Solid Transportation Problem Research Articles

Efficient Transportation Planning: A Case Study of Multi-Dimensional Solid Transportation Problem

Efficient Transportation Planning: A Case Study of Multi-Dimensional Solid Transportation Problem

An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems

An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems

Neutrosophic decision-making for allocations in solid transportation problems

Neutrosophic decision-making for allocations in solid transportation problems

A new iterative fuzzy approach to the multi-objective fractional solid transportation problem with mixed constraints using a bisection algorithm

A new iterative fuzzy approach to the multi-objective fractional solid transportation problem with mixed constraints using a bisection algorithm

An extended Vogel’s approximation algorithm for efficiently solving Fermatean fuzzy solid transportation problems

An extended Vogel’s approximation algorithm for efficiently solving Fermatean fuzzy solid transportation problems

A NOVEL METHOD FOR SOLVING FULLY FUZZY SOLID TRANSPORTATIONS PROBLEMS

In this paper, we proposes a new method for solving solid transportation problem under uncertainty environments. The fully fuzzy solid transportation problem has been formulated. To reduce the model into crisp equivalent, we have used existing method for approximation of fuzzy numbers by interval numbers and its arithmatics. A simplex method and existing method for solving Interval Linear Programming problems are used for solving solid transportation problem with fuzzy parameters and decision variables. Furthermore, for illustration, some numerical examples are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy and reasonable.

Analyze the Stochastic Solid Fuzzy Transportation Problem with Mixed Constraints through Weibull Distribution

This paper proposed a general formulation of the stochastic solid transportation problem (SSTP) with mixed constraints such as supply, demand and conveyance capacity taken as uncertain under stochastic environment, following the Weibull distribution (WD). The aim of this study is to minimize the transportation cost includes probabilistic constraints have inequalities of stochastic solid transportation problem (SSTP). SSTP with probabilistic constraints is represented as a chance constrained programming problem. Obtain alpha cut representation from cost coefficient of the fuzzy objective function. We have developed four models for stochastic solid transportation problem. The suggested models are demonstrated by taken as numerical example. A sensitivity analysis is performed to understand parameter’s sensitivity in the proposed model. Introduction: In system of transportation, goods are moved from various sources to destinations using different vehicles and organizational systems, involving both technology and human efforts. Efficient resource allocation in transportation system is crucial for industries and imprecision from factors like fluctuating demand, unreliable supply chains and unpredictable traffic. To address these complexities, advanced mathematical models are needed to manage stochasticity, fuzziness and mixed constraints. The study explores the stochastic solid fuzzy transportation problem with mixed constraint by utilizing the Weibull distribution to model uncertainties inherent in transportation systems. This research addresses the complexity introduced by stochastic variables and fuzzy parameters, particularly in situations where demand, supply and cost of transportation are not deterministic. Objectives: The aim of this study is to minimize the cost of transportation includes probabilistic constraints have inequalities of stochastic solid transportation problem (SSTP). Methods: Obtain alpha cut representation form the cost coefficient of the fuzzy objective function and four models are developed for stochastic solid transportation problem. These models are demonstrating by using a numerical example and a sensitivity analysis is conducted to understand the sensitivity of the parameters in the propose model. Results: Obtained optimal solutions for developed four models of SFSTPMC and sensitivity analysis shows that cost of transportation and flow of unit are sensitive to change in probabilities of demand. Improve transportation system by understanding sensitivity patterns that help decision maker choose appropriate supply availability probabilities. Conclusions: This study presented an approach for solving the SFSTPMC using the Weibull distribution for probabilistic constraints and fuzzy objective functions for transportation cost. Developed and optimized four models, focusing on stochastic parameters. Sensitivity analysis demonstrated the impact of these parameters on transportation cost and unit flow. The results validate the model’s effectiveness in practical resource allocation and decision making under uncertainty.

Improved of Multiobjective Fuzzy Probabilistic Solid Transportation Models in Transportation Systems

Transportation activities are stages in the product distribution system. The purpose of the transport system is to minimize the total cost. If there is more than one objective function and consider more than one type of vehicle, it is called a multiobjective solid transportation problem. In some cases, the parameter transportation model is under uncertainty. A probabilistic and fuzzy approach can be used. This research introduces a probabilistic fuzzy multiobjective solid transportation model where the source, destination and vehicle parameters follow the Pareto distribution. A triangular fuzzy number expresses the coefficient of the objective function. The obtained model is applied to the problem of the metal crate transportation system. There are two objective functions; the first is the objective function to minimize the total cost. The second is the objective function to minimize the total transportation time. Three types of vehicles are considered: HDL, Engkel and Wingbox. The result is that the total cost is Rp. 3836595, and the total time is 757.245 minutes or 13 hours.

