Multi-objective Transportation Research Articles

Genetic algorithm-based solution of multi-objective stochastic transportation problem

Genetic algorithm-based solution of multi-objective stochastic transportation problem

A new approach to multi-objective transportation problem forbinding relationship between warehouse to consumer and consumer to consumer

A special type of multi-objective transportation problem with emphasis on consumer to consumer relationship is presented. The objective is to minimise total transportation cost along with source to consumer and consumer to consumer association/relationship in vicinity of the source. A lexicographical goal programming model has been applied. Two phase approach has been made. In the first phase the total transportation cost is minimised. In the second phase, overall independence value of the consumer to consumer association/relation is minimised. This model can give a better result than a single objective transportation model. That is because the source to consumer association/relationship is considered in the first priority to get the lowest cost and the vicinity of consumers in the periphery of the source. In the second priority grouping is made for consumers to be served in the same warehouse, provided the capacity of the source is sufficient to meet the consumer's demand.

Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station

In this contribution, for the first time, an efficient model of multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station is formulated. Transfer station inserts transfer cost and type-I fixed-charge. Our aim is to analyze an extra cost that treats as type-II fixed-charge and truck load constraints in the designed model that required when the amount of items exceeds the capacity of vehicle for fulfilling the shipment by more than one trip. Type-II fixed-charge is added with transportation cost and other cost from transfer station. We consider here an important issue of the multi-objective transportation problem as product blending constraints for transporting raw materials with different purity levels for customers’ satisfaction. In realistic point of view, the parameters of the model are imprecise in nature due to existing several unpredictable factors. These factors are apprehended by incorporating the fuzzy-rough environment on the parameters. Expected-value operator is utilized to derive the deterministic form of fuzzy-rough data, and the model is experienced with help of fuzzy programming, neutrosophic linear programming and global criteria method. Two numerical examples are illustrated to determine the applicability of the proposed model.

Contiguous-cells transportation model for multi-objective non-pre-emptive production and maintenance scheduling

The long-standing issue of non-pre-emption in ‘multi-period’ production/maintenance (P/M) scheduling has always been a challenge and this has been the focus of many researchers. Recently, the Contiguous-Cells Transportation Model (CCTM) was proposed to address this problem. However, the CCTM is limited to non-pre-emptive P/M scheduling decision situations where only one objective is of concern. The multiple objective non-pre-emptive P/M scheduling are encountered more frequently in the real world than the single objective case. This study proposed the Multi-Objective Contiguous-Cells Transportation Model (MOCCTM) and the solution procedure for handling multi-objective cases of non-pre-emptive production/maintenance scheduling. The variables and parameters of the CCTM were adopted with modifications to cater for the multi-objective requirements. A composite multiple-objective function was formulated by employing multi-objective optimisation techniques of assigning weights to objectives and normalisation of objectives. An algorithm similar to the conventional least cost method was developed for the solution of the MOCCTM. A bi-objective non-pre-emptive maintenance scheduling problem of 5 production machines across an operation and maintenance planning horizon of 10 periods was used to demonstrate the application of the MOCCTM. The MOCCTM is a good approach to solving multi-objective P/M scheduling problems in a non-pre-emptive environment.

A new approach to multi-objective transportation problem forbinding relationship between warehouse to consumer and consumer to consumer

A special type of multi-objective transportation problem with emphasis on consumer to consumer relationship is presented. The objective is to minimise total transportation cost along with source to consumer and consumer to consumer association/relationship in vicinity of the source. A lexicographical goal programming model has been applied. Two phase approach has been made. In the first phase the total transportation cost is minimised. In the second phase, overall independence value of the consumer to consumer association/relation is minimised. This model can give a better result than a single objective transportation model. That is because the source to consumer association/relationship is considered in the first priority to get the lowest cost and the vicinity of consumers in the periphery of the source. In the second priority grouping is made for consumers to be served in the same warehouse, provided the capacity of the source is sufficient to meet the consumer's demand.

Genetic Algorithm Based Solution of Fuzzy Multi-Objective Transportation Problem

Optimizing problems in the modern era, the single objective optimization problems are insufficient to hold the full data of the problem. Therefore, multi-objective optimization problems come to the rescue. Similarly, in daily life problems, the parameters used in the optimization problem are not always fixed but there may be some uncertainty and it can characterize by fuzzy number. This work underlines the genetic algorithm (GA) based solution of fuzzy transportation problem with more than one objective. With a view to providing the multifaceted choices to decision-maker (DM), the exponential membership function is used with the decision-makers desired number of cases which consisted of shape parameter and aspiration level. Here, we consider the objective functions which are non-commensurable and conflict with each other. To interpret, evaluate and exhibit the usefulness of the proposed method, a numerical example is given.

