Research On Location Routing Problem In Emergency Logistics Under Stochastic Demand And Travel Time

Frequent natural disasters and public health emergencies cause serious personal and property losses to human beings every year.However,timely rescue measures can minimize the impact of disasters.Facility location and vehicle routing are two interrelated sub-problems in emergency logistics systems,and most of the current papers deal with them separately,which are prone to suboptimal solutions.Due to the great uncertainty in emergency logistics,demand is often unpredictable,and as disasters wreak havoc on roads,the travel times of vehicles in the road network are uncertain.In addition,the attitude of decision makers towards risk is crucial for emergency decision-making.However,for the time being,there has been no research on the impact of all the above factors on emergency logistics.Considering both stochastic demand and travel time factors,this paper aims to optimize the time efficiency and economic benefits of emergency rescue.Then,a bi-objective combinatorial optimization model based on conditional value-at-risk with regret(CVaR-R),which can grasp the attitude of decision makers towards risk and comprehensively capture the variability of uncertainties.The regret value is defined as the difference between the object value between the implemented solution and the optimal solution in the same situation,where the optimal value is obtained by a deterministic model with known solution demand and travel time.In view of this,the model based on CVaR-R solves the Pareto solution by designing a hybrid optimization algorithm(variable neighborhood search + non-dominated sorting genetic algorithm Ⅱ,VNS+NSGA-Ⅱ).At this time,the decision maker still cannot determine the optimal solution from the Pareto frontier.Therefore,the average sacrifice measured by ρ-mean is introduced to obtain the Nash bargaining solution.In this paper,two test examples are designed to verify the model and algorithm.The small-scale example is solved by the Cplex and VNS algorithms respectively,and the results are consistent.The large-scale example uses VNS+NSGA-Ⅱ to solve the Pareto solution set,and then determines the NBS from the Pareto front by setting the distance parameter ρ.The results show that the VNS algorithm can accurately obtain the exact solution of small-scale example,and the hybrid optimization algorithm can also solve the bi-objective combined optimization model based on CVaR-R for a large-scale example in a reasonable time.In addition,the study also found that both the confidence level and the distance parameter will affect the determination of NBS.By changing the distance parameter,a solution that meets the risk preference of decision makers can be obtained,which provides decision support for emergency logistics departments in facility location selection and vehicle routing design.