Fuzzy Goal Programming Algorithm Research Articles

A bi-level programming approach for improving relief logistics operations: A real case in Kermanshah earthquake

Due to its location on the world dry belt, Iran is known as a disaster-prone country. Regarding such a problem, planning for relief operations in disaster situations seems significant and undeniable. The literature on disaster management has mostly defined their problems in a single-level framework, ignoring the bi-level aspect of such problems in both preparedness and response phases. However, in the context of disaster in the real world, there is normally more than one decision-maker that each of them may have their own objective. In this study, a bi-level multi-objective programming approach is extended to design a pre-positioning and distribution network under disastrous conditions considering both preparedness and response phases. The extended framework takes into account simultaneous planning for the distribution of drug, blood and relief items among disaster victims, and transferring the injured to hospital in order to diminish the adverse effects of potential disasters in the response phase. Additionally, to determine suitable candidate places for locating relief centers in the preparedness phase, a modified version of data envelopment analysis model is utilized, something that is not frequently done for facility location planning in the disaster management field. On the other hand, to solve the bi-level multi-objective programming problem with decision-makers at the upper level (the affected country) and the lower level (the international organization), a fuzzy goal programming algorithm is proposed. Furthermore, a consolidated method with respect to a novel fuzzy measure is developed to keep the considered network safe against the inherent uncertainty. Finally, the extended framework is utilized to solve a case study in Kermanshah, the province of Iran.

Bi-level multi-objective programming problem with fuzzy demands: a fuzzy goal programming algorithm

In this paper, a fuzzy goal programming (FGP) algorithm for solving bi-level multi-objective programming problems with fuzzy demands is presented. These fuzzy demands reflect the experts' imprecise or fuzzy understandings of the nature of parameters in the problem formulation process are assumed to be characterized as fuzzy numbers. Using the level sets of fuzzy parameters, the corresponding non fuzzy bi-level programming problem is introduced. In the proposed algorithm, the membership functions for the defined fuzzy goals of all objective functions at the two levels, as well as the membership functions for the vector of decision variables controlled by FLDM are developed in the model formulation of the problem. Then FGP algorithm is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtaining the most satisfactory solution for all decision makers. Illustrative numerical example is given to demonstrate the proposed algorithm.

Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems

This paper presents fuzzy goal programming (FGP) algorithm for solving decentralized bi-level multi-objective programming (DBL-MOP) problems with a single decision maker at the upper level and multiple decision makers at the lower level. A FGP algorithm for DBL-multi-objective linear programming (DBL-MOLP) problems is proposed. This algorithm is extended to solve bi-level multi-objective linear fractional programming (DBL-MOLFP) problems. In the proposed algorithm, the membership functions for the defined fuzzy goals of all objective functions at the two levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by ULDM are developed in the model formulation of the problem. Then FGP approach is used to achieve highest degree of each of the membership goals by minimizing their deviational variables and thereby obtaining the most satisfactory solution for all decision makers. Illustrative numerical examples are given to demonstrate the proposed algorithm.

A note on a fuzzy goal programming algorithm by Tiwari, Dharmar, and Rao

We propose a new algorithm for solving a fuzzy goal programming (FGP) problem with symmetrically triangular membership functions of fuzzy goals and priority structure. The efficiency of the algorithm is justified by showing its computational superiority over that by Tiwari et al.