Objective Transportation Problem Research Articles

Investigation of Markovian Process in Server Break-down

In day to day life goods produced at a number of places are consumed at different locations and then the problem faced by producer or dealer is to transfer goods from numerous places of origin to various places of consumption such that cost of transportation, time required, damages to the product etc. are optimum. This is called classical transportation problem. In this study we have studied transportation problem solve by Markov Decision Process. Introduction to the operations research is made along with over view of optimization techniques of single objective transportation problem. For literature review in the subject of multi objective fractional as well as linear multi objective transportation problems. In basic concepts of Markov Decision Process are given for further usage in the thesis work. We have stated algorithms for solving different types of multi objective programming problems. In entire work we have used basically linear membership functions, hyperbolic membership function and exponential membership function. These membership functions are Markov Decision Process. In case of linear membership function weighted arithmetic mean, weighted quadratic mean, geometric mean is used to find compromise solution. Almost everywhere we have found that the compromise solutions are fairly close to optimal solution when the problem is solved as single objective function. We have solution procedure for multi objective linear transportation is given using Markov Decision Process. Introduction to fractional programming is made and solutions of multi objective linear fractional programming problems are discussed. We have solutions of multi objective linear fractional transportation problem. In this topic fractional objective functions are approximated as linear functions using Taylor’s theorem and then applied method to solve the multi objective linear transportation problem discussed earlier. We focus on solution to fractional transportation problem with Markov Process coefficients. To multi objective fractional transportation problem with goal programming approach. We deal with general integer programming problem along with fractional transportation problems. The main result of this thesis is a characterization of increasing Marko processes satisfying certain conditions. At the end bibliography and research papers published by authors are given. Keywords: Markov Process, Transportation, Queen analyses Server system.

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>

To Use an Ant Colony Technique to Solve a Crispy Type Bi- and Tri-Objective Transportation Problem

Transportation problem (TP) aims to reduce the entire transportation cost of moving resources from various supply hubs to various demand hubs. However, in real-life situations, all organizations want to achieve numerous objectives while making transportation of goods. The degree of deterioration may vary depending on the mode, route, and time of transport. In some cases, the multiobjective could be used to reduce the use of a scarce resource, such as energy. As a result, the proposed approach was discovered to be an algorithm that improves bi- and triobjective TP techniques. This is an innovative way for solving the new bi- and triobjective transportation algorithm using a modified ant colony optimization (ACO) algorithm. According to the literature, various strategies have been developed in the past to tackle the multiobjective transportation problem (MOTP). The MOTP is solved using goal programming, fuzzy programming, interactive solution algorithms, and other techniques. These strategies are occasionally good or bad in achieving better results in a reasonable amount of time. The heuristic technique used in this work is the improved ACO algorithm, which is based on the ant colony algorithm and has been found to provide solutions with a reasonable degree of satisfaction for two and three objective TPs. When the findings are compared, the solution achieved using the proposed method has delivered the best performance and provides a case study to show the new strategy.

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.

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.

A Predictive Control Approach for Cooperative Transportation by Multiple Underwater Vehicle Manipulator Systems

This article addresses the problem of cooperative object transportation for multiple underwater vehicle manipulator systems (UVMSs) in a constrained workspace involving static obstacles. We propose a nonlinear model predictive control (NMPC) approach for a team of UVMSs in order to transport an object while avoiding significant constraints and limitations, such as kinematic and representation singularities, obstacles within the workspace, joint limits, and control input saturation. More precisely, by exploiting the coupled dynamics between the robots and the object and using certain load sharing coefficients, we design a predictive controller for each UVMS in order to cooperatively transport the object within the workspace’s feasible region. Moreover, the control scheme adopts load sharing among the UVMSs according to their specific payload capabilities. In addition, the feedback relies on each UVMS’s onboard measurements and no explicit data are exchanged online among the robots, thus reducing the required communication bandwidth. Finally, realistic simulation results conducted in the UwSim dynamic simulator running in robot operating system (ROS) environment as well as real-time experiments employing two small UVMSs and demonstrated the effectiveness of the proposed control strategy.

On Solving a MFL Paradox in Linear Plus Linear Fractional Multi- Objective Transportation Problem Using Fuzzy Approach

On Solving a MFL Paradox in Linear Plus Linear Fractional Multi- Objective Transportation Problem Using Fuzzy Approach

Goal programming tactic for uncertain multi-objective transportation problem using fuzzy linear membership function

In a managerial position, the ultimate objective is to take the right decision for the decision maker (DM) when transportation parameters are uncertain due to the globalization and other uncontrollable influences. In this paper, fuzzy membership function tactic based on goal programming to obtain the desired compromise solution of a multi-objective transportation problem (MOTP) in uncertain environment is proposed where the DM can choose a confidence level for different parameters. On the basis of DM’s choice on a particular confidence level, a compromise solution is obtain indicating the satisfaction level of the DM if the problem is feasible for this chosen confidence level. Uncertain normal distribution is used to convert the parameters from uncertain to a certain one. Simple linear programming problem (LPP) is designed using fuzzy linear membership function where the upper and lower values of the objectives are the desired goals of the DM. A numerical illustration is furnished to establish the effectiveness of the designed model whereas the single objective transportation problems are solved by TORA and LPPs are solved by using LINGO for operations research.

