Multi-objective Transportation Problem Research Articles

Intuitionistic fuzzy-based TOPSIS method for multi-criterion optimization problem: a novel compromise methodology

<abstract><p>The decision-making process is characterized by some doubt or hesitation due to the existence of uncertainty among some objectives or criteria. In this sense, it is quite difficult for decision maker(s) to reach the precise/exact solutions for these objectives. In this study, a novel approach based on integrating the technique for order preference by similarity to ideal solution (TOPSIS) with the intuitionistic fuzzy set (IFS), named TOPSIS-IFS, for solving a multi-criterion optimization problem (MCOP) is proposed. In this context, the TOPSIS-IFS operates with two phases to reach the best compromise solution (BCS). First, the TOPSIS approach aims to characterize the conflicting natures among objectives by reducing these objectives into only two objectives. Second, IFS is incorporated to obtain the solution model under the concept of indeterminacy degree by defining two membership functions for each objective (i.e., satisfaction degree, dissatisfaction degree). The IFS can provide an effective framework that reflects the reality contained in any decision-making process. The proposed TOPSIS-IFS approach is validated by carrying out an illustrative example. The obtained solution by the approach is superior to those existing in the literature. Also, the TOPSIS-IFS approach has been investigated through solving the multi-objective transportation problem (MOTP) as a practical problem. Furthermore, impacts of IFS parameters are analyzed based on Taguchi method to demonstrate their effects on the BCS. Finally, this integration depicts a new philosophy in the mathematical programming field due to its interesting principles.</p></abstract>

Multi-objective optimization to the transportation problem considering non-linear fuzzy membership functions

<abstract> <p>Considering the uncertainty of transporting goods from numerous origins to diverse destinations is a critical task for the decision-maker (DM). The ultimate goal of the DM is to make the right decisions that optimize the profit or loss of the organization under the vagueness of the uncontrollable effects. In this paper, mathematical models are proposed using fuzzy non-linear membership functions for the transportation problem considering the parameters' uncertainty that can help the DM to optimize the multi-objective transportation problems (MOTP) and to achieve the desired goals by choosing a confidence level of the uncertain parameters. Based on DM's selection of the confidence level, a compromise solution of the uncertain multi-objective transportation (UMOTP) is obtained along with the satisfaction level in percent for the DM. Two non-linear fuzzy membership functions are considered: the exponential and the hyperbolic functions. Using both membership functions, the sensitivity analysis was implemented by considering different confidence levels. According to the experimental results, the hyperbolic membership function gives 100% DM's satisfaction in many instances. Moreover, it shows stability against the exponential and linear functions.</p> </abstract>

Optimization of Interval Cost Multi-objective Transportation Problem in Uncertain Parameters: A Modified Least-Cost Method

The goal of this research is to focuses on multi-objective transportation problems, to reduce the cost of transporting a good from a variety of sources or origins to a range of destinations while adhering to a predetermined mathematical framework. By using interval values, the policy maker indicated the parameters of source and destination. In this work, a novel approach for finding initial basic feasible solutions (IBFS) that are extremely near to the best ones for a variety of transportation problems is presented. The proposed method can become a milestone in resolving the constraints to achieve the goal in solving transport problem. For the decision maker, regarding logistics and supply chains, it may be quite profitable. The prediction model is supported by an illustration drawn from mathematical view. All the LPPs are evaluated with the help of LINGO. Bangladesh Acad. Sci. 46(2); 155-164: December 2022

A New Approach to Solve Fully Fuzzy Multi-Objective Transportation Problem

The transportation problem is the problem of transferring goods from several sources or producers to multiple destinations or consumers in a cost-effective way, which is one of the most important problems in the supply chain management problems. The application of this problem in addition to the distribution of goods in the location and production planning problems is also important. Many real-life transportation problems encounter multiple, conflicting, and incommensurable objective functions. In addition, in real applications, due to lack of information, it is not possible to accurately estimate the parameters of this problem. Therefore, the main goal of this paper is to find the Pareto optimal solutions of fully fuzzy multi-objective transportation problem under the conditions of uncertainty. In accordingly, a new approach based on nearest interval approximation is proposed to solve the problem. Numerical examples are provided to illustrate the proposed approach and results.

