Annals of Operations Research

, Volume 264, Issue 1–2, pp 477–498 | Cite as

Daily aircraft routing for amphibious ready groups

  • Ertan Yakıcı
  • Robert F. Dell
  • Travis Hartman
  • Connor McLemore
Original Research
  • 80 Downloads

Abstract

An Amphibious Ready Group (ARG) consists of ships capable of conducting flight operations that daily require the transport of personnel and cargo (PMC) to remain operationally viable. Planning daily PMC transport for ARG ships and nearby airfields is a unique vehicle routing problem characterized by a heterogeneous capacitated vehicle fleet, two cargo types, multiple depots, time windows, and synchronized routing of two aircraft required between some but not all node pairs. We formulate this problem as an integer linear program (ILP) with an objective function that expresses the cost of flight operations and a penalty for undelivered PMC. We perform extensive computational testing using an ILP solver and a tailored ant colony optimization with local search metaheuristic on test instances constructed to represent those found in practice. We find most instances difficult to solve optimally while our heuristic provides the best known or close to the best known solution in just a few minutes. We have embedded our heuristic in a decision support system complete with graphical user interface and sent this out for use by United States Navy ARG planners.

Keywords

Vehicle routing Integer linear programming Ant colony optimization Local search Military 

References

  1. Barbarosoğlu, G., Özdamar, L., & Cevik, A. (2002). An interactive approach for hierarchical analysis of helicopter logistics in disaster relief operations. European Journal of Operational Research, 140(1), 118–133.CrossRefGoogle Scholar
  2. Belanger, N., Desaulniers, G., Soumis, F., & Desrosiers, J. (2006). Periodic airline fleet assignment with time windows, spacing constraints, and time dependent revenues. European Journal of Operational Research, 175(3), 1754–1766.CrossRefGoogle Scholar
  3. Bent, R., & Van Hentenryck, P. (2006). A two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows. Computers & Operations Research, 33(4), 875–893.CrossRefGoogle Scholar
  4. Braekers, K., Caris, A., & Janssens, G. K. (2014). Exact and meta-heuristic approach for a general heterogeneous dial-a-ride problem with multiple depots. Transportation Research Part B: Methodological, 67, 166–186.CrossRefGoogle Scholar
  5. Bredström, D., & Rönnqvist, M. (2008). Combined vehicle routing and scheduling with temporal precedence and synchronization constraints. European Journal of Operational Research, 191(1), 19–31.CrossRefGoogle Scholar
  6. Brown, G. G., Carlyle, W. M., & Dell, R. F. (2013). Optimizing intratheater military airlift in iraq and afghanistan. Military Operations Research, 18(3), 35–52.CrossRefGoogle Scholar
  7. Cherkesly, M., Desaulniers, G., Irnich, S., & Laporte, G. (2016). Branch-price-and-cut algorithms for the pickup and delivery problem with time windows and multiple stacks. European Journal of Operational Research, 250(3), 782–793.CrossRefGoogle Scholar
  8. Cheung, R. K., Shi, N., Powell, W. B., & Simao, H. P. (2008). An attribute-decision model for cross-border drayage problem. Transportation Research Part E: Logistics and Transportation Review, 44(2), 217–234.CrossRefGoogle Scholar
  9. Cordeau, J.-F. (2006). A branch-and-cut algorithm for the dial-a-ride problem. Operations Research, 54(3), 573–586.CrossRefGoogle Scholar
  10. Cordeau, J.-F., & Laporte, G. (2003a). The dial-a-ride problem (darp): Variants, modeling issues and algorithms. Quarterly Journal of the Belgian, French and Italian Operations Research Societies, 1(2), 89–101.Google Scholar
  11. Cordeau, J.-F., & Laporte, G. (2003b). A tabu search heuristic for the static multi-vehicle dial-a-ride problem. Transportation Research Part B: Methodological, 37(6), 579–594.CrossRefGoogle Scholar
  12. Cordeau, J.-F., & Laporte, G. (2007). The dial-a-ride problem: Models and algorithms. Annals of Operations Research, 153(1), 29–46.CrossRefGoogle Scholar
  13. Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6(1), 80–91.CrossRefGoogle Scholar
  14. De Rosa, B., Improta, G., Ghiani, G., & Musmanno, R. (2002). The arc routing and scheduling problem with transshipment. Transportation Science, 36(3), 301–313.CrossRefGoogle Scholar
