Muṭāli̒āt-i Mudīriyyat-i Ṣan̒atī (Dec 2022)
Presenting a mathematical location-routing model for the perishable products considering dependency of fuel consumption to the vehicle' loading
Abstract
In this study, a location routing model has been considered for the distribution network of multiple perishable food products in a cold supply chain, where vehicles can refuel at filling stations. In this model, the fuel consumption is expected to vary based on the amount of load transported between nodes using a fleet that utilizes unconventional fuels. The objective of the study is to minimize the production of Carbon Dioxide, and therefore, the problem has been formulated as an integer linear programming model. To validate the model, several numerical examples were solved using GAMS software. The results indicate that, on average, fuel consumption decreases by 14 percent in this particular case. Due to the complexity of the problem, genetic simulated annealing algorithms were developed to solve real-sized instances of the problem, and their performance was also evaluated.IntroductionThe negative impacts of vehicle transportation on the environment are undeniable due to its effects on land and resource consumption. Therefore, efficient management of logistics activities and their optimization lead to providing differentiated services to customers, fast service delivery, reduced waiting times, damage reduction, customer support, and more. Considering the significant role of transportation in the generation and dissemination of environmental pollutants, as well as its irreversible impacts on the environment, the health of living beings, and ozone layer depletion, incorporating the concept of sustainability and considering environmental constraints alongside economic requirements in modeling and optimizing transportation and distribution networks can greatly contribute to environmental preservation and risk reduction.Materials and MethodsThe perishable food location-routing problem, considering the dependency of fuel consumption on the cargo load, has been formulated and solved on a complete graph consisting of customers, potential warehouse locations, and virtual refueling stations. The proposed model aims to minimize environmental impacts by minimizing fuel consumption, correlating vehicle fuel consumption with the amount of cargo transported between nodes, and optimizing the fleet composition for delivering customer orders, in addition to economic considerations and food freshness preservation. In the literature of classical location-routing problems, it is considered a challenging problem, and finding an optimal solution in this domain is difficult even for relatively small dimensions, let alone large-scale problems, where exact methods are computationally hard or nearly impossible to apply. For this reason, most research conducted to solve such problems has focused on the development of heuristic and metaheuristic methods. In this study, the genetic algorithm and simulated annealing are briefly described, and then the performance of these algorithms in solving the introduced mathematical model will be evaluated.Discussion and ResultsIn order to validate the proposed algorithms, the results obtained from these algorithms were compared to the optimal solutions of small-sized problems solved using the GAMS software. Reported numerical examples with processing times exceeding 3 hours in GAMS software were disregarded, and a total of 200 iterations were considered for the convergence of the algorithms, based on multiple experimental runs, to achieve reasonably good solutions within a reasonable time. In the solved numerical examples with small dimensions, the maximum deviation of the simulated annealing and genetic algorithms compared to the exact solution is 4.3% and 6.3%, respectively. Considering the negligible deviation values, the performance of both algorithms is acceptable for solving the proposed model. However, by comparing the solutions obtained from each algorithm, it is found that the genetic algorithm provides better solutions compared to the simulated annealing algorithm. In order to enhance the credibility of the proposed algorithms, pairwise t-tests were performed, in addition to comparing the solutions and solution times obtained. Firstly, the hypothesis of the genetic algorithm outperforming the simulated annealing algorithm in terms of solution quality was tested, followed by the hypothesis regarding solution times. According to the results, the null hypothesis was rejected in both tests, and the alternative hypothesis was accepted. In other words, the values of the simulated annealing algorithm solutions were larger than those of the genetic algorithm, as can also be observed in the box plot. Conversely, the solution time of the genetic algorithm was greater than that of the simulated annealing algorithm.ConclusionIn the conducted research, in order to further approximate the problem to real-world conditions and make it more practical, a heterogeneous fleet with non-conventional fuels was utilized, and the fuel consumption was correlated with the amount of cargo transported between nodes, aiming to minimize environmental risks alongside economic considerations in the logistics process. This problem was initially modeled by considering constraints and assumptions, and then, due to the computational complexity of solving the problem in medium and large dimensions, genetic and simulated annealing algorithms were developed to solve the proposed problem. To validate the presented mathematical model, a small numerical example was first solved accurately using the GAMS software, where the model demonstrated an average 14% fuel consumption reduction. In the next section, 15 numerical examples were generated and the performance of the algorithms in solving the proposed model was evaluated and tested in three categories: small, medium, and large. The obtained results indicate the superior quality of the genetic algorithm in finding suitable solutions for the model compared to the simulated annealing algorithm in cases where the solution time was less of a concern
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