At FedEx we have a performance computer in the cockpit that we use to calculate this stuff, and it keeps total control of the inputs and parameters in the cockpit (There are some other carriers using these now, includeing Southwest, all of those used ours as a template).
The V1 is calculated by first attempting to use the V1max, the highest speed you can go and still stop, except our computer deducts 3000' off the runway available length to make this calculation. If performance will not allow the use of V1max and still have 3000' remaining when we "rock to a stop", it starts backing V1 towards V1min (slowest speed you can be and still continue) to try to hold that 3000'. Eventually you reach the point where this is not possible, as you've reached V1min and there is less than the 3000' "stop margin", so then it holds that, and as you increase weight you eventually reach a balanced field. The latter is not usually a factor on the smaller stuff (727s, etc) as the runway length is such that you hit Vr before you hit V1max in the first place, so the V1 is almost always Vr limited. In the larger airplanes you will almost always have a V1/Vr split unless really light.