摘要<br>
　　規劃一個有效率、高品質的運輸系統，首先要構建一個適當的營運網路，以往的營運網路採用起點與迄點間的直接網路（direct network）運輸，然而此種營運模式，因每一運具的承載率低，故所耗用的運具較多。因此而有軸輻式網路（hub-and-spoke network）的提出，軸輻式網路(hub-and-spoke, H/S)的結構提供人流或物流於中繼站轉運的功能，替代運具低承載率的高運輸成本。

　　軸輻式網路於實務作業的應用上，由最初期的純軸輻式網路(pure Hub-and-Spoke,H/S)，逐漸隨著業者實務性的需求，而有層級式軸輻式網路(hierarchical H/S)、單向裝或卸具軸輻式(H/S with one-directed stopovers)、沿途裝卸軸輻式(stopovers network)以及含分支之軸輻式(stopovers with feeders network)等型態。

　　軸輻式網路中，中繼站之轉運成本具有規模經濟特性，達到旅客或貨物運輸業者經營的總營運成本最小化。因此軸輻式網路的結構，被廣泛的應用於旅客或貨物的路面與航空運輸以及通訊業中。

　　本研究之網路，為具規模經濟特性之軸輻式網路，在服務網路中，存在一個以上的場站(depot)，在單一週期內服務區內之需求，每架飛機在該週期內只能服務一條路線，並且在整個配送過程中不能違反時窗限制及容量限制的情況下，求業者之成本最小化或利潤最大化。

　　本研究以FedEX Express國際快遞公司及台南市區公車為例，首先構建具規模經濟特性之營運網路，並依其網路架構數學模式。以frank-wolfe algorithm 線性化成本函數，並以以商用軟體ampl呼叫cplex求解數學模式。
　
　　最佳規劃共需14 班MD-11 型飛機及8班A310型飛機，運輸成本929,242 美元，轉運成本為400,049美元，故總成本為1,329,291 美元。中繼轉運站之轉運量分別為，蘇比克灣：672,808磅、台北221,568磅以及東京248,137磅。台南市區公車方面，則為一小時可節省430.672元/小時。

Abstract<p>

　Before planning a transportation system with efficiency and high quality,，we should construct a suitable operational network. Former operational network uses direct network between origin and destination. However , the direct network is proposed because transport means having low load-factor, this pattern needs more fleet. The hub-and-spoke network provides passengers and cargo transfer function in hubs to substitute low load-factor modal which has expensive transportation cost.

　There are several types of H/S network. Application of the hub-and-spoke network, from the type of pure hub-and-spoke during the initial period becomes to types hierarchical H/S, H/S with one-directed stopovers, stopovers network and stopovers with feeders network because of need of carriers.

　Within the hub-and-spoke network，transfer cost of hubs has characteristics of economies of scale to make carriers minimize their total operational cost. Therefore, the construction of the hub-and-spoke network is applied in land and air transportation of passengers and cargo and in telecommunication industry.

　In this research, the definition of the H/S network is : there are more than one depot and we need to satisfy all needs in the H/S network during single cycle and each aircraft can provide service on only one route and this H/S network cannot violates limitation of time windows and volume. According to limitation above, we try to minimize the carriers’ cost.

　Take FedEX Express and the bus network in Tainan city for example. Optimize his hub-and-spoke network design problem with economies of scale. At first, construct the hub-and-spoke network design problem with economies of scale, and then according to its network to construct the mathematical model. Use frank-wolfe algorithm to linearize the cost function and use “ampl” to solve the mathematical model.

　The optimization needs 14 MD-11 aircrafts and 8 A310 aircrafts,and the transportation cost is 929,242 US dollar, transfer cost is 80,263 US dollar，and total cost is 1,009,505 US dollar. The amount that transfers in hubs is : Subic Bay,682,808 pounds; Taipei 221,568 pounds and Tokyo 248,137pounds. In the bus network in Tainan city, we can save 430.672 dollars per hour.

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