6. Please formulate the following problem as a Dynamic Programming problem and s

Question

6. 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 (l unit $10 million) and the feasible levels of invectment on any theral station are 0, 1, 2, or 3 umits. The electric power obtainable (rehurn fumction) for different immestments is given below: Thermal Station Return function, Ri(x) R,(O) Ri(1) R,(2) R (3) Find the investment policy for maximizing the total electric power generated

Explanation / 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.

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