The resource transfer problem a framework for integrated scheduling and routing problems

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 Appendix A 297 Table A.31 Results of the sc10 and sc11 instances (time limit 60 s) Test set sc10 sc10 sc10 sc10 sc10 sc10 sc10 sc11 sc11 sc11 sc11 sc11 sc11 sc11 Solver CPLEX B&B(Γ ) B&B FB(Γ ) FB = 0.05 = 0.1 CPLEX B&B(Γ ) B&B FB(Γ ) FB = 0.05 = 0.1 Closed (#) 9 10 10 10 10 6 6 Best k (#) 1 1 0 1 Feas (#) 0 0 0 0 0 0 0 Av dev (%) − 0 0 0 − 0 0 0 Max dev (%) − 0 0 0 − 0 0 0 Av time (s) 55.5 34.6 39.35 32.8 36.5 32 32 59.5 42.95 42 42.85 42 42.95 42 Max dev (%) − 0 0 0 − 0 0 0 Av time (s) 60 36.2 39.25 35.15 38.15 36.2 36.2 56.45 39.45 40.5 39.05 39.7 39.45 39.45 Table A.32 Results of the sc12 and sc13 instances (time limit 60 s) Test set sc12 sc12 sc12 sc12 sc12 sc12 sc12 sc13 sc13 sc13 sc13 sc13 sc13 sc13 Solver CPLEX B&B(Γ ) B&B FB(Γ ) FB = 0.05 = 0.1 CPLEX B&B(Γ ) B&B FB(Γ ) FB = 0.05 = 0.1 Closed (#) 8 7 7 7 Best k (#) 1 0 1 0 0 0 Feas (#) 0 0 0 0 0 0 0 Av dev (%) − 0 0 0 − 0 0 0 298 Appendix A Table A.33 Results of the sc14 and sc15 instances (time limit 60 s) Test set sc14 sc14 sc14 sc14 sc14 sc14 sc14 sc15 sc15 sc15 sc15 sc15 sc15 sc15 Solver CPLEX B&B(Γ ) B&B FB(Γ ) FB = 0.05 = 0.1 CPLEX B&B(Γ ) B&B FB(Γ ) FB = 0.05 = 0.1 Closed (#) 10 10 10 10 11 10 11 10 10 10 Best k (#) 0 1 0 0 0 0 Feas (#) 0 0 0 0 0 0 1 Av dev (%) − 0 0 0 − 0 0 0.07 0.07 Max dev (%) − 0 0 0 − 0 0 0.72 0.72 Av time (s) 58.4 30.65 36.95 30.65 36 30.65 30.65 60 30.5 33.05 30.3 31.3 30.55 30.55 Max dev (%) − 0 0 1.06 1.06 − 0 0 1.72 1.72 Av time (s) 57.9 27 33 27 33 27 27 60 45.8 45.05 45.1 45.1 46.1 46.1 Table A.34 Results of the sc16 and sc17 instances (time limit 60 s) Test set sc16 sc16 sc16 sc16 sc16 sc16 sc16 sc17 sc17 sc17 sc17 sc17 sc17 sc17 Solver CPLEX B&B(Γ ) B&B FB(Γ ) FB = 0.05 = 0.1 CPLEX B&B(Γ ) B&B FB(Γ ) FB = 0.05 = 0.1 Closed (#) 11 11 10 10 6 5 Best k (#) 0 0 0 0 0 0 0 Feas (#) 0 0 1 0 0 1 Av dev (%) − 0 0 0.1 0.1 − 0 0 0.29 0.29 Appendix A 299 Table A.35 Results of the sc18 and sc19 instances (time limit 60 s) Test set sc18 sc18 sc18 sc18 sc18 sc18 sc18 sc19 sc19 sc19 sc19 sc19 sc19 sc19 Solver Closed (#) CPLEX B&B(Γ ) B&B FB(Γ ) FB = 0.05 = 0.1 CPLEX B&B(Γ ) B&B FB(Γ ) 11 FB = 0.05 = 0.1 Best k (#) 0 1 1 1 Feas (#) 0 0 0 0 0 0 1 Av dev (%) − 0 0 0 − 0 0 0.14 0.14 Max dev (%) − 0 0 0 − 0 0 1.66 1.66 Av time (s) 56.25 39.95 43.75 36.35 43.6 39.3 39.3 60 35.8 33.4 31.1 33.25 32.9 32.9 Max dev (%) − 0 0 0 − 13.89 28.7 10.62 14.81 13.89 13.89 Av time (s) 58.05 34.5 36.55 34.55 36.25 34.7 34.7 60 46.4 49.65 41.35 39.45 45.1 45.1 Table A.36 Results of the sc20 and sc21 instances (time limit 60 s) Test set sc20 sc20 sc20 sc20 sc20 sc20 sc20 sc21 sc21 sc21 sc21 sc21 sc21 sc21 Solver CPLEX B&B(Γ ) B&B FB(Γ ) FB = 0.05 = 0.1 CPLEX B&B(Γ ) B&B FB(Γ ) FB = 0.05 = 0.1 Closed (#) 9 9 9 5 Best k (#) 0 0 0 0 0 0 Feas (#) 0 0 0 0 2 4 Av dev (%) − 0 0 0 − 2.93 4.37 1.49 3.41 3.11 3.32 References Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms, and applications Prentice Hall, Englewood Cliffs Akkerman R, Farahani P, Grunow M (2010) Quality, safety and sustainability in food distribution: a review of quantitative operations management approaches and challenges OR Spectr 32(4):863–904 Allahverdi A (2015) The third comprehensive survey on scheduling problems with setup times/costs Eur J Oper Res 246(2):345–378 Anbuudayasakar SP, Ganesh K, Mohapatra S (2014) Models for practical routing problems in logistics: design and practices Springer, Cham Archetti C, Speranza MG, Vigo D (2014) Vehicle routing problems with profits In: Toth P, Vigo D (eds) Vehicle routing: problems, methods, and applications, 2nd edn SIAM, Philadelphia, pp 273–297 Armstrong R, Gao S, Lei L (2008) A zero-inventory production and distribution problem with a fixed customer sequence Ann Oper Res 159(1):395–414 Arnold V, Bardhan I, Cooper WW, Gallegos A (1998) Primal and dual optimality in computer codes using two-stage solution procedures in DEA In: Aronson JE , Zionts S (eds) Operations research: methods, models and applications Quorum Books, Westport, pp 57–96 Artigues C, Rivreau D (2008) Heuristics In: Artigues C, Demassey S, Néron E (eds) Resourceconstrained project scheduling: models, algorithms, extensions and applications ISTE, London, pp 87–105 Artigues C, Koné O, Lopez P, Mongeau M (2015) Mixed-integer linear programming formulations In: Schwindt C, Zimmermann J (eds) Handbook on project management and scheduling, vol Springer, Cham, pp 547–564 Baldacci R, Mingozzi A (2009) A unified exact method for solving different classes of