Abstract
This paper has been designed to introduce the method for solving the Bi-level Multi-objective (BL-MO) Fully Quadratic Fractional Optimization Model through Fuzzy Goal Programming (FGP) approach by utilising non-linear programming. In Fully Quadratic Fractional Optimization Model, the objective functions are in fractional form, having quadratic functions in both numerator and denominator subject to quadratic constraints set. The motive behind this paper is to provide a solution to solve the BL-MO optimization model in which number of decision-makers (DM) exists at two levels in the hierarchy. First, the fractional functions with fuzzy demand, which are in the form of fuzzy numbers, are converted into crisp models by applying the concept of α-cuts. After that, membership functions are developed which are corresponding to each decision-maker’s objective and converted into simpler form to avoid complications due to calculations. Finally, the model is simplified by applying FGP approach, and a compromised solution to the initial model is obtained. An algorithm, flowchart and example are also given at the end to explain the study of the proposed model.
Highlights
Bi-level Multi-objective Fully Quadratic Fractional Optimization Model (BL-MOFQFOM) mostly arises in supply chains, agriculture, traffic control systems, biofuel production, and in many more cases
BL-MOFQFOM is a kind of decision structure in which more than one decision-makers are present at two levels
BLMOFQFOM is a demanding tool which has its utilization in the fields of banking, economic systems, healthcare planning, transportation, profit/cost, debt/equity, and so on
Summary
Bi-level Multi-objective Fully Quadratic Fractional Optimization Model (BL-MOFQFOM) mostly arises in supply chains, agriculture, traffic control systems, biofuel production, and in many more cases. BL-MOFQFOM is a kind of decision structure in which more than one decision-makers are present at two levels. First level decision-makers are called leaders and followers are the decision-makers on the second level, subject to quadratic constraints. A number of objectives emerge in such models, all of which are proposed to be optimized to the higher extent possible. They agree to compromise up to a certain limit so that every objective function can obtain a satisfactory solution
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