Contributions to Management Science Illa Weiss The Resource Transfer Problem A Framework for Integrated Scheduling and Routing Problems Contributions to Management Science More information about this series at http://www.springer.com/series/1505 Illa Weiss The Resource Transfer Problem A Framework for Integrated Scheduling and Routing Problems 123 Illa Weiss Clausthal-Zellerfeld Germany Dissertation Clausthal University of Technology, Germany, 2018, D 104 ISSN 1431-1941 ISSN 2197-716X (electronic) Contributions to Management Science ISBN 978-3-030-02537-3 ISBN 978-3-030-02538-0 (eBook) https://doi.org/10.1007/978-3-030-02538-0 Library of Congress Control Number: 2018959095 © 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, express 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 Foreword Due to their practical relevance and challenging intractability, scheduling and vehicle routing problems have been matters of intense research since the early days of operations research From the combinatorial perspective, scheduling and vehicle routing are closely related, both dealing with the allocation of resources and the sequencing of activities over time A large number of variants have been considered in the literature In industrial applications of complex scheduling problems, beyond precedence constraints and scarce renewable resources representing potential factors, generalized precedence relations, sequence-dependent changeover times, and storage resources for consumable factors like materials have to be taken into account Rich vehicle routing problems include such diverse requirements as temporal or spatial synchronization constraints, multi-dimensional capacity restrictions, incompatibilities between goods, restricted accessibility of roads and locations, working time regulations, or inter-route constraints arising from limited processing capacities at depots Despite their structural similarities, scheduling and vehicle routing problems were mostly considered separately Moreover, the overwhelming majority of models and methods proposed in the literature are dedicated to specific problem settings In real-world planning, however, scheduling and routing problems often arise jointly, and a large variety of individual requirements must be considered In supply chain operations planning, production and transportation must be coordinated to reduce order-to-delivery time and stocks Due to short shelf life times, aligning production scheduling and vehicle routing is frequently of particular importance in food supply chains Multi-site scheduling of distributed project portfolios involving resources that are transferred between the locations may be cited as a further example of an important problem setting including scheduling and routing aspects In industrial practice, scheduling and routing are generally performed sequentially This hierarchical approach, however, may lead to substantial performance losses, which could be avoided if scheduling and routing decisions were made simultaneously The need for general and integrated scheduling and routing approaches was the starting point for the research of Illa Weiss In her dissertation, she proposes the resource transfer problem (RTP) as a comprehensive reference model for complex v vi Foreword scheduling and rich vehicle routing problems The RTP model offers a compact unifying framework for modeling and solving scheduling and routing problems Activities and haulage are represented via events among which resource units are to be transferred, and the problem consists in allocating resource units and assigning occurrence times to the events The model also covers multi-modal settings, where each event can occur in alternative modes with different resource requirements Moreover, incompatibility and inclusions constraints can be formulated for the resource units allotted to distinct events Having devised a conceptual and a mathematical programming model of the RTP, the author demonstrates the modeling power of the framework by explaining how to express the various features of complex scheduling and rich vehicle routing problems within the RTP framework The book also presents major algorithmic achievements Generalizing classical results from resource-constrained project scheduling, Illa Weiss shows how for given occurrence modes and occurrence times of the events, a feasible assignment of resource units can be computed efficiently using a column-generation approach that is based on a path-based formulation of a minimum-flow problem with side constraints As a solver for RTP instances, she devises a time-oriented branch-andbound algorithm, which relies on constraint propagation and takes