A Compromise Decision-making Model for Multi-objective Large-scale Programming Problems with a Block Angular Structure under Uncertainty

Authors

1 Assistant Professor, Faculty of Industrial & Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 MSc, Faculty of Industrial & Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

Abstract

This paper proposes a compromise model, based on the technique for order preference through similarity ideal solution (TOPSIS) methodology, to solve the multi-objective large-scale linear programming (MOLSLP) problems with block angular structure involving fuzzy parameters. The problem involves fuzzy parameters in the objective functions and constraints. This compromise programming method is based on the assumption that the optimal alternative is closer to fuzzy positive ideal solution (FPIS) and at the same time, farther from fuzzy negative ideal solution (FNIS).An aggregating function that is developed from LP- metric is based on the particular measure of ‘‘closeness” to the ‘‘ideal” solution.An efficient distance measurement is utilized to calculate positive and negative ideal solutions. The solution process is as follows: first, the decomposition algorithm is used to divide the large-dimensional objective space into a two-dimensional space. A multi-objective identical crisp linear programming is derived from the fuzzy linear model for solving the problem. Then, a single-objective large-scale linear programming problem is solved to find the optimal solution. Finally, to illustrate the proposed method, an illustrative example is provided.

Highlights

  • This paper proposes a compromise model to solve multi-objective large-scale linear programming problems with block angular structure
  • An efficient distance measurement is utilized to calculate positive and negative ideal solutions
  • A decomposition algorithm is used to divide the large-dimensional objective space into a two-dimensional space

Keywords