考虑外包的货运航空公司货流分配问题

针对货运航空公司大量、纷繁交错的航空货运需求，制定合理的路径规划和配流方案可以降低运输成本、提高运输效率。考虑货机运输和外包运输2种运输方式，建立了运力配置和货流分配一体化的混合整数规划模型。以中国国际货运航空有限公司为例进行算例求解，根据不同运输距离对货流进行预分配，根据OD对机场所在集合预先规定货流可以中转的机场，不仅缩小了搜索空间，比两者均不处理时节省了85.12%的计算时间，而且中转货流运输路径总长度和中转货流周转量与不处理相比也分别降低了17.19%和28.99%，减少了大量绕路。得到的结果与不考虑外包的模型相比节省了4.87%的成本。引入外包价格系数进行灵敏度分析，随着外包价格系数从1.2到0.8不断减小，货运航空公司通过外包运输的货物量增加，同时小型货机执飞的航段不断减少，而大型货机执飞的航段没有变化。对不同运输方式的单位运输成本随运输量变化的曲线进行分析，当货运航空公司在面临新增局部货运需求时，可以不改变全局方案，而根据曲线及剩余运力情况做出较优的决策。 

Cargo flow distribution of cargo airlines considering outsourcing

For cargo airlines, in the face of a large number of complicated air cargo demands, formulating reasonable route planning and distribution schemes can reduce transportation costs and improve transportation effciency. We established a mixed integer programming model that integrates transport capacity allocation and cargo flow distribution and took Air China Cargo as an example to solve the model, in which airlines can use their self-owned cargo aircraft or outsourcing service for transportation. We proposed two data processing ways: pre-allocating cargo flow according to different transportation distances and pre-specifying transit airports according to OD pairs, which not only reduces the search space, but also saves 85.12% of the calculation time compared to the situation without data processing. The total length of freight transportation path and the turnover of transit freight flow are also reduced by 17.19% and 28.99% compared with non-preprocessing, which reduces a large number of detours. Compared with the model without outsourcing, the integrated model saves 4.87% of the cost. Then the outsourcing price coeffcient was introduced for sensitivity analysis. As the outsourcing price coeffcient decreases from 1.2 to 0.8, the outsourcing cargo volume increases. At the same time, the flight segments operated by small aircraft decrease, and the flight segments allocated to large aircraft do not change. Finally, we analyzed the curves of unit transportation cost varying with transportation volume on the same flight segment for different modes of transportation, which provides a reference for airlines to respond to the temporary segment demand, and provides a better solution according to curves and residual transport capacity without changing the overall plan.