Polynomial algorithms for some scheduling problems with one nonrenewable resource

This paper deals with the Extended Resource Constrained Project Scheduling Problem (ERCPSP) which is defined by events, nonrenewable resources and precedence constraints between pairs of events. The availability a resource depleted replenished at occurrence times set decision problem ERCPSP consists determining whether an instance has feasible schedule or not. When there only one resource, this equivalent to find that minimizes number units initially required. It generalizes maximum cumulative cost two-machine completion time flow-shop problem. In paper, we consider some specific constraints: parallel chains, series-parallel interval order constraints. For first two cases, polynomial algorithms based on linear decomposition chains are proposed. third case, algorithm introduced solve it. priority events using properties orders.