完全預購商品供貨之最適訂價策略

The Optimal Pricing Strategy of Complete Pre-Ordered Merchandise Supply

本研究係透過顧客對商品的需求率函數及顧客願意等待取貨的比率函數，來探討一個完全預購商店在缺貨期間之商品供貨的訂價策略問題，其中在缺貨期間之某時點的需求率函數是當時點之價格水準及價格變化率的線性函數。當顧客在缺貨期間之某時點進入一個完全預購的商店，且對當時點之價格水準與價格變化率之商品表明有需求意願時，他將會被告知必須等待一段時間之後才能取得該商品。此刻，顧客仍願意購買的比率是一個介於0 與1 之間的比率函數。如何建立一個可具體討論的數學模式並決定出在缺貨期間之每一個時點的最佳價格函數，才能使此完全預購商店之總利潤為最大，則為本研究的主要內容。本研究的結果顯示：在需求率函數假設為線性的假設條件下，完全預購商品之最佳價格函數依比率函數的型態而異；當比率函數為等待時間長度之指數函數型態時，最佳價格函數是一個與顧客預購商品之時點無關的常數函數；當比率函數假設為等待時間長度之線性函數型態時，最佳價格函數是顧客預購商品之時點的一個遞增函數。

In this study, we explored the pricing strategy problem at each point in time during the stock-out period for complete pre-ordered store through the demand rate function of merchandise and the ratio function for customer willingness to wait for taking merchandise, in which the demand rate function at certain point in time during the stock-out period is a linear function both with the price level and price variability at that point in time. When customers step into a complete pre-ordered store at certain point in time during the stock-out period, they will review the merchandise and consider the demands based on the merchandise price levels and price variability 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. At this moment, the ratio value for the customers still willing to pre-order is a ratio function of value between 0 and 1. The main part of this study is to construct a mathematical model that is concrete to discuss, and to determine the optimal price at each point in time during the stock-out period in order to maximize the total profit for the complete pre-ordered store. The findings of this study are as follows: Under the assumed condition that the potential demand rate function is a linear function of the price and price variability, the optimal price of complete pre-ordered merchandise is based on the type of ratio function. When the ratio function is assumed to be an exponential function of the length of waiting time for merchandise, the optimal price function is a constant that is irrelevant to the point in time for customer to pre-order merchandise. When the ratio function is assumed to be a linear function of the length of waiting time for merchandise, the optimal price function is an increasing function of the point in time for customer to pre-order merchandise.