以近似法求解考慮材積與重量之航空貨運營收管理問題

Abstract

在國際貿易自由化與全球供應鏈的發展下，航空貨運在過去數十年蓬勃發展，目前航空貨運之成長幅度已超越航空客運之成長。此外，自從美國航空公司利用營收管理成功地提高營收後，營收管理於航空客運業已是一項十分普及的技術。有鑑於此，本研究希望能將營收管理應用於航空貨運的艙位規劃上，將有限的艙位妥善使用，以增加航空公司的期望總收益。就營收管理的角度而言，目前航空客運之營收管理相當成功，而航空貨運尚須考慮許多重要的特性，如需考慮貨物材積與重量或是艙位供給之不確定性等等。 應用隨機序程之動態數學規劃(Dynamic Programming, DP)模式，建構一考慮貨物材積與重量隨機性之數學模式，並發展Joint Approximate Heuristics(JAH)近似法來求解期望收益函數。JAH近似法將以接受訂位之累積平均材積與重量的DP狀態變數，只運算其中之特定幾點，來簡化運算之複雜度。除此之外，還利用模擬需求到達，進而應用多元線性迴歸，求出DP模式邊界條件之超賣賠償函數。 本研究利用模擬之方式，對模式進行驗證，並對幾個模式中之重要因素進行敏感度分析。將結果與先前文獻之Decoupling Heuristics(HD)方法作比較，從小型範例之結果可以發現，HD啟發式解法所求出之艙位控管決策有其不合理之處。而在中型範例首先對材積與重量之間距(a, b)進行敏感度分析，由結果發現，平均模擬收益值隨著a、b值之增加，改善幅度越來越小，且不需很大的a、b值，即可獲得不錯之平均收益。進而探討HD啟發式解法、JAH演算法與無控管下之績效，HD與JAH兩者控管方式皆能夠獲得不錯的結果，與無控管之平均收益相比都能夠高出7%以上。又JAH控管與HD控管相比，JAH控管與HD控管在不同情形下，互有所長，JAH控管之平均收益普遍略低，差距在1%內，但同時標準差卻較低，收益較為穩定。並觀察到在材積容量為瓶頸限制，即材積較重量供給少時，以JAH控管會比HD控管好很多，可能因為HD演算法在材積之費率函數計算上過於簡化，造成對材積部分之控管較為不精確。

Due to world trade liberalization and global supply chain, air cargo industry has been booming for the past several decades. The growth rate of air cargo has surpassed that of air passengers. On the other hand, since American Airlines successfully applied revenue management to raise its profit, revenue management has become a common technique in air passenger business. Therefore, this study is aiming to apply the revenue management concept to the planning and control of air cargo space, so the airlines can fully utilize the limited cargo space to increase the expected revenue. This study develops a Joint Approximate Heuristics (JAH) based on approximating the expected revenue function in a dynamic programming (DP) model considering both the stochastic volume and weight of air cargo shipments. In order to alleviate the computational load, the approximation is achieved by computing only a specific numbers of data points, which evenly spaced in the ranges of the DP stage variables, the accumulated average weight and volume of the accepted bookings. In addition, the expected penalty due to overbooking, the boundary condition of the DP model, is estimated by simulating the arrivals and then by a multiple linear regression analysis. This study verifies the model by performing a series of simulation experiments, including the sensitivity analysis for several important factors. In particular, the result is compared with that of a decoupling heuristic (HD) of a key prior research work. It is found that it does not need a large number of sampling points to achieve a good solution quality. In general, the average revenue using JAH is 7% higher than the FCFS (first-come-first-serve) policy and roughly the same as that by the HD control, but the revenue variation by JAH is smaller, suggesting more stable revenue. Especially, if the volume is the bottleneck of the capacity, using JAH control could get better performance than the HD control.