在配銷系統面對隨機需求時，常利用水平轉運來共享存貨、降低缺貨機率，即系統中之零售點除供應其顧客直接需求外，亦可透過水平轉運的方式提供或接收存貨，以降低系統之整體需求風險；在實務上，當顧客所需之商品庫存不足時，可向系統中之其他分店進行緊急調貨，以避免缺貨的發生。決策者必須決定此系統之存貨控制政策，即為考慮水平轉運之存貨問題。在現有相關文獻中，討論水平轉運與隨機需求之理論模式發展未臻完善，除文獻十分稀少，亦多採用近似分析，本研究期望發展較精確之單位時間期望總成本模式，以決定各零售點之再訂購點與固定訂購批量。
本研究考慮單階層多個相同零售點之存貨系統，顧客需求為普瓦松隨機過程(Poisson process)，零售點以再訂購點決定是否提供緊急水平轉運，若存貨量低於再訂購點，則不提供轉運以防止零售點本身之缺貨，並向上游廠商訂購一個批量以補足存貨。模式中考量之相關總成本包含：訂購成本、存貨持有成本、缺貨成本以及水平轉運成本。
根據隨機過程與存貨理論，本研究以數學分析建構考慮水平轉運之存貨模式，探討期望成本模式之特性，並利用所發現之性質發展一求解方法，可快速求得最佳或近似最佳存貨政策。演算結果顯示，俱水平轉運系統其最佳存貨政策下之期望總成本明顯低於無水平轉運之古典存貨模式，亦透過模擬實驗驗證成本分析式之精確性，發現最佳政策下之平均成本估計偏差為0.41%，顯示其近似表現良好。在總共64組之演算實驗中，本解法可求得最佳決策之機率約為63%，而其餘組合皆可求得近似最佳解，平均成本偏差為0.22%，顯示其求解品質良好。另外，經統計分析亦發現，當需求速率較低、前置時間較長，缺貨與存貨持有成本較高，水平轉運與訂購成本較低時，使用水平轉運機制之效益越顯著。

An inventory replenishment problem with emergency lateral transshipment for a one-echelon supply chain is investigated in this thesis. The system consists of several identical retailers, where demand follows a Poisson process. The (reorder-point s, fixed-quantity Q) ordering policy is implemented; the optimal control policy is to be determined to minimize the expected total cost per unit time. The expected total cost includes ordering cost, inventory holding cost, emergency lateral transshipment cost, and backordering cost of shortage.
Via renewal reward process, an approximate expected cost model is analyzed. The convexity of the cost function with respect to the control policy has been established. An efficient solution procedure is then developed to find the near optimal or optimal (s, Q) policy. In comparison with the simulation models, computational result with 64 cases has demonstrated that the approximate analysis is very accurate. The approach finds the optimum solution for 40 out of 64 instances with an average cost deviation of 0.22% from those solution found with local enumeration. It indicates that the performance of the approximate model and the solution procedure is excellent. Statistical analysis in the numerical study also illustrates that the advantage of lateral transshipment when a supply chain has low demand rate, long lead time, high shortage and holding cost, or low transshipment and ordering cost.

一、中文部分
陳彥方（2007）。俱水平轉運之二階層存貨系統再訂購點暨固定訂購批量模式。國立成功大學工業與資訊管理學系碩博士班碩士論文，台南市。取自https://hdl.handle.net/11296/4b94za

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