Proportional optimization and fairness
type: Item
instance of: scholarly article
title: Proportional optimization and fairness
zbMATH Open document ID: 1169.90003
publication date: 2008-10-06T00:00:00Z
review text: The problem studied in the book is the one dealing with the very important question arising in scheduling theory: ``How to allocate resources to competing tasks that the assignment is ``fair''?'' Then an additional question arises: ``What is the meaning of fairness in this context?'' Here, the author gives a very comprehensive answer based on the apportionment theory. The proposed algorithm have their roots in house monotone methods and the results are especially welcome in the area of just-in-time scheduling. The book is a very solid piece of work with a thorough introduction to the field followed by a detailed presentation of several important topics. It is composed of 11 chapters complemented by an extensive bibliography and an index. Chapter 1 quotes in a very brief way basic definitions used throughout the book. Chapter 2 briefly reviews main results of the apportionment theory used in the remainder of the book. It emphasizes the axiomatic approach to the apportionment problem and to the construction of the just-in-ime sequences. The approach relies on the divisor methods, in particular parametric methods. Chapter 3 considers the problems of deviation minimization, the total and the maximum deviation, as tools for obtaining just-in-time sequences. It formulates these problems as nonlinear integer optimization and presents efficient algorithms for their solution. The algorithms are based on the concept of ideal positions, closely related to the Webster's apportionment method. Chapter 4 proves that there exist cyclic solutions that minimize the total deviation for symmetric point deviation functions, the same is shown for the maximum deviation. It also proves that limiting optimization to the sequences with the bottleneck deviation not exceeding. Chapter 5 gives a more efficient algorithm for the maximum absolute deviation (referred to as bottleneck) deviation. The absolute value function of deviation results in optimal bottleneck being always less than 1, and al…
Mathematics Subject Classification ID: 90-02
Mathematics Subject Classification ID: 90B05
Mathematics Subject Classification ID: 90B35
zbMATH DE Number: 5349203
zbMATH Keywords: fairness in scheduling
zbMATH Keywords: just-in-time scheduling
zbMATH Keywords: apportionment theory
author: Wieslaw Kubiak
reviewed by: Jacek Blazewicz
MaRDI profile type: Publication
published in: International Series in Operations Research & Management Science
description: scientific article; zbMATH DE number 5349203