I want to model the following situation: there is one production site (modelled by the source), a collection of depots (modelled by nodes without demand) and, of course many more customers (modelled by sinks). The production equals the demand and the transport of goods costs money; the costs are proportional to the amount of goods transported, but the factor may be different for different roads.
Now comes the twist: a depot may only be visited if also a specific customer nearby will be served from that depot.
The way I intend to model that requirement is by demanding that the flow from the depot to that customer shall be the maximum of all outflows from that depot.
The question is now, as to whether such a maximum restriction upon the outflows of a node will preserve integrality of the solution.