| Article ID: | iaor20071475 |
| Country: | Singapore |
| Volume: | 21 |
| Issue: | 1 |
| Start Page Number: | 127 |
| End Page Number: | 139 |
| Publication Date: | Jan 2004 |
| Journal: | Asia-Pacific Journal of Operational Research |
| Authors: | Jahanshahloo G.R., Shoja N., Tohidi G., Lotfi F. Hosseinzadeh |
| Keywords: | programming: integer |
In this paper, a method using the concept of l1-norm is proposed to find all the efficient solutions of a 0–1 Multi-Objective Linear Programming (MOLP) problem. These solutions are specified without generating all feasible solutions. Corresponding to a feasible solution of a 0–1 MOLP problem, a vector is constructed, the components of which are the values of objective functions. The method consists of a one-stage algorithm. In each iteration of this algorithm a 0–1 single objective linear programming problem is solved. We have proved that optimal solutions of this 0–1 single objective linear programming problem are efficient solutions of the 0–1 MOLP problem. Corresponding to efficient solutions which are obtained in an iteration, some constraints are added to the 0–1 single objective linear programming problem of the next iteration. Using a theorem we guarantee that the proposed algorithm generates all the efficient solutions of the 0–1 MOLP problem. Numerical results are presented for an example taken from the literature to illustrate the proposed algorithm.