Multi-objective green 4-dimensional transportation problems for damageable items through type-2 fuzzy random goal programming

Abstract

As per ECOFYS’s11https://ingmarschumacher.files.wordpress.com/2013/05/asn-ecofys-2013-world-ghg-emissions-flow-chart-2010.pdf. report, road transportation contributes 10.5% of the GHGE, which is the cause of global warming. With the infrastructural developments, there are several routes between different cities, even in developing countries. In a business, objectives’ goals are always uncertain. With these facts, in this investigation, a multi-objective green four-dimensional transportation problem for damageable items is formulated and solved. Here four objectives — minimization of operational cost, transportation time, carbon emission amount and maximization of retailers’ satisfaction, whose goals are type-2 fuzzy random are considered. There are several connecting paths between sources and destinations with varied traffic congestion and maximum possible velocities for different conveyances. To get a better compromise solution for multi-objectives, the type-2 fuzzy random goal programming method (T2FRGPM) is developed using the Enhanced Karnik-Mendel algorithm for type reduction of type-2 fuzzy set The model is solved by the proposed T2FRGPM and illustrated with some numerical data using Lingo 11.0. A real-life example and several particular models are presented. The effectiveness of the proposed method, the importance of the four-dimensional transportation problem, and the objectives are established. A trade-off between transportation time and carbon emission amount is presented.