vehicle routing problems Math Program 120(2):347–380 Baldacci R, Battarra M, Vigo D (2008) Routing a heterogeneous fleet of vehicles In: Golden B, Raghavan S, Wasil E (eds) The vehicle routing problem: latest advances and new challenges Springer, New York, pp 3–27 Baldacci R, Bartolini E, Mingozzi A, Roberti R (2010) An exact solution framework for a broad class of vehicle routing problems Comput Manag Sci 7(3):229–268 Baptiste P, Le Pape C (1996) Edge-finding constraint propagation algorithms for disjunctive and cumulative scheduling In: Proceedings of the 15th international conference of the U.K Planning Special Interest Group, Liverpool, United Kingdom, pp 339–345 Baptiste P, Le Pape C, Nuijten W (1999) Satisfiability tests and time-bound adjustments for cumulative scheduling problems Ann Oper Res 92(1–4):305–333 © Springer Nature Switzerland AG 2019 I Weiss, The Resource Transfer Problem, Contributions to Management Science, https://doi.org/10.1007/978-3-030-02538-0 301 302 References Baptiste P, Le Pape C, Nuijten W (2001) Constraint-based scheduling: applying constraint programming to scheduling problems Kluwer Academic Publishers, Dordrecht Baptiste P, Laborie P, Le Pape C, Nuijten W (2006) Constraint-based scheduling and planning In: Rossi F, van Beek P, Walsh T (eds) Handbook of constraint programming Elsevier, Amsterdam, pp 761–799 Bartels JH, Zimmermann J (2009) Scheduling tests in automative R&D projects Eur J Oper Res 193(3):805–819 Bartusch M, Möhring RH, Radermacher FJ (1988) Scheduling project networks with resource constraints and time windows Ann Oper Res 16(1–4):201–240 Battarra M, Cordeau JF, Iori M (2014) Pickup-and-delivery problems for goods transportation In: Toth P, Vigo D (eds) Vehicle routing: problems, methods, and applications, 2nd edn SIAM, Philadelphia, pp 161–192 Beck JC, Prosser P, Selensky E (2002) On the reformulation of vehicle routing problems and scheduling problems International symposium on abstraction, reformulation, and approximation Lecture notes in computer science, vol 2371 Springer, Berlin, pp 282–289 Beck JC, Prosser P, Selensky E (2003) Vehicle routing and job shop scheduling: What’s the difference? In: Proceedings of the 13th international conference on automated planning and scheduling, Trento, pp 267–276 Beck JC, Prosser P, Selensky E (2006) A case study of mutual routing-scheduling reformulation J Sched 9(5):469–491 Bellenguez-Morineau O, Néron E (2008) Multi-mode and multi-skill project scheduling problem In: Artigues C, Demassey S, Néron E (eds) Resource-constrained project scheduling: models, algorithms, extensions and applications ISTE, London, pp 149–160 Bertsekas DP (1998) Network optimization: continuous and discrete models Athena Scientific, Belmont Bła˙zewicz J, Lenstra JK, Rinnooy Kan AHG (1983) Scheduling subject to resource constraints: classification and complexity Discrete Appl Math 5(1):11–24 Braekers K, Ramaekers K, Van Nieuwenhuyse I (2016) The vehicle routing problem: state of the art classification and review Comput Ind Eng 99(C):300–313 Bredström D, Rönnqvist M (2008) Combined vehicle routing and scheduling with temporal precedence and synchronization constraints Eur J Oper Res 191(1):19–31 Brucker P (2007) Scheduling algorithms, 5th edn Springer, Berlin Brucker P, Knust S (2001) Resource-constrained project scheduling and timetabling In: Burke E, Erben W (eds) Practice and theory of automated timetabling III: third international conference, PATAT 2000 Konstanz, August 16–18, 2000 Selected Papers Lecture notes in computer science, vol 2079 Springer, Berlin, pp 277–293 Brucker P, Knust S (2003) Lower bounds for resource-constrained project scheduling problems Eur J Oper Res 149(2):302–313 Brucker P, Knust S (2012) Complex scheduling, 2nd edn Springer, Berlin Brucker P, Knust S, Schoo A, Thiele O (1998) A branch and bound algorithm for the resourceconstrained project scheduling problem Eur J Oper Res 107(2):272–288 Brucker P, Drexl A, Möhring R, Neumann K, Pesch E (1999) Resource-constrained project scheduling: notation, classification, models, and methods Eur J Oper Res 112(1):3–41 Carlier J, Moukrim A (2015) Storage resources In: Schwindt C, Zimmermann J (eds) Handbook on project management and scheduling, vol Springer, Cham, pp 177–189 Chen ZL (2010) Integrated production and outbound distribution scheduling: review and extensions Oper Res 58(1):130–148 Cordeau JF, Gendreau M, Laporte G (1997) A tabu search heuristic for periodic and multi-depot vehicle routing problems Networks 30(2):105–119 Correia I, Saldanha-da-Gama F (2015) A modeling framework for project