本研究透過時間向度上人口遷徙流量守恆的關係，整合靜態人口遷徙均衡模型(Nagurney, 1993)與動態用路人均衡路徑選擇模型(Chen, 1999)，構建動態人口遷徙均衡模型；並將動態人口分布問題構建為雙層規劃模型，上層為政府之社會福利政策最佳化系統，以追求系統遷徙總成本最小為目標；下層限制式則包含動態人口遷徙均衡限制式，對於任何遷徙者而言，必以遷徙總成本最小的節點為其遷徙目的地。 此外，根據變分不等式敏感度分析手法(Tobin and Friesz, 1988)進行路網測試，證實利用變分不等式敏感度分析可以獲得變分不等式模型決策變數對於微擾變數之一階偏微，有效預估參數微擾後路段上人口遷徙量的變動情況。透過變分不等式敏感度分析資訊手法，導入社會福利政策，來改善地區資源分布不均的潛在問題，達成人口重分配，區域均衡發展之目的。 This thesis integrates both static human migration equilibrium model (Nagurney, 1993) and dynamic user-optimal route choice model (Chen, 1999), by way of flow conservation over time to build the dynamic human migration equilibrium model. Furthermore, this thesis creates dynamic human redistribution to bilevel programming model. With the socialware polices optimal system by upper level, it minimizes the system migration total costs, and the lower level includes dynamic human migration equilibrium within certain limits to make sure each migrant will move to the destination based on minimum migration total costs. Besides, following variational sensitivity analysis manners (Tobin and Friesz, 1988) proceed the numerical examples, to verify that variational inequality model decision variable to perturb variable’s first order differential can estimate the change efficiently after parameter perturbed by the way. In view of sensitivity analysis information and guiding in socialware policies of the government, to improve the potential problems of resources disproportion to get population re-distribution and regional development be balanced.
