在這篇研究中，我們講考慮在一個線性市場中，兩家競爭廠商的最佳決策問
題；所謂的最佳決策問題包含了零售價格、商品的訂購量以及服務水準。在這篇
研究裡面所說的服務水準指的是一家廠商所宣稱能滿足前來消費顧客的比率，而
不是指服務的好壞。在定義了服務水準之後，我們的研究背景是在一條線性的市
場裡頭，有兩家競爭廠商座落在這個線性市場的兩個端點；而我們要研究的目的
是這兩家競爭廠商如何對零售價格、商品的訂購量以及服務水準做最佳的決策，
來使得其本身的期望利潤極大。因此，為了得到我們上面提到的最佳決策，我們
將建立顧客購買行為與廠商決策之間的關係，並利用報童模型與拉氏乘數方法來
建立模型尋找最佳解。
先前許多學者提出的線性市場的研究多注重於零售價格和顧客與商店之間的
距離對於消費者選擇的影響；而我們不僅探討這些已被學者提出的重要的影響，
我們再加上廠商設定的服務水準如何去影響消費者購買選擇，進而影響廠商的期
望利潤。我們希望能透過這些廠商的決策對於消費者的購買影響，去看看怎樣的
決策組合能夠使得廠商的利潤極大化。

In this study, we will consider optimal decisions problem of two competitive retailers about their price decision, order quantities decision and the service level decision in a linear market. The base situation of this linear market is consisted by two retailers which are located at the end points. To maximize the pure revenues of the two retailers, we wish to find out the optimal decisions of the retail prices, the order quantities of the product and the service level (which mean how percentage of consumers’ demand can be satisfied) of the two retailers. Therefore, for obtaining the anticipant result above mentioned, we hope to solve the problem by a variety newsvendor model and Lagrange multiplier method to see which selection combination will maximize their profit.
Unlike other literature which had been proposed, the distinct idea of this study is to consider the setting of the service level of the retailer, and how this service level affect the expected profit of the retailer. In this way, we can find out the variation of retailer’s decision of retail price and order quantities of the product when the retailer also has to consider the decision of the service level. Because of these decision variables are conditioned each other, we want to find out the optimal decision combination of these variables to maximize the expected profit of the retailer.
To discuss this phenomenon we mentioned above, we derived the expected profit function by the classical newsvendor model, to see what decisions combination will create the largest profit of them. The process of building of the expected function is as follow: When the retailer decides a service level, that can affect the decision of the retail price and the order quantities of both retailers, then affect the consumers’ demand (market share) of themselves at different decisions combination. So we will derive the relationship of these decision variables first, and then find an optimal equilibrium decision combination to maximize the expected profit of the retailer.

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