Most inventory modelling has assumed stochastic demands and constant lead times. However, here we consider a problem for which the opposite situation holds; namely, there is a known constant demand rate, but lead times are random variables. Moreover, the probability distributions of the lead times change in a seasonal fashion. Also, shortages of raw materials result in lost sales. The goal of this paper is to propose heuristic methods for minimizing the expected costs in such a situation. This study was motivated by a problem of management of raw material at a sawmill.