劉佳明臺灣大學：生物環境系統工程學研究所林昇賢Lin, Sheng-HsienSheng-HsienLin2007-11-272018-06-292007-11-272018-06-292005http://ntur.lib.ntu.edu.tw//handle/246246/56044本文考慮一個簡單的水庫標的線性規劃問題，這個水庫問題可以表示成一個位勢網絡的問題，另外水庫的對偶問題也可以用一個流量網絡問題來表達。標的模式考慮水庫的蓄洪、供水與貯水三類服務功能，並假定各時期各項服務功能的成本（收益）是供應量的片段線性函數。接著本文利用自對偶參數法，來處理具有網絡問題特性的原水庫問題及對偶問題。 文中採用網絡單純形法、對偶網絡單純形法及互補定理，來處理水庫問題及對偶問題。先利用自對偶參數法、網絡單純形法與對偶網絡單純形法，來處理原水庫問題。再利用互補定理，來處理水庫的對偶問題。A reservoir goal linear programming model was formulated for a simple reservoir in this thesis. It can be treated as a potential network model. The dual model of potential network is a network flow problem. The three functional services of the reservoir considered are: reserved space for flood control, water supply, and pooling of water. The reservoir is to be operated to meet minimum demands for each service item in each period. The profit for each service item is a piecewise linear function of supply and the total profit is to be maximized. In this thesis, self-dual parametric algorithm were presented for solving the reservoir and its dual problems. The network simplex, network dual simplex, and complimentary theorem were used to solve reservoir and its dual problems. First, self-dual parametric algorithm, network simplex, and network dual simplex were offered to solve reservoir problem. Then, complimentary theorem were used to solve the dual problem.摘要 Ⅰ Abstract Ⅱ 目錄 Ⅲ 表目錄 Ⅴ 圖目錄 Ⅵ 第一章 序論 1 1.1 前言 1 1.2 章節介紹 2 1.3 文獻回顧 2 第二章 自對偶參數法 3 2.1 簡例問題 3 2.2自對偶參數法的方法及應用 6 2.3自對偶參數法的優點 12 第三章 水庫規劃問題 13 3.1 水庫規劃問題介紹 13 3.2 水庫規劃問題簡例 16 3.3 水庫標的線性規劃模式 21 3.4 水庫問題的規劃方案 22 第四章 自對偶參數法在水庫規劃問題之應用 24 4.1 基本規劃方案及初始規劃方案 24 4.2 水庫問題與自對偶參數法-供應量為最小值 31 4.3 自對偶參數法求解-供應量為標的值 42 第五章 對偶問題與原問題間關係 50 5.1 對偶問題介紹 50 5.2 水庫對偶線性規劃模式 52 5.3 對偶問題的價格方案 54 第六章 結果與討論 58 參考文獻 60 附錄A 切割淨成本 62 附錄B 網孔值與淨成本 63 附錄C 對偶變數與淨成本 65 附錄D切割淨成本求法之比較 66922399 bytesapplication/pdfen-US水庫標的線性規劃問題對偶問題位勢網絡流量網絡網絡單純形法對偶網絡單純形法自對偶參數法互補定理reservoir goal linear programming problemdual problempotential network problemnetwork flow problemnetwork simplexnetwork dual simplexself-dual parametric algorithmcomplimentary theoremthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/56044/1/ntu-94-R92622033-1.pdf