Abstract
Transportation and logistic networks have always been offering significant practical applications for optimization and operations research techniques. Especially in the last two decades, numerous success stories for large-scale, realistic networks have attracted the interest of the scientific and research society. A typical example of such a success story is the vehicle routing problem, where recent advancements have made it possible for large, complex problems to be solved to optimality. This chapter is designed so as to introduce the reader in the notions tackled by important problems in transportation and logistics engineering and the algorithms that have been devised over the years to solve them. The problems presented and studied in this contribution include the traffic assignment, the vehicle routing problem, and the toll pricing among others.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Recommended Reading
H. Armelius, L. Hultkranz, The politico-economic link between public transport and road pricing: an ex-ante study of the Stockholm road-pricing trial. Transport. Policy 13(1), 167–172 (2006)
R. Arnott, K. Small, The economics of traffic congestion. Am. Sci. 82(5), 446–455 (1994)
A. Atamtürk, M.W.P. Savelsbergh, Integer programming software systems. Ann. Oper. Res. 140(1), 67–124 (2005)
A. Babin, M. Florian, L. James-Lefebvre, H. Spiess, EMME/2 An interactive graphic method for road and transit planning, in RTAC Annual Conference Preprints, vol. 1 (1981)
M.L. Balinski, R.E. Quandt, On an integer program for a delivery problem. Oper. Res. 12(2), 300–304 (1964). JSTOR
L.D. Baskar, B. De Schutter, H. Hellendoorn, Hierarchical traffic control and management with intelligent vehicles, in IEEE Intelligent Vehicles Symposium, 2007, pp. 834–839
L.D. Baskar, B. De Schutter, H. Hellendoorn, Optimal routing for ntelligent vehicle highway systems using mixed integer linear programming. Technical Report, Delft University, Netherlands, 2010
J.C. Bean, Genetic algorithms and random keys for sequencing and optimization. ORSA J. Comput. 6, 154–160 (1994)
M.J. Beckmann, C.B. McGuire, C.B. Winsten, Studies in the Economics of Transportation (Yale University Press, New Haven, 1956)
A. Bemporad, M. Morari, Control of systems integrating logic, dynamics and constraints. Automatica 35(3), 407–427 (1999)
A. Ben-Tal, A. Nemirovski, Robust optimization—methodology and applications. Math. Program. 92(3), 453–480 (2002)
D.P. Bertsekas, J.N. Tsitsiklis, Parallel and Distributed Computation (Prentice Hall, Old Tappan, 1989)
D.D. Bochtis, S.G. Vougioukas, H.W. Griepentrog, A mission planner for an autonomous tractor. Trans. ASABE 52(5), 1429–1440 (2009)
J.B. Bramel, D. Simchi-Levi, A location based heuristic for general routing problems. Oper. Res. 43, 649–660 (1995)
L.S. Buriol, M.G.C. Resende, C.C. Ribiero, M. Thorup, A hybrid genetic algorithm for the weight setting problem in OSPF/IS-IS routing. Networks 46, 36–56 (2005)
L.S. Buriol, M.J. Hirsch, P.M. Pardalos, T. Querido, M.G.C. Resende, M. Ritt, A hybrid genetic algorithm for road congestion minimization, in Proceedings of the XLI Simpósio Brasileiro de Pesquisa Operacional, 2009, pp. 2515–2526
L.S. Buriol, M.J. Hirsch, P.M. Pardalos, T. Querido, M.G.C. Resende, M. Ritt, A biased random-key genetic algorithm for road congestion minimization. Optim. Lett. 4(4), 619–633 (2010)
D.G. Cantor, M. Gerla, Optimal routing in a packet-switched computer network. IEEE Trans. Comput. C-23, 1062–1069 (1974)
M. Carey, A constraint qualification for a dynamic traffic assignment model. Transport. Sci. 20, 55–88 (1986)
