Please formulate the following problem as a Dynamic Programming problem and solv
ID: 2294097 • Letter: P
Question
Please formulate the following problem as a Dynamic Programming problem and solve it using a multi-stage optimization strategy. (Note: No credits will be given for solving it using any other means) It is proposed to build thermal stations at three different sites. The total budget available is 3 units (1 unit $10 million) and the feasible levels of investment on any thermal station are 0, 1, 2, or 3 units. The electric power obtainable (return fimction) for different investments is given below: Thermal Station, i Return function, Ri(x) R,(O) Ri(1) Ri(2) Ri(3) 4 Find the investment policy for maximizing the total electric power generatedExplanation / Answer
From return function table for thermal stations, it is clear that the return function for station 3 has maximum return for 1 unit investment Ri(1)=3. So, invest 1 unit on thermal station 3. Now, 2 more units are left.
From the return function table, if the remaining two units are invested on station 3, the overall return is only Ri(3)=6.
If we invest remaining 2 units on station 1, the return is,
Ri(1) of station 3 + Ri(2) of station 1=3+4=7.
If we invest remaining 2 units on station 2, the return is,
Ri(1) of station 3+Ri(2) of station 2=3+5=8.
Also one unit investment on each yields 2+1+3=6 and all the 3 units on any one of the station yields, Ri(3) of any station=6.
Therefore, the investment for maximizing the total electric power generated is 1 unit on station 3 and 2 units on station 2.