Comparative Analysis of Optimization Methods for Grey Fuzzy Transportation Problems in Logistics

Optimal dispatch of virtual power plant using interval and deterministic combined optimization

Multi-carrier energy systems (MESs) provide various types of energy to customers like natural gas, electricity, cool, and heat. The interdependency among natural gas, heating, and power systems is rising due to the extensive growth of electrically powered heating facilities and cogeneration systems. Energy hub (EH) performs as a transitional agent amid consumers and suppliers. Therefore, multi-energy incorporation is a prevailing tendency and the EH is supposed to perform a pivotal role in allotting energy sources more effectively. The influence of MESs in distribution systems attracts more and more researchers. The MESs’ uncertainties need to be addressed using efficient methods. This book chapter introduces the interval optimization to deal with the uncertainties. The uncertainties are modeled as interval numbers. Pessimistic predilection ordering and EHs’ pessimism levels are implemented in the optimization in order to make the comparison of interval numbers. The interval optimization minimizes the total cost interval instead of the worst-case scenarios in the robust optimization. It performs computationally better than stochastic optimization, as well. In comparison with the stochastic optimization, a precise probability distribution of random variables is not needed in the interval optimization. Further, it can diminish computational complexity. In this chapter, the stochastic optimization and interval optimization methods are being conducted for evaluation.

<p style='text-indent:20px;'>Transport and logistics systems include a range of activities that deal with all sorts of decisions and operations from material handling to vehicle routing. One of the main challenges for transport and logistics processes is to deal with large-scale and complex problems. However, with increasingly diverse sets of operational real-world data becoming available, data-driven heuristic approaches are promising to pave the path for solving the problems in the field of transport and logistics. Thus, a comprehensive review is needed to observe the reflections of this path in literature. To bridge this gap, a total of 40 papers on the topic of "data-driven heuristic approaches to logistics and transportation problems" are determined. Before the categorization and content analysis; descriptive, bibliometric and social network analysis are carried out to identify the current state of the literature. All the papers are systemically reviewed based on different perspectives, namely data-driven methodology, heuristics, sub-problems and etc. Based on the review, suggestions for future research are likewise provided. Subsequently, machine learning and deep learning methods are considered to be among the most promising data-driven methodologies. The review may be useful for academicians, researchers, and practitioners for a better understanding of data-driven heuristic approaches to transportation and logistics problems.</p>

There is a wide range of sequential decision problems in transportation and logistics that require dealing with uncertainty. There are four classes of policies that we can draw on for different types of decisions, but many problems in transportation and logistics will ultimately require some form of direct lookahead policy (DLA) where we optimize decisions over some horizon to make a decision now. The most common strategy is to use a deterministic lookahead (think Google maps), but what if you want to handle uncertainty? In this paper, we identify two major strategies for designing practical, implementable lookahead policies which handle uncertainty in fundamentally different ways. The first is a suitably parameterized deterministic lookahead, where the parameterization is tuned in a stochastic simulator. The second uses an approximate stochastic lookahead, where we identify six classes of approximations, one of which involves designing a “policy-within-a-policy,” for which we turn to all four classes of policies. We claim that our approximate lookahead model spans all the classical stochastic optimization tools for lookahead policies, while opening up pathways for new policies. But we also insist that the idea of a parameterized deterministic lookahead is a powerful new idea that offers features that, for some problems, can outperform the more familiar stochastic lookahead policies.

A transportation problem in its balanced form where all parameters and variables are of triangular intuitionistic fuzzy values is considered in this study. In the literature of the field, the existing proposed approaches have many shortcomings, e.g., obtaining negative solutions for the variables and obtaining negative objective function value in existence of positive unit transportation costs. In this study, considering the existing shortcomings, a new and effective solution approach is proposed to overcome such shortcomings. The performed computational experiments prove the superiority of the proposed approach over those of the literature from the results’ quality.

Naturally decision makers try to maximize ratio of return/risk, return/cost, and time/cost of transportation problem under uncertain environment. In such cases fractional transportation problem (FTP) play perfect role in instead of ordinary transportation problem. Some limited methods for the solution of fractional transportation problem using exact or fuzzy parameters are available in literature, and existing methods cannot deal uncertain FTP properly having hesitation factors due to inexact information. Here, I introduce the concept of intuitionistic fuzzy expectation of trapezoidal intuitionistic fuzzy numbers, and some related theorems are presented. Further, I present the concept of trapezoidal intuitionistic fuzzy fractional transportation (TIFFTP) problem, and a methodology for the solution of TIFFTP problem based on expectation of trapezoidal intuitionistic fuzzy numbers. Finally, I illustrate the presented TIFFTP problem by using an example.

