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Posts: 1

# Assignment problem with Multiple Constraint

I am trying to solve a Optimization problem, but having difficulty in building a complex constraint. I am trying to assign "House" (p0-p9) to "Stores". The usual constraint of Assignment problem remains the same.

num n = 10;

set NSET = {1..n};

num d {NSET, NSET};        /* Distance Matrix */
num t {NSET, NSET};          /* Price Matrix */

min z = sum{i in NSET, j in NSET} d[i,j] * x[i,j];        /* Minimize overall distance */

con assign_i{i in NSET}: sum{j in NSET} x[i,j] = 1;

con assign_j{j in NSET}: sum{i in NSET} x[i,j] = 1;

in addition I want to place a constraint based on Price. Its going to be standard deviation of PRICE of house-store pair to be less than a threshold (0.2)

I have attached an excel sheet with Distance table and Price Table.

Let me know if you need further clarifications.

SAS Employee
Posts: 32

## Re: Assignment problem with Multiple Constraint

Hi,

As I understand it you can compute the standard diviation of PRICE for all pairs before creating your model and then just have a simple constraint that says

deviation*binaryvariableforpair <= threshold

But since this just excludes certain pairs, I think you can just preprocess the pairs and only include the pairs which are below the threshold in your model, which is much more efficient. The best way to do this is probably to have a "set of pairs" and only add those pairs for which your condition is not violated.

Hope this helps

Philipp

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