The robust linear programming technique for multi-dimensional analysis of preferences

Abstract

The linear programming technique for multi–dimensional analysis of preferences (LINMAP) is one of the noted multi–attributes decision making (MADM) techniques and has been implemented in crisp and fuzzy environments. Robust optimisation attempts to obtain a solution which is feasible in all circumstances arising due to the uncertainty of parameters. The purpose of this study is to extend the LINMAP method for addressing robustness in MADM problems. In this methodology, robust optimisation concepts are used to describe robustness in decision information and decision making processes. Each alternative is evaluated based on its weighted distance to a robust positive ideal solution (RPIS). The RPIS and the robust weights of attributes are estimated using a new robust linear programming technique. Finally, Monte Carlo simulation is applied to test the robustness of the solution. A numerical example is provided to illustrate the effectiveness of the methodology.