advantage of several consistency tests that she adapted to the general RTP setting An extensive experimental performance analysis demonstrates that the solver is able to provide good solutions to complex instances of supply chain operations planning within a few minutes of CPU time The results obtained by Illa Weiss are highly relevant to scientists and practitioners in scheduling and transportation It is my hope that the ideas developed in this excellent thesis will achieve a wide dissemination and stimulate further research in these vital fields Clausthal-Zellerfeld, Germany Christoph Schwindt Acknowledgements This PhD thesis was created during my time at Clausthal University of Technology, where I worked as a scientific assistant in the Operations Management Group During this time, I had the privilege to meet many great people with whom I enjoyed spending my time First, I would like to thank my supervisor Prof Dr Christoph Schwindt, who taught me a lot and who was always available for support and interesting discussions I also thank Prof Dr Jürgen Zimmermann, who kindly agreed to be the second reviewer Furthermore, I would like to thank my colleagues from the Operations Management Group for excellent collaboration and a nice and inspiring working atmosphere: Tobias Paetz, Mario Sillus, Anja Heßler, Nora Krippendorff, Astrid Ludwig, and Michael Krause Special thanks go to Tobias Paetz, who shared an office with me for several years and who always took time for any question I had I enjoy remembering this beautiful time It was (and still is) a great pleasure to spend time with Mario Sillus, Anja Heßler, and Nora Krippendorff who did not only contribute to our great working atmosphere but with whom I also had many special moments outside the office Without Astrid Ludwig it would have been a lot harder to cope with all the administrative work Finally, I would like to thank Michael Smyth and Sophie Weiss for proofreading my thesis and Janis Kesten-Kühne who was always open for any discussion and supported me whenever needed Clausthal-Zellerfeld, Germany April 2018 Illa Weiss vii Contents Introduction Elements of Scheduling and Routing Theory 2.1 Scheduling Problems 2.1.1 Machine Scheduling Problems 2.1.2 Project Scheduling Problems 2.1.3 Resource Transfers in Project Scheduling 2.2 Vehicle Routing Problems 2.2.1 Standard Vehicle Routing Problems 2.2.2 Pickup and Delivery Problems 2.2.3 Additional Constraints and Further Variants of Vehicle Routing Problems 2.2.4 Rich Vehicle Routing Problems 2.3 Integrated Scheduling and Routing Problems 2.4 Reformulation of Scheduling and Vehicle Routing Problems 3 19 20 21 25 31 36 41 46 The Resource Transfer Problem 3.1 Problem Description 3.2 Conceptual Model and Mathematical Formulation 3.2.1 Conceptual Model 3.2.2 Mathematical Formulation 3.3 Graph-Based Representation 3.3.1 Time Lag Graph 3.3.2 Transfer Graph 3.3.3 Inclusion and Incompatibility Graphs 49 49 53 53 59 63 63 66 67 Modeling Power of the Framework 4.1 Scheduling Problems as Resource Transfer Problems 4.1.1 Machine Scheduling Problems 4.1.2 Project Scheduling Problems 4.1.3 Resource Transfers in Project Scheduling 69 69 69 75 84 ix x Contents 4.2 Vehicle Routing Problems as Resource Transfer Problems 92 4.2.1 Standard Vehicle Routing and Pickup and Delivery Problems 93 4.2.2 Further Variants of Vehicle Routing Problems and Additional Constraints 103 4.3 Integrated Scheduling and Routing Problems as Resource Transfer Problems 117 4.4 Summary of the Building Blocks 120 Solution Approach 5.1 Allocation of Resource Units 5.2 Branch-and-Bound Algorithm 5.2.1 Enumeration Scheme 5.2.2 Lower Bounds for the Makespan 5.2.3 Preprocessing 5.2.4 Truncated Branch-and-Bound Algorithm 5.3 Consistency Tests 5.3.1 Consistency Tests for Renewable Resources 5.3.2 Consistency Tests for Storage Resources 5.3.3 Consistency Tests for the Mode Selection 123 123 144 145 159 169 174 177 178 198 201 Experimental Analysis 6.1 Experimental Design 6.2 Validation 6.2.1 Results of RCPSP/Max Instances 6.2.2 Results of MRCPSP/Max Instances 6.2.3 Results of 1-PDVRPTW Instances 6.3 Generation of Test Sets 6.4 Evaluation of the Results 205 205 207 209 217 221 225 235 Conclusions 267 Appendix A 269 References 301 Index 309 ... routing problems, as well as integrated scheduling and routing problems that have been considered in the literature Chapter introduces the RTP and presents a conceptual and a mathematical formulation... 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... vi Foreword scheduling and rich vehicle routing problems The RTP model offers a compact unifying framework for modeling and solving scheduling and routing problems Activities and haulage are