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

Die Faszination des Verrats: Eine Studie zur Dekadenz im Ost‐West Konflikt. By Thomas Noetzel. Hamburg, Junius (1989) DM48.

Les Nations Armées. By Maurice Faivre (Preface by Pierre Messmer), Paris FEDN/Economica (1988).

Insurgency and Terrorism: Inside Modern Revolutionary Warfare. By Bard E. O'Neill, Brassey's (US), Washington, DC (1990), $19.00.

LIC 2010: Special Operations and Unconventional Warfare in the Next Century. By Rod Paschall, Brassey's (US), Washington, DC, $24.00.

Air Power and Colonial Conflict: The Royal Air Force 1919–1939. By D. E. Omissi, Manchester University Press, Manchester and New York (1990), ISBN 0–7190–2960–0. £35.00.

Key to the Sinai: The Battles for Abu Ageila in the 1956 and 1967 Arab‐Israeli Wars. By George W. Gawrych. Combat Studies Institute Research Survey No. 7, US Army Command and General Staff College, Fort Leavenworth, Kansas, 1990. $8.00.

Arms Export Regulations. Edited by Ian Anthony. SIPRI/Oxford University Press, Oxford (1991), ISBN 0–19–829158–2, £25.00.