Question

(5 points). OPG has six new power plants planned for the future. The anticipated useful life of these plants is 30 years for the non-renewable energy plants (plants 1, 2 and 3) and 40 years for the renewable energy plants (plants 4, 5 and 6). Plants 1, 2 and 4 will be on line in year 5. Plants 3 and 5 in year 15. Plant 6 in year 25. The cost of installing generating capacity at plant i, discounted to the present, is ci per megawatt, for i 1; 2: ...6. Projected power demand in year t is Di megawatts, for 10; 20:30; 40: Due to environmental regulations, the fraction of generating capacity at non-renewable energy plants in year t, relative to total generating capacity of the six new plants in year t, can be at most r: for 10; 20: 30; 40. The generating capacity (MW) of each plant must be determined. Formulate a linear program that assigns capacities to the six plants so as to minimize total present cost of installing generating capacity, while meeting demand and satisfying the environmental constraints in years t 10:20: 30:40

Answer 1

Linear program is following:

Let Pi be the generating capacity in megawatt installed at plant i, where i={1,2,3,4,5,6}

Minimize $\inline \sum$ci*Pi

s.t.

P1+P2+P4 >= D10   (demand for year t=10)

P1+P2+P3+P4+P5 >= D20   (demand for year t=20)

P1+P2+P3+P4+P5+P6 >= D30   (demand for year t=30)

P3+P5+P6 >= D40 (demand for year t=40)

(1-r10)*P1+(1-r10)*P2-r10*P4 <= 0   (environmental regulation for year t=10)

(1-r20)*P1+(1-r20)*P2+(1-r20)*P3-R20*P4-R20*P5 <= 0   (environmental regulation for year t=20)

(1-r30)*P1+(1-r30)*P2+(1-r30)*P3-r30*P4-r30*P5-r30*P6 <= 0   (environmental regulation for year t=30)

(1-r40)*P3-r40*P5-r40*P6 <= 0   (environmental regulation for year t=40)

Pi >= 0