The Package Server Location Problem

Arnaud Malapert, Jean-Charles Régin, Jean Parpaillon


In this paper, we introduce a new multi-objective optimization problem derived from a real-world application: the package server location problem. A number of package servers are to be located at nodes of a network. Demand for these package servers is located at each node, and a subset of nodes are to be chosen to locate one or more package servers. Each client is statically associated to a package server. The objective is to minimize the number of package servers while maximizing the efficiency and the reliability of the broadcast of packages to clients. These objectives are contradictory: the broadcast becomes more efficient as the number of servers increases. This problem is analyzed as a multi-objective optimization problem and a mathematical formulation is proposed. In addition, the criteria combination can be specified via a small dedicated language. Results for exact multi-objective solution approaches based on mixed integer linear programming are reported.


  1. Aboolian, R., Berman, O., and Drezner, Z. (2009). The multiple server center location problem. Annals of Operations Reseach, 167:337-352.
  2. Alves, M. J. and Clímaco, J. (2007). A review of interactive methods for multiobjective integer and mixed-integer programming. European Journal of Operational Research, 180(1):99 - 115.
  3. Beamon, B. M. (1998). Supply chain design and analysis:: Models and methods. International Journal of Production Economics, 55(3):281 - 294.
  4. Berman, O. and Drezner, Z. (2007). The multiple server location problem. The Journal of the Operational Research Society, 58(1):91-99.
  5. Berman, O. and Krass, D. (2002). Recent Developments in the Theory and Applications of Location Models: A Preview. Annals of Operations Reseach, 111:15-16.
  6. Dantzig, G. B. (1960). On the significance of solving linear programming problems with some integer variables. Econometrica, 28:30-44.
  7. Ehrgott, M. (2000). Multicriteria optimization. SpringerVerlag.
  8. Ferris, M., Meyer, R., and D'Souza, W. (2006). Radiation Treatment Planning: Mixed Integer Programming Formulations and Approaches. In Appa, G., Pitsoulis, L., and Williams, H., editors, Handbook on Modelling for Discrete Optimization, volume 88 of International Series in Operations Research & Management Science, pages 317-340. Springer US. (2012). GNU Linear Programming
  9. Guignard-Spielberg, M. and Spielberg, K., editors (2005). Integer Programming: State of the Art and Recent Advances-Part I, volume 139. Annals of Operations Reseach.
  10. Gurobi Optimization (2012).
  11. Guttierez, G., Janota, M., Lynce, I., Lhomme, O., Manquinho, V., Marques-Silva, J., and Michel, C. (2011). Final version of the optimizations algorithms and tools. Technical report, Project Mancoosi: Managing the Complexity of the Open Source Infrastructure.
  12. Hu, X. and Eberhart, R. (2002). Multiobjective Optimization Using Dynamic Neighborhood Particle Swarm Optimization. In Congress on Evolutionary Computation (CEC'2002), volume 2, pages 1677-1681, Piscataway, New Jersey. IEEE Service Center.
  13. IBM (2012). IBM Ilog Cplex Optimizer.
  14. Iyoob, I., Zarifoglu, E., and Dieker, A. B. (2012). Cloud computing operations research. Service Science, Accepted.
  15. Johnson, D. S., Lenstra, J. K., and Kan, A. H. G. R. (1978). The Complexity of the Network Design Problem. Networks, 8:279-285.
  16. Sawaragi, Y., Nakayama, H., and Tanino, T. (1985). Theory of Multiobjective Optimization. Mathematics in Science and Engineering. Academic Press.
  17. Sherali, H. D., Bae, K.-H., and Haouari, M. (2010). Integrated Airline Schedule Design and Fleet Assignment: Polyhedral Analysis and Benders' Decomposition Approach. INFORMS Journal on Computing, 22(4):500.
  18. Steuer, R. E. (1986). Multiple Criteria Optimization: Theory, Computation and Application. John Wiley, New York.
  19. Wu, T. and Shi, L. (2011). Mathematical models for capacitated multi-level production planning problems with linked lot sizes. International Journal of Production Research, 49(20):6227-6247.
  20. Wu, T., Shi, L., Geunes, J., and Akartunali, K. (2011). An optimization framework for solving capacitated multilevel lot-sizing problems with backlogging. European Journal of Operational Research, 214(2):428 - 441.
  21. Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making. Systems, Man and Cybernetics, IEEE Transactions on, 18:183-190.

Paper Citation

in Harvard Style

Malapert A., Régin J. and Parpaillon J. (2013). The Package Server Location Problem . In Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-8565-40-2, pages 193-204. DOI: 10.5220/0004282501930204

in Bibtex Style

author={Arnaud Malapert and Jean-Charles Régin and Jean Parpaillon},
title={The Package Server Location Problem},
booktitle={Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

in EndNote Style

JO - Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - The Package Server Location Problem
SN - 978-989-8565-40-2
AU - Malapert A.
AU - Régin J.
AU - Parpaillon J.
PY - 2013
SP - 193
EP - 204
DO - 10.5220/0004282501930204