An interactive multiple objective linear programming method based on piecewise-linear additive value functions. (English) Zbl 0644.90086

Stewart, Theodor J.

IEEE Trans. Syst. Man Cybern. 17, No. 5, 799-805 (1987).

The procedure proposed in this paper can be seen as an extension of the later version of the Zionts-Wallenius algorithm [cf. S. Zionts and J. Wallenius, Manage. Sci. 29, 519-529 (1983; Zbl 0519.90083)]. It uses the idea of approximating a utility function by a piecewise-linear additive form introduced in the UTA method by Jacquet-Lagrèze and Siskos [cf. E. Jacquet-Lagrèze and J. Siskos, Eur. J. Oper. Res. 10, 151-164 (1982; Zbl 0481.90078)]. Provided that the DM’s preferences can be represented by an additive value function with concave terms, the method, through a series of pairwise comparisons in the Zionts-Wallenius sense, allows the DM’s most preferred solution to be approximated, even when this is not a basic solution to the original problem.
It is worth noting that, independently, another procedure has been proposed, based on an interactive assessment of a piecewise-linear utility function for multiobjective linear programming [cf. E. Jacquet-Lagrèze, R. Meziani and the reviewer, ibid. 31, 350-357 (1987; Zbl 0636.90083)]. Instead of using the scheme of the Zionts-Wallenius algorithm, it uses a linear regression method for approximating the DM’s preferences by an additive utility function.

Reviewer: R.Słowinski

MSC:

90C31	Sensitivity, stability, parametric optimization
91B16	Utility theory
90B50	Management decision making, including multiple objectives
90C05	Linear programming

Keywords:

multiobjective linear programming; interactive method; additive utility function

Citations:

Zbl 0519.90083; Zbl 0481.90078; Zbl 0636.90083