臺灣國內路線貨運業提供時效性貨運服務，其營運網路皆採取沿途裝卸的方式運 送貨物，而不像國外的軸輻式運送網路。這種特殊的運送方式，使得臺灣在貨物路徑或車輛 路線規劃上異於國外。路線貨運業之營運規劃問題相當複雜，基本上區分為長、中、短期三 個規劃階段。長期規劃場站位置與大小，中期規劃車隊規模，而短期則規劃貨物路徑、貨櫃 指派與均衡及車輛路線。 　　貨物路徑問題是以營運成本最經濟的方式，在營運網路容量與作業條件限制下規劃貨物 的運送路徑。作業方式之限制包括每一起迄對單一貨物路徑及進入每一迄點的貨物路徑形成 一擴張樹結構。然而在每日的實務即時運作時，因每日的貨運量起伏不同，容許站所作業人 員按實際需要，對每一對貨物允許多重貨物路徑，形成即時性貨物排程問題。該問題已往的 研究多採用路徑為決策變數之模式與演算法。 然而路徑決策變數相當龐大，求解上常無法對所有可行路徑一併考量，因此先行選定K條成 本最小之可行貨物路徑，如此限制了較佳可行解之求取。因此本研究以節線流量為決策變數 來建構即時性貨物排程問題，並據以提出拉式鬆弛法與懲罰函數之Frank-Wolfe等不同的演 算法。最後本研究採用已往研究所使用的相同營運資料進行實證測試，測試結果顯示懲罰函 數法能求取更佳的解答。

　　　　　Time-definite common carriers collect, consolidate and transport time- definite small shipments for shippers. Their operation network consists of local service and line-haul operation networks. In Taiwan, the common carriers typically run their line-haul operations by making center-to-center direct feeds. As a result, their line-haul operation network is different from the most common network configuration, hub-and-spoke, in US. Despite this difference, the carriers still have to develop the most cost-effective operating plan to reduce their operating cost. The operating plan consists of long-term strategic decision which determines the size and location of facilities; the median-term tactical decision determines the fleet size; and the short-term operating decision determines freight routes, trailer assignment and balancing and feeder schedules. The freight routing problem is to determine freight routes so that the total operating cost is minimized while meeting the service and operational constraints. The operational constraints include network capacity, singular path for each O-D pair, and a directed in-tree for each destination center. However, due to daily volume fluctuation, operators are allowed to make multiple freight routes. As a result, the freight routing problem becomes real time freight routing problem. In the previous research, most of the studies use path as decision variable. However, there are enormous number of paths thus, they pre-determine k paths for each O-D pair. It results in an inferior solution. In this research, we formulate the problem by link variable. We also propose two algorithms, the Lagrangian Relaxation and penalty method. We perform the numerical testing on the same data set used by the previous research. The results demonstrate the penalty method which outperforms the previous approaches based on path formulation.