二階層動態批量問題包含供應鏈中的上游原物料及產品訂購、存貨管理與下游配銷商之進貨供貨控制等，如何有效地組織生產與採購活動以降低整體成本，是企業生產與存貨管理中重要的課題。目前動態批量相關研究雖然已經發展數十年，在求解方法與時間上均有很大的改良，但主要針對單階層生產存貨問題，二階層與多階層系統之動態存貨研究成果相對稀少，隨著供應鏈之廣泛運用，針對多階層系統之動態批量存貨研究有其理論與應用價值。
本研究探討有限期間內之二階層動態批量存貨問題，包含上游一個物流中心與下游一個配銷點，物流中心向外部訂貨，並根據配銷點的供貨需求，將產品由物流中心運送至下游配銷點。與古典動態問題相似，研究中假設每期的顧客需求為已知，在兩階層均不容許缺貨發生的狀況下，決定上下階層每一期的訂購批量，並使存貨相關總成本最小化，考慮成本包含：第一階層物流中心向外部訂購產品所產生的固定訂購成本與存貨持有成本，及第二階層配銷點向上游訂購產品所產生的固定訂購成本與存貨持有成本。在上下階層之運輸上，假設運輸或前置時間為零或固定常數，而運輸成本則依據古典動態存貨理論將其納入訂購成本中。
本研究以最小化總成本為目標，建立數學規劃模式，決定兩階層各期訂購批量，進而以目前文獻之理論基礎，建立二階層動態批量存貨問題最佳解特性，並利用其發展 之啟發式演算法，其中 為總規劃期數，以快速求得近似最佳或最佳存貨決策。演算實驗發現：在每期訂購成本與單位存貨持有成本皆固定的狀況下，演算法之求解品質優異，與最佳解比較，其總成本平均偏差為3.24%；在每期訂購成本為固定，而每期單位存貨持有成本變動之狀況下，啟發式解法與最佳解比較，其總成本平均偏差為9.39%，並發現需求平均值與總規劃期均會影響求解品質。

A two-echelon dynamic lot sizing problem without shortage has been addressed in this thesis. Demands of an item occur in finite planning periods, where warehouse at the upper echelon orders the item from supplier; and periodic delivery is made to distributor at the lower echelon. The demand at each period can only be satisfied from available stock at the distributor. Replenishment quantities for both warehouse and distributor at each period are to be determined to minimize the total relevant cost, which includes: ordering cost and inventory carrying cost at two echelons.
An integer programming model is developed to solve this dynamic lot sizing problem when the planning horizon is short or moderate. Four dominance properties of the optimal replenishment policy have been shown. Using these findings, a heuristic is developed to efficiently compute optimal or near optimal lot sizing policy, where n is the number of planning periods. The solution procedure consists of two phases: replenishment policy at the distributor is first determined by computing a proposed marginal cost ratio; and lot sizing policy at the warehouse is then determined, using the replenishment quantities obtained at phase one as input. In comparison with the optimum solutions obtained from integer programming models, the numerical study has shown that average cost deviations of solutions from the heuristic are 3.24% and 9.39% when ordering cost per period is fixed, while the inventory carrying cost per period is fixed and varied, respectively. It has also illustrated that both the mean demand per period and the length of planning horizon affect the solution quality.

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