Multi-objective optimization for multi-type transportation problem in intuitionistic fuzzy environment

Abstract

Multi-objective optimization is an emerging field concerning optimization problems associated with more than one objective function, each of them has to be optimized simultaneously. Multi-objective optimization is widely used in logistics and supply chains to reduce the cost and time involved in transportation. With the increase in Global Supply Chains, many organizations are facing the challenges of delivering products to their customers at a fast pace, low cost, and high reliability. There are numerous factors that may affect the goal of an organization to optimize the cost, time, and effort during the transportation of their products to the end customers. For instance, in the existing transportation problems, the type of vehicles used for the movement of the products is not focused. Transportation of the goods is considered to utilize any type of vehicle irrespective of the nature of the goods. However, in real-life scenarios, there are certain constraints in the vehicle used to transport the finished goods or raw materials from a source to a destination. Vehicles such as tanker trucks, top open trucks, closed trucks, etc. need to be booked based on the nature of goods to be transported. Also, the cost and time of transportation are uncertain in nature. In this paper, we formulate the Multi-Objective Solid Transportation Problem (MOSTP) by considering the above issue. The uncertain parameters of the problem are considered as Pentagonal Intuitionistic Fuzzy Numbers (PIFN). Magnitude method is used for defuzzification. An algorithm to find the solution of formulated Intuitionistic Fuzzy Multi-Objective Solid Transportation problem (IFMOSTP) is provided. The proposed model is illustrated by a numerical example which is solved with the help of LINGO software.