, estimation of a straight line approximation of the renewal function instead of direct estimation of the renewal function has proved successful. This approximation is based on a limit expression for large values of the argument, say t, of the renewal function. However, in warranty analusis, typically t is small compared to the mean failure time of the unit. Hence, alternative methods for renewal function estimation, both parametric and nonparametric, are presented and discussed. An important aspect of this paper is to discuss the performance of the renewal function estimators when only a small number of failed units is available. A Monte Carlo study is given which suggests guidelines for choosing an estimator under various circumstances.     

Relationships among potential sorties,ground support,and aircraft reliability

A methodology is developed for assessing tactical airfield/aircraft system effectiveness, and for evaluating effectiveness changes resulting from incremental investments in ground support resources and/or aircraft reliability. Two categories of ground support functions–turnaround and maintenance–are distinguished. The measure of effectiveness is the maximum potential sortie rate achievable by the system. The methodology enables empirical derivation of the general equation of the tactical airfield/aircraft system. It also enables graphical presentation of the system tradeoffs in the form of a System Analysis Chart.     

A mathematical programming approach to the scheduling of sorting operations

In this paper we describe an approach to the scheduling and/or real-time control of sorting operations in the presence of deadlines. The problem arises in the postal service where mail has to be sorted by zip codes, and in the banking system where checks have to be sorted according to the bank on which they are drawn. In both applications losses are incurred if items miss their clearing deadlines. For example, in check-sorting an extremely important objective of the control system is to reduce the “float” i.e., the total dollar value of the checks which miss their deadlines. The proposed real-time control system utilizes a linear program which chooses between alternative sort-patterns and assigns the various processing steps to the time periods between deadlines.     

Minimizing flow time on a single machine with job classes and setup times

We examine the static sequencing problem of ordering the processing of jobs on a single machine so as to minimize the average weighted flow time. It is assumed that all jobs have zero ready times, and that the jobs are grouped into classes with the property that setup tasks are only required when processing switches from jobs of one class to jobs of another class. The time required for each setup task is given by the sum of a setdown time from the previous class and a setup time for the new class. We show that an algorithm presented in the literature for solving a special case of this problem gives suboptimal solutions. A number of properties of the optimal solution are derived, and their use in algorithms is evaluated. Computational results are presented for both a branch-and-bound procedure and a simpler depth-first search.