1. ¹Algorithmics Incorporated, Ontario, Canada
2. ²University of Colorado, Colorado, USA

Correspondence: Dr M Laguna, Graduate School of Business Administration, University of Colorado at Boulder, Boulder, Colorado, 80309-0419 USA. E-mail: manuel.laguna@colorado.edu

Received October 1997; Accepted April 1999.

Abstract

The minimax relative regret solution to a linear programme with interval objective function coefficients can be found using an algorithm that, at each iteration, solves a linear programme to generate a candidate solution and a mixed integer programme (MIP) to find the corresponding maximum regret. This paper first shows that there exists a regret-maximising solution in which all uncertain costs are at a bound, and then uses this to derive a MIP formulation that maximises the regret of a candidate solution. Computational experiments demonstrate that this approach is effective for problems with up to 50 uncertain objective function coefficients, significantly improving upon the existing enumerative method.