An Algorithm to Solve a Two-Level Resource Control Pre-Emptive Hierarchical Programming Problem

  • C. Subhash Narula
  • D. Adiele Nwosu
Part of the International Centre for Mechanical Sciences book series (CISM, volume 289)


Recently the two¡ªlevel resource control pre¡ªemptive hierarchical programming problem has attracted much attention in the literature. However it is usually discussed under the misnomer 2¡ªlevel linear programming problem. By taking into consideration the sequential nature of the decision making process in this problem, we develop an efficient algorithm to solve the problem. The proposed algorithm uses regular simplex pivots with a few modifications to select the variables to enter and leave the basis. The algorithm is illustrated with an example.


Linear Programming Problem Resource Control Regular Simplex Level Decision Maker Pivot Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Bard, J. F. (1983). An efficient point algorithm for a linear two—stage optimization problem. Operations Research, 31, 670–684.CrossRefMATHMathSciNetGoogle Scholar
  2. Bard, J. F. and Falk, J. E. (1982). An explicit solution to the multilevel programming problem. Comput. Opns. Res., 9, 77–100.Google Scholar
  3. Bialas, W. F. and Karwan, M. H. (1981). Two—level linear programming: A primer. Technical Report, Department of Industrial Engineering, SUNY at Buffalo.Google Scholar
  4. Bialas, W. F. and Karwan, M. H. (1982). On two—level optimization. IEEE Transactions on Automatic Control, AC-27, 211–214.Google Scholar
  5. Bialas, W. F.,Karwan, M. H. and Shaw, J. P. (1980). A parametric complementary pivot approach for two—level linear programming. Research Report No. 80–2, Dept. of Industrial Engineering, SUNY at Buffalo.Google Scholar
  6. Candler, W. and Townsley, R. (1982). A linear two—level programming problem. Comput. Opns. Res., 9, 59–76.CrossRefMathSciNetGoogle Scholar
  7. Fortuny—Amat and McCarl, B. (1981). A representation and economic interpretation of a two—level programming problem. J. Operational Res. Soc., 32, 783–792.Google Scholar
  8. Narula, S. C. and Nwosu, A. D. (1983). Two—level hierarchical programming problem. Multiple Criteria Decision Making — Theory and Application (P. Hansen, Editor ), Springer Verlag, 290–299.Google Scholar
  9. Nwosu, A. D. (1983). Pre—emptive hierarchical programming problem: A decentralized decision model. Unpublished Ph.D. dissertation. Department of Operations Research and Statistics, Rensselaer Polytechnic Institute, Troy, New York.Google Scholar
  10. Wen, U. (1981). Mathematical methods for multi—level linear programming. Unpublished Ph.D. dissertation, Department of industrial Engineering, SUNY at Buffalo, Buffalo, New York.Google Scholar

Copyright information

© Springer-Verlag Wien 1985

Authors and Affiliations

  • C. Subhash Narula
    • 1
  • D. Adiele Nwosu
    • 2
  1. 1.School of BusinessVirginia Commonwealth UniversityUSA
  2. 2.Department of MathematicsUniversity of NigeriaNigeria

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