由於市場中流行性產品不斷的推陳出新，愈來愈多的產品符合單期模式在價格的假設條件：在銷售期開始時價格較高；而銷售期結束時，僅有殘值，而使得單期模式的研究與應用逐漸受到重視，各種不同的模式已逐漸被提出，例如：數量折扣、允許退貨…等。這些模式的提出都是為了促使原本的單期模式更符合現實生活中的情況。然而以往的文獻中，較少有學者討論現實生活中的預購現象。
本研究建立考慮預購策略的單期模式，模式中引進預購意願率函數來說明當零售商提供相當的折扣率給予消費者時，市場中會有部份比例的消費者會願意提早進行購買，而進行預購的消費者比例即為預購意願率。
本研究探討預購策略對單期模式的影響，目標為最大化期望利潤，零售商以折扣率與訂購量作為決策變數，討論當消費者的預購意願率型態為理性型、衝動型、保守型、門檻型與複合型時對利潤函數的影響，並求解各預購意願型態的公式解。此外考慮產品數與需求型態之不同，本研究將預購策略納入單期模式後，可分為三種模式類型：單一產品預購單期模式、多產品預購單期模式與模糊需求預購單期模式。預購單期模式討論預購策略對單期模式之影響；多產品預購單期模式延伸預購單期模式，考慮決策者面對多產品且具有採購預算限制情況下，預購策略對多產品單期模式之影響，並提出可行之演算法來找出在採購預算限制下的最佳折扣率與訂購量。而與預購單期模式及多產品預購單期模式不同，單一產品模糊需求預購單期模式考慮當欠缺歷史資料造成需求之不確定性無法以隨機變數之形式來呈現時，採用模糊數來描述需求之不確定性，進而求解最佳折扣率與訂購量。
經由數值範例，本研究發現考慮預購策略的單期模式，在任何預購意願型態所得到的期望利潤中，皆大於原有單期模式的期望利潤，而此增量可視為預購意願率函數的資訊價值。

Some fashionable products are considered single-period products, which are products whose value is high/low at the beginning/end of the selling period. Researchers have extensively studied single-period problems. Quantity discounts, price discounts, and returns have been considered However, few studies have discussed the reservation policy in single-period models even though it is commonly used in business.
This study considers the reservation policy and the associated price discount in single-period models. The willingness rate, which is a function of the discount rate, is used to represent the proportion of the potential market that is attracted to make a reservation when a discount is offered. Several types of willingness function, i.e., rational, impulsive, conservative, threshold, and compound, are discussed to construct the profit function. The objective is to maximize the profit function with two decision variables: order quantity and discount rate.
The discount rate may have an impact on the extra-demand which is independent of the potential market. Based on demand variable types, the number of product types, and extra-demand, five single-period models are established. In the models, demand is considered as a random variable that follows a normal distribution, or is defined as a fuzzy number. An algorithm that solves the optimal discount rates and order quantities, restricted by a retailer’s purchasing budget, is proposed for cases that include several product types.
Numerical examples show that the optimal profits of the proposed models are higher than those of single-period models. The increase in profit could be considered as the information value of the willingness function.

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