Markovian multiechelon repairable inventory system

In this article we model a two-echelon (two levels of repair, one level of supply) repairable-item inventory system using continuous-time Markov processes. We analyze two models. In the first model we assume a system with a single base. In the second model we expand this model to include n bases. The Markov approach gives rise to multidimensional state spaces that are large even for relatively small problems. Because of this, we utilize aggregate/disaggregate techniques to develop a solution algorithm for finding the steady-state distribution. This algorithm is exact for the single-base model and is an approximation for the n-base model, in which case it is found to be very accurate and computationally very efficient.     

Production lot sizing under setup and worker learning

Previous lot-sizing models incorporating learning effects focus exclusively on worker learning. We extend these models to include the presence of setup learning, which occurs when setup costs exhibit a learning curve effect as a function of the number of lots produced. The joint worker/setup learning problem can be solved to optimality by dynamic programming. Computational experience indicates, however, that solution times are sensitive to certain problem parameters, such as the planning horizon and/or the presence of a lower bound on worker learning. We define a two-phase EOQ-based heuristic for the problem when total transmission of worker learning occurs. Numerical results show that the heuristic consistently generates solutions well within 1% of optimality.     

A logistic regression/Markov chain model for NCAA basketball

Each year, more than $3 billion is wagered on the NCAA Division 1 men's basketball tournament. Most of that money is wagered in pools where the object is to correctly predict winners of each game, with emphasis on the last four teams remaining (the Final Four). In this paper, we present a combined logistic regression/Markov chain model for predicting the outcome of NCAA tournament games given only basic input data. Over the past 6 years, our model has been significantly more successful than the other common methods such as tournament seedings, the AP and ESPN/USA Today polls, the RPI, and the Sagarin and Massey ratings. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006.     

Book Reviews

Strategic Views from the Second Tien The Nuclear Weapons Policies of France, Britain and China. Edited by J.C. Hopkins and W Hu, New Brunswick and London, Transaction Publishers, (1995) ISBN 1-56000-7907. $ 21.95

Multinational Military Forces: Problems and Prospects. By Roger H. Palin. Adelphi Paper 294, 11SS/Oxford University Press (1995) ISBN 0-19-828025-4 ISSN 0567 932X

South Africa in the Global Economy. Edited by Greg Mills, et al. South African Institute of International Affairs, Johannesburg, (1995) ISBN 1-874890-58-7. R. 45.60

The Limits of Air Powen The American Bombing of North Vietnam. By Mark Clodfelter, The Free Press. New York (1989). ISBN 0-02-905990-9. $22.95.

Guy Gibson. By Richard Morris with Colin Dobinson. Viking. London (1994). ISBN 0-670-82878-5. £18.00.

Dambuster: A Life of Guy Gibson VC. By Susan Ottway. Leo Cooper, London (1994). ISBN 0-85052-427. £16-95.     

Exploiting self‐canceling demand point aggregation error for some planar rectilinear median location problems

When solving location problems in practice it is quite common to aggregate demand points into centroids. Solving a location problem with aggregated demand data is computationally easier, but the aggregation process introduces error. We develop theory and algorithms for certain types of centroid aggregations for rectilinear 1‐median problems. The objective is to construct an aggregation that minimizes the maximum aggregation error. We focus on row‐column aggregations, and make use of aggregation results for 1‐median problems on the line to do aggregation for 1‐median problems in the plane. The aggregations developed for the 1‐median problem are then used to construct approximate n‐median problems. We test the theory computationally on n‐median problems (n ≥ 1) using both randomly generated, as well as real, data. Every error measure we consider can be well approximated by some power function in the number of aggregate demand points. Each such function exhibits decreasing returns to scale. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 614–637, 2003.     

Partitioning of biweighted trees

A districting problem is formulated as a network partitioning model where each link has one weight to denote travel time and another weight to denote workload. The objective of the problem is to minimize the maximum diameter of the districts while equalizing the workload among the districts. The case of tree networks is addressed and efficient algorithms are developed when the network is to be partitioned into two or three districts. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 143–158, 2002; DOI 10.1002/nav.10003     

Analysis of down times of jib cranes—A stochastic approach

In this paper a case study dealing with the maintenance problem of jib cranes is presented. A jib crane is viewed as a complex system whose performance is observed as a single realization over period of time. After pointing out limitations of existing stochastic models to analyze the observed realization a new family of bivariate stochastic processes is introduced. The data of jib crane is analyzed using new model and cross‐validated using part of the data set. It is noted that the new family of stochastic processes is useful to analyze bivariate data where one of the variables is finitely valued and the other is nonnegative and continuous. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 231–243, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10006     

The one‐warehouse multiretailer problem with an order‐up‐to level inventory policy

We consider a two‐level system in which a warehouse manages the inventories of multiple retailers. Each retailer employs an order‐up‐to level inventory policy over T periods and faces an external demand which is dynamic and known. A retailer's inventory should be raised to its maximum limit when replenished. The problem is to jointly decide on replenishment times and quantities of warehouse and retailers so as to minimize the total costs in the system. Unlike the case in the single level lot‐sizing problem, we cannot assume that the initial inventory will be zero without loss of generality. We propose a strong mixed integer program formulation for the problem with zero and nonzero initial inventories at the warehouse. The strong formulation for the zero initial inventory case has only T binary variables and represents the convex hull of the feasible region of the problem when there is only one retailer. Computational results with a state‐of‐the art solver reveal that our formulations are very effective in solving large‐size instances to optimality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010