Proposed by Peter Nightingale, Emir Demirović
The resource-constrained project scheduling problem is a classical well-known problem in operations research. A number of activities are to be scheduled. Each activity has a duration and cannot be interrupted. There are a set of precedence relations between pairs of activities which state that the second activity must start after the first has finished. The set of precedence relations are usually given as a directed acyclic graph (DAG), where the edge (u,v) represents a precedence relation where u must finish before v begins. The DAG contains two additional activities with duration 0, the source and sink, where the source is the first activity and sink is the last activity (these are dummy activities).
There are a set of renewable resources. Each resource has a maximum capacity and at any given time slot no more than this amount can be in use. Each activity has a demand (possibly zero) on each resource. The dummy source and sink activities have zero demand on all resources.
The problem is usually stated as an optimisation problem where the makespan (i.e. the completion time of the sink activity) is minimised.
An extension of the basic RCPSP is the multi-mode variant where activities may have multiple modes. The mode dictates the duration and resource demands of the activity. In this variant, the schedule must give the mode of each activity as well as its starting time.
Another extension concerns non-renewable resources. Each non-renewable resource has a capacity for the entire schedule. An example would be a financial budget that applies to the entire project. Modes of activities must be chosen to avoid exceeding the capacity of each of the non-renewable resources.