  15. Del Pia, A., & Filippi, C. (2006). A variable neighborhood descent algorithm for a real waste collection problem with mobile depots. International Transactions in Operational Research, 13(2), 125–141.CrossRefGoogle Scholar
  16. Desaulniers, G., Desrosiers, J., Erdmann, A., Solomon, M. M., & Soumis, F. (2002). Vrp with pickup and delivery. In SIAM monographs on discrete mathematics and applications, pp. 225–242.Google Scholar
  17. Desrosiers, J., Dumas, Y., & Soumis, F. (1986). A dynamic programming solution of the large-scale single-vehicle dial—a-ride problem with time windows. American Journal of Mathematical and Management Sciences, 6(3–4), 301–325.CrossRefGoogle Scholar
  18. Detti, P., Papalini, F., & de Lara, G. Z. M. (2017). A multi-depot dial-a-ride problem with heterogeneous vehicles and compatibility constraints in healthcare. Omega, 70, 1–14.CrossRefGoogle Scholar
  19. Dorigo, M., & Stützle, T. (2010). Ant colony optimization: overview and recent advances. In M. Gendreau & J.-Y. Potvin (Eds.), Handbook of metaheuristics (pp. 227–263). Springer.Google Scholar
  20. Drexl, M. (2012). Synchronization in vehicle routing-a survey of vrps with multiple synchronization constraints. Transportation Science, 46(3), 297–316.CrossRefGoogle Scholar
  21. Drexl, M. (2014). Branch-and-cut algorithms for the vehicle routing problem with trailers and transshipments. Networks, 63(1), 119–133.CrossRefGoogle Scholar
  22. Drexl, M., Rieck, J., Sigl, T., & Press, B. (2013). Simultaneous vehicle and crew routing and scheduling for partial- and full-load long-distance road transport. BuR Business Research, 6(2), 242–264.CrossRefGoogle Scholar
  23. Dumas, Y., Desrosiers, J., & Soumis, F. (1991). The pickup and delivery problem with time windows. European Journal of Operational Research, 54(1), 7–22.CrossRefGoogle Scholar
  24. Gribkovskaia, I., Halskau, O., & Kovalyov, M. Y. (2015). Minimizing takeoff and landing risk in helicopter pickup and delivery operations. Omega, 55, 73–80.CrossRefGoogle Scholar
  25. Grimault, A., Bostel, N., & Lehuédé, F. (2017). An adaptive large neighborhood search for the full truckload pickup and delivery problem with resource synchronization. Computers & Operations Research, 88, 1–14.CrossRefGoogle Scholar
  26. Gschwind, T. (2015). A comparison of column-generation approaches to the synchronized pickup and delivery problem. European Journal of Operational Research, 247(1), 60–71.CrossRefGoogle Scholar
  27. Halskau, Ø. (2014). Offshore helicopter routing in a hub and spoke fashion: Minimizing expected number of fatalities. Procedia Computer Science, 31, 1124–1132.CrossRefGoogle Scholar
  28. Ioachim, I., Desrosiers, J., Soumis, F., & Bélanger, N. (1999). Fleet assignment and routing with schedule synchronization constraints. European Journal of Operational Research, 119(1), 75–90.CrossRefGoogle Scholar
  29. Li, Y., Lim, A., & Rodrigues, B. (2005). Manpower allocation with time windows and job-teaming constraints. Naval Research Logistics (NRL), 52(4), 302–311.CrossRefGoogle Scholar
  30. Lim, A., Rodrigues, B., & Song, L. (2004). Manpower allocation with time windows. Journal of the Operational Research Society, 55(11), 1178–1186.CrossRefGoogle Scholar
  31. Madsen, O. B., Ravn, H. F., & Rygaard, J. M. (1995). A heuristic algorithm for a dial-a-ride problem with time windows, multiple capacities, and multiple objectives. Annals of operations Research, 60(1), 193–208.CrossRefGoogle Scholar
  32. Masmoudi, M. A., Braekers, K., Masmoudi, M., & Dammak, A. (2017). A hybrid genetic algorithm for the heterogeneous dial-a-ride problem. Computers & Operations Research, 81, 1–13.CrossRefGoogle Scholar
  33. Masmoudi, M. A., Hosny, M., Braekers, K., & Dammak, A. (2016). Three effective metaheuristics to solve the multi-depot multi-trip heterogeneous dial-a-ride problem. Transportation Research Part E: Logistics and Transportation Review, 96, 60–80.CrossRefGoogle Scholar
  34. Masson, R., Lehuédé, F., & Péton, O. (2013). An adaptive large neighborhood search for the pickup and delivery problem with transfers. Transportation Science, 47(3), 344–355.CrossRefGoogle Scholar
  35. Moreno, L., de Aragao, M. P., & Uchoa, E. (2006). Column generation based heuristic for a helicopter routing problem. In Experimental algorithms, pp. 219–230. Springer.Google Scholar
