Fully Fuzzy Fractional Capacitated Multi-Objective Solid Transportation Problem with Blended Fuel Emission and Bounds on Rim Conditions

The fractional programming is a generalization of linear programming. The objective function in a linear fractional program is a ratio of two linear functions. As the ratio of two functions is considered the fractional programming models become more suitable for real life problems. Due to uncontrollable factors the parameters in the transportation problem may not be known precisely in real life situations. Oxygenated diesel fuel blends have a potential to reduce the emission of particulate matter (PM) and to be an alternative diesel fuel. This paper focuses on fully fuzzy fractional capacitated multi objective solid transportation problem with blended fuel emission and bounds on rim conditions. Three models have been discussed in which one consulting of emission related to diesel and another two are emissions related to B20 and B50. In this model, some objectives functions are linear , some are fractional and are conflicting in nature with each other. The optimal solution is obtained by using fuzzy programming approach through LINGO software. The main aim of this paper is to determine a transportation schedule that maximizes the profit percentage and also minimizes the transportation cost, time, emission cost of a trading firm. Keywords - Fractional transportation problem, Hexagonal fuzzy number, Emission related to blended fuels, fuzzy programming approach.