A design trade-off is a condition in which no single desirable attribute is maximized for the sake of not minimizing any other desirable attribute.
The classic example is quality and cost; one always prefers designs that are of the highest quality and the lowest cost, yet increasing quality typically requires increased cost, and decreasing cost typically requires decreasing quality.
Consider figure 1 (source). Each curve represents the variation of a characteristic of interest in our design; they could be literally any characteristic at all. Assume, for the sake of argument, that their variation over some range is well known and depicted by the given curves.
Consider the red curve. If we maximize that value, then you'll notice the black value is terrible. So while it might be good to maximize red, the resulting design will be terrible because of the terrible black value. Similarly, if we maximize black, the value of red will be awful.
So any design that maximizes either of the two characteristics alone will be a bad design.
The best design possible here (assuming red and black are the only two characteristics about which we care) is at the point where the two curves intersect. Neither red nor black are maximized, but each of their values is as good as they can get without unnecessarily lowering the other value. This is the trade-off.
figure 2 (source) we have two characteristics again, each represented by a unique curve, but we see that there are now two intersection points. That means there are two designs which are good trade-offs.Of course, it's almost never this simple. In
So, in this case, which trade-off point do we choose? Choosing the right one could make all the difference to come up with a truly superior design, but you will need to supplement your decision-making with added information - which can impose its own problems and costs.
Exercise for the Reader Consider figure 2. How might you decide which of the two trade-off points to use? What information might you need to make that decisions? What assumptions are you making? Are those assumptions valid?
It gets worse. In real life, there are very few situations such as those sketched above. Usually, you will have many - often more than a half-dozen - different characteristics to trade off against each other simultaneously. What's more, you will likely not have enough information to describe pretty curves as is done above, so you won't be able to use a simple algebraic algorithm to find the trade-off points.
This is why a decision matrix or weighted decision matrix is so useful: it allows you to find trade-off points based on your best available information - something that just isn't possible if you expect mathematically perfect results.