A Network Model for the Hospital Routing Problem

Arash Rafiey, Vladyslav Sokol, Ramesh Krishnamurti, Snezana Mitrovic Minic, Abraham Punnen, Krishna Teja Malladi

Abstract

We consider the problem of routing samples taken from patients to laboratories for testing. These samples are taken from patients housed in hospitals, and are sent to laboratories in other hospitals for testing. The hospitals are distributed in a geographical area, such as a city. Each sample has a deadline, and all samples have to be transported within their deadlines. We have a fixed number of vehicles as well as an unlimited number of taxis available to transport the samples. The objective is to minimize a linear function of the total distance travelled by the vehicles and the taxis. We provide a mathematical programming formulation for the problem using the multi-commodity network flow model, and solve the formulation using CPLEX, a general-purpose MIP solver. We also provide a computational study to evaluate the solution procedure.

References

  1. Brønmo, G., Christiansen, M., Fagerholt, K., and Nygreen, B. (2007). A multi-start local search heuristic for ship scheduling - a computational study. In Computers & Operations Research 34(1), pp 900-917.
  2. Brysy, O. and Gendreau, M. (2005). Vehicle routing problem with time windows, part i: Route construction and local search algorithms. In Transportation Science 39(1), pp 104-118.
  3. Ceder, A. (2003). Designing public transport network and routes. In Advanced Modeling for Transit Operations and Service Planning, W. H. K. Lam, M. G. H. Bell (eds), pp 59-91. Emerald Group Publishing Limited, Bingley.
  4. Christiansen, M., Fagerholt, K., and Ronen, D. (2004). Ship routing and scheduling: Status and perspectives. In Transportation Science 38(1), pp 1-18.
  5. Cordeau, J. F., Laporte, G., Savelsbergh, M. W. P., and Vigo, D. (2007). Vehicle routing. In Transportation, Handbooks in Operations Research and Management Science, Volume 14, C. Barnhart and G. Laporte (eds), pp 367-428. Elsevier, Amsterdam.
  6. Cortés, C. E., Matamala, M., and Contardo, C. (2010). The pickup and delivery problem with transfers: Formulation and a branch-and-cut solution method. In European Journal of Operational Research 200, pp 711- 724.
  7. Desrochers, M., Desrosiers, J., and Solomon, M. (1992). A new optimization algorithm for the vehicle routing problem with time windows. In Operations Research 40, pp 342-354.
  8. Golden, B. L., Raghavan, S., and Wasil, E. A. (2008). The vehicle routing problem: Latest advances and new challenges. In Operations Research/Computer Science Interfaces Series, Vol. 43. Springer.
  9. Gopalan, R. and Talluri, K. T. (1998). Mathematical models in airline schedule planning: A survey. In Annals of Operations Research 76, pp 155-185.
  10. Grasas, A., Ramalhinho, H., Pessoa, L. S., Resende, M. G. C., Caball, I., and Barba, N. (2014). On the improvement of blood sample collection at clinical laboratories. In BMC Health Services Research 14(12), 9 pages (DOI:10.1186/1472-6963-14-12).
  11. Kallehauge, B., Larsen, J., Madsen, O. B. G., and Solomon, M. M. (2005). Vehicle routing problem with time windows. In Column Generation, G. Desaulniers, J. Desrosiers, M. M. Solomon (eds), pp 67-98. Springer.
  12. Karapetyan, D. and Punnen, A. P. (2013). A reduced integer programming model for the ferry scheduling problem. In Public Transport 4(3), pp 151-163.
  13. Kohl, N., Desrosiers, J., Madsen, O. B. G., Solomon, M. M., and Soumis, F. (1999). 2-path cuts for the vehicle routing problem with time windows. In Transportation Science 33(1), pp 101-116.
  14. Kohl, N. and Madsen, O. B. G. (1997). An optimization algorithm for the vehicle routing problem with time windows based on lagrangian relaxation. In Operations Research 45(3), pp 395-406.
  15. Laporte, G. (1992). The vehicle routing problem: An overview of exact and approximate algorithms. In European Journal of Operational Research 59(3), pp 345-358.
  16. Laporte, G., Gendreau, M., Potvin, J.-Y., and Semet, F. (2000). Classical and modern heuristics for the vehicle routing problem. In International transactions in operational research 7(4-5), pp 285-300.
  17. Minic, S. M. (1998). Pickup and delivery problem with time windows: A survey. In Simon Fraser University, School of Computing Science, CMPT TR 1998-12.
  18. Minic, S. M. and Laporte, G. (2006). The pickup and delivery problem with time windows and transshipment. In INFOR 44(3), 217-227.
  19. Minic, S. M. and Punnen, A. (2011). Scheduling of a heterogeneous fleet of re-configurable ferries: a model, a heuristic, and a case study. In OR 2011 - International Conference on Operations Research, Zurich, Switzerland.
  20. Rais, A. and Viana, A. (2010). Operations research in healthcare: a survey. In International Transactions in Operational Research 18, pp 1-31.
  21. Savelsbergh, M. W. P. and Sol, M. (1995). The general pickup and delivery problem. In Transportation Science, 29 (1), pp 17-29.
  22. Toth, P. and Vigo, D. (2002). The vehicle routing problem. In SIAM.
Download


Paper Citation


in Harvard Style

Rafiey A., Sokol V., Krishnamurti R., Mitrovic Minic S., Punnen A. and Teja Malladi K. (2015). A Network Model for the Hospital Routing Problem . In Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-075-8, pages 353-358. DOI: 10.5220/0005219203530358


in Bibtex Style

@conference{icores15,
author={Arash Rafiey and Vladyslav Sokol and Ramesh Krishnamurti and Snezana Mitrovic Minic and Abraham Punnen and Krishna Teja Malladi},
title={A Network Model for the Hospital Routing Problem},
booktitle={Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2015},
pages={353-358},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005219203530358},
isbn={978-989-758-075-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - A Network Model for the Hospital Routing Problem
SN - 978-989-758-075-8
AU - Rafiey A.
AU - Sokol V.
AU - Krishnamurti R.
AU - Mitrovic Minic S.
AU - Punnen A.
AU - Teja Malladi K.
PY - 2015
SP - 353
EP - 358
DO - 10.5220/0005219203530358