staffing and scheduling problems In: Schwindt C, Zimmermann J (eds) Handbook on project management and scheduling, vol Springer, Cham, pp 547564 Correia I, Lampreia-Lourenỗo L, Saldanha-da-Gama F (2012) Project scheduling with flexible resources: formulation and inequalities OR Spectr 34(3):635–663 References 303 Dantzig GB, Ramser JH (1959) The truck dispatching problem Manage Sci 6(1):80–91 De Reyck B, Herroelen WS (1998) A branch-and-bound procedure for the resource-constrained project scheduling problem with generalized precedence relations Eur J Oper Res 111(1):152– 174 De Reyck B, Herroelen WS (1999) The multi-mode resource-constrained project scheduling problem with generalized precedence relations Eur J Oper Res 119(2):538–556 Demassey S (2008) Mathematical programming formulations and lower bounds In: Artigues C, Demassey S, Néron E (eds) Resource-constrained project scheduling: models, algorithms, extensions and applications ISTE, London, pp 49–62 Demeulemeester EL, Herroelen WS (2002) Project scheduling: a research handbook Kluwer Academic Publishers, Boston Derigs U, Vogel U (2014) Experience with a framework for developing heuristics for solving rich vehicle routing problems J Heuristics 20(1):75–106 Derigs U, Gottlieb J, Kalkoff J, Piesche M, Rothlauf F, Vogel U (2011) Vehicle routing with compartments: applications, modelling and heuristics OR Spectr 33(4):885–914 Desaulniers G, Desrosiers J, Ioachim I, Solomon MM, Soumis F, Villeneuve D (1998) A unified framework for deterministic time constrained vehicle routing and crew scheduling problems In: Crainic TG, Laporte G (eds) Fleet management and logistics Springer Science+Business Media, New York, pp 57–93 Desaulniers G, Madsen OBG, Ropke S (2014) The vehicle routing problem with time windows In: Toth P, Vigo D (eds) Vehicle routing: problems, methods, and applications, 2nd edn SIAM, Philadelphia, pp 119–159 Doerner KF, Salazar-González JJ (2014) Pickup-and-delivery problems for people transportation In: Toth P, Vigo D (eds) Vehicle routing: problems, methods, and applications, 2nd edn SIAM, Philadelphia, pp 193–212 Dohn A, Rasmussen MS, Larsen J (2011) The vehicle routing problem with time windows and temporal dependencies Networks 58(4):273–289 Domschke W, Scholl A (2010) Logistik: Rundreisen und Touren Oldenbourg, München Dorndorf U (2002) Project scheduling with time windows: from theory to applications PhysicaVerlag, Heidelberg Dorndorf U, Phan-Huy T, Pesch E (1999) A survey of interval capacity consistency tests for timeand resource-constrained scheduling In: We¸glarz J (ed) Project scheduling: recent models, algorithms and applications Kluwer Academic Publishers, Dordrecht, pp 213–238 Dorndorf U, Pesch E, Phan-Huy T (2000a) A time-oriented branch-and-bound algorithm for resource-constrained project scheduling with generalised precedence constraints Manage Sci 46(10):1365–1384 Dorndorf U, Pesch E, Phan-Huy T (2000b) Constraint propagation techniques for the disjunctive scheduling problem Artif Intell 122(1):189–240 Drexl M (2012a) Synchronization in vehicle routing: a survey of VRPs with multiple synchronization constraints Transp Sci 46(3):297–316 Drexl M (2012b) Rich vehicle routing in theory and practice Logist Res 5(1):47–63 Dror M, Fortin D, Roucairol C (1998) Redistribution of self-service electric cars: a case of pickup and delivery Technical Report 3543, Institut National de Recherche en Informatique et en Automatique, Rocquencourt Ehrenberg C (2015) Lösung komplexer Ablaufplanungsprobleme: Modelle, Methoden und Fallstudien Shaker, Aachen Eksioglu B, Vural AV, Reisman A (2009) The vehicle routing problem: a taxonomic review Comput Ind Eng 57(4):1472–1483 Elmaghraby SE, Kamburowski J (1992) The analysis of activity networks under generalized precedence relations (GPRs) Manage Sci 38(9):1245–1263 Fagerholt K, Christiansen M (2000) A combined ship scheduling and allocation problem J Oper Res Soc 51(7):834–842 Farahani P, Grunow M, Günther HO (2012) Integrated production and distribution planning for perishable food products Flex Serv Manuf J 24(1):28–51 304 References Floyd RW (1962) Algorithm 97: shortest path Commun ACM 5(6):345 Franck B, Neumann K, Schwindt C (2001) Truncated branch-and-bound, schedule construction, and schedule-improvement procedures for resource-constrained project scheduling OR Spectr 23(3):297–324 Goel A (2009) Vehicle routing and scheduling with drivers’ working hours Transp Sci 43(1):17–26 Goel A, Gruhn V (2008) A general vehicle routing problem Eur J Oper Res 191(3):650–660 Goel A, Irnich S (2017) An exact method for vehicle