Cooperative Impedance Control for Multiple Underwater Vehicle Manipulator Systems Under Lean Communication

This article addresses the problem of cooperative object transportation for multiple underwater vehicle manipulator systems (UVMSs) in a constrained workspace with static obstacles, where the coordination relies solely on implicit communication arising from the physical interaction of the robots with the commonly grasped object. In this article, we propose a novel distributed leader-follower architecture, where the leading UVMS, which has knowledge of the object's desired trajectory, tries to achieve the desired tracking behavior via an impedance control law, navigating in this way, the overall formation toward the goal configuration while avoiding collisions with the obstacles. On the other hand, the following UVMSs estimate locally the object's desired trajectory via a novel prescribed performance estimation law and implement a similar impedance control law that achieves tracking of the desired trajectory despite the uncertainty and external disturbance in the object and the UVMS dynamics, respectively. The feedback relies on each UVMS's force/torque measurements and no explicit data is exchanged online among the robots, thus reducing the required communication bandwidth and increasing robustness. Moreover, the control scheme adopts load sharing among the UVMSs according to their specific payload capabilities. Finally, various simulation studies clarify the proposed method and verify its efficiency.

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.

Goal programming technique for solving fully interval-valued intuitionistic fuzzy multiple objective transportation problems

In transportation problems, the cost depends on various irresistible factors like climatic conditions, fuel expenses, etc. Consequently, the transportation problems with crisp parameters fail to handle such situations. However, the construction of the problems under an imprecise environment can significantly tackle these circumstances. The intuitionistic fuzzy number associated with a point is framed by two parameters, namely membership and non-membership degrees. The membership degree determines its acceptance level, while the non-membership measures its non-belongingness (rejection level). However, a person, because of some hesitation, instead of giving a fixed real number to the acceptance and rejection levels, may assign them intervals. This new construction not only generalizes the concept of intuitionistic fuzzy theory but also gives wider scope with more flexibility. In the present article, a balanced transportation problem having all the parameters and variables as interval-valued intuitionistic fuzzy numbers is formulated. Then, a solution methodology based on goal programming approach is proposed. This algorithm not only cares to maximize the acceptance level of the objective functions but simultaneously minimizes the deviational variables attached with each goal. To tackle the interval-valued intuitionistic fuzzy constraints corresponding to each objective function, three membership and non-membership functions, linear, exponential and hyperbolic, are used. Further, a numerical example is solved to demonstrate the computational steps of the algorithm, and a comparison is drawn amidst linear, exponential and hyperbolic membership functions.

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.

Solution of Multi Objective Transportation Problem Under Fuzzy Environment

The crisp transportation problem is one of the special case of linear programming problems. It is explained with the hypothesis that the cost parameters are indicated inaccurate way. But in the present world, the transportation parameters may be uncertain due to many uncontrolled factors; this gives rise to fuzzy environment. Here, we proposed a method for the solution of fully fuzzy multi objective transportation problems involving triangular fuzzy numbers. We solve the fully fuzzy multi objective transportation problems without converting it into crisp form. A numerical example is discussed to demonstrate the theory formulated in this article.

A multiple objective transportation problem approach to dynamic truck dispatching in surface mines

In surface mining operations, fleet management systems seek to make optimal decisions to handle material in two steps: path production optimization and real-time truck dispatching. This paper develops a multiple objective transportation model for real-time truck dispatching. The model addresses two major drawbacks of former models. The proposed model dispatches the trucks to destinations trying to simultaneously minimize shovel idle times, truck wait times, and deviations from the path production requirements established by the production optimization stage. To evaluate the performance of the proposed model, we developed a benchmark model based on the backbone of the most widely used fleet management system in the mining industry (Modular Mining DISPATCH). Afterward, we built a discrete event simulation model of the truck and shovel operation using an iron ore mine case study, implemented both of the dispatching models, and compared the results. The implementation of the models suggests that the multiple objective model developed in this paper is able to meet the production requirements of the operation using a fleet at 85% of the size of the deterministically calculated desired fleet. In addition, the model is able to meet the full capacity of the processing plants with a fleet of 30% less trucks than the desired fleet.