Traditional reactive power optimization mainly considers the constraints of active management elements and ignores the randomness and volatility of distributed energy sources, which cannot meet the actual demand. Therefore, this paper establishes a reactive power optimization model for active distribution networks, which is solved by a second-order cone relaxation method and interval optimization theory. On the one hand, the second-order cone relaxation technique transforms the non-convex optimal dynamic problem into a convex optimization model to improve the solving efficiency. On the other hand, the interval optimization strategy can solve the source–load uncertainty problem in the distribution network and obtain the interval solution of the optimization problem. Specially, we use confidence interval estimation to shorten the interval range, thereby improving the accuracy of the interval solution. The model takes the minimum economy as the objective function and considers a variety of active management elements. Finally, the modified IEEE 33 node arithmetic example verifies the feasibility and superiority of the interval optimization algorithm.

Solving a fuzzy fixed charge solid transportation problem using batch transferring by new approaches in meta-heuristic

Objectives: To find the best optimal solution of transportation problem in fuzzy environment Method: We proposed a new method to find the optimal solution. Findings: This study introduces a Median method. By applying the same we transform the fuzzy transportation problem to an exquisite valued one and subsequently into a new proposed process to uncover the fuzzy realistic solution. Also, we find a minimum transportation cost. Novelty: The numerical illustration demonstrates that the new projected method for managing the transportation problems on fuzzy algorithms. AMS Mathematics Subject Classification (2010): 90C08, 90C90 Keywords Median, Median of Trapezoidal Fuzzy Numbers, Median of Triangular Fuzzy Numbers, Trapezoidal Fuzzy Numbers, Transportation Problem, and Fuzzy Transportation Problem

In this study, the paper delves into precision challenges within traditional transportation problem solutions, which rigidly define cost, supply, and demand. Acknowledging the inherent vagueness in real world contexts, the research explores the efficacy of intuitive fuzzy sets as a potent tool. Organized into four distinct sections, this work utilizes decagonal intuitionistic fuzzy numbers for managing supply and demand, while upholding conventional approaches for cost considerations. Employing a fuzzy ordering method, optimal solutions are derived by adjusting the configuration of decagonal intuitive fuzzy numbers across each segment. Through a comparative analysis, the Study identifies the most effective solution, with initial sections addressing balanced geometric intuitionistic fuzzy transportation problems and the final part focusing on unbalanced scenarios, specifically emphasizing supply and demand complexities.

In This Issue

Robust optimization of uncertain structures based on normalized violation degree of interval constraint

The purpose of the article is to develop the method for solving two‐ and three‐index fuzzy transportation problems. The fuzzy models of transportation problems allow formalizing situation for the using of fuzzy resources which should take into account in case of the uncertainty in the determination of the volume of production and consumption. Additional information is introduced in these models about the possible values of the needs in the form of fuzzy sets. The corresponding membership functions can be viewed as a way to approximate an expert display of available non‐formalized his ideas about the real value of the parameter on the basis of which the various possible values of each particular parameter values are assigned to the membership functions. Research methods is a mathematical modeling based on transport problem, solved on a network, that consists of a finite number of nodes and arcs between them, is a linear programming problem (LPP), if the total cost of transport and restrictions on traffic volumes are defined by linear functions. Scientific novelty of the research is to solve transportation problems with intermediate points that reduce to solving two‐index and three‐index tasks are considered. The ways to find the optimal solution of fuzzy transportation problem, in which resources are given in the form of triangular fuzzy numbers. Conclusions. Method of transformation in the system of constraints for the solving the crisp and fuzzy transportation problems with intermediate points has been proposed. The proposed method is illustrated by the example of real transportation problem.

Day-ahead interval scheduling strategy of power systems based on improved adaptive diffusion kernel density estimation

The transportation problem is a special case for linear programming. Sometimes, the amount of demand and supply in transportation problems can change from time to time, and thus it is justified to classify the transportation problem as a fuzzy problem. This article seeks to solve the Fuzzy transportation problem by converting the fuzzy number into crisp number by ranking the fuzzy number. There are many applicable methods to solve linear transportation problems. This article discusses the method to solve transportation problems without requiring an initial feasible solution using the ASM method and the Zero Suffix method. The best solution for Fuzzy transportation problems with triangular sets using the ASM method was IDR 21,356,787.50, while the optimal solution using the Zero Suffix method was IDR 21,501,225.00. Received February 5, 2021Revised April 16, 2021Accepted April 22, 2021