Hi Mahdi,
I don't believe that it is possible to do what you want. If I am understanding this correctly you want to compile a C/C++ program on a windows machine using Cygwin, gcc and Gurobi Linux libraries. Cygwin does not make a windows machine a Linux machine (it is still a windows machine with UNIX like tools). Thus, you cannot link the Gurobi Linux libraries on a windows machine. Also, we don't support gcc on windows. Thus we don't have a windows port for gcc. On windows we only provide libraries for Microsoft Visual Studio. Thus, I think you have three choices.
1) Create a Linux Virtual Machine (VM) on your windows machine and compile your program using gcc and link to the gurobi linux libraries
2) Use MS Visual Studio command line tool to build you application using the Gurobi windows libraries. See:
https://msdn.microsoft.com/en-us/library/f35ctcxw.aspx3) Use the MS Visual Studio IDE (integrated development environment) to build the app on windows. This what we would recommend on windows.
I hope this helps
Amal de Silva
Gurobi Optimization