Collaborative Multi-Robot Transportation in Obstacle-Cluttered Environments via Implicit Communication.

This paper addresses the problem of cooperative object transportation in a constrained workspace involving static obstacles, with the coordination relying on implicit communication established via the commonly grasped object. In particular, we consider a decentralized leader-follower architecture for multiple mobile manipulators, where the leading robot, which has exclusive knowledge of both the object's desired configuration and the position of the obstacles in the workspace, tries to navigate the overall formation to the desired configuration while at the same time it avoids collisions with the obstacles. On the other hand, the followers estimate the object's desired trajectory profile via novel prescribed performance estimation laws that drive the estimation errors to an arbitrarily small predefined residual set. Moreover, a navigation function-based scheme is innovatively combined with adaptive control to deal with parametric uncertainty. Hence, the current state of the art in robust motion planning and collision avoidance is extended by studying second order non-linear dynamics with parametric uncertainty. Furthermore, the feedback relies exclusively on each robot's force/torque, position as well as velocity measurements and no explicit information is exchanged online among the robots, thus reducing the required communication bandwidth and increasing robustness. Finally, two simulation studies clarify the proposed methodology and verify its efficiency.

Fuzzy multi objective transportation problem – evolutionary algorithm approach

This paper deals with fuzzy multi objective transportation problem. An fuzzy optimal compromise solution is obtained by using Fuzzy Genetic Algorithm. A numerical example is provided to illustrate the methodology.

Bi-criteria transportation problem with multiple parameters

This paper introduces a bi-criteria transportation problem with multiple parameters which brings together the concept of price discrimination from the area of marketing management to the world of multi objective transportation problems. The problem deals with two objectives, the overall shipment cost and the bottleneck time of shipment. Both the objectives are of minimization type and have multi-choice coefficients pertaining to differential marketing strategies or different modes of transportation available. First, the problem with minimum availability and demand of goods is solved and then the problem is extended to the case of interval demand and supply. By iteratively solving multi-choice variants of a cost minimizing transportation problem/minimum cost flow problem, all Pareto optimal time–cost pairs are obtained. The proposed algorithm for both the variants is successfully implemented and solved using the CPLEX optimization package.

Paradox in a Linear Multi Objective Transportation Problem

Paradox in a Linear Multi Objective Transportation Problem

Design and Coordination of Cooperative Mobile Robots

<p>Object transportation is an important task considered in mobile robotics. For many years, it has been performed by single robots, capable to transport payload of moderate size and mass with respect to the robot size and mass. But if the payload gets bigger, the robot fails in the transporting task. For wider or heavier payloads, human operators improve their capacities by working in group. A similar improvement should be expected with a group of mobile robots.</p><p>In this paper, we proposed a new concept of cooperative mobile robots to deal with the problem of long object transportation in unstructured environment whatever the payload length. The proposed C3Bots AT/VLP robot is formed by the association of two or more mono-robots with simple kinematics forming a poly-robot system.</p><p>The paper presents several kinematic schemes and the corresponding obstacle-crossing processes. It deals with the problem of how to maintain stable motion for the poly-robot during obstacle crossing. Changes in the internal configuration of the robot adjust the center of gravity to guarantee stable motion. A specific stability criterion for contact on three wheels is presented. By adjusting the relative poses of the front and rear axles with respect to the payload, it is possible to maximize the stability of the poly-robot and its payload during obstacle crossing.</p>

A novel algorithm for solving two-objective fuzzy transportation problems

Fuzzy two-objective transportation Satisfaction level percent Efficient solution Fuzzy number A-level set A B S T R A C T A new method is proposed for finding efficient solution sets for fuzzy two objective transportation problems using ranking function and percent of function one solution is introduced for transportation problem and explained with the proposed model. Decision maker can obtain efficient solutions with the proposed method and selects the most preferred one among them. Objective of classic transportation problem is minimizing cost but generally, problems which are formulated are multi-purpose and these purposes will be measured in different scales and are inconsistent with each other. In practice, ideal solution for multi-objective problem is always impossible. When objectives are in conflict with each other, we cannot reach these solutions. For this purpose, efficient solution will be introduced instead of ideal solution. Often, objective functions and right-hand columns are considered as fuzzy data in multi-objective transportation problems that these values are determined by decision-maker; then, he will reach solution by analyzing data with required method. In 1979, an algorithm was introduced by Izerman for multi-objective transportation problems. in 2005, an algorithm was proposed by Omar and Yunes for solving multi-objective transportation problems using fuzzy factors. In 2011, a new method was presented by Pendian for solving two- objective transportation problem. In this article, a new method is suggested for finding efficient solution sets for two-objective fuzzy transportation using ranking function. In proposed method, solution of next problem could be