流體分派環狀網路系統之最佳解

Optimization of a Closed-Loop Fluid Distribution Network System

林百洲(Pai-Chou Lin)

《國防管理學報》 9卷2期 (1988/06) Pp. 27-41

https://doi.org/10.29496/JNDM.198806.0003

摘要

本文係探討滿足流體網路系統中，各需求點之流量及壓力需求，使系統投資成本為最低的一套演算法。此投資成本包括管線成本及供給壓力成本。文中之演算法係使用疊代（Iterative）的過程，利用泰勒級數第一階段展開式將數學模式中的非線性限制式轉換成線性方程式，再利用線型規劃之解法求出網路系統中各管線內之流最及其使用之口徑大小，而此時系統之投資成本為最低。基於線性近似造成的誤差，在每次疊代過程中求出來之流量的解必須經由「流量分析方法」加以修正，同時在生另一線性近似模式，再求其解。這疊代過程一直到線性近似求出來的各管線內之流量與修正後之流量之誤差在允許之範圍內，則停止。

並列摘要

This paper presents an algorithm for minimizing the cost of fluid distribution network system while meeting the flow demand and the pressure head requirements at the demand nodes. The cost includes the cost of the pipe and the supply head.The algorithm is an iterative procedure which approximates the nonlinear constraints with a Taylor's series first order expansion and uses linear programming algorithm to solve the resulting linear programming problem. The linear programming solution yields the flow and the length of each pipe segment of different diameter, In each Iteration, the correct flow rate, are calculated using a flow rate analysis method, and new linear approximations are obtained. The process is repeated until the difference between the flow rate in pipe-line and its corrected (low rate is within a specified limit.