M. Carey, Nonconvexity of the dynamic traffic assignment problem. Transport. Res. 26B, 127–133 (1992)
Y.P. Chan, Optimal travel time reduction in a transport network: an application of network aggregation and branch-and-bound techniques. Research Report R, vol. 69, pp. 693–695, 1969
C.K. Chau, K.M. Sim, The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands. Oper. Res. Lett. 31(5), 327–334 (2003)
N. Christofides, A. Mingozzi, P. Toth, Exact algorithms for the vehicle routing problem based on the spanning tree and shortest path relaxations. Math. Program. 20, 255–282 (1981)
E.G. Coffman Jr, Scheduling in Computer and Job Shop Systems (Wiley, New York, 1976)
J.R. Correa, A.S. Schulz, N.E. Stier-Moses, Selfish routing in capacitated networks. Math. Oper. Res. 29(4), 961–976 (2004)
S. Dafermos, Convergence of a network decomposition algorithm for the traffic equilibrium model, in Proceedings of the 8th International Symposium on Transportation and Traffic Theory, Toronto, ed. by V.F. Hurdle et al. (University of Toronto Press, Toronto, 1983), pp. 43–156
C. Daganzo, The cell transmission model: a simple dynamic representation of highway traffic consistent with the hydrodynamic theory. Transport. Res. 28B(4), 269–287 (1994)
C. Daganzo, The cell transmission model, Part II: network traffic. Transport. Res. 29B(2), 79–93 (1995)
G.B. Dantzig, J.H. Ramser, The truck dispatching problem. Manag. Sci. 6(1), 80–91 (1959)
J. Descrosiers, Y. Dumas, M.M. Solomon, F. Soumis, Time constrained routing snad scheduling, in Network Routing, Handbooks in Operations Research and Management Science, ed. by M.O. Ball, T.L. Magnanti, C.L. Monma, G.L. Nemhauser (North-Holland, Amsterdam, 1995), pp. 35–139
M. Desrochers, J. Descrosiers, M.M. Solomon, A new optimization algorithm for the vehicle routing problem with time windows. Oper. Res. 40, 342–354 (1992)
M. Dror, Note on the complexity of the shortest path models for column generation in VRPTW. Oper. Res. 42, 977–978 (1994)
J. Eliasson, L.-G. Mattsson, Equity effects of congestion pricing: Quantitative methodology and a case study for Stockholm. Transport. Res. A 40(7), 602–620 (2006)
M. Ericsson, M.G.C. Resende, P.M. Pardalos, A genetic algorithm for the weight setting problem in OSPF routing. J. Combin. Optim. 6(3), 299–333 (2002)
S.P. Evans, Derivation and analysis of some models for combining trip distribution and assignment. Transport. Res. 10, 37–57 (1976)
M.L. Fisher, R. Jaikumar, A generalized assignment heuristic for vehicle routing. Networks (Wiley Online Library) 11(2), 109–124 (1981)
L.R. Ford Jr, D.R. Fulkerson, Solving the transportation problem. Manag. Sci. 3(1), 24–32 (1956)
M. Florian, D. Hearn, Network equilibrium models and algorithms, in Handbooks in OR and MS, vol. 8, Chap. 6, ed. by M.O. Ball et al. (North-Holland, Amsterdam, 1995), pp. 485–550
M. Florian, D.W. Hearn, Traffic assignment: equilibrium models, in Pareto Optimality, Game Theory and Equilibria (Springer, New York, 2008) (pp. 571–592)
M. Frank, P. Wolfe, An algorithm for quadratic programming. Nav. Res. Logist. Q. 3(1–2), 95–110 (1956), Wiley
R.S. Garfinkel, G.L. Nemhauser, Integer Programming, vol. 4 (Wiley, New York, 1972)
J. Geunes, P.M. Pardalos, Supply Chain Optimization, vol. 98 (Springer, New York, 2005)
B.E. Gillett, L.R. Miller, A heuristic algorithm for the vehicle dispatch problem. Oper. Res. 22, 240–349 (1974)
A. Glazer, E. Niskanen, Parking fees and congestion. Reg. Sci. Urban Econ. 22, 123–132 (1992)
B. Golden, A problem in network interdiction. Nav. Res. Logist. Q. 25(4), 711–713 (1978), Wiley
B.L. Golden, A minimum-cost multicommodity network flow problem concerning imports and exports. Networks (Wiley) 5(4), 331–356 (1975)
