Hello everyone,

I would like to solve a mathematical model with GAMS and unfortunately I can’t find the solution. I would like to solve the following problem with the GAMS programme:

I would like to carry out location planning taking a barrier into account. I will take the federal state of Brandenburg as an example. My demand/requirement locations are all cities in Brandenburg. I get the coordinates of the cities from Excel using geocoordinates and can thus determine the respective distances between the cities. To do this, I form a distance matrix between the cities and insert the values in a table in GAMS. I have one demand point per 200 inhabitants. For example, if I have 1000 inhabitants in a small town, then I have 5 demand points for this town. My barrier should be Berlin. The barrier area is represented by a circle or, even more simply, by the corner points of the rectangle as an area. The corner points of the rectangle represent the area for the barrier zone. The new locations should be shown with X and Y coordinates. If a new location falls on the barrier area, the location is moved to the edge of the barrier. There should also be a capacity limit for the new location. For example, a location can only cover 20 demand points.

My objective function is to minimise the distance between demand points and new locations.There should also be the possibility to limit the number of new locations.

How can I create a formula, that moves locations out of the barrier zone to the edge of the barrier zones?

Many thanks in advance