routing and truck driver scheduling problems Transp Sci 51(2):737–754 Gonỗalvez JF, de Magalhóes Mendes JJ, Resende MGC (2015) The basic multi-project scheduling problem In: Schwindt C, Zimmermann J (eds) Handbook on project management and scheduling, vol Springer, Cham, pp 667–683 Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey Ann Discrete Math 5:287–326 Gromicho J, Hoorn JJ, Kok AL, Schutten JMJ (2012) Restricted dynamic programming: a flexible framework for solving realistic VRPs Comput Oper Res 39(5):902–909 Gschwind T (2015) A comparison of column-generation approaches to the synchronized pickup and delivery problem Eur J Oper Res 247(1):60–71 Gunes C, van Hoeve WJ, Tayur S (2010) Vehicle routing for food rescue programs: a comparison of different approaches In: Lodi A, Milano M, Toth Paolo (eds) Integration of AI and OR techniques in constraint programming for combinatorial optimization problems Lecture notes in computer science, vol 6140 Springer, Berlin, pp 176–180 Hartmann S (2015) Time-varying resource requirements and capacities In: Schwindt C, Zimmermann J (eds) Handbook on project management and scheduling, vol Springer, Cham, pp 163–176 Hartmann S, Briskorn D (2010) A survey of variants and extensions of the resource-constrained project scheduling problem Eur J Oper Res 207(1):1–14 Hartmann J, Makuschewitz T, Frazzon EM, Scholz-Reiter B (2012) A genetic algorithm for the integrated scheduling of production and transport systems In: Helber S, Breitner M, Rösch D, Schön C, Graf von der Schulenburg JM, Sibbertsen P, Steinbach M, Weber S, Wolter A (eds) Operations research proceedings 2012 Springer, Cham, pp 533–539 Hasle G, Kloster O (2007) Industrial vehicle routing In: Hasle G, Lie KA, Quak E (eds) Geometric modelling, numerical simulation, and optimization: applied mathematics at SINTEF Springer, Berlin, pp 397–435 Heilmann R (2000) Ressourcenbeschränkte Projektplanung im Mehr-Modus-Fall Gabler, Wiesbaden Heilmann R (2001) Resource-constrained project scheduling: a heuristic for the multi-mode case OR Spectr 23(3):335–357 Heilmann R (2003) A branch-and-bound procedure for the multi-mode resource-constrained project scheduling problem with minimum and maximum time lags Eur J Oper Res 144(2):348–365 Hempsch C, Irnich S (2008) Vehicle routing problems with inter-tour resource constraints In: Golden B, Raghavan S, Wasil E (eds) The vehicle routing problem: latest advances and new challenges Springer, New York, pp 421–444 Herroelen WS, De Reyck B, Demeulemeester EL (1998) Resource-constrained project scheduling: a survey of recent developments Comput Oper Res 25(4):279–302 Herroelen WS, Demeulemeester EL, De Reyck B (1999) A classification scheme for project scheduling In: We¸glarz J (ed) Project scheduling: recent models, algorithms and applications Kluwer, Boston, pp 1–26 Irnich S (2008) A unified modeling and solution framework for vehicle routing and local searchbased metaheuristics INFORMS J Comput 20(2):270–287 Irnich S, Toth P, Vigo D (2014a) The family of vehicle routing problems In: Toth P, Vigo D (eds) Vehicle routing: problems, methods, and applications, 2nd edn SIAM, Philadelphia, pp 1–33 References 305 Irnich S, Schneider M, Vigo D (2014b) Four variants of the vehicle routing problem In: Toth P, Vigo D (eds) Vehicle routing: problems, methods, and applications, 2nd edn SIAM, Philadelphia, pp 241–271 Jungnickel D (2005) Graphs, networks, and algorithms, 2nd edn Springer, Berlin Klein R, Scholl A (1999) Computing lower bounds by destructive improvement: an application to resource-constrained project scheduling Eur J Oper Res 112(2):322–346 Kok AL, Meyer CM, Kopfer H, Schutten JMJ (2010) A dynamic programming heuristic for the vehicle routing problem with time windows and European Community social legislation Transp Sci 44(4):442–454 Kolisch R, Hartmann S (2006) Experimental investigation of heuristics for resource-constrained project scheduling: an update Eur J Oper Res 174(1):23–37 Kolisch R, Meyer K (2006) Selection and scheduling of pharmaceutical research projects In: Józefowska J, We¸glarz J (eds) Perspectives in modern project scheduling Springer Science+Business Media, New York, pp 321–344 Kolisch R, Padman R (2001) An integrated survey of deterministic project scheduling Omega 29(3):249–272 Kolisch R, Schwindt C, Sprecher A (1999) Benchmark instances for project scheduling problems In: We¸glarz J (ed) Project scheduling: recent models, algorithms and applications Kluwer Academic Publishers, Dordrecht, pp 213–238 Krüger D, Scholl A (2009) A heuristic solution framework for the resource