Do note that that Location-Allocation is not trying to balance all choosen facilities with the same amount of demand, so each facility can have a wide range of demand points assigned to it.
However, you should not get two different solutions on the same data/problem on two different machines.
If you are geting different behavior then it could be a difference in the underlying network dataset (restrictions, impedance, etc)
or the locations are not correct. By that I mean you may have loaded the locations using "network locations" instead of geometry when in fact the network locations have become stale. You could create a new Location-Allocation layer on your problem layer, re-load the locations making sure to check on the Use Geometry and not the Use Network Location Fields and re-solve.
If this does not solve the issue, then perhaps you can post a screen-shot of what you are getting.
Jay Sandhu