Multi-objective Solid Transportation Problem Research Articles

A belief-degree-based two-stage multi-objective solid transportation problem in a green supply chain

A belief-degree-based two-stage multi-objective solid transportation problem in a green supply chain

Solving a multi-objective solid transportation problem: a comparative study of alternative methods for decision-making

The transportation problem in operations research aims to minimize costs by optimizing the allocation of goods from multiple sources to destinations, considering supply, demand, and transportation constraints. This paper applies the multi-dimensional solid transportation problem approach to a private sector company in Egypt, aiming to determine the ideal allocation of their truck fleet.In order to provide decision-makers with a comprehensive set of options to reduce fuel consumption costs during transportation or minimize total transportation time, a multi-objective approach is employed. The study explores the best compromise solution by leveraging three multi-objective approaches: the Zimmermann Programming Technique, Global Criteria Method, and Minimum Distance Method. Optimal solutions are derived for time and fuel consumption objectives, offering decision-makers a broad range to make informed decisions for the company and the flexibility to adapt them as needed.Lingo codes are developed to facilitate the identification of the best compromise solution using different methods. Furthermore, non-dominated extreme points are established based on the weights assigned to the different objectives. This approach expands the potential ranges for enhancing the transfer problem, yielding more comprehensive solutions.This research contributes to the field by addressing the transportation problem practically and applying a multi-objective approach to support decision-making. The findings provide valuable insights for optimizing the distribution of the truck fleet, reducing fuel consumption costs, and improving overall transportation efficiency.

Interactive strategy of carbon cap-and-trade policy on sustainable multi-objective solid transportation problem with twofold uncertain waste management

Interactive strategy of carbon cap-and-trade policy on sustainable multi-objective solid transportation problem with twofold uncertain waste management

Fuzzy Multi-objective Solid Transportation Problem: Genetic Algorithm Based Solution Approach

Fuzzy Multi-objective Solid Transportation Problem: Genetic Algorithm Based Solution Approach

A Belief-degree Based Two Stage Multi-objective Solid Transportation Problem in a Green Supply Chain

A Belief-degree Based Two Stage Multi-objective Solid Transportation Problem in a Green Supply Chain

Non-dominated sorting genetic algorithm III with stochastic matrix-based population to solve multi-objective solid transportation problem

Non-dominated sorting genetic algorithm III with stochastic matrix-based population to solve multi-objective solid transportation problem

New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators

A solid transportation problem emerges when the decision variables are represented by three items: the source, the destination, and the mode of transport. In applications, the STP generally requires considering multiple objectives such as cost minimization, time minimization, security level maximization, etc. In this way, a multi-objective solid transportation problem arises. This paper deals with the solution of the problem and analyzes the effect of several important fuzzy aggregation operators on the solution of the problem. In this context, the most commonly used aggregation operators are investigated for this problem. To explain the solution approach, a numerical example from the literature is given and a Pareto-optimal solution set is provided to offer the decision-maker. Furthermore, graphical comparisons and sensitivity analysis are presented with the solution obtained.

The Multi-objective Solid Transportation Problem with Preservation Technology Using Pythagorean Fuzzy Sets

The Multi-objective Solid Transportation Problem with Preservation Technology Using Pythagorean Fuzzy Sets

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.

Carbon mechanism on sustainable multi-objective solid transportation problem for waste management in Pythagorean hesitant fuzzy environment

Waste management involved in various fields of global ecosystem that provides several positive effects for green environment and sustainable development. We devise a multi-objective solid transportation model of waste management problem in agriculture field and forest department for urban or rural development. Starting to end point of the problem covered by considering the objective functions as transportation cost, job opportunity and carbon emission. Carbon emission is restricted by the combination of several policies of carbon mechanism (carbon tax, cap-and-trade and offset policy). Various critical sitchs appear in such realistic process and uncertainty attached with related data. Here we prefer Pythagorean hesitant fuzzy environment to overcome deep uncertainty rather than single uncertainty. After that, we initiate a ranking approach to convert uncertain data into crisp data. To justify the appropriateness of the formulated model and to select the best policy of carbon mechanism, we study two industrial applications with various cases of such mechanism. To derive the Pareto-optimal solution of the problems, two fuzzy techniques, namely, fuzzy programming and Pythagorean hesitant fuzzy programming, are utilized here. Comparative study, model validation, sensitivity analysis, managerial insights and conclusions with future research scopes are outlined at last.

