不确定性条件下的设备替换优化的随机动态规划方法

A Stochastic Dynamic Programming Approach for the Equipment Replacement Optimization under Uncertainty

本文提出了一种解决设备更新换代优化(ERO)问题的随机动态规划(SDP)模型,用以明确地解释在车辆利用中的不确定性,并采用Bellman算法解决ERO SDP问题.针对SDP状态空间的增长,提出了特殊简化算法,以解决动态规划方法中固有的'维数灾'问题,确保所需的内存和计算时间不会随着时间范围的增加而成倍增长.并对SDP软件的实现技术、功能和图形用户界面(GUI)进行了讨论,开发了基于SDP的ERO软件,并使用美国得克萨斯交通局(TxDOT)现有车辆数据进行验证.对统计结果、软件计算时间和求解效果进行综合分析,结果显示,使用该ERO软件,估计大量成本可以节省.

In this paper, a stochastic dynamic programming（SDP） based optimization model is formulated for the equipment replacement optimization（ERO） problem that can explicitly account for the uncertainty in vehicle utilization. The Bellman approach is developed and implemented to solving the ERO SDP problem.Particular attention is paid to the SDP state-space growth and special scenario reduction techniques are developed to resolve the＂curse of dimensionality＂issue that is inherent to the dynamic programming method to ensure that the computer memory and solution computational time required will not increase exponentially with the increase in time horizon. SDP software computer implementation techniques, functionalities and the Graphical User Interfaces（GUI） are discussed. The developed SDP-based ERO software is tested and validated using the current Texas Department of Transportation（TxDOT） vehicle fleet data. Comprehensive numerical results, such as statistical analyses, the software computational time and solution quality, are described and substantial cost-savings have been estimated by using this ERO software.