We present a mathematical model in an integer programming (I.P.) framework for non-linear delay costing in the airline industry. We prove the correctness of the model mathematically. Time is discretized into intervals of, for example, 15 minutes. We assume that the cost increases with increase in the number of intervals of delay in a piecewise linear manner. Computational results with data obtained from Sydney airport (Australia) show that the integer programming non-linear cost model runs much slower than the linear cost model; hence fast heuristics need to be developed to implement non-linear costing, which is more accurate than linear costing. We present a greedy heuristic that produces a solution only slightly worse than the ones produced by the I.P. models, but in much shorter time.

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关于航空业分段线性时延成本优化模型的说明

我们在整数编程（IP）框架中提出了一种数学模型，用于航空业中的非线性延迟成本核算。我们用数学方法证明了模型的正确性。时间被离散为例如15分钟的间隔。我们假设，成本随着分段时间间隔的增加而增加，且呈分段线性方式。根据从悉尼机场（澳大利亚）获得的数据进行的计算结果表明，整数规划非线性成本模型的运行速度比线性成本模型慢得多。因此，需要开发快速启发式方法来实施非线性成本核算，该方法比线性成本核算更准确。我们提出了一种贪婪的启发式方法，该方法产生的解决方案仅比IP模型产生的解决方案稍差，但时间却短得多。