Fixed-charge solid transportation problem with budget constraints based on carbon emission in neutrosophic environment

This paper is to integrate among solid transportation problem, budget constraints and carbon emission with probable maximum profit. The range of air pollution and climate change are effected by \({\text {CO}_2}\) gas emission and other greenhouse gases from myriad transportation systems. Henceforth, our target is to minimize carbon emission for pollution-free environment. Transportation system with single objective is hardly applicable to the situation with more than one criterion. Therefore multi-objective decision making is incorporated for designing real-life transportation problem. Due to time pressure, data limitation, lack of information or measurement errors in practical problems, there exist some hesitations. Based on the fact, decision maker considers indeterminacy in the designed problems. To overcome such hesitancy of occurrence and non-occurrence in fuzzy and intuitionistic fuzzy, neutrosophic set is very important and suitable to accommodate such general structure of problems. Therefore neutrosophic environment with neutrosophic linear programming, fuzzy programming and global criterion method is utilized here to find the compromise solution of the multi-objective transportation problem. Thereafter, the performance of the considered model is useful by evaluating a numerical example, and then the derived results are compared. Finally sensitivity analysis and conclusions with upcoming works of this research are stated hereafter.

Solving Multi Objective Transportation Problems using Harmonic Mean and Graph Theory

Operations research is frequently applied to economics activities, where more attention has also been directed to transportation problems (TP). Another application of this type of transportation problem can be shown as multi objective transportation problems (MOTPs). Usually, in a transportation problem, only one objective of transporting goods from source to destination is considered. However, in a MOTP, different objectives such as time, cost, and risk must be considered. The basic requirement of a multi objective transportation problem in such way as to obtain a minimum value for the objectives mentioned above. Therefore, researchers are developing various algorithms to find an efficient solution to these specific problems. Also, in this paper, we focus on presenting a new approach for an efficient solution to the MOTP. It is recommended to build the method based on the harmonic mean algorithm and spanning tree, compare its solutions with the methods of other concurrent researchers and check the effectiveness of this article. We can say that this new approach is an efficient and easy-to-understand method that provides relatively accurate solutions.

Geometric Mean Method Combined With Ant Colony Optimization Algorithm to Solve Multi-Objective Transportation Problems in Fuzzy Environments

The transportation problem (TP) is a well-known subject in the field of optimization and a very prevalent challenge for businesspeople. The goal is to reduce the total transportation cost, of delivering resources from sources to destinations. The literature demonstrates that various approaches have been designed with a single goal in mind, although TPs are not always developed with a bi-goal in mind. Solving transportation difficulties with several objectives is a common task. In this study, a new method for addressing multi-criteria TP using geometric means, along with a novel approach of the Ant Colony Optimization algorithm (ACO) for solving multi-objective TP in a fuzzy environment. Fuzzy numbers have been used to solve real-world problems in various domains, including operations research and optimization. The ACO Algorithm has long been recognized as a viable alternative strategy for solving optimization problems. The purpose of this study is to provide a unique approach for organizing fuzzy numbers as well as enhancements to the ACO algorithm for solving the Multi-Objective TP model. Our method, such as Geometric Mean Ant Colony Optimization Algorithm (GMACOA), outperforms other methods in terms of objective values. Numerical examples are provided to demonstrate the method in comparison to various current methods.

