Multi-objective Transportation Model Research Articles

A cost-efficient relocation model minimizing economic and social disruption of the disaster-affected population of the Kedarnath considering uncertainty

In 2013, Kedarnath, India, faced a devastating landslide-induced flood, causing substantial damage, loss of life, and displacement. This event highlights a gap in post-disaster relocation models, hindering efficient transportation to preferred locations. The challenge intensifies as coordinating relocation with individual preferences, coupled with post-disaster data uncertainty, complicates efforts and triggers a series of effects on community acceptance, psychological well-being, and overall resilience. The study addresses post-disaster relocation gaps by introducing a multi-objective transportation model (MOTM) with psychological support, optimizing resettlement to minimize budget impact, distance, and economic and social disruption (ESD). The proposed interval-valued pentagonal neutrosophic number (IVPN) and defuzzification technique advances disaster management theory and offers a practical solution for uncertainty in data, bridging theory, and practical application in the disaster response phase. The MOTM efficiently minimizes transportation, psychological intervention, and rental costs through fuzzy goal programming (FGP), global criterion method (GCM), and neutrosophic compromise approach (NCA), implemented with LINGO optimization software. The values of parameters considered in the MOTM are captured in IVPN format and converted to crisp values, availing the proposed defuzzification technique. The performance evaluation of the defuzzification technique is carried out through a comparative analysis of past literature. The proposed MOTM and IVPN were implemented in the 2013 Kedarnath flood case study to generate diverse relocation options. GCM provides relocation options at a higher cost and distance but with minimal ESD by providing a preferred location to a family count as high as 3324 out of 3491 families. The FGP technique provides results similar to NCP that reduce the costs and distance of the relocation process by 6.95% and 0.88%, respectively; however, it increases ESD by allocating preferred locations to only 2623 out of 3491 families. The study provides Pareto optimal solutions for the smooth application of MOTM for diverse post-disaster instances.

Intuitionistic fuzzy multi-objective transportation model during pandemic COVID-19

The given paper discusses an intuitionistic fuzzy discrete time-space optimization model while taking into account the COVID-19 pandemic. The novelty of this study is characterized by the proposal of a distinctive multi-objective intuitionistic fuzzy transportation model in which the demand function varies with time as the number of infected, exposed and susceptible persons increase. Forecasting of demand is executed using the epidemic diffusion model. Also, a new approach to defuzzify triangular intuitionistic fuzzy numbers, depending upon the concept of the golden ratio, is presented. Intuitionistic fuzzy programming approach is used to obtain the pareto-optimal solution. A real-life numerical illustration is explained using the proposed methodology to examine its practical suitability. Outperforming the existing traditional method of solving a transportation problem verifies its proficiency.

A fully Fermatean fuzzy multi-objective transportation model using an extended DEA technique

A fully Fermatean fuzzy multi-objective transportation model using an extended DEA technique

An extended multi-objective transportation model based on Fermatean fuzzy sets

An extended multi-objective transportation model based on Fermatean fuzzy sets

Convex Combination Method on Probabilistic Fuzzy Multiobjective Transportation Problem with Pareto Distribution

This article introduces a transportation model with two objective functions. The first objective function is the function which minimizes the total cost and the second objective function is the function which minimizes the total time. Parameters of source, destination and maximum capacity of transportation means are assumed to follow the Pareto distribution. The multiobjective transportation model is the development of a single objective transportation model. Parameters of the objective function are expressed by triangular fuzzy numbers. Fuzzy multi objective problems are transformed into a deterministic single objective using the convex combination method. The formulated model is applied to the problem of shipping metal crates. There are 3 types of conveyances namely HDL, Engkel and Wingbox. Obtained the optimal total cost of Rp. 3,770,294 and metal crates delivery time to be for 13 hours.

Multi stage Multi-objective Transportation Problem under Uncertainty Environment

In present scenario due to high competition in market, there are lots of pressures on organizations involbs with transportation industry, to provide the service in a better and effective manner. The distribution of products among the customers in systematic manner is not an easy task. Transportation models provide an effective framework to meet these challenges. If the parameters involved with multi-objective transportation model are expressed in terms of fixed parameter then it is not easy to address them in an uncertainty environment, rather it is easy to handle them when they are represented in terms of linguistic variables. It is noticed that, all the objectives of a transportation model are affected by different criteria like route of transportation, weather condition, vehicles used for transportation etc. In the present study a multi-stage transportation model with multiple numbers of objectives is developed with fuzzy relations. Minimization of both transportation cost and transportation time are considered as two different objectives of first stage which are associated with a number of different criteria like deterioration time, fixed charge and mode of transportation. In second stage, another objective i.e quantity of transported amount is considered on the performance basis of objectives of first stage. All these factors considered for this model are fuzzy parameters and are expressed in terms of linguistic variables. The fuzzy rule based transportation model is developed and the solution is obtained by Genetic Algorithm for multi-objective problems (MOGA). The model is presented with a numerical problem and optimum result is discussed.

