經濟訂購量於前置時間不確定之 (r, S) 排隊系統應用

Abstract

由於供應商訂購前置時間的不確定性，導致備貨時需面臨下列兩個問題：何時該訂貨及該訂多少貨。本論文情境為客人依卜瓦松過程進入系統；系統有一個無限大等候區、系統有一個服務站及一個服務人員。服務時間服從指數分配，服務方式為先到先服務，每一次需要一單位存貨，當存貨為零時則停止服務，等待的客人繼續等待，此時外面的客人不允許進入系統，拒絕客人進入系統將造成損失。系統使用的存貨管理方式為，當存貨降至再訂購點r時立刻訂貨，訂購前置時間服從指數分配，貨物送達時補貨人員將存貨補充至存貨水準S。本論文構建經濟訂購量模型，成本包含訂購成本、存貨成本及缺貨成本，求出經濟訂購量模型的最佳r及S水準，並利用此水準訂定排隊存貨模型搜尋最佳r及S水準的範圍，以改善窮舉法搜尋的缺失。

Due to the uncertainty of the replenishment lead time, inventory manager faces the following two issues: when to order and the order quantity. In this study, we consider a (r, S) inventory policy where the order point is r and order-up-to-level is S. Customers enter the system following a Poisson process. The system has an infinite waiting room, and there is only one service station and one server. The service time is exponentially distributed and the service discipline is first-come-first-served. When inventory is zero, the service stops, and customer at the waiting line continue to wait. No customers are allowed to enter the system when the stock is empty. These rejected customers bring the lost sales. The mentioned-above problem is known as queueing inventory system. Queueing method and Brute Force Search (BFS) method are generally used to define the optimal levels of (r, S). In this study we establish an economic order quantity (EOQ) model to approach the queueing inventory system. We prove the unit time total cost function in the EOQ model is an unimodal with respect to r and S. Based on the optimal values of r and S, we defined the searching range of optimal values of (r, S) in the queueing inventory system to improve the BFS.