Development of a Novel Fuzzy Hierarchical Location-Routing Optimization Model Considering Reliability

Abstract

Background: This paper discusses the optimization of a novel fuzzy hierarchical location-routing problem, taking into consideration reliability. The mathematical model presented aims to determine the optimal locations of production centers and warehouses, as well as the optimal routing of vehicles, in order to minimize total costs. Methods: Because of the uncertainty surrounding the demand and transportation cost parameters, a fuzzy programming method was employed to control the model. To solve the mathematical model, both GA and PSO algorithms were used. Results: The results show that as the uncertainty rate increases, the total costs also increase. Additionally, the results indicate that the maximum relative difference percentage between the solutions of the GA and PSO, and the optimal solutions are 0.587 and 0.792, respectively. On the other hand, analysis of numerical examples demonstrates that the Baron Solver is unable to solve large-scale numerical examples. Conclusions: By comparing the results of GA and PSO, it is observed that PSO was able to solve numerical examples in less time than GA, while GA obtained better results than PSO. Therefore, the TOPSIS method was used to rank the different solution methods, which resulted in GA being recognized as an effective algorithm with a utility weight of 0.972.

Sustainable Multi-Objective Models for Waste-to-Energy and Waste Separation Site Selection

“…If it is assumed that the problem is of the graph type, it can be stated that G = (N, S) is a graph consisting of N nodes and a set of edges, S, representing communication pathways between nodes [27]. Some nodes, based on feasibility and other considerations, can serve as candidate locations [28] for setting up WtE centers (energy parks or plants). The distribution for the model was determined using MATLAB R2020b's distribution fitting tools, with historical data.…”

“…This objective function is of paramount importance because waste shipments should be dispatched in a way that covers the shortest distance to minimize potential environmental pollution. Moreover, considering that organic waste materials typically have a high moisture content, it is better to avoid long-distance transport [28], especially during very hot or very cold seasons. Icing can lead to difficulties in waste sorting, and exposure to heat and dry conditions can result in moisture loss and reduced WtE efficiency.…”