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Maximize capacitated coverage model

Question asked by H.J.vanToor_tudelft on Apr 28, 2020

I try to understand how the maximize capacitated coverage exactly works. I've already done many iterations for my facility location problem and during the analysis of the output i don't understand why some decisions are taken by the solver. For example; if i select 238 facilities i serve 9360 demand points. If i select 239 facilities i serve 9331 demand points, which is less demand points with more facilities while opposite was expected. Could someone provide me the integer programming model/math behind this solver? It would be much appreciated. Thank you! 

 

My unfinished model description is attached. 

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