Stability set for integer linear goal programming Omar M. Saad, Walied H. Sharif * Department of Mathematics, College of Science, Qatar University, P.O. Box 2713, Doha, Qatar Abstract In this paper we present an iterative goal programming approach for solving mul- tiobjective integer linear programming problems. After illustrating the approach we give the definition of, and an algorithm to determine the stability set of the first kind for multiobjective problems of all-integer variables and with parameters in the right-hand side of the constraints. Finally, the paper is concluded together with some points for further research. Ó 2003 Elsevier Inc. All rights reserved. Keywords: Goal programming; Multiobjective integer linear programming; Stability 1. Introduction Goal programming is one of several approaches that have been proposed for the modeling, solution and analysis of multiobjective mathematical program- ming problems. There are a wide variety of goal programming models in- cluding weighted goal programming [2,5], lexicographic goal programming i.e. the use of the so-called ‘‘preemptive priority’’ concept [5,7], minimax goal programming includes fuzzy programming [13], and interactive goal pro- gramming which is used to generate a subset of non-dominated solutions [6,11]. Integer goal programming methods for all-integer, mixed-integer and zero- one multiple objective problems have been introduced by Lee and Morris [9]. * Corresponding author. E-mail address: w.sharif@qu.edu.qa (W.H. Sharif). 0096-3003/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0096-3003(03)00669-6 Applied Mathematics and Computation 153 (2004) 743–750 www.elsevier.com/locate/amc