Hello !

could anybody help me by modeling constraints Nr.4 on the screenshot in the Attachment. M is a subset of N and there are always 2^n subsets of a set N. As example if i have N with 3 Cities {1,2,3} than there are M = 2^3 = 8 different M: M1 = {1}, M2 = {2}, M3 = {3}, M4 = {1,2}, M5 = {1,3}, M6 ={2,3}, M7 = {1,2,3} and M8 = { “empty subset” }. What i need is a loop which build all this subsets M1…M, such that i could use it in the constraints Nr.4 (for all M with more than 1 member, that would be M4 to M7 in the example wit N = 3). I also attached a screenshot of the .gms script for the constraints Nr.1- Nr.3. x(i,j) is a binary variable and c(i,j) is the costs parameter. I’m really thankful for any help.

Best regards

Mahdi Alazzeh