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 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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 ) 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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