Management of projects often requires decisions concerning the choice of alternative activities. The completion time of the whole project (i.e. the makerpan) is computed subsequently. In this paper, we aim at selecting the activities and computing the makespan simultaneously. This problem is referred to as PERT Problem with Alternatives (PPA). The corresponding model is similar to a conventional PERT graph, except that two types of nodes are introduced to represent either the choice between activities, or the fact that a set of activities should be completed before starting a subsequent set of activities. In this paper, we analyse the PPA and we propose a pseudo-polynomial algorithm to solve it.