考虑随机需求的高铁快运专列停站与运能分配协同优化OA

With the growing demand for express transportation,high-speed railway(HSR)express delivery has new development opportunities.A collaborative optimization method of train stopping plan and capacity allocation scheme for HSR freight trains considering stochastic demand was proposed to utilize HSR transportation resources efficiently,align capacity allocation with actual demand fluctuations,and avoid underutilization or insufficiency of train capacity.First,accounting for demand randomness,this developed a two-stage stochastic programming model to maximize expected profit under the constraints of train stopping,train transportation capacity and station loading-unloading efficiency.In the first stage,the stopping plan and capacity allocation scheme for each train were determined to maximize the total expected profit of operating HSR express freight trains.In the second stage,based on all possible values of stochastic demand following a discrete probability distribution,the optimal actual express delivery transportation plan was formulated to maximize the operational revenue of HSR express freight trains.Then,the two-stage stochastic programming model was equivalently reconstructed into a nonlinear model according to the inherent attributes of the model.Leveraging these model characteristics,linearization techniques were devised to convert the nonlinear programming model into an equivalent linear programming model.The utilization of the commercial solver GUROBI ensured the attainment of precise solutions.Case studies on the Nanjing-Hangzhou HSR line confirmed the method's effectiveness.The results show that this method can effectively determine the optimal train stopping plan and capacity allocation for HSR express freight trains under random demand.Compared with the scheme obtained based on deterministic demand,it has a higher expected revenue,and can well adapt to stochastic demand.Meanwhile,it can avoid the intractable solution problem of scenario-based mathematical programming models caused by an excessive number of demand scenarios.The method can provide a reference for the organization of express delivery under the HSR freight train mode and helps improve service efficiency and enterprise revenue.