constrained (multi-)project scheduling problem with sequence-dependent transfer times Eur J Oper Res 197(2):492–508 Krüger D, Scholl A (2010) Managing and modelling general resource transfers in (multi-)project scheduling OR Spectr 32(2):369–394 Laborie P (2003) Algorithms for propagating resource constraints in AI planning and scheduling: existing approaches and new results Artif Intell 143(2):151–188 Lahyani R, Khemakhem M, Semet F (2015) Rich vehicle routing problems: from a taxonomy to a definition Eur J Oper Res 241(1):1–14 Lawler EL, Lenstra JK, Rinnooy Kan AHG, Shmoys DB (1993) Sequencing and scheduling: algorithms and complexity In: Graves SC, Rinnooy Kan AHG, Zipkin P (eds) Handbooks in operations research and management science Vol 4: logistics of production and inventory North-Holland, New York, pp 445–522 Li F, Chen ZL,Tang L (2017) Integrated production, inventory and delivery problems: complexity and algorithms INFORMS J Comput 29(2):232–250 Mankowska DS, Meisel F, Bierwirth C (2014) The home health care routing and scheduling problem with interdependent services Health Care Manag Sci 17(1):15–30 Meinecke C, Scholz-Reiter B (2014a) A representation scheme for integrated production and outbound distribution models Int J Logist Syst Manag 18(3):283–301 Meinecke C, Scholz-Reiter B (2014b) A heuristic for the integrated production and distribution scheduling problem Int J Mech Ind Sci Eng 8(2):280–287 Mika M, Waligóra G, We¸glarz J (2006) Modelling setup times in project scheduling In: Józefowska J, We¸glarz J (eds) Perspectives in modern project scheduling Springer Science+Business Media, New York, pp 131–163 Mika M, Waligóra G, We¸glarz J (2015) Overview and state of the art In: Schwindt C, Zimmermann J (eds) Handbook on project management and scheduling, vol Springer, Cham, pp 445–490 Möhring RH, Schulz AS, Stork F, Uetz M (1999) Resource-constrained project scheduling: computing lower bounds by solving minimum cut problems In: Nešetˇril J (ed) Algorithms - ESA’99 Lecture notes in computer science, vol 1643 Springer, Berlin, pp 139–150 Nag B, Golden B, Assad A (1988) Vehicle routing with site-dependencies In: Golden B, Assad A (eds) Vehicle routing: methods and studies Studies in management science and systems Elsevier, Amsterdam, pp 149–159 Nemati S, Shylo OV, Prokopyev OA, Schaefer AJ (2016) The surgical patient routing problem: a central planner approach INFORMS J Comput 28(4):657–673 Neumann K, Morlock M (2002) Operations research, 2nd edn Hanser, München 306 References Neumann K, Schwindt C (1995) Activity-on-node networks with minimal and maximal time lags and their application to make-to-order production Technical Report WIOR-447, University of Karlsruhe Neumann K, Schwindt C (1997) Projects with minimal and maximal time lags: construction of activity-on-node networks and applications OR Spektr 19(3):205–217 Neumann K, Schwindt C (2002) Project scheduling with inventory constraints Math Meth Oper Res 56(3):513–533 Neumann K, Schwindt C, Zimmermann J (2003) Project scheduling with time windows and scarce resources, 2nd edn Springer, Berlin Parragh SN, Doerner KF, Hartl RF (2008a) A survey on pickup and delivery problems Part I: transportation between customers and depot J Betriebswirt 58(1):21–51 Parragh SN, Doerner KF, Hartl RF (2008b) A survey on pickup and delivery problems Part II: transportation between pickup and delivery locations J Betriebswirt 58(2):81–117 Pinedo ML (2016) Scheduling: theory, algorithms, and systems, 5th edn Springer, Cham Pisinger D, Ropke S (2007) A general heuristic for vehicle routing problems Comput Oper Res 34(8):2403–2435 Pollaris H, Braekers K, Caris A, Janssens GK, Limbourg S (2015) Vehicle routing problems with loading constraints: state-of-the-art and future directions OR Spectr 37(2):297–330 Poppenborg J, Knust S (2016) A flow-based tabu search algorithm for the RCPSP with transfer times OR Spectr 38(2):305–334 Ropke S, Pisinger D (2006) A unified heuristic for a large class of Vehicle Routing Problems with Backhauls Eur J Oper Res 171(3):750–775 Roy B (1964) Physionomie et traitement des problèmes d’ordonnancement In: Carré D, Darnaut P, Guitard P, Nghiem PT, Pacaud P, de Rosinski J, Roy B, Sandier G (eds) Les Problèmes d’Ordonnancement Dunod, Paris, pp 1–18 Salewski F, Schirmer A, Drexl A (1997) Project scheduling under resource and mode identity constraints: model, complexity, methods, and application Eur J Oper Res 102(1):88–110 Sariklis D, Powell S (2000) A heuristic method for the open vehicle routing problem J Oper Res Soc 51(5):564–573 Schmid V, Doerner KF, Laporte G (2013) Rich routing problems arising in supply chain management Eur J Oper Res 224(3):435–448 Schnell A, Hartl RF (2016) On the efficient modeling and solution of the multi-mode resourceconstrained project scheduling problem with generalized precedence relations OR Spectr 38(2):283–303 Scholz-Reiter B, Frazzon EM, Makuschewitz T (2010a) Integrating manufacturing and logistic systems along global supply chains CIRP J Manuf Sci Technol 2(3):216–223 Scholz-Reiter B, Schwindt C, Makuschewitz T, Frazzon EM (2010b) An approach for the integration of production scheduling and inter-facility transportation within global supply chains In: Hanna MD (ed) Proceedings of the POMS 21st annual conference, Vancouver, Paper 015-0387 Schutt A, Feydy T, Stuckey PJ, Wallace MG (2013) Solving RCPSP/max by lazy clause generation J Sched 16(3):273–289 Schwindt C (1998a) Generation of resource-constrained project scheduling problems subject to temporal constraints Technical Report WIOR-543, University of Karlsruhe Schwindt C (1998b) Verfahren zur Lösung des ressourcenbeschränkten Projektdauerminimierungsproblems mit planungsabhängigen Zeitfenstern Shaker, Aachen Schwindt C (2005) Resource allocation in project management Springer, Berlin Selensky E (2001) On mutual reformulation of shop scheduling and vehicle routing In: Proceedings of the 20th UK PLANSIG, pp 282–291 Sprecher A, Kolisch R, Drexl A (1995) Semi-active, active, and non-delay schedules for the resource-constrained project scheduling problem Eur J Oper Res 80(1):94–102 Subramanian A, Uchoa E, Ochi LS (2013) A hybrid algorithm for a class of vehicle routing problems Comput Oper Res 40(10):2519–2531 References 307 Ullrich CA (2013) Integrated machine scheduling and vehicle routing with time windows Eur J Oper Res 227(1):152–165 Vidal T, Crainic TG, Gendreau M, Prins C (2013) Heuristics for multi-attribute vehicle routing problems: a survey and synthesis Eur J Oper Res 231(1):1–21 Vidal T, Crainic TG, Gendreau M, Prins C (2014) A unified solution framework for multi-attribute vehicle routing problems Eur J Oper Res 234(3):658–673 Viergutz C (2011) Integrated production and distribution scheduling PhD thesis, Osnabrück University, Osnabrück Viergutz C, Knust S (2014) Integrated production and distribution scheduling with lifespan constraints Ann Oper Res 213(1):293–318 Villeneuve D, Desaulniers G (2005) The shortest path problem with forbidden paths Eur J Oper Res 165(1):97–107 Vogel U (2012) A flexible metaheuristic framework for solving rich vehicle routing problems Shaker, Aachen We¸glarz J, Józefowska J, Mika M, Waligóra G (2011) Project scheduling with finite or infinite number of activity processing modes: a survey Eur J Oper Res 208(3):177–205 Wendt R (2016) Integrierte Produktions- und Distributionsplanung mit Routingentscheidungen: Modellierungsbaukasten und Lösungsverfahren PhD thesis, TU Dortmund University, Dortmund Xu H, Chen ZL, Rajagopal S, Arunapuram S (2003) Solving a practical pickup and delivery problem Transp Sci 37(3):347–364 Index Activities, 2, 9, 19, 46, 49, 51, 75, 117, 123, 145 Activity durations, 9, 14, 49, 51, 76, 117, 123 mode-dependent, 14, 15, 17, 52, 78 Activity interval capacity test, 182, 185 Activity-on-node-network, 10 Algorithm of Bellman, 132 Alternative execution modes, 14, 15, 17, 51, 78, 232 Alternative occurrence modes, 51, 53, 59, 71, 73, 74, 78, 80, 83, 84, 89, 91, 93, 94, 97, 107–110, 112, 114–116, 118, 120, 124, 145, 206 Alternative process plans, 118, 226 Backhauls, 26, 98, 99, 101 Balance test, 200 Beam width, 175, 176, 206 Binary search, 167, 182, 199 Blocking of machines, 74 Branch-and-bound algorithm, 2, 144, 145, 157, 175, 205, 206 truncated, 174, 205 Capacities, 2, 9, 21, 32, 33, 48, 50, 52, 53, 60, 63, 70, 111, 112, 230 multi-dimensional, 32, 37, 50, 97 time-varying, 14, 34, 50, 78 Capacity profile, 180, 181 Changeover times, see Setup times Classification scheme for integrated production and distribution scheduling problems, 42 for machine scheduling problems, for project scheduling problems, 18 for rich vehicle routing problems, 36 for synchronization requirements, 37 for vehicle routing problems, 35 Column generation, 129, 140 Combined vehicle routing and scheduling problem, 38 Compartments, 32, 33, 40, 111 Complexity hierarchy, Consistency tests, 2, 145, 153, 174, 177, 205, 206 Constraint propagation, 2, 46, 144, 153, 168, 177 Core loading profile, 180, 181 Customer demands, 21, 25, 28, 93, 97 Customer services, 21, 34, 35, 38, 46, 50, 93, 97, 117 Deadlines, 8, 13, 19, 72, 73, 77 Depots, 21, 23, 25, 26, 34, 93–95, 97, 102, 114 Destructive