Telephone: +43 2236 71521Telex: 079 137 iiasa a D Telefax: +43 2236 71313 ForewordOne of the main problems with mathematical modelling is always the lack of knowledge about the real world to be modelled. There are several quite natural approaches for modelling uncertainty, vagueness and lack of knowledge. However, it is usually not easy to find modelling approaches which are intuitively clear as well as analytically tractable.In the present paper, lack of knowledge is represented by interval values for coefficients of the objective function in a linear programming model. This modelling approach is natural and straightforward. In the present paper, the authors enhance the analytical tractability of this model by introducing a new way of generating solutions, which are frequently more preferable than the ones obtained by previous treatments. AbstractIn this paper, we focus on a treatment of a linear programming problem with an interval objective function. From the viewpoint of the achievement rate, a new solution concept, a maximin achievement rate solution is proposed. Nice properties of this solution are shown: a maximin achievement rate solution is necessarily optimal when a necessarily optimal solution exists, and if not, then it is still a possibly optimal solution. An algorithm for a maximin achievement rate solution is proposed based on a relaxation procedure together with a simplex method. A numerical example is given to demonstrate the proposed solution algorithm.