C.P. Gomes, B. Selman, N. Crato, Heavy-tailed distributions in combinatorial search, in Principles and Practice of Constraint Programming-CP97 (Springer, Berlin/Heidelberg 1997), pp. 121–135
P. Goodwin, Congestion charging in central London: lessons learned. Plann. Theor Pract. 5(4), 501–505 (2004)
E. Hadjiconstantinou, N. Christofides, An exact algorithm for general, orthogonal, two-dimensional knapsack problems. Eur. J. Oper. Res. (Elsevier) 83(1), 39–56 (1995)
R. Hamerslag, Prognosemodel voor het personenvervoer in Nederland (Technische Hogeschool Delf, Delft, 1971)
D.W. Hearn, S. Lawphongpanich, J.A. Ventura, Restricted simplicial decomposition: computation and extensions, in Computation Mathematical Programming (Springer, Berlin/Heidelberg, 1987), pp. 99–118
D.W. Hearn, S. Lawphongpanich, J.A. Ventura, Finiteness in restricted simplicial decomposition. Oper. Res. Lett. (Elsevier) 4(3), 125–130 (1985)
D.W. Hearn, M.B. Yildirim, A toll pricing framework for traffic assignment problems with elastic demand. Appl. Optim. 63, 135–143 (2001)
D.W. Hearn, M.B. Yildirim, M.V. Ramana, L.H. Bai, Computational methods for congestion toll pricing models. In Proceedings of the Intelligent Transportation Systems, 2001, pp. 257–262. IEEE
D.W. Hearn, M.V. Ramana, in Solving Congestion Toll Pricing Models, University of Florida, Department of Industrial & Systems Engineering
D.W. Hearn, J. Ribera, Convergence of the Frank–Wolfe method for certain bounded variable traffic assignment problems. Transport. Res. B Methodol. (Elsevier) 15(6), 437–442 (1981)
M. Held, R.M. Karp, The traveling salesman problem and minimum spanning trees: Part II. Math. Program. 1, 6–25 (1971)
J.M. Henderson, R.E. Quandt, Microeconomic Theory: A Mathematical Approach (McGraw-Hill, New York, 1958)
D.A. Hensher, K.J. Button, Handbook of Transport Modelling, 2nd edn. (Emerald, Bingley, 2007)
C.A. Holloway, An extension of the Frank–Wolfe method of feasible directions. Math. Program. 6, 14–27 (1974)
S.P. Hoogendoom, P.H. Bovy, State-of-the-art of vehicular traffic flow modelling. In Proceedings of the Institution of Mechanical Engineers. Part I: J. Syst. Control Eng. 215(4), 283-303
B. Kallehauge, J. Larsen, O.B. Madsen, M.M. Solomon, Vehicle Routing Problem with Time Windows (Springer, New York 2005), pp. 67–98
D. Kim, P.M. Pardalos, A solution approach to the fixed charge network flow problem using a dynamic slope scaling procedure. Oper. Res. Lett. (24), 195–203 (1999)
D. Kim, P.M. Pardalos, Dynamic slope scaling and trust interval techniques for solving concave piecewise linear network flow problems. Network (35–3), 216–222 (2000)
F. Knight, Some fallacies in the interpretation of social cost. Q. J. Econ. 38(4), 582–606 (1924)
J. Kohl, Der Verkehr und die Ansiedlungen der Menschen (Dresden/Leipzig, 1841)
A.W.J. Kolen, A.H.G. Rinnoy Kan, H.W.J.M. Trienekens, Vehicle routing with time windows. Oper. Res. 35, 266–273 (1987)
G. Laporte, M. Gendreau, J.Y. Potvin, F. Semet, Classical and modern heuristics for the vehicle routing problem. Int. Trans. Oper. Res. (Wiley) 7(4–5), 285–300 (2000)
T. Larsson, A. Migdalas, M. Patriksson, A partial linearization method for the traffic assignment problem. Report LiTH-MAT-R-89-06, Optimization, Linköping Institute of Technology, Department of Mathematics, Linköping, 1989
E.L. Lawler, D.E. Wood, Branch and bound methods: a survey. Oper. Res. 14(4), 699–719 (1966)
J. Leape, The London congestion charge. J. Econ. Perspect. 20(4), 157–176 (2006)
L.J. Leblanc, Mathematical Programming Algorithms for Large Scale Network Equilibrium and Network Design Problems (Northwestern University, Evanston, 11973)