  36. Nanry, W. P., & Barnes, J. W. (2000). Solving the pickup and delivery problem with time windows using reactive tabu search. Transportation Research Part B: Methodological, 34(2), 107–121.CrossRefGoogle Scholar
  37. Nguyen, P. K., Crainic, T. G., & Toulouse, M. (2017). Multi-trip pickup and delivery problem with time windows and synchronization. Annals of Operations Research, 253(2), 899–934.CrossRefGoogle Scholar
  38. Ozdamar, L. (2011). Planning helicopter logistics in disaster relief. OR Spectrum, 33(3), 655–672.CrossRefGoogle Scholar
  39. Paquette, J., Cordeau, J.-F., Laporte, G., & Pascoal, M. M. (2013). Combining multicriteria analysis and tabu search for dial-a-ride problems. Transportation Research Part B: Methodological, 52, 1–16.CrossRefGoogle Scholar
  40. Parragh, S. N., Doerner, K. F., & Hartl, R. F. (2008). A survey on pickup and delivery problems. Journal für Betriebswirtschaft, 58(1), 21–51.CrossRefGoogle Scholar
  41. Pimenta, V., Quilliot, A., Toussaint, H., & Vigo, D. (2017). Models and algorithms for reliability-oriented dial-a-ride with autonomous electric vehicles. European Journal of Operational Research, 257(2), 601–613.CrossRefGoogle Scholar
  42. Rekiek, B., Delchambre, A., & Saleh, H. A. (2006). Handicapped person transportation: An application of the grouping genetic algorithm. Engineering Applications of Artificial Intelligence, 19(5), 511–520.CrossRefGoogle Scholar
  43. Ritzinger, U., Puchinger, J., & Hartl, R. F. (2016). Dynamic programming based metaheuristics for the dial-a-ride problem. Annals of Operations Research, 236(2), 341–358.Google Scholar
  44. Røpke, S., Cordeau, J.-F., & Laporte, G. (2007). Models and a branch-and-cut algorithm for pickup and delivery problems with time windows. Networks, 49(4), 258–272.CrossRefGoogle Scholar
  45. Røpke, S., & Pisinger, D. (2006). An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation Science, 40(4), 455–472.CrossRefGoogle Scholar
  46. Rousseau, L.-M., Gendreau, M., & Pesant, G. (2003). The synchronized vehicle dispatching problem. New York: Citeseer.Google Scholar
  47. Savelsbergh, M., & Sol, M. (1998). Drive: Dynamic routing of independent vehicles. Operations Research, 46(4), 474–490.CrossRefGoogle Scholar
  48. Schmid, V., Doerner, K. F., Hartl, R. F., & Salazar-González, J.-J. (2010). Hybridization of very large neighborhood search for ready-mixed concrete delivery problems. Computers & Operations Research, 37(3), 559–574.CrossRefGoogle Scholar
  49. Stentoft Arlbjørn, J., Qian, F., Gribkovskaia, I., & Halskau, Ø, Sr. (2011). Helicopter routing in the norwegian oil industry: Including safety concerns for passenger transport. International Journal of Physical Distribution & Logistics Management, 41(4), 401–415.CrossRefGoogle Scholar
  50. Stützle, T., & Hoos, H. (1997). Max-min ant system and local search for the traveling salesman problem. In 1997, IEEE international conference on evolutionary computation, pp. 309–314. IEEE.Google Scholar
  51. Stützle, T., & Hoos, H. H. (1996). Improving the ant system: A detailed report on the max–min ant system. FG Intellektik, FB Informatik, TU Darmstadt, Germany, Tech. Rep. AIDA–96–12.Google Scholar
  52. Stützle, T., & Hoos, H. H. (2000). Max–min ant system. Future Generation Computer Systems, 16(8), 889–914.CrossRefGoogle Scholar
  53. Timlin, M. T. F., & Pulleyblank, W. R. (1992). Precedence constrained routing and helicopter scheduling: Heuristic design. Interfaces, 22(3), 100–111.CrossRefGoogle Scholar
  54. Toth, P., & Vigo, D. (1996). Fast local search algorithms for the handicapped persons transportation problem. In Meta-Heuristics, pp. 677–690. Springer.Google Scholar
  55. Velasco, N., Castagliola, P., Dejax, P., Guéret, C., & Prins, C. (2009). A memetic algorithm for a pick-up and delivery problem by helicopter. In Bio-inspired algorithms for the vehicle routing problem, pp. 173–190. Springer.Google Scholar
  56. Wray, J. D. (2009). Optimizing helicopter assault support in a high demand environment. Master’s thesis, Monterey, California. Naval Postgraduate School.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Industrial Engineering Department, Turkish Naval AcademyNational Defense UniversityIstanbulTurkey
  2. 2.Operations Research DepartmentNaval Postgraduate SchoolMontereyUSA
  3. 3.Navy AssessmentsArlingtonUSA

Personalised recommendations