資源配置最適化二階層線性規劃模型之研究－以科技專案計畫預算分配為例

Abstract

在「資源有限」而「需求無度」的現實環境下，有效的資源分配一直是公民營機構不斷追求的理想。傳統上資源分配的方法多傾向依據專家的主觀經驗來判斷，而衡量指標大部分仍以申請單位過去的績效表現為主，以作為資源分配的依據。這種單向思維的分配模式很難達到資源配置最適化之目標。因此，如何突破過去由上而下的單向資源分配思維，建構一套客觀、公平、及可量化的「資源配置最適化」模型，來克服因資源配置不當所衍生的相關問題，是值得深入研究的議題。 本研究的目的係在有限的資源條件下，避免資源過度集中，讓資源分配者與被分配者均覺得公平與滿意，使資源配置能發揮最大效益。基此，本研究運用二階層線性規劃的數學模式，建構資源配置模型，要求下階層資源使用者創造資源的總效益為最大，同時控管每個資源使用者所獲資源分配的差異為最小，藉以達到資源配置最適化的目標。 為驗證此模型的實用性與有效性，本研究結合改良式Fishbein模式，再透過預算分配二階層線性規劃模型，採取線性規劃法及「漸近法(successive approximations)」求解，對經濟部2003年「法人科技專案」之87筆研發計畫進行實證研究，結果發現運用二階層線性規劃模式進行預算分配時，可使各產業分別累積的貢獻度達到最大，且可使不同產業的滿意程度落差由40.8%大幅縮減至2.6%。

Due to the fact that precious resource is always limited but the demand for it is unlimited, the optimal allocation of resource is a problem of paramount importance in government or in business. Existing practices of resource allocation are generally based on past performance measures by projects or by organizations. Simple arithmetic average of such performance measures was used to calculate the average unit of resource that an average performer can receive. However, other important criteria should be considered to make resource allocation more objective and more acceptable to resource contenders. Additional resource allocation objectives include: maximizing the overall potential benefits of projects to be funded, minimizing the difference between the highest and the lowest hit rates of resource contending organizations, and selecting projects with strategic importance etc. To formulate a mathematical resource allocation model with the above objectives and constraints is a challenging problem. To solve this type of problems is even a bigger challenge. The mathematical model of bi-level linear programming will be attempted to address this problem. The R&D funding subsidy of Ministry of Economic Affairs’ “Technology Development Program” was used as an example to demonstrate the feasibility of our proposed model formulation and solution algorithms in resource allocation.