Fuzzy harmonic mean technique for solving fully fuzzy multi-objective transportation problem

In this research article, an algorithm is developed using a fuzzy harmonic mean technique to solve a fully fuzzy multi-objective transportation problem (FFMOTP). First, the FFMOTP will be formalized mathematically, and then by using fuzzy arithmetic, it will be decomposed into three-level (lower, middle, & upper) multi-objective linear programming problems. After then, by using the fuzzy harmonic mean as a tool, the three-level multi-objective linear programming problems are converted into three-level single objective linear programming problems. Further, these single objective linear programming problems for all the three levels are solved to give the Combine fuzzy optimal solution. In the end, two numerical examples are solved to elaborate our proposed algorithm completely and compare the result obtained by our proposed algorithm with the results obtained using the other methods.

A belief-degree based multi-objective transportation problem with multi-choice demand and supply

This paper focusses on the development of a Multi-choice Multi-objective Transportation Problem (MCMOTP) in the uncertain environment. The parameters associated with the objective functions in MCMOTP are regarded as uncertain variables and the other parameters associated with supply capacity and demand requirements are considered under the multi-choice environment. In this paper, two ranking criteria have been utilized to convert the uncertain objectives into their crisp form. Using these two ranking criteria for the uncertain MCMOTP model, two deterministic models have been developed namely, Expected Value Model (EV Model) and Optimistic Value Model (OV Model). The multi-choice parameters in the constraints are converted to a single choice parameters with the help of binary variable approach. The EV and OV models are solved directly in the LINGO 18.0 software using minimizing distance method and fuzzy programming technique. At last, a numerical illustration is provided to demonstrate the application and algorithm of the models. The sensitivity of the objective functions in OV Model is also examined with respect to the confidence levels to investigate variation in the objective functions.

Intuitionistic Fuzzy Programming Technique to Solve Multi- Objective Transportation Problem

This paper presents a solution of the multi-objective transportation problem via Fuzzy Programming Algorithm and the product is to be transported from source i to destination j. The time and cost of transportation from source i to destination j were recorded. Here we have considered MOTP with intuitionistic fuzzy numbers and completed the problem in both ways. Therefore the optimal compromise solution will remain same both the exponential and linear membership function. For the solution the membership functions are used for such a problem. LINDO/TORA statistical software was employed in the data analysis and is completed in two stages.

Goal programming approach for multi-objective optimization to the transportation problem in uncertain environment using fuzzy non-linear membership functions

The ultimate goal of the decision maker (DM) is to take right decisions to optimize the profit or loss of the organization when the parameters of the transportation problem are ambiguous because of some uncontrollable effects. In this paper, mathematical models are proposed using fuzzy non-linear membership functions and the inverse uncertain normal distribution has been used to eliminate the uncertainty in the parameters which will help the DM to find a compromise solution of the uncertain multi-objective transportation problem (UMOTP) and to achieve the desired goals for a chosen level of confidence for the uncertain parameters. The compromise solutions of the uncertain multi-objective transportation problem are presented to obtain the DM satisfaction if the problem becomes achievable for this preferred confidence level of the parameters. Numerical illustration is given where Linear Programming Problems (LPPs) are resolved with LINGO and the graphs are designed with the help of MATLAB 18.00. J. Bangladesh Acad. Sci. 46(1); 101-115: June 2022

A multi-objective transportation problem with cost dependent credit period policy under Gaussian fuzzy environment

A multi-objective transportation problem with cost dependent credit period policy under Gaussian fuzzy environment

Solving multi-objective linear fractional transportation problem under neutrosophic environment

We are discussing multi-objective linear fractional transportation problem (MOLFTP) under neutrosophic environment in the present paper. In proposed methodology, we characterize each objective of our MOLFTP in three different ways such that truth membership; indeterminacy membership and falsity membership functions. Proposed methodology gives us best neutrosophic compromise programming model under the given membership functions. In the given approach, we convert MOLFTP model into the non-linear integer programming model using proposed approach and solve it using MATLAB. To support the theory a numerical example is also discussed.

