344 European Journal of Operational Research 68 (1993)344-351 North-Holland Theory and Methodology An interactive procedure for multiple objective integer linear programming problems Jasmina N. Karaivanova Institute of Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria Subhash C. Narula * Department of Mathematics, Link6ping Institute of Technology, S-581 83 Link6ping, Sweden Vassil Vassilev Institute of lnformatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria Received October 1990; revised March 1991 Abstract: There are many practical problems where the objective functions and the constraints can be represented by linear functions but the decision variables are restricted to only integer values. Our objective is to present an interactive procedure for the multiple objective integer linear programming problem that is fast, does not place too many demands on the decision maker and can be implemented without requiring any special software. We illustrate the proposed procedure with a numerical example and report some computational experience. Keywords: Algorithm; Chebychev norm; Integer programming; Multiple criteria; Multiple objectives Introduction Consider the multiple objective integer linear programming (MOILP) problem: Maximize Cx * Professor Narula's work was partially supported by partici- pation in the National Academy of Sciences/Bulgarian Academy of Sciences interacademy exchange program and the Institute of Informatics, Bulgarian Academy of Sci- ences. Correspondence to: S.C. Narula, Department of Mathematics, Link6ping Institute of Technology,S-58l 83 Link6ping, Swe- den. Subject to Ax<b, x> 0 and integer where C is a (k ×n)-matrix, A is an (m ×n)- matrix, b is an (m x 1)-vector, and x is an (n x 1)-vector of decision variables. Compared to the multiple objective linear pro- gramming (MOLP) problem, very little research has been reported on the MOILP problem. At present a few algorithms are available to solve the MOILP problem. However, a number of methods, for example, the algorithms of Bitran (1979), Burkard, Krarup and Pruzan (1982), 0377-2217/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved