MIP Models for Solving 3-Dimensional Packing Problems Arising in Space Engineering

  • Giorgio Fasano
Part of the Applied Optimization book series (APOP, volume 79)


In space engineering payload or cargo accommodation activities are quite challenging. Hard combinatorial multidimensional packing issues, in the presence of additional conditions, frequently arise and a specific approach is necessary. The work presented in this chapter focuses on a modeling (non-algorithmic) approach. A basic mixed integer programming model has been implemented to treat an orthogonal three-dimensional packing issue with rotations. The approach proposed seems quite suitable in practice, as the introduction of additional conditions is straightforward for significant applications (including tetris-like problems). The basic mixed integer programming mathematical model is described together with an extended formulation. A heuristic procedure is presented and some data concerning the computational experience are reported.


three-dimensional orthogonal packing additional conditions tetris-like problems mixed integer programming heuristics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Amadieu P. The European Transfer Vehicle Mission and System Concept. 48th International Astronautical Federation Congress, Turin (Italy), Oct.1997.Google Scholar
  2. [2]
    Amiouny S., Bartholdi J., Vate J.V., Zhang J. Balanced loading. Operations Research, 40 238–246, 1992.zbMATHCrossRefGoogle Scholar
  3. [3]
    Bischoff E., Marriott M. A comparative evaluation of heuristics for container loading. European Journal of Operational Research, 44 267–276, 1990.zbMATHCrossRefGoogle Scholar
  4. [4]
    Brinkley R. H. et al. International Space Station: an Overview. 48th International Astronautical Federation Congress, Turin (Italy), Oct. 1997.Google Scholar
  5. [5]
    Bussolino L., Fasano G., Novelli A. A cargo accommodation problem for a space vehicle: The CAST project. In this book 13–26.Google Scholar
  6. [6]
    Coffman E., Garey J.M., Johnson D. Approximation Algorthms for Bin Packing: A Survey. Boston: PWS Publishing Company, 1997Google Scholar
  7. [7]
    Colaneri L., Delia Croce F., Perboli G., Tadei R. A Heuristic Procedure for the Space Cargo Rack Configuration Problem. In this book 27–42.Google Scholar
  8. [8]
    Daughtrey R. S. et al. A Simulated Annealing Approach to 3-D Packing with Multiple Constraints, Boeing Huntsville AI Center. Huntsville (Alabama): Cosmic Program MFS28700, 1991.Google Scholar
  9. [9]
    Dyckhoff H., Scheithauer G., Terno J. Cutting and Packing. In Annotated Bibliographies in Combinatorial Optimization, M. Del Pamico et al. (eds), Chichester: Wiley, 1997.Google Scholar
  10. [10]
    Fasano G., Cargo analytical integration in space engineering: A three-dimensional packing model. In Operations Research in Industry, Ciriani T. A., Gliozzi S., Johnson E.L., R. Tadei (eds), London: Macmillan, 1999.Google Scholar
  11. [11]
    Fekete S.P., Schepers J. On more-dimensional packing. Tech. Report 288–9–90, ZPR, 1997.Google Scholar
  12. [12]
    Hadjiconstantinou E., Christofides N. An exact algorithm for general orthogonal two-dimensional knapsack problems. European Journal of Operational Research, 83 39–56, 1995.zbMATHCrossRefGoogle Scholar
  13. [13]
    IBM, Optimization Subroutines Library Guide and Reference, Version 3. Form SC23–0519, IBM Corporation, 2001.Google Scholar
  14. [14]
    Martello S., Pisinger D., Vigo D. The three-dimensional bin packing problem. Operations Research, 48 256–267, 2000.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    Martello S., Vigo D. Exact solution of the two-dimensional finite bin packing problem. Management Science, 44 388–399, 1998.zbMATHCrossRefGoogle Scholar
  16. [16]
    Mathur K. An Integer Programming-based Heuristic for the Balanced Loading Problem. Operations Research Letters, 22 19–25, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  17. [17]
    Mohanty B.B., Mathur K., Ivancic N.J. Value considerations in three-dimensional packing — a heuristic procedure using the fractional knapsack problem. European Journal of Operational Research, 74 143–151, 1994.zbMATHCrossRefGoogle Scholar
  18. [18]
    Nemhauser G.L., Wolsey L.A., Integer and Combinatorial Optimization. New York: Wiley, 1988.zbMATHGoogle Scholar
  19. [19]
    Padberg M. Packing Small Boxes into a Big Box, New York Univ. Off. of Naval Research, N00014–327, 1999.Google Scholar
  20. [20]
    Williams H.P. Model Building in Mathematical Programming, 4th Edition, London: Wiley, 1999.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Giorgio Fasano
    • 1
  1. 1.Alenia Spazio S.p.A.TorinoItaly

Personalised recommendations