Estimating the probability that a simulated system will be the best

Consider a stochastic simulation experiment consisting of v independent vector replications consisting of an observation from each of k independent systems. Typical system comparisons are based on mean (long‐run) performance. However, the probability that a system will actually be the best is sometimes more relevant, and can provide a very different perspective than the systems' means. Empirically, we select one system as the best performer (i.e., it wins) on each replication. Each system has an unknown constant probability of winning on any replication and the numbers of wins for the individual systems follow a multinomial distribution. Procedures exist for selecting the system with the largest probability of being the best. This paper addresses the companion problem of estimating the probability that each system will be the best. The maximum likelihood estimators (MLEs) of the multinomial cell probabilities for a set of v vector replications across k systems are well known. We use these same v vector replications to form v^k unique vectors (termed pseudo‐replications) that contain one observation from each system and develop estimators based on AVC (All Vector Comparisons). In other words, we compare every observation from each system with every combination of observations from the remaining systems and note the best performer in each pseudo‐replication. AVC provides lower variance estimators of the probability that each system will be the best than the MLEs. We also derive confidence intervals for the AVC point estimators, present a portion of an extensive empirical evaluation and provide a realistic example. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 341–358, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10019     

Optimal stocking policies for low usage items in multi-echelon inventory systems

Multi-echelon logistic systems are essential parts of the service support function of high technology firms. The combination of technological developments and competitive pressures has led to the development of services systems with a unique set of characteristics. These characteristics include (1) low demand probabilities: (2) high cost items; (3) complex echelon structures; (4) existence of pooling mechanisms among stocking locations at the same echelon level; (5) high priority for service, which is often expressed in terms of response time service levels for product groups of items: (6) scrapping of failed parts; and (7) recycling of issued stock due to diagnostic use. This article develops a comprehensive model of a stochastic, multi-echelon inventory system that takes account of the above characteristics. Solutions to the constrained optimization problem are found using a branch and bound procedure. The results of applying this procedure to a spare parts inventory system for a computer manufacturer have led to a number of important policy conclusions.     

A branch and bound algorithm for solving a class of nonlinear integer programming problems

This article presents a branch and bound method for solving the problem of minimizing a separable concave function over a convex polyhedral set where the variables are restricted to be integer valued. Computational results are reported.     

Rescheduling to minimize makespan on a changing number of identical processors

We consider the problem of rescheduling n jobs to minimize the makespan on m parallel identical processors when m changes value. We show this problem to be NP-hard in general. Call a list schedule totally optimal if it is optimal for all m = 1, …,n. When n is less than 6, there always exists a totally optimal schedule, but for n ≥ 6 this can fail. We show that an exact solution is less robust than the largest processing time first (LPT) heuristic and discuss implications for polynomial approximation schemes and hierarchical planning models.     

Optimal refueling sequence for a mixed fleet with limited refuelings

Consider a fleet of vehicles comprised of K₁ identical tankers and K₂ identical nontankers (small aircraft). Tankers are capable of refueling other tankers as well as nontankers. The problem is to find that refueling sequence of the tankers that maximizes the range simultaneously attainable by all K₂ nontankers. A recent paper established that the “unit refueling sequence,” comprised of one tanker refueling at each of K₁ refueling operations, is optimal. The same paper also proffered the following conjecture for the case that the number of refueling operations is constrained to be less than the number of tankers: A nonincreasing refueling sequence is optimal. This article proves the conjecture.     

Test for the extreme value and weibull distributions based on normalized spacings

Discussed in this article are tests for the extreme-value distribution, or, equivalently, for the two-parameter Weibull distribution when parameters are unknown and the sample may be censored. The three tests investigated are based on the median, the mean, and the Anderson-Darling A² statistic calculated from a set zⁱ of values derived from the spacings of the sample. The median and the mean have previously been discussed by Mann, Scheuer, and Fertig [10] and by Tiku and Singh [14]. Asymptotic distributions and points are given for the test statistics, based on recently developed theory, and power studies are conducted to compare them with each other and with two other statistics suitable for the test. Of the normalized spacings tests, A² is recommended overall; the mean also gives good power in many situations, but can be nonconsistent.     

Book reviews

Managing International Conflict, From Theory to Practice: a Teaching Tool Using CASCON by Lincoln P. Bloomfield and Allen Moulton, New York: St Martin's Press, 1997, ISBN 0-312-13675-7 (pbk), £18.99.

The American Century: the Rise and Decline of the United States as a World Power by Donald W. White, London: Yale University Press, 1997, ISBN 0-300-05721-0 (hbk), £25.

Humanitarian Intervention in Contemporary Conflict by Oliver Ramsbotham and Tom Woodhouse, Cambridge: Blackwell, 1996.

The US Military/NGO Relationship in Humanitarian Interventions by Chris Seiple, Peacekeeping Institute, Center for Strategic Leadership, US Army War College, 1996.

Uncivil Wars: International Security and the New Internal Conflicts by Donald M. Snow, London: Lynne Rienner Publishers, 1996, ISBN 1-55587-655-2 (pbk), £15.50, ISBN 1-55587-648-X (hbk), £33.50.

Intelligence Power in Peace and War by Michael Herman, Royal Institute for International Affairs, Cambridge: Cambridge University Press, 1996, ISBN 0-521-56231-7 (hbk), £50, ISBN 0-521-56636 (pbk), £16.95.

UK Eyes Alpha: Inside British Intelligence by Mark Urban, London: Faber and Faber, 1996, ISBN 0-571-17689-5 (hbk), £16.99.

New Cloak, Old Dagger by Michael Smith, London: Victor Gollancz, 1996, ISBN 0-575-06150-2 (hbk), £20.

Conversion Survey 1997: Global Disarmament and Disposal of Surplus Weapons by Bonn International Center for Conversion, Oxford: Oxford University Press, 1997.

Plutonium and Highly Enriched Uranium 1996: World Inventories, Capabilities and Policies by David Albright, Frans Berkhout and William Walker, Oxford: SIPRI and Oxford University Press, 1997.

The Wars of Eduard Shevardnadze by Carolyn McGiffert Ekedahl and Melvin A. Goodman, University Park, PA: Penn State University Press, 1997.