L.J. LeBlanc, K. Farhangian, Efficient algorithms for solving elastic demand traffic assignment problems and mode split-assignment problems. Transport. Sci. 15(4), 306 (1981)
L.J. LeBlanc, R.V. Helgason, D.E. Boyce, Improved efficiency of the Frank–Wolfe algorithm for convex network programs. Transport. Sci. (Institute for Operations Research and the Management Sciences) 19(4), 445–462 (1985)
K. LeBlanc Edward, J. Larry, An efficient approach to solving the road network equilibrium traffic assignment problem. Transport. Res. 9(5), 309–318 (1975), Elsevier
H. Lévy-Lambert, Tarification des services à qualité variable: application aux péages de circulation. Econometrica 36(3–4), 564–574 (1968)
J. Linderoth, T. Ralphs, Noncommercial Software for Mixed Integer Linear Programming. Optimization Online, 2005
D.G. Luenberger, Investment Science (Oxford University Press, New York, 1998)
L.-G. Mattsson, Road pricing: consequences for traffic, congestion and location, in Road Pricing, the Economy and the Environment, ed. by C. Jensen-Butler, B. Sloth, M.M. Larsen, B. Madsen, O.A. Nielsen, (Springer, Berlin, 2008), pp. 29–48
T.L. Magnanti, Combinatorial optimization and vehicle fleet planning: perspectives and prospects. Networks (Wiley Online Library) 11(2), 179–213 (1981)
R.S. Markovits, Second-best theory and law & economics: an introduction. Chi.-Kent L. Rev. 73, 3 (1997)
K. McAloon, C. Tretkoff, G. Wetzel, Sports league scheduling, in Proceedings of Third Ilog International Users Meeting, Paris, July 1997
D.K. Merchant, G. Nemhauser, A model and an algorithm for the dynamic traffic assignment problem. Transport. Sci. 12, 183–199 (1978)
D.K. Merchant, G. Nemhauser, Optimality conditions for a dynamic traffic assignment model. Transport. Sci. 12, 200–207 (1978)
D.L. Miller, A matching based exact algorithm for capacitated vehicle routing problems. INFORMS J. Comput. 7(1), 1–9 (1995)
J.D. Murchland, Road network traffic distribution in equilibrium. Math. Model Soc. Sci. 8, 145–183 (1970)
K. Murty, Solving the fixed charge problem by ranking the extreme points. Oper. Res. (16), 268–279 (1968)
A. Nahapetyan, S. Langpopanich, Discrete-time dynamic traffic assignment problem with periodic planning horizon: system optimum. J. Global Optim. 38(1), 41–60 (2007)
A. Nahapetyan, P.M. Pardalos, Adaptive dynamic cost updating procedure for solving fixed charge network flow problems. Comput. Optim. Appl. 39(1), 37–50 (2008)
G. Nemhauser, M. Trick, Scheduling a major college basketball conference, Georgia Tech., Technical Report, 1997
S. Nguyen, An algorithm for the traffic assignment problem. Transport. Sci. 8(3), 203 (1974)
S. Nguyen, others, Equilibrium traffic assignment for large scale transit networks. Eur. J. Oper. Res. 37(2), 176–186 (1988)
S. Nguyen, L. James, TRAFFIC: An Equilibrium Traffic Assignment Program (University of Montreal, Montreal, 1975)
W. Ochoa-Rosso, Applications of Discrete S Optimization Techniques to Cq Capital Investment and Network Synthesis Problems (1968)
W. Ochoa-Rosso, A. Silva, Optimum project addition in urban transportation networks via descriptive traffic assignment models. Research Report R, vol. 44, 1968
T. Oksanen, A. Visala, Coverage path planning algorithms for agricultural field machines. J. Field Robot. 26(8), 651–668 (2009)
K.R. Overgaard, Urban transportation planning traffic estimation. Traffic Q. 21(2) (1967)
P.M. Pardalos, M.G.C. Resende, Handbook of Applied Optimization (Oxford University Press, Oxford, 2002)
P. Patriksson, The traffic assignment problem: models and methods (1994)
