在現今供應鏈合作的環境中，成員之間多以策略結盟的方式進行合作，藉此來降低彼此各項作業的成本。同時在利益的考量上，不再只是單方面的針對供應商或採購者，而是必須考慮整個供應鏈成員的共同利益。本研究的問題背景為：單一供應商在購買原物料後，經過加工生產，製造成完成品，最後將完成品配送給多個採購者。本研究的決策變數分別為：供應商之生產週期數與採購者之補貨週期；即期望透過尋找最佳的供應商生產週期數以及採購者的補貨週期，降低整體供應鏈的平均總成本。在理論分析的探討中，我們首先先推導出由供應商和所有採購者所組成的聯合總平均成本，接下來再針對聯合總平均成本曲線的最佳解結構特性進行探討(如片段凸性、接合點等)。其中我們證明得到聯合總平均成本函數對時間T具有片段凸性的性質。同時，針對在聯合總平均成本曲線的最佳解位置，即在其接合點及區域最低值的發生點，我們推導出其封閉解的公式。上述之理論分析的結果，將有助於提出一有效的搜尋演算法，以求取本模式的最佳解。論文中也將舉一範例與多個隨機實驗之數據來驗證並說明本研究中得的理論結果。 In this paper, we consider an integrated inventory model with one vendor and multiple buyers. In this 3-tier supply chain, this vendor purchases raw material, produces into finished items, and delivers finished items to multiple buyers. The focus of this study is to secure the optimal common cycle for the vendor’s production and all the buyers’ replenishment to minimize the average total cost. To approach this problem, we first derive the joint total average cost that occurs from the vendor and all buyers. Then, we analyze the optimality structure of the optimal joint total average cost curve with respect to the value of common cycle (T). We show that the joint total average cost curve is piece-wise convex. The junction points on the optimal joint total average cost curve can be easily located by a closed-form formula. We propose an efficient search algorithm for securing the optimal solution of this problem. In order to improve the effectiveness of the search algorithm, we derive an upper and a lower bound on the value of common cycle. A numerical example demonstrate that our search algorithm secures the optimal solution in a very short run time.
