Allocating resources offers a good example of this phenomenon. Let's assume that C consumers must choose among R resources; to make it simple, let's limit ourselves to the case where:

The apparent complexity of the problem depends on the kind of model. In practice, there are two possible models:

In the first case, if we associate a constrained variable representing the chosen resource with each consumer, we get C variables with a domain of size R+1, where R is the number of possible resources. The apparent complexity of the problem in this model is thus (R+1)C.

The second case is, of course, analogous to the first: we associate a constrained variable with each resource such that the variable represents the chosen consumer, so we get R variables with a domain of size C+1, where C is the number of possible consumers. The apparent complexity of the problem in this model is thus (C+1)R.

When the difference in apparent complexity is great, we must consider the magnitude of C and R very carefully.