Problem 2 Duke Energy needs to determine how much electricity to produce from each of their generators in order to meet their demand in the next hour. They have 5 available generators. The generators differ in the fixed cost of operating the generator (which is paid only if the generator is turned on and produces a positive amount of electricity), the variable cost per MW, and the maximum amount of electricity (in MW) they can produce. The table below lists these values for each of the generators. Generator 1 2 3 4 5 Fixed cost: F; ($) Variable cost: Cj ($ per MW) Max Capacity: M, (MW) 300 250 200 500 700 500 450 300 250 4 5 8 7 9 400 Suppose that Duke Energy must produce electricity to meet demand of 600 MW this hour. 1. Formulate an integer programming problem that helps Duke determine which generator(s) should be turned on and how much electricity should be produced from each of these generators in order to meet the demand at minimum total cost. Clearly define the decision variables, objective and constraints. (Hint: you will need one continuous variable x, for each generator j, representing the amount of electricity generated by each generator j; additionally, you will need one binary variable y, for each generator j, representing whether or not generator j will be used at all. You should model the connection between x and y using logic constraints and then formulate them using big-M inequalities.) 2. Solve this integer program using Jupyter notebook. You may use hwk9-2.ipynb provided on Canvas as a starting point.
Problem 2 Duke Energy needs to determine how much electricity to produce from each of their generators in order to meet their demand in the next hour. They have 5 available generators. The generators differ in the fixed cost of operating the generator (which is paid only if the generator is turned on and produces a positive amount of electricity), the variable cost per MW, and the maximum amount of electricity (in MW) they can produce. The table below lists these values for each of the generators. Generator 1 2 3 4 5 Fixed cost: F; ($) Variable cost: Cj ($ per MW) Max Capacity: M, (MW) 300 250 200 500 700 500 450 300 250 4 5 8 7 9 400 Suppose that Duke Energy must produce electricity to meet demand of 600 MW this hour. 1. Formulate an integer programming problem that helps Duke determine which generator(s) should be turned on and how much electricity should be produced from each of these generators in order to meet the demand at minimum total cost. Clearly define the decision variables, objective and constraints. (Hint: you will need one continuous variable x, for each generator j, representing the amount of electricity generated by each generator j; additionally, you will need one binary variable y, for each generator j, representing whether or not generator j will be used at all. You should model the connection between x and y using logic constraints and then formulate them using big-M inequalities.) 2. Solve this integer program using Jupyter notebook. You may use hwk9-2.ipynb provided on Canvas as a starting point.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem 2 Duke Energy needs to determine how much electricity to produce from each of their
generators in order to meet their demand in the next hour. They have 5 available generators. The
generators differ in the fixed cost of operating the generator (which is paid only if the generator
is turned on and produces a positive amount of electricity), the variable cost per MW, and the
maximum amount of electricity (in MW) they can produce. The table below lists these values for
each of the generators.
Generator
1
2 3 4 5
Fixed cost: F; ($)
Variable cost: Cj ($ per MW) 4 5 8 7
Max Capacity: M; (MW) 300 250 200 500
Suppose that Duke Energy must produce electricity to meet demand of 600 MW this hour.
1. Formulate an integer programming problem that helps Duke determine which generator(s)
should be turned on and how much electricity should be produced from each of these generators
in order to meet the demand at minimum total cost. Clearly define the decision variables,
objective and constraints. (Hint: you will need one continuous variable x, for each generator
j, representing the amount of electricity generated by each generator j; additionally, you will
need one binary variable y, for each generator j, representing whether or not generator j will
be used at all. You should model the connection between x and y using logic constraints and
then formulate them using big-M inequalities.)
700
500 450 300 250
9
400
2. Solve this integer program using Jupyter notebook. You may use hwk9-2.ipynb provided on
Canvas as a starting point.
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