improvement, 167 Dial-a-ride problem, 30, 103 Domain, 146, 152 Driving hour regulations, 31, 36, 41, 105 Due dates, 8, 55 Edge-finding, 185 Eligible event-mode combinations, 148, 149 Energetic reasoning, 178, 195 Energy precedence test, 197, 206 Events, 49–51, 69, 75, 93, 117, 123, 145 © Springer Nature Switzerland AG 2019 I Weiss, The Resource Transfer Problem, Contributions to Management Science, https://doi.org/10.1007/978-3-030-02538-0 309 310 scheduled, 146 unscheduled, 146, 147 Feasible path, 131, 140 Filtered beam search algorithm, 175, 206 Filter width, 175 Floyd Warshall algorithm, 153, 155, 156, 178 Forbidden paths, 129, 131, 136, 137, 140 General interval capacity test, 195 Giant-tour representation, 39 Heterogeneous fleet, see Vehicles, heterogeneous Home health care routing problem, 38, 50 Inclusion graph, 67, 71, 95 Incompatibility constraints, 33, 39, 40, 103, 112, 120, 233 Incompatibility graph, 67 Input negation test, 191, 206 Input-or-output test, 189 Input test, 185, 206 Instance generator, 225 Inter-route resource constraints, 34, 38, 110 Interval capacity, 178, 180 Interval capacity consistency test, 178, 179, 182 Jobs, 4, 19, 69 Linehauls, 26, 98, 99, 101 Load transshipments, 37, 109 Lower bound critical-path based, 159, 205 on the objective function value, 154, 155, 159, 167, 205, 206 on the time lags, 153, 155 on the transfer times, 155 workload-based, 160, 205 Machine downtimes, 8, 73 Machines, 4, 19, 46, 47 heterogeneous, 5, 71, 73, 74 identical, 5, 70, 71, 73 uniform, 5, 51 unrelated, 44, 51 Index Machine scheduling problem, 3, 4, 69 flexible flow shop, 5, 72 flexible job shop, 6, 48, 72 flexible open shop, flow shop, 5, 71 job shop, 6, 43, 46, 48, 71 multiprocessor flow shop, multiprocessor job shop, multiprocessor open shop, open shop, 6, 46, 72 parallel machines, 4, 43, 70, 71 single machine, 4, 70 Makespan, see Objective function, makespan Many-to-many problem, 26, 28, 102 Maximum driving times, 31 Maximum ride times, 30, 103 Maximum route duration, 95, 110 Minimal problem instance, 146, 161, 177, 178 Minimum-flow problem, 20, 124–127, 129, 139, 154 path-flow formulation, 128 Minimum overlaps, 38, 77 Mode activities, 168 Mode allocation, 123 Mode assignment, 53, 56, 64, 126 time-feasible, 64 Mode-identity constraints, 15, 79, 120 Mode shaving, 201, 203 Modified algorithm of Bellman, 133, 134, 137 Multi-start procedure, 207 Negative reduced cost, 129, 130 Node capacities, 124, 125, 127, 129 Non-Archimedean infinitesimal, 60 Not-first condition, 185 Not-last condition, 185 Objective function makespan, 8, 10, 15, 18, 47, 52, 55, 62, 76, 84, 147, 155, 198, 205 maximum lateness, 8, 18 maximum tardiness, maximum weighted lateness, 84 mean weighted earliness, 18 mean weighted lateness, 18, 84 mean weighted tardiness, 18, 84 total earliness, 18 total tardiness, 18, 43, 55 total travel cost, 21, 93 total travel distance, 21 total travel time, 21, 47 Index total weighted completion time, weighted sum of completion times, 18, 84 One-to-many-to-one problem, 26 One-to-one problem, 26, 28, 29, 102 Operations, 4, 5, 46, 69, 73, 117 Output negation test, 194, 206 Output test, 186, 206 Parallelity constraints, 14 Partially ordered destructive relations, 17, 82 Partially regular, 55, 56, 84, 117, 144, 147 Partial schedule, 146 Penalty cost, 23, 44, 117 Performance-guarantee algorithm, 174, 206 Perishability, see Short shelf-life Pickup and delivery problem, 26, 30, 39, 102 many-to-one, 31, 103 one-to-many, 31, 103 with synchronization requirements, 38 Precedence consistency test, 177 Precedence relations, 8–10, 19, 37–39, 46–48, 51, 70–72, 76, 87, 91, 95, 99, 103, 104, 106 completion-to-completion, 12 generalized, 2, 12, 15, 20, 38, 51, 64, 72, 76, 77, 79, 80 start-to-completion, 12 Preprocessing, 155, 157, 169, 172, 181, 205 Pricing problem, 129–131, 140 Processing times, 4, 5, 70, 71, 73, 117 mode-dependent, 226, 232 Production and distribution scheduling problems, 42 Profile test, 198 Project duration, see Makespan Project net present value, 18 Project scheduling problem, 3, 75 multi-mode resource-constrained, 14, 78, 167 multi-mode resource-constrained with generalized precedence constraints, 146, 167, 207, 217 multi-project, 17, 19, 83 multi-site, 83 multi-skill, 15, 80 resource-constrained, 9, 10, 19, 76, 167 resource-constrained with generalized precedence constraints, 145, 160, 167, 170, 174, 177, 207, 209 resource-constrained with sequencedependent changeover times, 123 resource-feasible, 54 311 Quarantine times, 8, 72, 73 Release dates, 8, 13, 19, 72, 73, 77 Removal times, 16 Resource requirements, 9, 