A discrete problem of optimal resource allocation in a network-like set of activities

The paper is concerned with optimization of a network-like set of activities. With specified dependences of times for completion of activities on the resource it is required either to minimize the time for completing the entire set (the total amount of the resource being fixed) or the total resource (the time of completion being fixed). The problem is solved in the assumption that these dependencies are uniformly discrete in time, monotone, and convex.