A multi-objective transportation model under neutrosophic environment

A multi-objective transportation model under neutrosophic environment

An Empirical Study on Multi-objective Transportation Problem in Fuzzy Environment

For both in economical and social development of country transportation system plays a vital role. As it is directly involved with financial growth of the country, for that a complete well planned transportation infrastructure is necessary. Most of the transportation models are formulated with minimization of transportation cost as the basic objective. But consideration of transportation system with a single objective is not able to meet the various requirements of transportation industry for which it may not lead to the practical optimal solution. It bounds the decision makers (DMs) to consider several objectives at a time instead of single objective. To handle a multi-objective transportation problem with fixed parameters is a challenging issue; rather it is easy to consider all parameters in terms of linguistic variables. In this paper, a multi criteria multi-objective transportation models is formulated based on fuzzy relations under the fuzzy logic with several objectives like (i) minimization of total transportation cost and (ii) minimization of total transportation time. Another objective, maximization of the transported amount from a source to a destination is determined on the basis of previous two objectives. All the objectives are associated with multiple numbers of criteria like breakable items, shipping distance, service charge, mode of transportation etc. These relations are imprecise in nature and represented in terms of verbal words such as low, medium, high and very high. The fuzzy rule based multi-objective transportation problem is formulated and result is discussed.

A multi-objective transportation model under neutrosophic environment

In this paper, a new compromise algorithm for multi-objective transportation problem (MO-TP) is developed, which is inspired by Zimmermann's fuzzy programming and the neutrosophic set terminology. The proposed NCPA is characterized by assigning three membership functions for each objective namely, truth membership, indeterminacy membership and falsity membership. With the membership functions for all objectives, a neutrosophic compromise programming model is constructed with the aim to find best compromise solution (BCS). This model can cover a wide spectrum of BCSs by controlling the membership functions interactively. The performance of the NCPA is validated by measuring the ranking degree using TOPSIS approach. Illustrative examples are reported and compared with exists models in the literature. Based on the provided comparisons, NCPA is superior to fuzzy and different approaches.

Fuzzy multi objective transportation model based on new ranking index on generalized LR fuzzy numbers

In this paper, we present a new method for analyzing a fuzzy multi objective transportation problem using a linear programming model based on a new method for ranking generalized LR fuzzy numbers. First, we present a new method for ranking generalized LR fuzzy numbers from its λ-cut.To the best of our knowledge till now there is no method in the literature to find the ranking order of the generalized LR fuzzy numbers to various linear and non-linear functions of LR fuzzy numbers from its  -cut based on area, mode and spread. Our method can efficiently rank various LR fuzzy numbers, their images and crisp numbers which are consider to be a special case of fuzzy numbers (normal/nonnormal, triangular/trapezoidal, and general), which could not be ranked by the existing ranking methods. Our ranking method also satisfies the linearity property condition. For the corroboration, we used some comparative examples of different existing methods to illustrate the advantages of the proposed method.The reference functions of LR fuzzy numbers of fuzzy multi objective transportation problem are considered to be linear and non-linear functions. This paper develops a procedure to derive the fuzzy objective value of the fuzzy multi objective transportation problem, in that the fuzzy cost coefficients and the fuzzy time are LR fuzzy numbers. The method is illustrated with an example by various cases.

Transportation policies for single and multi-objective transportation problem using fuzzy logic

In this paper, single and multi-objective transportation models are formulated with fuzzy relations under the fuzzy logic. In the single-objective model, objective is to minimize the transportation cost. In this case, the amount of quantities transported from an origin to a destination depends on the corresponding transportation cost and this relation is verbally expressed in an imprecise sense i.e., by the words ‘low’, ‘medium’, ‘high’. For the multi-objective model, objectives are minimization of (i) total transportation cost and (ii) total time for transportation required for the system. Here, also the transported quantity from a source to a destination is determined on the basis of minimum total transportation cost as well as minimum transportation time. These relations are imprecise and stated by verbal words such as ‘very high’, ‘high’, ‘medium’, ‘low’ and ‘very low’. Both single objective and multi-objective problems using Real coded Genetic Algorithms (GA and MOGA) are developed and used to solve the single level and bi-level logical relations respectively. The models are illustrated with numerical data and optimum results are presented.

Multiobjective Transportation Model with Fuzzy Parameters: Priority based Fuzzy Goal Programming Approach

This paper presents a priority based fuzzy goal programming approach for solving a multiobjective transportation problem with fuzzy coefficients. In the model formulation of the problem, first the membership functions for the fuzzy goals are defined. Subsequently, the membership functions are transformed into membership goals, by assigning the highest degree (unity) of a membership function as the aspiration level and introducing deviational variables to each of them. In the solution process, negative deviational variables are minimized to obtain the most satisficing solution. Sensitivity analysis of the solution, with a change in priorities of the fuzzy goals is performed. Next the Euclidean distance function is used to identify the appropriate priority structure of the goals, thereby obtaining the most satisficing decision for the decision-making unit, by minimizing their regrets of achieving the ideal point dependent decision in the decision-making context. A numerical example is solved to demonstrate the potential use of the proposed approach.