- 學位論文
季節性商品多期隨機需求問題之最佳訂購量
The Optimal Order Quantity for Seasonal Products Multi-Period Stochastic Demand Problem
摘要
多期隨機需求問題又稱多期報童問題，乃單期隨機需求問題之延伸，主要針對具時效或易腐商品於各期初決定使得總成本極小化之最佳訂購量。然而，日常生活中許多商品之需求量於有限規劃期內具有季節性，例如牛奶、羊肉等商品，本研究遂針對這類商品建立多期隨機需求問題之最佳訂購量模型。目前多期隨機需求問題的研究，大多採用頻率學派的統計方法，僅依賴歷史銷售資料進行決策，忽略人對市場需求的主觀判斷。故本研究採用貝氏學派的觀點，結合决策者對商品季節需求先驗知識與實際銷售量資訊，建構多期隨機需求問題之季節性動態貝氏模型。模型由觀測方程式與狀態方程式組成，觀測方程式是用來描述需求量如何隨機地依賴狀態參數，而狀態方程式則是描述前後季狀態參數之動態變化。當各期內發生供過於求或供不應求的情形時，分別以常態分配與二階動差近似法，將前一季的後驗分配修正為下一季的先驗分配，逐季迭代建立期望總損失成本最小之決策模型，根據此模型便可求出當季之最佳訂購量。最後，以數值範例說明季節性動態貝氏模型的具體應用。
並列摘要
The multi-period stochastic demand problem, also known as the multi-period newsboy problem, is an extension of the single-period stochastic demand problem. It is mainly aimed at determining the optimal order quantity for timeliness or perishable products at the beginning of each period to minimize the total cost. However, many daily products' demand is seasonality in the finite-horizon planning, such as milk, mutton and other products. This research establishes the optimal order quantity model for the multi-period stochastic demand problem for this kind of products. The current multi-period research on stochastic demand issues mostly uses statistical methods of the Frequentist, relying only on historical sales data to make decisions, ignoring people's subjective judgments on market demand. Therefore, this study adopts the Bayesian of view, combining the decision makers' prior knowledge of the seasonal demand for products and the actual sales volume information to construct a seasonal dynamic Bayesian model of the multi-period stochastic demand problem. The model is composed of observation equation and state equation. The observation equation is to describe how demand randomly relies on current season state parameter and the state equation is to describe the former one and the next season dynamic changes in parameter. When over-stock or under-stock occurs in each period, we use the normal distribution theory and two moment approximation method to adjust the posterior distribution of the previous season to the prior distribution of the next season. In this way, establish a decision model with the minimum expected total loss cost can be obtained by iteration. According to this model, we can be found the optimal order quantity in each period. In the end, we use numerical examples to illustrate the specific application of the seasonal dynamic Bayesian model.