Individuals arrive at a geographical area that is initially empty, in accordance with a pure birth process with birth parameters λj = jλ + θ, j ≧ 0. Due to contamination, this geographical area is unsafe for its population and at some fixed time T in the future everyone in the area will be evacuated and no further immigration will be allowed.

Suppose now than an intermediate evacuation time τ, 0 ≦ τ ≦ T, at which time everyone present in the area would be evacuated, is to be chosen. The area would then again fill up with individuals between times τ and T, and, at T, the final evacuation would be made and the area would be permanently sealed off. The problem is to choose τ so as to minimise the total expected cost incurred by time T, where a cost g(x) is incurred for each individual that spends a time x in the area.