## Finding all maximal efficient faces in multiobjective linear programming.(English)Zbl 0795.90054

Summary: An algorithm for finding the whole efficient set of a multiobjective linear program is proposed. From the set of efficient edges incident to a vertex , a characterization of maximal efficient faces containing the vertex is given. By means of the lexicographic selection rule of Dantzig, Orden and Wolfe, a connectedness property of the set of dual optimal bases associated to a degenerate vertex is proved. An application of this to the problem of enumerating all the efficient edges incident to a degenerate vertex is proposed. Our method is illustrated with numerical examples and comparisons with Armand-Malivert’s algorithm show that this new algorithm uses less computer time.

### MSC:

 90C29 Multi-objective and goal programming 90C05 Linear programming
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### References:

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