A novel Approach for Fully Intuitionistic Fuzzy Multi-Objective Fractional Transportation Problem

This paper exhibits a novel approach for solving fully intuitionistic fuzzy multi-objective fractional transportation problem (FIF-MOFTP). Because of the change of market policies, we expect that the transportation cost, the shipped quantity, the source, and the destination parameters are not generally exact. In this paper, a theorem which demonstrate that FIF-MOFTP is ever solvable was presented. In our approach, the problem is converted into a linear one based on some transformations. Then the linearized model is reduced to a crisp multi-objective transportation problem utilizing the accuracy function for each objective. Moreover, various theorems that set up the relation among the FIF-MOFTP and its equivalent crisp model using linear, hyperbolic, and parabolic membership functions are also proofed. To approve the proposed approach, a numerical example is incorporated. Deductions and future exploration of this paper are depicted at end.

A Multi-objective Transportation Data Problems and their Based on Fuzzy Random Variables

A Multi-objective Transportation Data Problems and their Based on Fuzzy Random Variables

Solving Multi-Objective Transportation Problem Using Opportunity Cost Method

Solving Multi-Objective Transportation Problem Using Opportunity Cost Method

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.

Analyzing a Two-Staged Multi-objective Transportation Problem Under Quantity Dependent Credit Period Policy Using q-fuzzy Number

Recently, the inclusion of a credit period policy becomes a beneficial strategy to improve a transportation business from the point of views of source and destination. In this regard, this study addresses a two-staged multi-objective transportation problem to transport the products from a production house to some retailers through some distributors by minimizing total transportation cost of retailers and by maximizing total profit of distributors simultaneously. Here, distributors offer a quantity dependent credit period policy to the retailers to induce them to procure the items from that distributors. Under this policy, those retailers who collect the materials more than a threshold value, would get this facility. Ideally, to assign a value of the credit period, there is no specific rule. It is totally the own strategy of the distributors with uncertainty. So, it takes different amounts at different times depending on the market situations. In that sense, it has been considered as q-fuzzy number, which is a combination of linear and non-linear memberships. To simplify the model, some arithmetic operations on q-fuzzy number and its defuzzification procedure have been introduced. Finally, two examples have been considered to examine the feasibility for both the cases (crisp and fuzzy) of the model and a non-elitist multi-objective genetic algorithm has been used to find the optimal solution.

Fuzzy arithmetic DEA approach for fuzzy multi-objective transportation problem

In this paper, a transportation problem (TP) with fuzzy costs in the presence of multiple and conflicting objectives is investigated. In fact, a fuzzy data envelopment analysis (DEA) approach is proposed to solve the fuzzy multi-objective TP (FMOTP). To this end, each arc in FMOTP will be considered as a decision-making unit (DMU). Next, those objective functions that needs to be maximized will be used to define the outputs of DMU and those that needs to be minimized will be used to define the inputs of DMU. Consequently, two different fuzzy efficiency scores will be derived for each arc by solving fuzzy DEA models. So, a unique fuzzy attribute will be defined for each arc by combining the resulting fuzzy efficiency scores. Therefore, the FMOTP will be converted into a single objective fuzzy TP that can be solved using the standard algorithms. Finally, using a numerical example the proposed approach has been illustrated.

Interactive Pythagorean-hesitant fuzzy computational algorithm for multiobjective transportation problem under uncertainty

ABSTRACT Transportation problems inherently involve uncertainty in real life. The uncertain framework for optimization of transportation models depends on various aspects. Therefore the effective modeling and optimization configuration is needed to solve such transportation problems. In this study, we have considered a multiobjective transportation problem with fuzzy parameters and developed a new Pythagorean-hesitant fuzzy computational algorithm to solve the problem under uncertainty. The proposed approach is based on Pythagorean-hesitant fuzzy decision set which captures a set of possible values for membership and non-membership degrees of each objective function under the Pythagorean-hesitant fuzzy environment. To show the applicability and validity of the proposed approach a numerical example has been presented. The efficiency performance of the proposed approach has also been discussed along with the comparative study with other existing approaches.

Tolerance Approach to Sensitivity Analysis in Multiobjective Transportation Problem

This paper represents ordinary sensitivity analysis and tolerance approach to sensitivity analysis in supply and demand values of the multiobjective transportation problem. Our proposed approach allows simultaneous and independent changes in the supply and demand values. The aim of this paper is to find the ranges for each supply and demand value within which the changes can occur without affecting the current basis of the best compromise solution. We have used the best compromise solution obtained using fuzzy programming technique for the postoptimality analysis of the multiobjective transportation problem. The approach is illustrated by a numerical example.

