衡量報童類型產品的獲利能力之可達成能力指標及其應用

Abstract

本論文提出一新指標“可達成能力指標I A ”，此可準確且簡易測量出常態需求的報童類型產品之獲利能力。此獲利能力定義為最佳訂貨條件下，達成目標利潤的機率。當分配的參數未知時，一個不偏並且有效的I A 估計量將被導出來估計實際的I A。藉由所提出的指標，此論文也研究兩個常在存貨系統所發生的問題，產品評估問題和產品選擇問題。 首先，我們先考慮單一種舊產品被儲存。當新產被引進時，由於受到儲存空間的限制，某人應當決定舊產品是否依然值得被訂購或是應當被削減。因此，我們研究產品評估，即檢測舊產品的獲利能力是否達到所設定之需求。我們利用統計檢定方法來處理此問題。檢定的臨界值將被計算來決定評估的結果。在設定的檢定力與信賴水準下，樣本數所需的大小也被研究。生鮮產品的實例被呈現來討論所提出方法的適用性。 實際上，需求資料有時是多組樣本而非單一樣本。因此，我門估計及檢定I A 基於多組樣本。基於多組樣本的假設檢定用來處理產品評估問題被呈現出。實際案例有關甜甜圈的銷售被呈現出來探討此方法的適用性。 假如多種舊產品被考慮來互相比較，我們就得研究產品選擇問題，即比較兩產品並選擇其中一個具有最低獲利能力的產品。同樣的，統計的假設檢定被利用來處理產品選擇問題。檢定的臨界值將被計算出來去決定選擇的結果。在設定的檢定力與信賴水準下，樣本數所需的大小也被研究。應用實例關於英語教材雜誌的比較被呈現出來討論此方法的適用性。

In this dissertation, we develop a new index “Achievable Capacity Index, I A ”, which can accurately and simply measure the rofitability of newsboy-type product with normally distributed demand. Note that the profitability defines as the probability of achieving the target profit under optimal ordering condition. An unbiased and effective estimator of I A is derived to estimate actual I A as the parameters of distribution are unknown. By using the proposed index, this dissertation also investigate two common problems in the inventory systems, product evaluation problem and product selection problem. First, we consider the single old stock product. If the new product is introduced, one ought to judge whether the old product is unworthy of being ordered or is curtailed due to the spatial constraint in the warehouse. Therefore, we investigate the product evaluation which examines whether the profitability meets a designated requirement. We utilize the statistical hypothesis testing methodology to tackle this problem. The critical value of the test is calculated to determine the evaluation results. The sample size required for the designated power and confidence level is also investigated. An application example for a fresh food product is provided to illustrate the practicality of the proposed approach. Practically, the market information regarding demand is sometime obtained from multiple samples rather than single sample. Therefore, we estimate and test I A based on multiple samples. A hypothesis testing for tackling the product evaluation problem based on multiple samples is presented. Critical values of the test are calculated to determine the evaluation results. A real case on the sales of donuts is presented to illustrate the applicability of our approach. If the multiple old products are considered to compare each other, we study the product selection problem which deals with comparing two old products and selecting the one that has a significantly lower rofitability. Also, the statistical hypothesis testing methodology is performed to tackle this selection problem. Critical value of the test is calculated to determine the selection decision. Sample size required for a designated power and confidence level is also investigated. An application example on comparing English-teaching magazines is presented to illustrate the practicality of our approach.