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[Help-glpk] [Fwd: Modeling GLPK problem statement]
From: |
Andrew Makhorin |
Subject: |
[Help-glpk] [Fwd: Modeling GLPK problem statement] |
Date: |
Sun, 03 Nov 2013 03:15:51 +0400 |
-------- Forwarded Message --------
From: Pankhuri Gupta <address@hidden>
To: address@hidden
Subject: Modeling GLPK problem statement
Date: Sat, 2 Nov 2013 18:14:42 -0400
Hi,
I am trying to solve a maximization optimization problem using the GLPK
software. This is my first time and I am having difficulty in
formulating my model. I have tried reading through the entire GLPK
programming manual and other places on the internet, but am not able to
get any handle on how I should formulate my model for these equations.
Can anybody give me an idea as to how can I proceed or any other
material I should look into/refer to? It would be of great help.
I have been trying to solve it using API routine calls in C (as
mentioned in the start of the GLPK manual kit)
The problem is mentioned below:
The objective function that is to be maximized is of
the form:
objFunc = (A[1] * y[1]) + (A[2] * y[2]) + (A[3] *
y[3]) + (A[4] * y[4])
Constraints:
P = B[1]z[1] + B[2]z[2] + B[3]z[3] +
B[4]z[4] + B[5]z[5] + B[6]z[6] + B[7]z[7]
y[1] <= max ( C[1]z[1] , C[4]z[4] ,
C[7]z[7])
y[2] <= max ( C[2]z[2], C[4]z[4])
y[3] <= max ( C[1]z[1] , C[2]z[2],
C[5]z[5] , C[7]z[7])
y[4] <= max ( C[3]z[3] , C[5]z[5] ,
C[6]z[6])
Bounds:
0 <= P <= 500
0 <= y[1] <= 1
0 <= y[2] <= 1
0 <= y[3] <= 1
0 <= y[4] <= 1
z[1], z[2] ….. , z[7] : all are
binary variables.
The structural variables (for which I have to find the
values) : z[1], … , z[7]
1. Adding Constraints for y’s:
I was trying to build a constraint matrix with 7 columns (one for each
z[i]) (and one row for each constraint). However, with this approach I
was not able to model addition of constraints on the y’s (since in this
case it is selecting one maximum value and not a summation of all
values).
Even if I model y’s as:
Y[1] = C[1]z[1]W[1] + C[4]z[4]W[2] + C[7]z[7]W[3]
where, only one of W[1], W[2], W[3] can be one, this calls for adding
several more structural variables into my set of equations.
2. Objective Coefficients:
The objective function is in terms of y’s (and has only 4 values).
Hence, I was confused as to how should I set up my objective
coefficients in the matrix.
Thanks,
Pankhuri
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