Three electric power plants with capacities of 25, 40, and 30 MW-hr (mega-watt h
ID: 444538 • Letter: T
Question
Three electric power plants with capacities of 25, 40, and 30 MW-hr (mega-watt hours) supply electricity to three cities (Bend, Redmond, and LaPine). The maximum demands of these three cities (in order given) are 35, 25, and 30 MW-hr. The prices per MW-hr to these three cities are:
City
Bend
Redmond
LaPine
Plant
1
$600
$700
$400
2
$320
$300
$350
3
$500
$480
$450
During the month of January, there will be a 20% increase in the given maximum demands above for each city due to a forecasted arctic freeze. This increase in demand can be covered with a 4th plant on another grid but at a premium price of $1,000 per MW-hr. However, this grid is not connected to LaPine since that town is in the boonies.
The electric utility wants to determine the most economic allocation for distribution and purchase of electricity during January to all three cities from the three existing plants augmented by the 4th plant.
a) Formulate the problem as a general LP model.
City
Bend
Redmond
LaPine
Plant
1
$600
$700
$400
2
$320
$300
$350
3
$500
$480
$450
Explanation / Answer
Key decision to to be mase is to determine the optimization of distribution and purchase of electricity from all 4 plant to three cities
Let the cost factor be Xij, i = no. of plants (1,2,3,4) and j = three cities (B-Bend, R-Redmond, L -Lapine)
Feasible alternatives are X1B, X2B, X3B, X4B, X1R, X2R..... X4L where each of them are non-integers
Objective is to minimize the cost of electricty distribution and purchase,
Zmin = (600X1B+320X2B+500X3B+1000X4B) + (700X1R+300X2R+480X3R+1000X4R) + (400X1L+350X2L+450X3L+ 1000X4L)
Constraints:
The max. capacity (in MW-hr) of Plant1 = 25, Plant2 = 40, Plant3 = 30. Forecasted 20% increase in maximum demand of three cities is = (35+25+30) x 20% = 18MW-Hr. So total power required from plant4 = 13 which is arrived from = max. power demand + 20% increase in demand - capcity of plant1, plant2 and plant3.
X1B+X1R+X1L = 25
X2B+X2R+X2L = 40
X3B+X3R+X3L = 30
X4B+X4R+X4L = 13
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