Abstract
Network models are attractive because of their computational efficiency. Network applications can involve multiple objective analysis. Multiple objective analysis requires generating nondominated solutions in various forms. Two general methods exist to generate new solutions in continuous optimization: changing objective function weights and inserting objective bounds through constraints. In network flow problems, modifying weights is straightforward, allowing use of efficient network codes. Use of bounds on objective attainment levels can provide a more controlled generation of solutions reflecting tradeoffs among objectives. To constrain objective attainment, however, would require a side constrained network code, sacrificing some computational efficiency for greater model flexibility. We develop reoptimization procedures for the side constrained problem and use them in conjunction with simplex-based techniques. Our approach provides a useful tool for generating solutions allowing greater decision maker control over objective attainments, allowing multiobjective analysis of large-scale problems. Results are compared with solutions obtained from the computationally more attractive weighting technique. Reoptimization procedures are discussed as a means of more efficiently conducting multiple objective network analyses.
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References
V. Srinivasan and G.L. Thompson, Accelerated algorithms for labeling and relabeling of trees, with applications to distribution problems, Journal of the Association for Computing Machinery 19, 4(1972)712.
V. Srinivasan and G.L. Thompson, Benefit-cost analysis of coding techniques for the primal transportation algorithm, Journal of the Association for Computing Machinery 20, (1973)194.
J. Kennington and R. Helgason,Algorithms for Network Programming (Wiley, New York, 1980).
S. Chen and R. Saigal, A primal algorithm for solving a capacitated network flow problem with additional linear constraints, Networks 7(1977)59.
B. Roy and P. Vincke, Multicriteria analysis: Survey and new directions, Eur. J. Oper. Res. 8(1981)207.
G.W. Evans, An overview of techniques for solving multiobjective mathematical programs, Management Science 30(1984)1268.
R.E. Rosenthal, Principles of multiobjective optimization, Decision Sciences 16(1985)133.
R.E. Steuer,Multiple Criteria Optimization: Theory, Computation and Application (Wiley, New York, 1986).
S. Ziontz and J. Wallenius, Identifying efficient vectors: Some theory and computational results, Oper. Res. 28(1980)788.
R.E. Steuer, An interactive multiple objective linear programming procedure, TIMS Studies in the Management Sciences 6(1977)225.
V. Srinivasan and G.L. Thompson, Algorithms for minimizing total cost bottleneck time and bottleneck shipment in transportation problems, Naval Research Logistics Quarterly 23 (1976)567.
Y.Y. Haimes, W. Hall and H. Freedman,Multiobjective Optimization in Water Resource Systems: The Surrogate Worth Trade-Off Method (Elsevier, Amsterdam, 1975).
D. Klingman and N. Phillips, Topological and computational aspects of preemptive multicriteria military personnel assignment problems, Management Science 30(1984)1362.
T.T. Liang and T.J. Thompson, A large-scale personnel assignment model for the Navy, Decision Sciences 18, 2(1987)234.
R. Benayoun, O. Larichev, J. de Montgolfier and J. Tergny, Linear programming with multiple objective functions: The method of constraints, Automatic and Remote Control 32(1971)1257.
A. Ali, E. Allen, R. Barr and J. Kennington, Reoptimization procedures for bounded variable primal simplex network algorithms, Eur. J. Oper. Res. 23(1986)256.
E. Hellerman and D. Rarick, Reinversion with the preassigned pivot procedure, Math. Progr. 1(1971)195.
F. Glover, D. Karney and D. Klingman, Implementation and computational comparisons of primal, dual and primal-dual computer codes for minimum cost network flow problems, Networks 4(1974)191.
D. Klingman, A. Napier and J. Stutz, NETGEN: A program for generating large-scale minimum cost flow network problems, Management Science 20(1974)814.
R.S. Barr, F. Glover and D. Klingman, Enhancements of spanning tree labeling procedures for network optimization, INFOR 17(1979)16.
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Olson, D.L., Shetty, B., Venkataramanan, M.A. et al. Network reoptimization procedures for multiobjective network probelems. Ann Oper Res 20, 219–232 (1989). https://doi.org/10.1007/BF02216930
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DOI: https://doi.org/10.1007/BF02216930