Suppose we want to maximize our combined number of X and Y products over 10 days, and each day we can either:
Get 3 copies of X if Y<7, otherwise get 4 copies of X.
Get 2 copies of Y if X<5, otherwise get 3 copies of Y.
Over 10 days, how should we structure our choice to obtain the maximum number for X + Y?
If you have a strategy bent, then this problem will be a bit of fun, and a bit more complex than it seems at first. This is a type of problem that strategy and resource management games depend on often – when multiple resources have growth patterns that are co-dependent, simple rules can give rise to unexpectedly nuanced problems. Even better, the formula is pretty modular and simple to tweak, so it’s easy to introduce variations.
I call these type of problems resource entanglement problems, since their hallmark is multiple valuable resources with co-dependent growth curves. This type of problem rely on straightforward goals and rules to attract new players and keep those players with unexpected depth. The high ratio between depth and complexity of rules is a hallmark of good game design.
But I’m not here today to talk about game design.
These problems are not always hypothetical. Resource management is a real field of study, and even outside of business there’s plenty of tradeoffs in everyday life. Consider a classic: time vs. money. With money, we can purchase services to save time. With time, we can put additional effort into making money. Since we value both time and money, we find ourselves in an intriguing cycle.
But there is a trap. Elegant optimization problems are fun to think about, but elegance does not correlate with necessity. Elegant problems grabs our attention but may distract us from more important problems. For example, resource management problems are often much more trivial when the ultimate value of one resource is removed. What if hypothetically, we were to demote our value of money? How much does money mean? What about time? These problems risk sounding senseless initially, but depending on the person may have surprising answers.
If you find yourself working on some intricate problem, perhaps the first thing to ask is what you can demote.