A Fuzzy Approach to Multi-Objective Solid Transportation Problem with Mixed Constraints Using Hyperbolic Membership Function

Abstract Multi-objective Solid Transportation Problem (MSTP) is known as a special class of vector-minimization (or maximization) problems and has three parameters: source, destination, and conveyance. The objectives such as transportation cost, transportation time, transportation safety level, and objectives in terms of environmental and social issues are generally in conflict with each other. In this paper, we present a fuzzy approach to bring these conflicting objectives together as high as possible. Instead of using the linear membership function, which is frequently used in the literature for ease of use, we use the hyperbolic membership function in our approach. Also, while most of the papers in the literature deal with the standard equality constrained form of MSTP, the mixed constrained form is addressed in this paper. Finally, a numerical example from the literature is used to illustrate the construction of the hyperbolic membership function and how well it represents the objective functions’ degree of satisfaction.

A Restricted Multi-Objective Solid Transportation Problem with Budget Constraint Involving Stochastic Variable and Interval Type-2 Fuzzy Number

This paper proposes a new concept in transportation problem in which if the negligible amount quantity is transported through a distribution center, then the decision maker (DM) cannot deliver that negligible amount quantity through the particular distribution center and the DM puts some restriction on transportation problem. Here, we develop six transportation models with budget at each destination, of which three models are without restriction and another three models are with restriction. Also, apart from source, demand and capacity constraints, an extra constraint on the total budget at each destination is also imposed. Here, all the parameters in Models 1 and 2 are crisp in nature and are solved in crisp environment, whereas all the parameters in Models 3–6 are interval type-2 fuzzy and random in nature, respectively, and are solved in uncertain environment. To reduce Models 3–6 into its crisp equivalent, we use the expected value of fuzzy number and chance constraint programming technique, respectively. Weighted sum method is also used to give the preference of the objective function and a gradient-based optimization technique-generalized reduced gradient (GRG) method are applied and using LINGO-13 software to get the optimal solutions. A numerical example is provided to illustrate the models and programming. Finally, a sensitivity analysis is presented for Models 1 and 2 with respect to the weight function.

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.

A Humanitarian Green Supply Chain Management Considering Minimum Cost and Time

Disaster is the sudden problem of the world. There is no time bound. By disaster, all the creatures of the earth are affected. Here, the authors have tried to show some issues which are related to the natural calamities and green transportation. The main investigation of the paper is to describe about humanitarian supply chain management with optimized transportation cost, time, and carbon emission. Here a real-life problem of flood affected area has been chosen. When such disasters happen, quick response can reduce the devastation and save lives, and thus, it requires fulfilling the basic humanitarian needs of the affected population. In such case, organizations should also maintain the emission of the vehicles in safe range to mitigate the further disaster by pollution. A multi-objective solid transportation problem considering cost, time, and emission has been presented here. To solve the problem, this paper has used goal programming method and pareto optimal solution method. A comparison of results is also shown later. Some managerial insights are drawn to describe the situation.

A Multiobjective Multi-Product Solid Transportation Model with Rough Fuzzy Coefficients

Transportation management is one of the key success factors to keep an organization competitive, sustain its growth pace, and raise profits not only at a local but also a global scale. Therefore, planning and designing a transport system are prerequisite and vital topics for achieving these goals. In this paper, a multiobjective multi-product solid transportation problem (MOMPSTP) under uncertainty is formulated and solved by two different methods of multiobjective optimization problems (MOPs). The system parameters namely unit transportation cost, availability of products at source points, demands of products at destinations and the capacity of transportation mode all are taken as rough fuzzy variables (RFVs). A chance constraint programming model for MOP with RFVs is developed in order to obtain satisfactory solutions when decision makers (DMs) aim to optimize multiple objectives (cost, time, profit, etc.) simultaneously. For given credibility (Cr) and trust (Tr) levels of RFVs, Cr-Tr constraint programming technique is used to reduce the uncertain transportation problem into equivalent deterministic form. Two classical solution techniques-weighted sum method (WSM) and ideal point method (IPM) are utilized to solve the problem. Finally, a numerical example is provided to illustrate the usefulness of our proposed model and then a sensitivity analysis is performed to verify different solutions due to different level of satisfaction.

