In this paper, a parametric programming approach is proposed for the analysis of linear process engineering problems under uncertainty. A novel branch and bound algorithm is presented for the solution of mixed-integer linear programming problems where n right-hand-side parameters are allowed to vary independently. The procedure, based on the solution of multiparametric linear programs at each node of the tree search and special bounding procedures, identifies the different optimal integer solutions and their corresponding optimal value functions as the uncertain parameters vary within given ranges. Three examples are presented to illustrate the basic steps of the algorithm and its applicability to process engineering problems.