Abstract The bicriterion problem formulated as a 0–1 mixed integer linear programming problem is considered. The problem will be applied to a variety of applications, for example, process synthesis, process design, etc. By employment of the ϵ-constrained approach, the bicriterion problem is reformulated as a 0–1 parametric mixed integer linear programming problem. It is shown that a branch-and-bound algorithm for 0–1 parametric mixed integer linear programming developed previously by the present authors is successfully applied to obtain the complete set of Pareto optima for the bicriterion problem.