本研究探討二階供應鏈中之整合生產與配送批量決策問題，其中考慮訂貨式生產系統，上游俱一供應商與下游俱一零售商，在滿足需求且不容許缺貨下，採用單批次生產、多批次配送政策，決定供應商之最佳生產批量與供應商至零售商之最佳配送批量，以最小化相關整合總成本，總成本包含：上游生產整備成本，下游訂購成本，上、下游之存貨持有成本，與其間之配送成本，其中配送部分考慮實務上之比例遞減混合型運輸成本。
比例遞減混合型運輸成本其結構較傳統遞減型成本為複雜，總成本在不同配送量區段間可能不連續，屬間斷型階梯連續函數，總成本模式中包含整數與實數變數，故在求解上亦較俱挑戰性。本研究首先建立一考慮比例遞減混合型運輸成本之整合型總成本模式，進而探討其理論性質，並證明總成本函數之特性，依據此發現發展兩個快速啟發式演算法，以求得最佳或近似最佳之生產與配送批量，並與傳統文獻中所得到之結果和以窮舉法所求得之最佳解進行比較，探討模式與解法之表現。
實驗結果發現，兩種演算方法在求解品質上表現優良，其中第一種區段近似法所求解目標值與窮舉法最佳解目標值之平均偏差小於百分之一，第二種二維搜尋法則在所有實驗中皆能求得最佳解。在求解速度上，兩方法之求解時間皆小於一秒，相對而言，窮舉法之平均求解時間會因參數變化而大幅改變。在二階供應鏈整合成本模式參數方面，大部分參數對總成本皆有顯著影響，但對配送批量與配送次數而言，其影響顯著之參數相對較少，在其中，需求率與下游訂購成本同時對配送批量、配送次數與總成本皆有顯著影響，由於比例遞減混合型運輸成本之高複雜度，因此不易歸納出部分參數其特殊性質。

The purpose of this thesis is to analyze an integrated production and delivery quantity problem in a two-echelon supply chain with mixed transportation cost. It consists of a supplier at the upper echelon and a retailer at the lower echelon. The production and delivery quantities are jointly optimized to minimize the total cost per unit time, where shortage is not permitted. The total relevant cost includes setup cost at the supplier, ordering cost at the retailer, inventory carrying costs at both echelons, and transportation cost of each delivery.
To analyze the delivery cost, a mixed transportation cost is considered in the integrated cost model. It includes both the tapering and stepwise cost components, and real transportation cost/rate data from the shipping industry is used for analysis. The minimization of the integrated cost model consists of both integer and real variables. Four analytic properties are established for expediting the optimization process.
Two efficient heuristics are developed to find the near optimal or optimum production and shipment lot sizes. Numerical experiment with 64 instances has shown that both proposed approaches are efficient and effective. The interval approximation heuristic finds near optimal/optimum solution with an average cost deviation 0.02% when compared with the results using enumeration. The enhanced 2-D search algorithm finds the optimum solution in all instances when compared with that using enumeration. The average computational time in both approaches is less than one second.

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