Compromise Solutions for a Special Type of Stochastic Multi-Level Linear Multiple Objective Decision Making Problems

Compromise Solutions for a Special Type of Stochastic Multi-Level Linear Multiple Objective Decision Making Problems

Tarek H.M. Abou-El-EnienShereen F. El-Feky 

Department of Operations Research & Decision Support, Faculty of Computers & Information, Cairo University, 5 Dr. Ahmed Zoweil St., Orman 12613, Giza, Egypt

Teaching Assistant at Faculty of Computer Science, Department of Computer Science, Modern Science and Arts University, 6th of October city-Giza, Egypt

Corresponding Author Email: 
t.hanafy@fci-cu.edu.eg
Page: 
222-231
|
DOI: 
https://doi.org/10.18280/ama_a.550407
Received: 
29 August 2018
|
Accepted: 
16 November 2018
|
Published: 
31 December 2018
| Citation

OPEN ACCESS

Abstract: 

We introduce the concept of the technique for order preference by similarity to ideal solution (TOPSIS) to develop a methodology to find compromise solutions for the multi-level linear multiple objective decision making (MLLMODM) problems of block angular structure with stochastic parameters in the right hand side of the independent constraints (SMLLMODM) of mixed (Maximize/Minimize)-type. We propose a modified formulas for the distance function from the positive ideal solution (PIS) and the distance function from the negative ideal solution (NIS). We present a new interactive hybrid algorithm based on the proposed TOPSIS approach, the chance constrained programming method and the decomposition method to generate a compromise solutions for these types of mathematical optimization problems. Also, we give an illustrative numerical example to clarify the main results developed in the paper. The solutions of the numerical example by the proposed interactive hybrid algorithm is compared with the solutions of the ideal point (IP) method. In general, the results show that, the proposed hybrid TOPSIS method is a good tool to generate compromise solutions for the SMLLMODM problems of mixed type.

Keywords: 

compromise programming, stochastic programming, decomposition techniques, multiple objective decision making, multi-level programming

1. Introduction
2. Formulation of the Problem
3. TOPSIS for (SMLLMODM) of Block Angular Structure
4. Illustrative Numerical Example for the Hybrid Algorithm
5. Conclusions and Future Works
Appendix
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