| Summary: | 博士 === 淡江大學 === 管理科學研究所 === 79 === Electric power is an important factor for the development of the national
economy and for the improvement of prople''s living standard.Taipower is a
state-run and the sole electric utility in Taiwan.It is responsible for
stpplying the whole island with sufficient,reliable,responsible for
supplying the whole island with sufficient,reliable,and rational pricing
ro meet the requirements for the industrial establishments and the
economic growth of this nation.The planning environment faced by electric
utilities has been becoming more and more complicated and uncertain.In
response to the ever-changing environment,utilities have recognized the
need for better planning tools or models.Among Taipower''s planning
models,System Expansion Planning Model and Long-term Fuel Coal Supply
Model are of importment ones.In mathematical formulation,These model will
be classified as Minimal Cost Capacity Expansion Problem and Minimal Cost
Network Flow with Capacity Expansion Prlblem,respectively.These problems
have high dimensionality and complexity.In order to handle these
problems,the development of the computational tools of ecomposition and
multilevel optimization will be required.In this dissertation,the
application are emphasized for solving the above problems,At the same
time,we extend the application of Gineralized Benders Decomposition for
solving the Block Triangular problem.In order to implimint the application
of Generalized Benders Decompositon for solving above problems,two cases
are presented with the result of some experimertal runs.These results
indicate that the algorithm can indeed produce a sequential of trial
solution from which optimal feasible solution can be successively
abtained.
有關數學分解技巧與最佳化，自Dantize與Wolife
研究提出一些大型特殊結構線性規劃解法之演算程多（Algorithm）
以來，大型數理規劃分解理論的研究持續進行，而應用方面亦陸續受到重視。惟至目
前為止，對於塊狀三角問題（Block Triangular
Problem）尚未有效的分解技巧去分解它。本論文嘗試用Benders分解技巧應用於塊狀
三角形問題及步階箱疊型（Staircase）問題分解上，從基本構想， 分解方法加以探
討，並研提演算程序（Algorithm）。
最小成本容量擴充問題（Minimal Cost Capacity Expansion
Problem） 可供作系統容量擴充規劃上使用，其數學結構形態屬塊狀三角形問題的特
例，故可用相同的方法加以分析。並應用線性規劃雙階法（Two
Phase）理論，推導邊切（Bender Cut）限制式之通式。
兼具容量擴充最小成本網路問題（Minimal Cost Network Flow with Capacity
Expansion Problem）及兼具容量擴充最小成本多產品網路問題（Minimal Cost
Multicommodity Network Flow with Capacity
Expansion Probiem）是將過去最小成本網路問題或者最小成本多產品網路問題加以
延伸，將「上限容量」假定已知（Given） 或固定值改為變數處理。由於此兩問題經
由數學建構形態亦屬塊狀三角形的特例，故仍可用相同的方法加以分析。
長期電源開發模式之建構是容量擴充問題典型應用之一。該模式可供作機組增加電廠
增設、輸變電容量擴充等規劃的補助工具。本論文除探討線性規劃模式外，尚有非線
性規劃模式及機率性規劃模式。該等模式與Bloom[54] 不同的是採整數解且以彭水木
、張建隆、周錦雲[58]為基礎。最後用機率規劃模式以實例加以研究。
長期燃料煤供應模式建構，是兼具容量擴充最小成本網路問題或兼具容量擴充最小成
本多產品網路問題應用之一，該模式以張建隆[56]為基礎探討如何向國外採購煤，如
何運儲煤使總成本最低，討論該模式分解及以實例加以研究。
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