Multi-objective solid transportation problem under stochastic environment

In real life, three-dimensional (solid) transportation problem is an uncertain multi-objective decision-making (MODM) problem. In particular, it involves searching for the best transportation set-up that meets the decision maker’s preferences by considering the conflicting objectives/criteria such as transportation cost, transportation time, environmental and social issues. To tackle such complex situations, this paper proposes a general formulation of the multi-objective solid transportation problem (STP) with some random parameters. The paper makes the following contributions: (i) proposes a solution methodology based on chance-constraint programming technique to solve an STP with the uncertainty characterized by gamma distribution, (ii) proposes the initial feasibility conditions for the problem and (iii) extends fuzzy programming approach for solving the multi-objective stochastic problems. A numerical example is presented to illustrate the model and methodology.

A gamma type-2 defuzzification method for solving a solid transportation problem considering carbon emission

This paper intends to develop a multi-objective solid transportation problem considering carbon emission, where the parameters are of gamma type-2 fuzzy in nature. This paper proposed the defuzzification process for gamma type-2 fuzzy variable using critical value (CV ) and nearest interval approximation method. A chance constraint programming problem is generated using the CV based reduction method to convert the fuzzy problem to its equivalent crisp form. Applying the $\alpha $ -cut based interval approximation method, a deterministic problem is developed. Some real life data are used to minimize the cost and carbon emission. LINGO standard optimization solver has been used to solve the multi-objective problem using weighted sum method and intuitionistic fuzzy programming technique. The Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithm are implemented to generate efficient optimal solution by converting the multi-objective problem to a single objective problem using penalty cost for carbon emission. After solving the problem, analysis on some particular cases has been presented. The sensitivity analysis has been shown to different credibility levels of cost, emission, source, demand, conveyance to find total cost, emission and transported amount in each level. A comparison study on the performance of three algorithms (LINGO, GA and PSO) is presented. At the end, some graphs have been plotted which shows the effect of emission with different emission parameters.

A multi-objective solid transportation problem with reliability for damageable items in random fuzzy environment

In this paper, a multi-objective solid transportation problem (MOSTP) for damageable item is formulated and solved. First, we minimised the total cost of transportation and transportation time and maximise the reliability of transportation system. Here, transportation costs, resources, demands and capacities of conveyances are random fuzzy in natures. The transported item is likely to be damaged during transportation and damageability are different for different conveyances along different roots. The solid transportation problem (STP) is formulated as a decision making model optimising possibilistic value at risk (pVaR) by incorporating the concept of value at risk (VaR) into possibility and necessity measure theory. The reduced deterministic constrained problem is solved using generalised reduced gradient (GRG) method (LINGO-14.0). Some particular models has been presented. The model is illustrated with numerical examples and some sensitivity analysis is made on damageability.

A multi-objective solid transportation problem with reliability for damageable items in random fuzzy environment

A multi-objective solid transportation problem with reliability for damageable items in random fuzzy environment

Multi-objective Solid Transportation Problem in Uncertain Environment

Although new information technologies decrease information and transaction costs, transportation problem of physical goods is still relevant. Globalization of trade increased the uncertainty that companies are facing, it also increased the importance of supply chain management in world economies drastically. Because transportation systems are crucial for operation management, the problem of finding efficient and sustainable solutions under such uncertain environments needs to be studied. Thus, this paper focuses on “multi-objective solid transportation problem (STP) in uncertain environment” and presents some approaches to find the compromised optimal solution of multi-objective STP. Then, compatible with uncertainty, fuzzy programming and some techniques of the fuzzy set theory are implemented to solve the problem by using Maple 17.02. A numerical example is executed and presented here to illustrate suggested procedures.