折現收益之完全預購商品的供貨訂價策略及週期控制

The Pricing Strategy and Period Control of Complete Pre-Ordered Merchandise Supply under Discounted

本研究是聚焦在完全預購商品的訂價策略及週期性供貨，其中供貨的週期長度及在預購期間每一個時點之商品的價格水準皆為決策變數。當一位顧客在商品預購期間的某時點進入一個完全預購的商店，且對當時點之商品的售價水準表明其需求意願時，商品供應商將會告訴他，必須等待一段時間之後才能取得該商品。本研究假設：(1)潛在顧客對於商品的需求率是當時點之價格水準的線性遞減函數；(2)顧客願意訂購的比率是等待取貨之時間長度的指數遞減函數；(3)完全預購商店對於顧客在每一個時點之預購的收益採取折現處理（考慮連續複利之未來值）。基於上述的假設，本研究建立一個可具體討論的數學模式。如何決定出預購商品之最佳供貨週期長度及預購期間每一個時點之最佳價格水準，才能使完全預購商店在此預購期間之單位時間利潤為最大，則為本研究的主要內容。此外，本研究更進一步探討所得到的最佳解之特性，以提供行銷實務之運作參考。characteristics of optimal solutions in order to provide a reference for marketing practice.

This study focuses on the pricing strategy and period control of complete pre-ordered merchandise. The supply period length and the price level at each point in time during the pre-ordered period are decision variables. When customers step into a complete pre-ordered store at a certain point in time during the pre-ordered period of merchandise, they will review the merchandise and consider the demands based on the price level at that point in time. However, after declaring the intension to purchase the merchandise, the store assistant informs that the merchandise will not be available for a period of time. The assumptions in this study are: (1) the demand rate of merchandise for potential customers is a linear decreasing function of price level at that point in time; (2) the rate for the customers’ willings to pre-order is an exponential decreasing function of the waiting time length for taking merchandise; (3) the revenue for customers’ pre-ordering at each point in time are processed by discounted by the complete pre-ordered store (consider the future value with continuous compound interest). Based on the assumptions, we constructed a mathematical model that is concrete to discuss. The main part of this study is how to determine the optimal supply period length and the optimal price level at each point in time during the pre-ordered period of merchandise in order to maximize the unit time profit for the complete pre-ordered store. Furthermore, we discussed the characteristics of optimal solutions in order to provide a reference for marketing practice.