等效化简连续型时间-费用权衡问题

Equivalent Simplification for Continuous Time-Cost Tradeoff Problem

大型工程项目中的连续型时间-费用权衡问题是复杂的项目调度问题,特别是非线性问题,需要先用适当的分段线性函数近似逼近原先的非线性时间-费用函数。等效化简是有效减少其计算量,进而使其便于求解的理想方法。针对该问题,本文采用等效化简的方法,把大型问题转化为等价的小型问题,即在不影响解的最优性的前提下,减少问题所涉及的工序数量,并减小工序的工期范围,使原来不可计算的问题变得可以计算,使复杂的问题变得简单。另外,减小工序的工期范围,便于用更精细的分段线性函数来近似逼近原非线性函数,从而提高解的准确性。在该原理的基础上,本文以CPM网络为工具,利用机动时间与网络中路长的关系,寻找求解原问题过程中的冗余工序,以及非冗余工序的冗余工期,并将其去掉,进而实现问题的等效简化。

The continuous time-cost tradeoff problem in a large-scale project is a complex project scheduling problem, especially for the non-linear problem, we need apply a piecewise linear function to approximate the primal nonlinear time-cost function. The equivalent simplification is an ideal method to effectively reduce computation and then easily solve the problem. Aiming at the problem, the paper use the method of equivalent simplification to transform a large-scale problem into an equivalent and small-scale one, that is, under the precondition of keeping the optimal solution, reducing the activities and narrowing the scope of activity duration, and then making an incalculable problem be calculable and making an complex one be simple. In addition, narrowing the scope of activity duration is conducive to apply a more detailed piecewise linear function to approximate the primal nonlinear one, which improves the efficiency and accuracy. Based on the principle, the paper makes CPM network as a tool, and applies the relationship between float and path length in the network to search redundant activities and redundant durations of non-redundant activities in the process of solving the primal problem, and then remove them to realize the equivalent simplification for the problem.