## On Optimal Construction Oredr of Power Stations in Water Energy Developed by Stairs

**Guo Qingfeng Luo Zhihui Sun Xingming Normmal College of Xiang Tan**

This paper is on a practical problem of plan-order.suppose there are n hydropower stations in a river to be built,how do you make a construction order to get the maximum total profits?It is difficult。however,to find out an optimal construction order from ni ones.This paper is making a useful attempt to present the brief optimal principles as follows: Theorem 1:Given that there is not a key-station in a river,then the optimal construction order of stations should be P_1-I_1qP_2-I_2q……P_n-I_nq Theorem 3:If there is a key-station on headwaters of of a river(a common practice),the efficient algorithm to Look for optimal construction order of stations is a:jγ P_1-I_1qP_2-I_2q……P_(γ-1)-I_(γ-1)q b:jγ P_(γ+1)-I_(γ+1)q+△P_(γ+1)P_(γ+2)-I_(γ+2)q+△P_(γ+2)……P_n-I_nq+△P_n (Where:P,I:the profits per year and total investment(inclusive of interest)of a station,q:interest rate,γ:the ordinal number of the key- station built,△P:increment of profits per year,n:total number of stations,j=1,2,……,n.) Finally,a vivid example is taken to demonstrate the important economic significance both of the models and the theorems.

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