The authors consider an optimization problem in which Max[cjxj,1•i•p;j∈Si] is to be minimized subject to linear constraints, where (S1,S2,...,Sp) is a partition of the index set of the decision variables. The parametric analysis of a linear programme with parametric generalised upper bounds, equivalent to this problem, is developed. Using this parametric analysis, two algorithms have been designed to solve the problem. Computational results show that both these algorithms are better than the simplex algorithm used directly on a linear programme equivalent to the problem considered in this paper.
