近年來，隨著外食人口的增加，以及社群網路資訊流通發達，導致餐飲需求增加，加上不同地區文化造成飲食的多樣性，各式各樣不同風格的餐飲業者數量眾多，以至於餐飲業者間的競爭相當激烈，連鎖化經營成為餐飲業近年來的發展趨勢，然而因台灣市場規模發展有限，已經有不少本地餐飲業者透過連鎖、品牌授權等模式轉往國際市場，台灣傳統小吃業者多是家族式傳統經營模式，往往缺乏組織化及系統式的專業經營，以致於營業規模大多處於微型或小型企業型態，若有好的管理及服務理念，經由連鎖化擴大市場，相信在國際市場上也能擁有足夠的發展潛力。
雖然近年來許多企業藉由連鎖加盟體系在快速發展，但同時也出現許多問題，像是加盟總部與加盟者之間的資訊不對稱容易導致代理問題的產生，造成雙方利益上層出不窮的衝突與矛盾，而這些問題的根源往往在於不合理的合約費用設計上，當加盟者無法了解加盟業主實際營運狀況，或者加盟業主無法有效區分優良加盟者等狀況下，可能會影響雙方的獲利情形，本研究希望用數學模型建構市場環境，分析加盟業主及加盟者之最適決策和獲利。
研究結果發現，對加盟業主而言，若想要提高自身總利潤，可以考慮建立加盟者成功關鍵指標並藉由某些事前調查方式事先了解加盟者自身能力，再根據加盟者自身能力設計個別之加盟金，接著在新市場的選擇上應該要考慮一投入資金彈性係數較高且當地加盟市場平均報酬率較低之市場，並且試著提高單位商品利潤及降低教育訓練成本之彈性係數。本研究亦發現加盟業主在設定投入營運資金最低要求時，能有一最適之投入營運資金最低要求可使得自身利潤最大化。

In this study, we explored the franchise chain model for a Taiwanese snacks firm. We established a mathematical model by designing the initial fee and royalty fee of a franchise contract. Then, we derived the profit function and best strategy for the franchiser. In addition, we discussed whether the franchiser can get a higher profit when it knows the franchisee's ability in advance. Through numerical analysis, we found that the franchiser can limit the franchisees’ ability by setting a proper minimum investment fund, and increase the profit through designing the initial fee for each individual franchisee.

中文部分
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