Two-level solid transportation problem

Two-level solid transportation problem

"Efficient and Versatile Methodology for Solving Solid Transportation Problem Using Excel Solver: A Comparative Study with LINGO Code"

"Efficient and Versatile Methodology for Solving Solid Transportation Problem Using Excel Solver: A Comparative Study with LINGO Code"

A Systematic Formulation into Neutrosophic Z Methodologies for Symmetrical and Asymmetrical Transportation Problem Challenges

This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the interval solid transportation problem. The first scenario arises when we represent data problems as intervals instead of exact values, while the second scenario arises when the information is not entirely clear. We address both models when the uncertainty alone impacts the constraint set. In order to find a solution for the interval case, we generate an additional problem. Since this auxiliary problem is typical of solid transportation, we can resolve it using the effective techniques currently in use. In the fuzzy scenario, a parametric method is used to discover a fuzzy solution to the earlier issue. Parametric analysis identifies that the best parameterized approaches to complementary problems are characterized by the application of parametric analysis. We present a suggested algorithm for determining the stability set. Finally, we provide a numerical example and sensitivity analysis for the transportation problem, which is both symmetrical and asymmetrical.

Solving a multi-choice solid fractional multi objective transportation problem: involving the Newton divided difference interpolation approach

<abstract> <p>Multi-objective transportation problems (MOTPs) are mathematical optimization problems that involve simultaneously considering multiple, often conflicting objectives in transportation planning. Unlike traditional transportation problems, which typically focus on minimizing a single objective such as cost or distance, MOTPs aim to balance multiple objectives to find the optimal solution. These problems appear in various real-world applications such as logistics, supply chain management, and transportation, where decision-makers need to consider multiple criteria when designing transportation networks, routing vehicles, or scheduling deliveries. The primary challenge lies in the uncertainty in real-world transportation scenarios, where logistics involve factors beyond cost and distance. We investigated a multi-choice solid fractional multi-objective transportation problem (MCSF-MOTP) based on supply, demand, and conveyance capacity, where the coefficients of the objective functions were of the multi-choice type due to uncertainty. To address this uncertainty, the proposed model employed the Newton divided difference interpolation polynomial method, and the suitability of this model was validated through a numerical illustration employing a ranking approach.</p> </abstract>

Profit maximization multi-item Just-in-Time solid transportation problem with budget constraints based on carbon emission

Profit maximization multi-item Just-in-Time solid transportation problem with budget constraints based on carbon emission

Time-sequential probabilistic fermatean hesitant approach in multi-objective green solid transportation problems for sustainable enhancement

In order to delineate the randomness and imprecision in a single framework of time-sequential information, we proposed the notion of a time-sequential probabilistic fermatean hesitant set (TS-PFHS). Triangular time-sequential probabilistic fermatean hesitant number (Tr-TS-PFHN) is also initiated as a triangular version of TS-PFHS along with its fundamental operations and a ranking function. For the employment of our proposed set, we formulated a solid transportation problem (STP) with multiple objectives with TS-PFHS parameters for a sustainable green environment. Consequently, we proposed an algorithm by utilizing fuzzy programming (FP) and weighted sum technique (WST) to address proposed green transportation model. Additionally, to highlight the significance of the suggested technique, a numerical instance based on the transportation of electric vehicles in India is also investigated. Finally, conclusion along with the future prospects and limitations of the work done are discussed.

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

Solid Transportation Problem with Multiple Objectives under Integer and Non-integer Solution

Solid Transportation Problem with Multiple Objectives under Integer and Non-integer Solution

Optimizing bi-objective solid transportation problem using hierarchical order goal programming technique: a case study problem

Optimizing bi-objective solid transportation problem using hierarchical order goal programming technique: a case study problem

A pentagonal type-2 fuzzy variable defuzzification model with application in humanitarian supply chains

Disasters can be caused by humans or natural hazards, and they impact the vulnerability of communities worldwide. This study considers disasters caused by humans, including the rescue operation taken post-accidents. The objective of the research is to minimise time and cost to save people’s lives in the early stages of rescue operations from the fuzzy logic perspective by proposing a novel pentagonal type-2 fuzzy variable (PT2FV) defuzzification method. The multi-objective multi-modal services at the crucial early hours of a disaster solve a solid transportation problem mathematically using a weighted sum method and neutrosophic compromise programming in Lingo solver software. The novelty of the research has been justified by the sensitivity analysis test on various levels of credibility at different intervals of PT2FV. The various credibility level intervals have also been discussed, and the best possible interval is suggested. The outcome suggests an effective plan for humanitarian relief in difficult areas using multiple modes of transit for delivery of reliefs, availing rescue team and saving of victims along with a notion of an efficient contingency planning.

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.