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題名 | 水庫線性標的規劃模式與其對偶模式--互補解=A Linear Goal Programming Model and Its Dual for Reservoir Planning--Complimentary Solutions |
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作者 | 劉佳明; | 書刊名 | 農業工程學報 |
卷期 | 50:4 2004.12[民93.12] |
頁次 | 頁1-13 |
分類號 | 443.96 |
關鍵詞 | 多功能水庫; 水庫規劃; 線性規劃; 標的規劃; 網路規劃; Multi-functional reservoir; Reservoir planning; Linear programming; Goal programming; Network programming; Complimentary slackness; |
語文 | 中文(Chinese) |
中文摘要 | 本文藉簡單案例,以圖與表說明水庫規劃標的模式,對偶模式與原、偶二模式的關係。標的模式考慮水庫的蓄洪、供水與貯水三類服務功能,並假定各時期各項目服務功的成本(收益)是供應量的片段線性函數。模式所史決定的是水庫容量與各時期放水量,在滿足各項服務的預定需求條件下,使淨收益最大。其對偶模式則是,提供替代服務的水庫同業訂定服務價格的問題:所訂需求服務價格能為水庫單位接受,且使服務所得總收益最高。 水庫線性標的規劃模貸能以特定網絡的位勢關係,表示水庫的庫頂、庫底與水面三點位勢(容積)的時間變動歷程。對偶模式則能以同一網路的流量關係,表示水庫接受替代服務參數的影子價格條件。 除了以位勢網絡說明水庫標的規劃案例問題的變數,限制式與模式,文中又根據線性規劃對偶原理,建立水庫案例標的規劃模式的對偶模式,並且利用位勢與流量網絡圖、供應量與影子價格坐標圖、單純形法演算表,說明原、偶二模式互補解與其互補鬆弛條件:資源(或服務)有剩餘者,其影子價格是零,產品(或需求)有價差(目前與替代二方案之間)者,其數量是零。這二者是模式網絡演算與影子價格分析的利器。 |
英文摘要 | A linear goal reservoir planning model, its dual model and the relations among the two are introduced with simple examples. The three functional series of the reservoir considered are: reserved space for flood control, water supply, and pooling of water. The reservoir is to be operated to meet the 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. The dual model concerns the shadow prices of functional goals and minimum demands in each period. It is constructed from the viewpoint of a trader who is trying to convince the reservoir management to trade all the services. The accepted terms for the trade constitute the constrains of the dual model. Its objective function is, to minimize the total cost of purchasing (or to maximize the total profit of providing), the services. A primal model example and its dual are interpreted respectively as a potential network and a flow network. Their complimentary slackness conditions are explained in some details with diagrams and networks. The conditions are implied in the objective row and the right-hand side constant column of the simplex tableaux for the primal and its dual. There are closely examined. |
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