An improved approach for solving fuzzy transportation problem with triangular fuzzy numbers

A new method to determine the Fermatean fuzzy optimal solution of transportation problems

 Transportation Problems (TP) have multiple applications in supply chain management to reduce costs. Efficient methods have been developed to address TP when all factors, including supply, demand, and unit transportation costs, are precisely known. However, due to uncertainty in practical applications, it is necessary to study TP in an uncertain environment. In this paper, we define the Trapezoidal Fermatean Fuzzy Number (TrFFN) and its arithmetic operations. Then we introduce a new approach to solve TP, where transportation cost, supply, and demand are treated as TrFFN, and we call it Fermatean Fuzzy TP (FFTP). We illustrate the feasibility and superiority of this method with two application examples, and compare the performance of this method with existing methods. Furthermore, the advantages of the proposed method over existing methods are described to address TP in uncertain environments.

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

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.

Solving the fully fuzzy multi-objective transportation problem based on the common set of weights in DEA

A transportation problem basically deals with the problem which aims to minimize the total transportation cost or maximize the total transportation profit of distributing a product from a number of sources or origins to a number of destinations. While, in general, most of the real life applications are modeled as a transportation problem (TP) with the multiple, conflicting and incommensurate objective functions. On the other hand, for some reason such as shortage of information, insufficient data or lack of evidence, the data of the mentioned problem are not always exact but can be fuzzy. This type of problem is called fuzzy multi-objective transportation problem (FMOTP). There are a few approaches to solve the FMOTPs. In this paper, a new fuzzy DEA based approach is developed to solve the Fully Fuzzy MOTPs (FFMOTPs) in which, in addition to parameters of the MOTPs, all of the variables are considered fuzzy. This approach considers each arc in a FFMOTP as a decision making unit which produces multiple fuzzy outputs using the multiple fuzzy inputs. Then, by using the concept of the common set of weights (CSW) in DEA, a unique fuzzy relative efficiency is defined for each arc. In the following, the unique fuzzy relative efficiency is considered as the only attribute for the arcs. In this way, a single objective fully fuzzy TP (FFTP) is obtained that can be solved using the existing standard algorithms for solving this kind of TPs. A numerical example is provided to illustrate the developed approach.

Time Variant Multi-Objective Interval-Valued Transportation Problem in Sustainable Development

Sustainable development is treated as the achievement of continued economic development without detriment to environmental and natural resources. Now-a-days, in a competitive market scenario, most of us are willing to pay less and to gain more in quickly without considering negative externalities for the environment and quality of life for future generations. Recalling this fact, this paper explores the study of time variant multi-objective transportation problem (MOTP) with consideration of minimizing pollution. Time of transportation is of utmost importance in reality; based on this consideration, we formulate a MOTP, where we optimize transportation time as well as the cost function. The parameters of MOTP are interval-valued, so this form of MOTP is termed as a multi-objective interval transportation problem (MOITP). A procedure is taken into consideration for converting MOITP into deterministic form and then for solving it. Goal programming is applied to solve the converted transportation problem. A case study is conducted to justify the methodology by utilizing the environmental impact. At last, conclusions and future research directions are included regarding our study.

Dichotomized Incenter Fuzzy Triangular Ranking Approach to Optimize Interval Data Based Transportation Problem

This research article discusses the problems having flexible demand, supply and cost in range referred as interval data based transportation problems and these cannot be solved directly using available methods. The uncertainty associated with these types of problems motivates authors to tackle it by converting interval to fuzzy numbers. This confront of conversion has been achieved by proposing a dichotomic fuzzification approach followed by a unique triangular incenter ranking approach to optimize interval data based transportation problems. A comparison with existing methods is made with the help of numerical illustrations. The algorithm proposed is found prompt in terms of the number of iteration involved and problem formation. This method is practical to handle the transportation problems not having a single valued data, but data in form of a range.