MULTI-OBJECTIVE TRANSPORTATION PROBLEM UNDER TYPE-2 TRAPEZOIDAL FUZZY NUMBERS WITH PARAMETERS ESTIMATION AND GOODNESS OF FIT

The problem of transportation in real-life is an uncertain multi-objective decision-making problem. In particular, by taking into account the conflicting objectives, Decision-Makers (DMs) are looking for the best transport set up to determine the optimum shipping quantity subject to certain capacity constraints on each route. This paper presented a Multi-Objective Transportation Problem (MOTP) where the objective functions are considered as Type-2 trapezoidal fuzzy numbers (T2TpFN), respectively. Demand and supply in constraints are in multi-choice and probabilistic random variables, respectively. Also considered the “rate of increment in Transportation Cost (TC) and rate of decrement in profit on transporting the products from ith sources to jth destinations due to” (or additional cost) of each product due to the damage, late deliveries, weather conditions, and any other issues. Due to the presence of all these uncertainties, it is not possible to obtain the optimum solution directly, so first, we need to convert all these uncertainties from the model into a crisp equivalent form. The two-phase defuzzification technique is used to transform T2TpFN into a crisp equivalent form. Multi-choice and probabilistic random variables are transformed into an equivalent value using Stochastic Programming (SP) approach and the binary variable, respectively. It is assumed that the supply and demand parameter follows various types of probabilistic distributions like Weibull, Extreme value, Cauchy and Pareto, Normal distribution, respectively. The unknown parameters of probabilistic distributions estimated using the maximum likelihood estimation method at the defined probability level. The best fit of the probability distributions is determined using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), respectively. Using the Fuzzy Goal Programming (FGP) method, the final problem is solved for the optimal decision. A case study is intended to provide the effectiveness of the proposed work.

Multi-Objective Capacitated Solid Transportation Problem with Uncertain Variables

This paper investigates a multi-objective capacitated solid transportation problem (MOCSTP) in an uncertain environment, where all the parameters are taken as zigzag uncertain variables. To deal with the uncertain MOCSTP model, the expected value model (EVM) and optimistic value model (OVM) are developed with the help of two different ranking criteria of uncertainty theory. Using the key fundamentals of uncertainty, these two models are transformed into their relevant deterministic forms which are further converted into a single-objective model using two solution approaches: minimizing distance method and fuzzy programming technique with linear membership function. Thereafter, the Lingo 18.0 optimization tool is used to solve the single-objective problem of both models to achieve the Pareto-optimal solution. Finally, numerical results are presented to demonstrate the application and algorithm of the models. To investigate the variation in the objective function, the sensitivity of the objective functions in the OVM model is also examined with respect to the confidence levels.

From fuzzy transportation problem to non-linear intuitionistic fuzzy multi-objective transportation problem: A literature review

ABSTRACT To deal with the unpredictability of certain parameters of the transportation problem like fuel charges, climatic conditions, supply and demand of the product, etc., the concept of fuzzy transportation problem came into the limelight. It has been proved to be an efficient approach and extended in literature by various scholars. In the given paper, the existing methods to obtain the solution of different types of fuzzy transportation problem and its extensions are critically reviewed. Intuitionistic fuzzy transportation problems having single and multiple objectives have been focused upon. A review of the past ten years has been done to know the recent advancement. Tabular and graphical comparisons of different approaches are incorporated to understand their benefits and drawbacks.

An efficient stochastic programming approach for solving integrated multi-objective transportation and inventory management problem using goodness of fit

