The old saw of "Time, Budget, Scope," pick two is attributed to Greg Larman. I can't say that Greg is the author of this quote or not. But it's referenced in a paper "Quantum Mechanics, Buddhism and Projects," which itself is referenced on Requirements Networking Group. RNG is a great source of all things requirements management. Expect it seems sources for quantum mechanics and particle physics.
Rolf Goetz's paper, linked above makes the statement.
Recent results from quantum mechanics could be fruitful in finding an answer. Let us have a look at what the scientists found out. A neutron consists of 3 quarks of different 'colour'. Say, they are red, green and blue. If you really want, you can separate one from the other two. You will need A LOT of energy to do that, but you can do it. In the same instant you separate the, say, green quark, two things happen simultaneously: Next to the two remaining quarks, a fourth quark comes into existence, a green one. And, next to the separated quark, two more quarks form, one red one blue. In effect, you get two neutrons from the process of splitting one into pieces. (One can argue that splitting must me the wrong word here.)
WRONG, the neutron has three quarks - 1 Up and 2 Downs and the proton has three quarks 2 Ups and 1 Down. The details of this arrangement can be found at the wonderful HyperPhysics site. Which by the way is a great resource for your high school childrens physics homework. It is the evidence of deep inelastic scattering where I started writing FORTRAN code to capture signals buried deep in the noise that started my career as a radar systems software engineer, than a project manager.
Now To The PointThat saw of "time, cost, scope," or "time, cost, quality," pick two is flawed at its core.
It's the role of planning, engineering, cost management, project managers, and program managers to make all three of the attributes (variables) balance. You can start with any two - preferably start with one - of the variables as independent. Then adjust the dependent variables accordingly.
The notion of dependence and independence of variables of an equation is poorly understood in the project management business. If we treat all three variables as independent, balancing the equation that represents the project's "Plan" is straight forward. When one variable is dependent - derived from another - then the balancing becomes easier.
But the quote "time, cost, scope - pick means" does NOT mean the one not picked is not driven by the other two. All three can be picked. The equation is not "balanced" but that is simply the next step. And picking two may result in an imbalance as well.
The final "correction"
So it seems we can separate things from one another. However, we can not observe something without observing its environment.
Is old school quantum. It comes from the populist understanding of quantum mechanics in the 30's, 40's and 50's, picked up by writers and adapted to non-physics world. Nice analogy, but now based on a false understanding of the mechanics of things "quantum."
So What's the Solution?Start with the work breakdown structure. Describe the work needed to be done. Size this work using a probabilistic model. Don't have a probabilistic model for past work, then make one up. Get some bounds on the duration and cost of the work. Any bounds other than pure guessing. Delphi, Monte Carlo, something. Don't guess - ESTIMATE.
Put these estimates into a schedule, sequence the work. See what you get. Don't like the outcome? Adjust One, Two, or Three of the variables and repeat the process.
Repeat until all three variables balance - fit into the acceptable norms of acceptance.
This is the method used for our aerospace and defense programs, where scope is emerging (some programs are actually science projects), budget is variable (thanks to politics and congress), and of course time is very fluid. So all three variables are "dependent" in some way - directly or indirectly. But all three can be "balanced" to produce a credible Integrated Master Schedule. This is the definition of credible - that all three variables represent the current "reality" and its associated probabilistic confidence for the project at this point in time.
Somethings changes - congress cuts funding, the launch vehicle blows up on the test pad, the mission requirements change - what ever. We need a new Integrated Master Schedule.