This paper studied the shunting engine scheduling at a railway technical station with considerations of both shunting tasks(including break-up,make-up,and pick-up and delivery tasks)and non-shunting tasks(including shift,and meal tasks),time windows of non-shunting tasks,and waiting cost and outfit requirements of engines.Given the set of shunting engines and that of shunting tasks in the planning horizon,this problem lay in assigning a sequence of shunting tasks and determining the start time of shift,meal and outfit tasks(if any)for each engine.A connection net-work was constructed for each engine to describe its time-space utilization process of executing shunting/non-shunting tasks and connections between tasks.By utilizing the modeling framework for the node-arc model of the multi-commodity network flow problem,the problem was formulated into a mixed integer nonlinear programming model with the objective of minimizing the sum of total deadheading cost,total wheel stop waiting cost,total deviation penalty cost of non-shun-ting tasks and total outfit cost.The model was further transformed into a linear model,which can be solved quickly to op-timality by invoking commercial solvers.Finally,computational experiments on a realistic instance constructed based on a station were conducted to validate the feasibility and efficiency of the proposed approach.
维普
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