PurposeLogistics is the part of the supply chain (SC) that plans, executes and handles forward and reverse movement and storage of products, services and related information, in order to respond to customers' needs effectively and efficiently. The main concern for logistics is to ensure that the correct product is placed at the right time. This paper introduces a linear model of shipping focused on decision-making, which includes configuration of shipping network, choosing of transport means and transfer of individual customer shipments through a particular transport system.Design/methodology/approachIn this study, authors try to address the problem of supply chain network (SCN) where the primary goal is to determine the appropriate order allocation of products from different sources to different destinations. They also seek to minimize total transportation cost and inventory cost by simultaneously determining optimal locations, flows and shipment composition. The formulated problem of getting optimal allocation turns out to be a problem of multi-objective programming, and it is solved by using the max-addition fuzzy goal programming approach, for obtaining optimal order allocation of products. Furthermore, the problem demand and supply parameters have been considered random in nature, and the maximum likelihood estimation approach has been used to assess the unknown probabilistic distribution parameters with a specified probability level (SPL).FindingsA case study has also been applied for examining the effectiveness and applicability of the developed multi-objective model and the proposed solution methods. Results of this study are very relevant for the manufacturing sector in particular, for those facing logistics issues in SCN. It enables researchers and managers to cope with various types of uncertainty and logistics risks associated with SCN.Research limitations/implicationsThe principal contribution of the proposed model is the improved modelling of transportation and inventory, which are affected by different characteristics of SCN. To demonstrate computational information of the suggested methods and proposed model, a case illustration of SCN is provided. Also, environmentalism is increasingly becoming a significant global concern. Hence, the concept proposed could be extended to include environmental aspects as an objective function or constraint.Originality/valueEfficient integration of logistical cost components, such as transportation costs, inventory costs, with mathematical programming models is an important open issue in logistics optimization. This study expands conventional facility location models to incorporate a range of logistic system elements such as transportation cost and different types of inventory cost, in a multi-product, multi-site network. The research is original and is focused on case studies of real life.

Solving Bi-Level Multi-Objective Transportation Problem under Fuzziness

This paper describes a study on bi-level multi-objective transportation problem in fuzzy environment. To alleviate a difficulty of transporting goods within nodes for long distances, we venture to formulate a transportation problem using bi-level criteria. Again, in this paper, we incorporate the real-life uncertain situation in bi-level transportation system through fuzziness. It produces a new class of transportation problem, namely fuzzy bi-level multi-objective transportation problem (FBMOTP). We solve FBMOTP with and without priority of the 1st level of transportation problem (TP) using the Vogal Approximation Method (VAM) which are called respectively Approach 1 and Approach 2. A special emphasis of this paper is to introduce a new approach namely Approach 3 for solving the FBMOTP in addition to the considered two approaches. In this regard, we incorporate an algorithm for Approach 3 to find compromise solution of the FBMOTP using VAM. Thereafter, the proposed algorithm is illustrated to show the usefulness by taking a numerical example. A comparative analysis with the existing studies is provided to understand the effectiveness of the proposed methodology. At last, conclusions are described with the lines of future study of the paper.

A novel approach for solving rough multi-objective transportation problem: development and prospects

A novel approach for solving rough multi-objective transportation problem: development and prospects

Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

This article presents a multiple objective fractional fixed-charge transportation problem (MFFTP) in a rough decision-making framework. A transformation procedure is modified to convert non-linear multi-objective transportation problem to its linear version. The parameters of the designed model are considered to be fuzzy. We employ separate kinds of fuzzy scale, i.e., possibility, credibility and necessity measures, to deal with the fuzzy parameters. Using the fuzzy chance-constrained rough approximation (FCRA) technique, we extract the more preferable optimal solution from our suggested MFFTP. The initial result is compared with that of the robust ranking (RR) technique. We also use the theory of rough sets for expanding as well as dividing the feasible domain of the MFFTP to accommodate more information by considering two approximations. Employing these approximations, we introduce two variants, namely, the lower approximation (LA) and the upper approximation (UA), of the suggested MFFTP. Finally, by using these models, we provide the optimal solutions for our proposedproblem. We also associate our MFFTP with a real-world example to showcase its applicability as well as performance. Our core concept of this article is that it tackles an MFFTP using two separate kinds of uncertainty and expands its feasible domain for optimal solutions. Optimal solutions of the designed model (obtained from FCRA technique) belong to two separate regions, namely, “surely region” and “possible region”. The optimal solution which belongs to the “surely region” is better (as these are minimum values) than the one in the “possible region” and other cases. An interpretation of our approach along with offers about the intended future research work are provided at last.