Duke energy coal allocation Purcsae contract
Minimg Co.
Fixed Tonnage: Variable Tonnage:
RAG Peabody American Consol Cyprus Addington Waterloo
Power Demand
Amount Avl. (tons)
RAG Peabody American Consol Cyprus Addington Waterloo Total
350,000 300,000 275,000 200,000 175,000 200,000 180,000
Cost ($/tons) BTUs/lb
22 26 22 32 35 31 33
13000 13300 12600 12250 12000 12000 11300
Generating Unit Mimai Fort #5 Mimai Fort #7 Beckjord East Bend Zimmer Total
1,680,000
Transportation cost ($/Ton) Mimai Fort #5 Mimai Fort #7 Beckjord East Bend Zimmer Mimai Fort #5 5 5 4.75 5 4.75 3.75 3.75 3.5 3.75 3.5 3 3 2.75 3 2.75 3.25 3.25 2.85 3.25 2.85 5 5 4.75 5 4.75 2.25 2.25 2 2.25 2 2 2 1.6 2 1.6
10 10 13 10 10 5 11
Duke Energy Coal Allocation Model
RAG Peabody American Consol Cyprus Addington Waterloo
Objective Function coefficients Mimai Fort #5 Mimai Fort #7 Beckjord East Bend Zimmer 37 37 36.75 32 32.75 39.75 39.75 40.5 35.75 36.5 38 38 39.75 34 33.75 45.25 45.25 45.85 42.25 41.85 50 50 49.75 45 45.75 38.25 38.25 39 37.25 37 46 46 45.6 42 43.6
Minimization of Coal Cost Decision variables matrix RAG
53407249.329
Mimai Fort #5 Mimai Fort #7 Beckjord East Bend Zimmer Total shipped 0 0 61538.46 288461.5 0 350000
Peabody American Consol Cyprus Addington Waterloo
36654.135338 191729.32331 71616.54 0 0 0 0 0 33877.55 0 0 0 200000 0 0 0 0 98672.57
Total mWh
550000 Equals
mWh Required
500000
Equals 550,000
0 0 0 275000 0 166122.4 0 0 0 0 0 0
650000 750000 1100000 Equals Equals Equals 500,000 650,000 750,000 1,100,000
300000 275000 200000 0 200000 98672.5663716815
Amont Required Heat Rate (mWh) (BTU/kWh) 550,000 10,500 500,000 10,200 650,000 10,100 750,000 10,000 1,100,000 10,000 3,550,000
Add-On cost Beckjord
Mimai Fort #7 10 10 13 10 10 5 11
East Bend Zimmer 10 5 11 6 15 9 11 7 10 5 6 4 11 7
6 7 9 7 6 4 9
Demand constrant matrix Mimai Fort #5 Mimai Fort #7 Beckjord East Bend Zimmer 2.4761904762 2.5490196078 2.5742574 2.6 2.6 2.5333333333 2.6078431373 2.6336634 2.66 2.66 2.4 2.4705882353 2.4950495 2.52 2.52 2.3333333333 2.4019607843 2.4257426 2.45 2.45 2.2857142857 2.3529411765 2.3762376 2.4 2.4 2.2857142857 2.3529411765 2.3762376 2.4 2.4 2.1523809524 2.2156862745 2.2376238 2.26 2.26
equals
350,000
equals equals <= <= <= <=
300,000 275,000 200,000 175,000 200,000 180,000