A.C. Pigou, The Economics of Welfare, vol. 2 (Cosimo, New York, 2006)
J. Renaud, F.F. Boctor, G. Laporte, A fast composite heuristic for the symmetric traveling salesman problem. INFORMS J. Comput. 8, 134–143 (1996)
T.M. Ridley, An Investment Policy to Reduce the Travel Time in a Transportation Network (Operations Research Center, University of California, Berkeley, 1965)
M.G. Richards, Congestion harging in London, in The Policy and the Politics (Palgrave Macmillan, Basingstoke, 2006)
T. Roughgarden, Selfish Routing and the Price of Anarchy (MIT, Cambridge, 2005)
T. Roughgarden, E. Tardos, Bounding the inefficiency of equilibria in nonatomic congestion games. Games Econ. Behav. 47(2), 389–403 (2002)
D.M. Ryan, B.A. Foster, An integer programming approach to scheduling, in Computer Scheduling of Public Transport Urban Passenger Vehicle and Crew Scheduling (1981), pp. 269–280
D.M. Ryan, C. Hjorring, F. Glover, Extensions of the petal method for vehicle routing. J. Oper. Res. Soc. 44, 289–296 (1993)
A. Sorokin, V. Boginski, A. Nahapetyan, P.M. Pardalos, Computational risk management techniques for fixed charge network flow problems with uncertain arc failures. J. Comb. Optim. 25(1), 99–122 (2013)
P.A. Steembrink, Optimization of Transport Networks (Wiley, 1979)
P. Toth, D. Vigo (eds.), The Vehicle Routing Problem, vol. 9 (Society for Industrial and Applied Mathematics, 1987)
T. Tsekeris, S. Voß, Design and evaluation of road pricing. Netnomics 10(1), 5–52 (2009)
E.J. Van Henten, J. Hemming, B.A. Van Tujil, J.G. Kornet, J. Bontsema, Collision-free motion planning for a cucumber picking robot. Biosyst. Eng. 86(2), 135–144 (2003)
J.A. Ventura, D.W. Hearn, Restricted simplicial decomposition for convex constrained problems. Math. Program. 59(1), 71–85 (1993)
T.E. Verhoef, Second-best congestion pricing in general static transportation networks with elastic demands. Reg. Sci. Urban Econ. 32, 281–310 (2002)
T.E. Verhoef, P. Nijkamp, P. Rietveld, Second-best congestion pricing: the case of an untolled alternative. J. Urban Econ. 40(3), 279–302 (1996)
W.S. Vickrey, Congestion theory and transport investment. Am. Econ. Rev. 59(2), 251–260 (1969)
B. Von Hohenbalken, Simplicial decomposition in nonlinear programming algorithms. Math. Program. 13, 49–68 (1977)
S. Vougioukas, S. Blackmore, J. Nielsen, S. Fountas, A two-stage optimal motion planner for autonomous agricultural vehicles. Precis. Agr. 7, 361–377 (2006)
J.G. Wardrop, Some theoretical aspects of road traffic research. Oper. Res. 4(4), 72–73 (1953)
S.T. Waller, A.K. Ziliaskopoulos, A combinatorial user optimal dynamic traffic assignment algorithm. Ann. Oper. Res. 144(1), 249–261 (2006)
B.-W. Wie, R.L. Tobin, D. Bernstein, T.L. Friesz, A comparison of system optimum and user equilibrium dynamic traffic assignments with schedule delays. Transport. Res. C 3(6), 389–411 (1995)
W.I. Zangwill, Convergence conditions for nonlinear programming algorithms. Manag. Sci. 16(1), 1–13 (1969)
Q.P. Zheng, A. Arulselvan, Discrete time dynamic traffic assignment models and solution algorithm for managed lanes. J. Global Optim. 51(1), 47–68 (2011)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this entry
Cite this entry
Vogiatzis, C., Pardalos, P.M. (2013). Combinatorial Optimization in Transportation and Logistics Networks. In: Pardalos, P., Du, DZ., Graham, R. (eds) Handbook of Combinatorial Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7997-1_63
Download citation
DOI: https://doi.org/10.1007/978-1-4419-7997-1_63
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-7996-4
Online ISBN: 978-1-4419-7997-1
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering