Location-routing Problem Of Emergency Relief Based On Fairness

In 2020,the COVID-19 has trapped people home and prevented them from traveling.In the meantime,rainstorms in Shanxi Province,China,caused significant disruptions.The closure of the epidemic,the inability of relief supplies to reach the affected areas,and the inability of rescue troops to reach the affected areas in time are all problems worth studying.Destructive emergency may cause severe damage and colossal property losses.Various uncertainties force us to find a highly reliable emergency relief distribution network.In addition,how to take into account the psychological state of the people to avoid the secondary psychological trauma caused by an uneven distribution of relief is another problem we need to consider.Therefore,we established a three-level relief allocation network based on Central Resources Warehouse-Distribution Center-Disaster Area.Considering the uncertainty of the demand and transportation time,we use a robust optimization method to achieve a better solution so that the uncertain parameters have immunity.Firstly,we established a relief allocation model without considering fairness.Secondly,considering the psychology of the people,the square of the difference between the proportion of relief received and the average proportion of relief received is used to measure whether the allocation method is fair.An allocation model considering fairness is established.We used Python and Gurobi solver to solve the model with an accurate algorithm.A small-scale example is used to test the feasibility of the proposed model,then the effect of the exact algorithm is explored in large-scale samples.We use a Genetic Algorithm to improve applicability in large-scale.In addition,a more advanced algorithm is proposed by combining the Attention mechanism artificial intelligence method.Further,we gather some actual data of the rainstorms in China and then use the exact and heuristic methods to evaluate the performance.Considering fairness and efficiency,we find out the optimal location-route decision.The insights are listed below:(1)The MTZ elimination method could eliminate the sub tours;(2)Small-scale examples can be solved quickly by using Exact algorithms,while large-scale cannot find the optimal solution within a limited time.When the number of points increases by two times,the size of the adjacency matrix increases by eight times,but the pre-processing time increases by two orders of magnitude.(3)The Genetic Algorithm shows that,under the same circumstances,the transportation time of relief considering fairness will take longer than without fairness.Compared to the Exact algorithms,the Genetic Algorithm could solve large-scale instances quickly;(4)The result of using the Attention Mechanism shows that after training for a while,the model could obtain a better result in a short time.With the increase in the number of instances and training turns,the target results decreased,which is what we want.(5)The number of vehicles and the scope of the service time window will also impact the allocation.Selecting larger fleets or increasing the number of vehicles can help meet the needs of disaster areas.When the restriction of the service time window is relaxed,fairness can be improved.