An interactive multiple objective linear programming method based on piecewise-linear additive value functions

Zionts and Wallenius have recently discussed how their method for interactive multiple objective linear programming may be extended to handle pseudoconcave utility functions. They do not, however, specify how an implied interactive search over faces of the simplex is to be done. In a different development, Jacquet-Lagrèze and Siskos have introduced, in their UTA method, the idea of approximating a utility function by a piecewise-linear additive form, i.e., a separable programming approach. It is shown how these two concepts can be brought together in an interactive method for multiple objective linear programming, which avoids the unspecified search of Zionts and Wallenius but is nevertheless still able to approximate the true preferred solution when the utility function is concave. This method is applied to two hypothetical problems, and its performance is compared with that of the Zionts-Wallenius procedure.