Minimum up time MINLP

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Sankarshan Durgaprasad
Sankarshan Durgaprasad 2023년 3월 1일
답변: Shubham 2023년 5월 5일
I have 2 generator and 5 time periods. I wish to inclue a minimum uptime for my generators as 2 time periods. How do I go about doing this? Im not able to figure out how to represent this interms of the inequality matrix A.

답변 (1개)

Shubham
Shubham 2023년 5월 5일
Hi Sankarshan,
To represent the minimum uptime constraint for the generators in terms of the inequality matrix A, you can follow the steps below:
  1. Define your decision variables: Let x1 and x2 be the binary decision variables representing the on/off status of generator 1 and generator 2, respectively. Let y1, y2, y3, y4, and y5 be the binary decision variables representing the time periods.
  2. Define the objective function: Since there is no objective function given in the problem statement, assume that the objective is to maximize the total uptime of the generators. Maximize: x1*y1 + x1*y2 + x1*y3 + x1*y4 + x1*y5 + x2*y1 + x2*y2 + x2*y3 + x2*y4 + x2*y5
  3. Define the constraints:
  • Generator uptime constraint: The total uptime of each generator should be at least 2 time periods.x1*y1 + x1*y2 + x1*y3 + x1*y4 + x1*y5 >= 2x2*y1 + x2*y2 + x2*y3 + x2*y4 + x2*y5 >= 2
  • Time period constraint: Each time period should have only one state (either generator 1 is on or generator 2 is on).x1*y1 + x2*y1 <= 1x1*y2 + x2*y2 <= 1x1*y3 + x2*y3 <= 1x1*y4 + x2*y4 <= 1x1*y5 + x2*y5 <= 1
  • Binary constraints: The decision variables should be binary.x1, x2, y1, y2, y3, y4, y5 ∈ {0, 1}.
4. Write the constraints in matrix form:
[1 1 1 1 1 0 0 0 0 0] [x1] [2]
[0 0 0 0 0 1 1 1 1 1] * [x2] >= [2]
[1 0 0 0 0 1 0 0 0 0] [y1]
[0 1 0 0 0 0 1 0 0 0] [y2]
[0 0 1 0 0 0 0 1 0 0] [y3]
[0 0 0 1 0 0 0 0 1 0] [y4]
[0 0 0 0 1 0 0 0 0 1] [y5]
The first row of the matrix represents the generator 1 uptime constraint, the second row represents the generator 2 uptime constraint, and the remaining rows represent the time period constraints.
The inequality matrix A is the left-hand side of the matrix equation, and the decision variables are the column vector on the right-hand side. The right-hand side of the matrix equation is the vector of constants representing the minimum uptime constraint for the generators.

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