Credit linked two-stage multi-objective transportation problem in rough and bi-rough environments

With a rapid growth of research in multi-objective transportation problem, rough and bi-rough sets are two new mathematical ideas for formulating real-world-based problems involving uncertain data. In this study, we have investigated a two-stage multi-objective transportation problem by considering credit period policy under rough and bi-rough environments. In this regard, three conflicting objective functions have been optimized simultaneously under the same restrictions. In first objective function, we have presented the minimization of transportation cost of a production house. In second objective function, total transportation cost of retailers has been minimized. But, in last one, we have maximized total profit of distributors. Besides, due to existence of different types of uncertainties in our real-life problems, in the proposed model, independent parameters (including, actual transportation cost, requirement of the retailers, and cost per unit distance) have been considered as rough in nature and dependent parameters such as demanded transportation cost and demand of the distributors have been considered as bi-rough in nature. Moreover, to convert the uncertain model into an equivalent deterministic form, a rough and bi-rough programming approach has been derived along with the expected value approach. Finally, by using these ideas, the mathematical model of our considered transportation problem has been illustrated. After that, the proposed model has been solved by applying NSGA-II algorithm (elitist non-dominated sorting genetic algorithm) with some simulated numerical data. Some sensitivity analysis associated with our proposed model has also been discussed to show the effectiveness of the model.

A Fuzzy Goal Programming Approach to Multiobjective Transportation Problems

The current paper focuses on a multiobjective transportation problem which is a special type of vector minimum problem. In order to deal with such a problem, a new model based on fuzzy goal programming is suggested. Different solutions are obtained according to the priorities of the decision maker in the proposed model. With respect to its properties, at least a weakly efficient solution is yielded by solving the new model. To demonstrate the validity and strengths of the suggested model, some numerical examples are given. Further, a comparison is made with different existing methods.

Geometric Mean Method to Solve Multi Objective Transportation Problem Under Fuzzy Environment

Transportation problem is a very common problem for a businessman. Every businessman wants to reduce cost, time and distance of transportation. There are several methods available to solve the transportation problem with single objective but transportation problems are not always with single objective. To solve transportation problem with more than one objective is a typical task. In this paper we explored a new method to solve multi criteria transportation problem named as Geometric mean method to Solve Multi-objective Transportation Problem Under Fuzzy Environment. We took a problem of transportation with three objectives cost, time and distance. We converted objectives into membership values by using a membership function and then geometric mean of membership values is taken. We also used a procedure to find a pareto optimal solution. Our method gives the better values of objectives than other methods. Two numerical examples are given to illustrate the method comparison with some existing methods is also made.

Soft Set Based Intelligent Assistive Model for Multiobjective and Multimodal Transportation Problem

The real world conditions of transportation pose new challenges for development of intelligent assistive systems for effective decision making. The ignorance of relationships among various attributes and parameters is one of the major causes of uncertainty in existing models of transportation problems. Fuzzy sets have been explored by various investigators to address the uncertainty issues due to relationships among various attributes. However fuzzy sets are not fully capable of dealing all kinds of uncertainty to provide intelligent solutions of transportation problems. A soft set is explored in this paper to model the uncertainty arising from the relationships of attributes with the parameters in a multimodal and multi objective transportation problem. The three modes of transportation incorporated in this model are road, rail and air. The real data set is prepared using the tariff, distance and time duration of transport available on websites of transport service agencies. The objectives are to minimize the cost and time duration of transportation. The proposed model evaluates multiple criteria using various combinations of different modes of transport to optimize the objectives of the problem. The model has been illustrated using the real data set using existing methods of solution. The soft set approach is found to be quite effective in dealing with the relationships of attributes with the parameters arising due to multi criteria decision making and leads to intelligent optimal solutions. The proposed model can be used as intelligent assistive system for decision making of multi objective and multimodal transportation problems.

An Extended Multi-Objective Capacitated Transportation Problem with Mixed Constraints in Fuzzy Environment

In this paper, we study a multi-objective capacitated transportation problem (MOCTP) with mixed constraints. This paper is comprised of the modelling and optimisation of an MOCTP in a fuzzy environment in which some goals are fractional and some are linear. In real life application of the fuzzy goal programming (FGP) problem with multiple objectives, it is difficult for the decision maker(s) to determine the goal value of each objective precisely as the goal values are imprecise or uncertain. Also, we developed the concept of linearisation of fractional goal for solving the MOCTP. In this paper imprecision of the parameter is handled by the concept of fuzzy set theory by considering these parameters as a trapezoidal fuzzy number. α-cut approach is used to get the crisp value of the parameters. Numerical examples are used to illustrate the method for solving MOCTP.

Multi-objective fixed-charge transportation problem using rough programming

This paper analyses the multi-objective fixed-charge transportation problem (MOFCTP) using rough programming. Due to globalisation of market, the parameters of MOFCTP may not be defined precisely, so the parameters of the MOFCTP are treated as rough intervals. Expected value operator is used to convert rough MOFCTP to deterministic MOFCTP. Fuzzy programming method and linear weighted-sum method are used to obtain Pareto-optimal solution from deterministic MOFCTP. A comparative study is made between the obtained solutions extracted from the methods; and thereafter we perform a procedure to analyse the sensitive analysis of the parameters in MOFCTP. Finally, in order to show the applicability of our proposed study, an example on MOFCTP is included in this paper.