49–51, 53, 56, 61, 63, 77, 91, 94, 97, 101, 102, 145, 234 mode-dependent, 14, 17, 51, 53, 78, 95 time-varying, 14, 78 Resource-resource tradeoffs, 14, 51, 78 Resources doubly-constrained, 12, 77 globally limited, 34, 38, 39, 110 nonrenewable, 12, 19, 46, 77, 90, 91 partially renewable, 12 renewable, 9, 19, 49–53, 56, 59, 61, 70, 71, 73, 75, 76, 86, 87, 91, 95, 109, 110, 116, 118–120, 124, 178, 233 storage, 12, 49–53, 60, 72, 75–77, 83, 86, 90, 91, 93, 94, 97, 99, 101, 102, 106, 107, 109–112, 115, 118, 120, 124, 145, 198, 206 unary, 9, 46, 50, 77, 93, 94, 96, 97, 118, 120, 124, 178, 206 Resource transfers, 19, 84 completion-to-completion, 19, 84 completion-to-start, 19, 84 non-physical, 19, 85 physical, 19, 85 resource-consuming, 19, 90, 108, 114, 120 resource-using, 19, 81, 86, 89, 110, 120 stand-alone, 19, 20, 86 start-to-completion, 19, 84 start-to-start, 19, 84 Routes, 20 Schedule, 4, 14, 53, 58, 59 active, 147 changeover-feasible, 124 feasible, 55, 177 partial, 145 partially active, 147, 149, 177 resource-feasible, 54, 146 time-feasible, 54, 146, 153, 171 transfer-feasible, 126, 127, 139 Separating times, 14, 105, 120 Service times, 21, 46, 47, 93, 97 vehicle-dependent, 113 Setup external, 82 inseparable, 16, 80, 87 separable, 16, 80 312 Setup times, 8, 15, 44, 47, 51, 52, 74, 77, 80, 81, 117, 124 machine-dependent, 8, 74 resource-dependent, 19 schedule-dependent, 16, 82 sequence-dependent, 8, 16, 19, 74, 123, 124 Shaving, 181, 206 Shortest path problem with forbidden paths, 131 Short shelf-life, 41, 43, 44, 117, 118 Simplex algorithm, 138 Staff qualifications, 36, 38 Storage cost, 44 Supply chain operations planning, 225 Surgical patient routing problem, 45 Symmetric triples, 172, 178 Synchronization requirements, 35, 37, 38, 51, 104, 109 intra-route, 38 Time-cost tradeoffs, 14, 15, 51, 78 Time lag graph, 63, 95, 154 Time lags, 52–54, 62, 63, 71, 72, 82, 90, 97, 120, 145 finish-to-start, 77 maximum, 38, 41, 51, 64, 72, 73, 77, 79, 93, 95, 103, 104, 106, 107, 113, 115, 117, 118 minimum, 2, 12, 38, 41, 51, 64, 70, 72, 73, 76, 77, 79, 93, 95, 103, 104, 113, 115, 118 start-to-start, 77 Timetable, 53 Timetable constraint propagation, 179 Time windows, 23, 29, 31, 34, 37–39, 43, 44, 46, 47, 51, 93, 95, 97, 103, 114, 118, 226, 234 multiple, 31, 37, 40, 41, 44, 104 Topologically sorted network, 132 Transfer cost, 56 Transfer graph, 66, 95 Transfer times, 51–54, 57, 61, 63, 66, 73–76, 78, 81, 82, 84, 86, 91, 93, 95, 97, 106, 107, 113, 119, 120, 123, 145 asymmetric, 23 resource-dependent, 2, 20, 91, 120 sequence-dependent, 2, 19, 20, 91 symmetric, 23 time-dependent, 40, 41 vehicle-dependent, 33, 37, 112, 226, 230 Transportation planning in food distribution, 42 Transportation problem, 163, 165 Index Transportation times see Travel times Travel cost, 21, 23, 37, 95 Travel distances, 21, 23, 34, 46, 97 Truck dispatching problem, 21 Unit-assignment problem, 56, 58, 95 Unit-identity constraints, 55, 67, 74, 79, 94, 97, 102, 103, 110, 116, 119 Unit-inclusion constraints, 52, 54, 55, 57, 62, 63, 67, 68, 70, 73, 76, 79, 87, 94, 95, 102, 117, 120, 126, 127, 131, 133, 136, 139, 145, 203 Unit-incompatibility constraints, 52, 55, 58, 62, 63, 67, 68, 104, 112, 117, 126, 127, 132, 136, 139, 145, 203 Unit-interval capacity test, 179, 180 Upper bound, 154, 155, 167 Vehicle routing problems, 20 with additional temporal constraints, 38 with backhauls, 26, 39, 41, 99 capacitated, 21, 39–41, 43, 93 with clustered backhauls, 26 with compartments, 33, 40, 111 distance-constrained, 31, 40 with divisible delivery and pickup, 28, 101 with a heterogeneous fleet, 34, 39, 40, 112 industrial, 40 many-to-one, 25 with mixed linehauls and backhauls, 26, 27, 39, 40, 99 multi-attribute, 40 multi-depot, 34, 39–41, 114 one-commodity pickup and delivery, 28, 102, 208, 221 one-commodity pickup and delivery with time windows, 208, 221 one-to-many, 25 open, 34, 39, 40, 114 periodic, 34, 39–41, 115 with pickup and delivery, 39 prize-collecting, 35, 116 with profit, 35, 37, 116 rich, 36 with simultaneous pickup and delivery, 27, 39–41, 101 site-dependent, 33, 39, 113 with split deliveries, 34, 40, 114 with synchronization requirements, 37 with temporal dependencies, 38 with three-dimensional loading constraints, 32 Index with time windows, 23, 39–41, 43, 46, 93 truck and trailer, 37, 40 with two-dimensional loading constraints, 32 Vehicles, 2, 23, 46, 50 heterogeneous, 2, 33, 34, 37, 39, 40, 42, 44, 51, 112, 118, 119, 226, 230 313 homogeneous, 21, 42–44, 50, 93, 94, 206, 230 Working hour regulations, 31, 37, 40, 105 ... 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