Hi I have a VRP problem where a complete graph $G=(V,E)$ is given, a fleet of vehicles is given all with capacity of 3 units $Q = 3$. I am looking to add the generalized large multistar (GLM) inequality but I am having some trouble. The GLM formulation I have found is as follows:
We study the decomposition of multigraphs with a constant edge multiplicity into copies of a fixed star H=K"1","t: We present necessary and sufficient conditions for such a decomposition to exist where t=2 and prove NP-completeness of the corresponding decision problem for any t>=3. We also prove NP-completeness when the edge multiplicity function is not restricted either on the input G or on the fixed multistar H.