Methods and Models in Mathematical Programming

This book focuses on mathematical modeling, describes the process of constructing and evaluating models, discusses the challenges and delicacies of the modeling process, and explicitly outlines the required rules and regulations so that the reader will be

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thods and Models in Mathematical Programming

Methods and Models in Mathematical Programming

S. A. MirHassani • F. Hooshmand

Methods and Models in Mathematical Programming

S. A. MirHassani Department of Mathematics and Computer Science Amirkabir University of Technology (Tehran Polytechnic) Tehran, Iran

F. Hooshmand Department of Mathematics and Computer Science Amirkabir University of Technology (Tehran Polytechnic) Tehran, Iran

ISBN 978-3-030-27044-5 ISBN 978-3-030-27045-2 https://doi.org/10.1007/978-3-030-27045-2

(eBook)

© Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Abbreviations and Acronyms

The following table summarizes all abbreviations and acronyms, used throughout this book, and the reader can turn to this list at any time. Abbreviation B&B B&C BIP CLP CSP CTP DCP FSSP IFP IIS IP IPM KKT LHS LP LPR (mu) MCER MILP MINLP MIP MIS MPDP NDP NFP NLP

Definition Branch-and-bound Branch-and-cut Binary integer programming Constraint logic programming Cutting stock problem Course timetabling problem Disease control problem Flow shop scheduling problem Inner fit polygon Irreducible infeasible subsystem Integer programming Interior point method Karush Kuhn Tucker Left hand side Linear programming Linear programming relaxation Monetary unit McCormick envelope relaxation Mixed integer linear programming Mixed integer nonlinear programming Mixed integer programming Minimal infeasible subsystem Multi-parametric disaggregation technique Network design problem No fit polygon Nonlinear programming (continued) v

vi Abbreviation OR PDIP PIP PLF PPSP PSP QP RHS RLT SHP SNP SOS1 SOS2 SSP TSP VRP VRPTW WRMP

Abbreviations and Acronyms Definition Operations rese