Operations Research Letters 24 (1999) 139–148 www.elsevier.com/locate/orms An algorithm for multiparametric mixed-integer linear programming problems Joaqu n Acevedo 1 , Efstratios N. Pistikopoulos ∗ Centre for Process Systems Engineering, Imperial College, London SW7 2BY, UK Received 1 November 1996; received in revised form 1 December 1998 Abstract In this paper, the problem of solving multiparametric 0 –1 mixed-integer linear programming models is considered. A novel Branch and Bound algorithm is described based on successive solutions of parametric linear programs where n right-hand side parameters are allowed to vary independently. Numerical examples are presented to illustrate the basic steps and the potential of the proposed procedure. c  1999 Elsevier Science B.V. All rights reserved. Keywords: Parametric programming; Mixed-integer optimization; Optimization under uncertainty 1. Introduction Mathematical models involving uncertainty arise naturally in practical applications primarily due to the lack of exact and reliable data to model real systems. It is not surprising then that the eld of optimization under uncertainty has received a lot of attention over the last decades. For example, sensitivity analysis and parametric programming have been widely used to an- alyze the eect of parameter changes on the optimal solution of a linear programming model, to quantify the robustness of this solution and to compare it to other optimal or near optimal solutions that may arise * Corresponding author. Fax: +44 0171 594 6606. E-mail addresses: jacevedo@campus.mty.itesm.mx (J. Acevedo), e.pistikopoulos@ic.ac.uk (E.N. Pistikopoulos). 1 Present address: Dept. of Chem. Eng., ITESM, Monterrey, Mexico. as the parameters of the model move away from a “nominal” point. The extension of these techniques to mixed-integer problems, however, has been rather limited, mainly due to the computational complexity of the prob- lem, and the theoretical limitations of the algo- rithms presented (e.g. monotonicity, single-parameter changes, etc.). For parametric mixed-integer linear (pMILP) programs, approaches that have been pro- posed in the open literature can be broadly classied as (i) generalizations of the Branch and Bound al- gorithm (see e.g. [6]), (ii) cutting plane methods (e.g. [5]), and (iii) bounding procedures based on the convexity= concavity properties of the paramet- ric LP solution (e.g. [3]). A thorough review of the theory and applications of pMILP can be found in [4]. All these algorithms, however, share a com- mon limitation: they are applicable to the case of single parameterization, i.e. they do not explicitly 0167-6377/99/$ - see front matter c  1999 Elsevier Science B.V. All rights reserved. PII:S0167-6377(99)00017-6