Lower bounds for the Event Scheduling Problem with Consumption and Production of Resources

The Event Scheduling Problem with Consumption and Production of Resources (ESPCPR) is a general scheduling problem where the availability of a resource is depleted and replenished at the occurrence times of a set of events. This problem is an extension of the Resource Constrained Project Scheduling Problem (RCPSP) where activities are replaced by events, which have to be scheduled subject to generalized precedence relations. The aim of this paper is to show the connections between ESPCPR and classical scheduling problems in order to bring new lower bounds for ESPCPR. We start by recalling some similar models in literature such as the Project Scheduling with Inventory Constraints and the Financing Problem. Subsequently, we describe how to model classical scheduling problems using ESPCPR. Finally, we propose four lower bounds for this problem. The obtained computational results confirm their effectiveness.