matching otherwise set domain constraints math display block le x ij le text ij math math display block x ij mathbb z text ij math total weight matching math sum ij times w ij x ij math goal find maximum weight perfect matching guarantee variables indeed represent perfect matching add constraints saying vertex adjacent exactly one edge matching ie math display block sum j x ij text sum x ij text j math following lp math display block text maximize sum ij
Applied science Transportation Operations research Assignment problem