Flexible Services and Manufacturing Journal

, Volume 26, Issue 4, pp 565–584 | Cite as

Scheduling movements in the network of an express service provider

  • Ilse Louwerse
  • Jos Mijnarends
  • Ineke Meuffels
  • Dennis Huisman
  • Hein Fleuren


Express service providers manage shipments from senders to receivers under strict service level agreements. Such shipments are usually not sufficient to justify a single transportation, so it is preferred to maximize consolidation of these shipments to reduce cost. The consolidation is organized via depots and hubs: depots are local sorting centers that take care of the collection and delivery of the parcels at the customers, and hubs are used to consolidate the transportation between the depots. A single transportation between two locations, carried out by a certain vehicle at a specific time, is defined as a movement. In this paper, we address the problem of scheduling all movements in an express network at minimum cost. Our approach allows to impose restrictions on the number of arriving/departing movements at the hubs so that sufficient handling capacity is ensured. As the movement scheduling problem is complex, it is divided into two parts: one part concerns the movements between depots and hubs; the other part considers the movements between the hubs. We use a column generation approach and a local search algorithm to solve these two subproblems, respectively. Computational experiments show that by using this approach the total transportation costs are decreased.


Express service provider Movement scheduling Integer programming Column generation Local search 


  1. Aarts EHL, Lenstra JK (2003) Local search in combinatorial optimization. Princeton University Press, PrincetonMATHGoogle Scholar
  2. Armacost AP, Barnhart C, Ware KA (2002) Composite variable formulations for express shipment service network design. Transp Sci 36(1):1–20MATHCrossRefGoogle Scholar
  3. Armacost AP, Barnhart C, Ware KA, Wilson AM (2004) UPS optimizes its air network. Interfaces 34(1):15–25CrossRefGoogle Scholar
  4. Baltz A, Dubhashi D, Srivastav A, Tansini L, Werth S (2007) Probabilistic analysis for a multiple depot vehicle routing problem. Random Struct Algorithms 30(1–2):206–225MATHMathSciNetCrossRefGoogle Scholar
  5. Barnhart C, Johnson EL, Nemhauser GL, Savelsbergh MWP, Vance PH (1998) Branch-and-price: column generation for solving huge integer programs. Oper Res 46(3):316–329MATHMathSciNetCrossRefGoogle Scholar
  6. Barnhart C, Schneur RR (1996) Air network design for express shipment service. Oper Res 44(6):852–863MATHCrossRefGoogle Scholar
  7. Cordeau JF, Gendreau M, Laporte G (1997) A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks 30(2):105–119MATHCrossRefGoogle Scholar
  8. Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to algorithms. The MIT University Press, CambridgeMATHGoogle Scholar
  9. Crainic TG (2000) Service network design in freight transportation. Eur J Oper Res 122(2):272–288MATHCrossRefGoogle Scholar
  10. Dejax PJ, Crainic TG (1987) A review of empty flows and fleet management models in freight transportation. Transp Sci 21(4):227–248CrossRefGoogle Scholar
  11. Farvolden JM, Powell WB (1994) Subgradient methods for the service network design problem. Transp Sci 28(3):256–272MATHMathSciNetCrossRefGoogle Scholar
  12. Holmberg K, Hellstrand J (1998) Solving the uncapacitated network design problem by a lagrangean heuristic and branch-and-bound. Oper Res 46(2):247–259MATHMathSciNetCrossRefGoogle Scholar
  13. Leung JMY, Magnanti TL, Singhal V (1990) Routing in point-to-point delivery systems: Formulations and solution heuristics. Transp Sci 24(4):245–260MATHCrossRefGoogle Scholar
  14. Lübbecke ME, Desrosiers J (2005) Selected topics in column generation. Oper Res 53(6):1007–1023MATHMathSciNetCrossRefGoogle Scholar
  15. Magnanti TL, Mirchandani P (1993) Shortest paths, single origin-destination network design, and associated polyhedra. Networks 23(2):103–121MATHMathSciNetCrossRefGoogle Scholar
  16. Magnanti TL, Wong RT (1984) Network design and transportation planning: Models and algorithms. Transp Sci 18(1):1–55CrossRefGoogle Scholar
  17. Meuffels I, Fleuren H, Poppelaars J, Hoornenborg H, De Rooij F (2010) The design of express networks in a nutshell—playing the global optimisation game (GO-Game). OR News 39:6–8Google Scholar
  18. Mitrović-Minić S, Laporte G (2006) The pickup and delivery problem with time windows and transshipment. INFOR 44(3):217–228MathSciNetGoogle Scholar
  19. Pedersen MB, Crainic TG, Madsen OBG (2009) Models and tabu search metaheuristics for service network design with asset-balance requirements. Transp Sci 43(2):158–177CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Ilse Louwerse
    • 1
  • Jos Mijnarends
    • 1
  • Ineke Meuffels
    • 2
  • Dennis Huisman
    • 1
  • Hein Fleuren
    • 2
  1. 1.Erasmus University RotterdamRotterdamThe Netherlands
  2. 2.Tilburg UniversityTilburgThe Netherlands

Personalised recommendations