空服員排班網路模式與求解演算法之研究

The Network Model and Solution Algorithm for Airline Cabin Crew Scheduling Problem

傳統上，航空公司之空服員排班問題一般定式為集合涵蓋問題或集合分割問題，而近十幾年來，對於室服員排班問題多以變數產生法求解之，並常需進一步配合整數規劃之演算法求得整數解。然而，當航空公司在考量不同機型接續、不同艙位等級服務限制及多基地型態之實際營運服務情形峙，將使問題更趨複雜，因此若以上述演算法求解之，將無法有效求解此類問題。為改善上述情形，本研究以網路流動方式重新定式空服員排班問題，此模式可定式為一多重貨物網路流動問題。為有效求解大規模問題，本研究利用拉氏鬆施法暨次梯度法、網路草種法、及自行發展之是先發式解法加以求解，並以流量分解法產生所有可行組員行程。最後本研究以圈內一主要航空公司之實際國際線營運資料為倒，進行測試分析，結果顯示本研究所提出之排班網路模式及求解演算法，可有效地處理大型排班問題。

Airline cabin crew scheduling problems have been traditionally formulated as set covering problems or set partitioning problems. To resolve large-scale problems in practice, the column generation approach with integer programming algorithms has usually been employed in decades. When airline carries face the the multi base operations as well as aircraft type continuity and cabin classes in practical operations, these problems become more complicated and difficult to solve. In this research, taking into account the aforementioned factors, we introduce a new network modelthat can improve both efficiencyand and effectiveness of solving cabin crew scheduling problems to help air carriers minimize crew cost and plan proper crew service rotations under the real constraints. Mathematically, the model is formulated as a multi-commodity network flow problem. A Lagrangian relaxation-based algorithm, coupled with a subgradient method, the network simplex method and a heuristic for upper bound solution, is suggested to solve the problem. Furthermore, the flow decomposition algorithm is applied to generate all pairings for cabin crews. In order to evaluate the model in practice, computational tests referring the international operation of a major airline in Taiwan were performed. The results show the networkmodel and the Lagrangian relaxation-based algorithm can be useful for efficiently solving large-scale airline cabin crew scheduling problems.