本研究之目的在建立一個隨機模型可以描述接單生產環境之下單一最終產品的生產規劃。已知最終產品的物料清單且已將其中的半成品或原物料以分割線分為庫存生產(MTS )或訂單生產(MTO)。在本文中，訂單需求發生在最終產品，且為一隨機過程，產能與服務時間符合M/G/1等候線，庫存生產的半成品需服從連續盤存制之庫存策略(Q, r)，且所有被規劃為庫存生產式之半成品均不在廠內生產，全部採外購制，因為採行外購制所以所有與第一層存貨生產相關的半成品均不需考慮，反之其他相關生產活動均在廠內進行。 在此一環境下本研究利用Busy period、Exceptional First Service與Light Traffic Heuristic建立隨機模型，此模型可以同時處理生產與存貨之間的關聯性，包含顧客在等候線中之延遲時間、存貨機率、缺貨機率。我們利用數值分析的方式來驗證此模型是否可行，在將其結果與利用模擬實際情況生產方式產生的數據進行比較，發現結果良好。最後透過參數設定可以看出存貨策略(Q, r)對延遲時間的影響的變化。 In practice, manufacturers often produce their end products by a mix make-to-order (MTO) and make-to-stock (MTS) strategy. That is, manufacturers produce the products according to the orders arrival to satisfy customer’s demand of variety or keep products in advance to shorten the lead-time of demand. This mix production system could be use to produce for single end product that is assembled by many components. The problem of making decision for which sub-item to be MTO or MTS is important. In this study, we consider the above decision problem as determine a partition line in a bill of material (BOM) of the end product. Given a partition line in a BOM, we address the problem of determine the performance measure of this production system. We consider the light traffic heuristic proposed by Sigman and Simchi-Levi (1992) and busy period to derive the distribution of delay over all customers and inventory level distribution. We evaluate the accuracy of our model by comparing it to simulation results. We also conduct a numerical analysis to explore the effect of different parameter settings impact of various parameters on performance measures of this joint production system.
