internal static bool CalculateCriticalPathForwardFlow <T, TResourceId, TActivity, TEvent>
(this VertexGraphBuilderBase <T, TResourceId, TActivity, TEvent> vertexGraphBuilder)
where TActivity : IActivity <T, TResourceId>
where TEvent : IEvent <T>
where T : struct, IComparable <T>, IEquatable <T>
where TResourceId : struct, IComparable <TResourceId>, IEquatable <TResourceId>
{
if (vertexGraphBuilder is null)
{
throw new ArgumentNullException(nameof(vertexGraphBuilder));
}
if (!vertexGraphBuilder.AllDependenciesSatisfied)
{
return(false);
}
if (vertexGraphBuilder.FindInvalidConstraints().Any())
{
return(false);
}
// We can assume at this point that all the activity constraints are valid.
var completedEdgeIds = new HashSet <T>();
var remainingEdgeIds = new HashSet <T>(vertexGraphBuilder.EdgeIds);
// First complete the Isolated nodes.
foreach (Node <T, TActivity> node in vertexGraphBuilder.IsolatedNodes)
{
// Earliest Start Time.
int earliestStartTime = 0;
if (node.Content.MinimumEarliestStartTime.HasValue)
{
int proposedEarliestStartTime = node.Content.MinimumEarliestStartTime.Value;
// Augment the earliest start time artificially (if required).
if (proposedEarliestStartTime > earliestStartTime)
{
earliestStartTime = proposedEarliestStartTime;
}
}
if (node.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestStartTime = node.Content.MaximumLatestFinishTime.Value - node.Content.Duration;
// Diminish the earliest start time artificially (if required).
if (proposedLatestStartTime < earliestStartTime)
{
earliestStartTime = proposedLatestStartTime;
}
}
node.Content.EarliestStartTime = earliestStartTime;
// Latest Finish Time.
int latestFinishTime = node.Content.EarliestFinishTime.Value;
if (node.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestFinishTime = node.Content.MaximumLatestFinishTime.Value;
// Diminish the earliest finish time artificially (if required).
if (proposedLatestFinishTime < latestFinishTime)
{
latestFinishTime = proposedLatestFinishTime;
}
}
else if (node.Content.MinimumFreeSlack.HasValue)
{
int proposedLatestFinishTime = latestFinishTime + node.Content.MinimumFreeSlack.Value;
// Augment the latest finish time artificially (if required).
if (proposedLatestFinishTime > latestFinishTime)
{
latestFinishTime = proposedLatestFinishTime;
}
}
node.Content.LatestFinishTime = latestFinishTime;
}
// Complete the Start nodes first to ensure the completed edge IDs
// contains something.
foreach (Node <T, TActivity> node in vertexGraphBuilder.StartNodes)
{
int earliestStartTime = 0;
if (node.Content.MinimumEarliestStartTime.HasValue)
{
int proposedEarliestStartTime = node.Content.MinimumEarliestStartTime.Value;
// Augment the earliest start time artificially (if required).
if (proposedEarliestStartTime > earliestStartTime)
{
earliestStartTime = proposedEarliestStartTime;
}
}
if (node.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestStartTime = node.Content.MaximumLatestFinishTime.Value - node.Content.Duration;
// Diminish the earliest start time artificially (if required).
if (proposedLatestStartTime < earliestStartTime)
{
earliestStartTime = proposedLatestStartTime;
}
}
node.Content.EarliestStartTime = earliestStartTime;
foreach (T outgoingEdgeId in node.OutgoingEdges)
{
Edge <T, TEvent> outgoingEdge = vertexGraphBuilder.Edge(outgoingEdgeId);
int earliestFinishTime = node.Content.EarliestFinishTime.Value;
if (node.Content.MinimumFreeSlack.HasValue)
{
int proposedEarliestFinishTime = earliestFinishTime + node.Content.MinimumFreeSlack.Value;
// Augment the earliest finish time artificially (if required).
if (proposedEarliestFinishTime > earliestFinishTime)
{
earliestFinishTime = proposedEarliestFinishTime;
}
}
outgoingEdge.Content.EarliestFinishTime = earliestFinishTime;
completedEdgeIds.Add(outgoingEdgeId);
remainingEdgeIds.Remove(outgoingEdgeId);
}
}
// Forward flow algorithm.
while (remainingEdgeIds.Any())
{
bool progress = false;
foreach (T edgeId in remainingEdgeIds.ToList())
{
Edge <T, TEvent> edge = vertexGraphBuilder.Edge(edgeId);
// Get the dependency node and its incoming edges IDs.
var dependencyNode = vertexGraphBuilder.EdgeTailNode(edgeId);
var dependencyNodeIncomingEdgeIds = new HashSet <T>(dependencyNode.IncomingEdges);
// If calculations for all the dependency edges have been completed, then use them
// to complete the calculations for this edge.
if (dependencyNodeIncomingEdgeIds.IsSubsetOf(completedEdgeIds))
{
if (!dependencyNode.Content.EarliestStartTime.HasValue)
{
int earliestStartTime = dependencyNodeIncomingEdgeIds
.Select(vertexGraphBuilder.Edge)
.Max(x => x.Content.EarliestFinishTime.Value);
if (dependencyNode.Content.MinimumEarliestStartTime.HasValue)
{
int proposedEarliestStartTime = dependencyNode.Content.MinimumEarliestStartTime.Value;
// Augment the earliest start time artificially (if required).
if (proposedEarliestStartTime > earliestStartTime)
{
earliestStartTime = proposedEarliestStartTime;
}
}
if (dependencyNode.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestStartTime = dependencyNode.Content.MaximumLatestFinishTime.Value - dependencyNode.Content.Duration;
// Diminish the earliest start time artificially (if required).
if (proposedLatestStartTime < earliestStartTime)
{
earliestStartTime = proposedLatestStartTime;
}
}
dependencyNode.Content.EarliestStartTime = earliestStartTime;
}
int earliestFinishTime = dependencyNode.Content.EarliestFinishTime.Value;
if (dependencyNode.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestFinishTime = dependencyNode.Content.MaximumLatestFinishTime.Value;
// Diminish the earliest finish time artificially (if required).
if (proposedLatestFinishTime < earliestFinishTime)
{
earliestFinishTime = proposedLatestFinishTime;
}
}
else if (dependencyNode.Content.MinimumFreeSlack.HasValue)
{
int proposedEarliestFinishTime = earliestFinishTime + dependencyNode.Content.MinimumFreeSlack.Value;
// Augment the earliest finish time artificially (if required).
if (proposedEarliestFinishTime > earliestFinishTime)
{
earliestFinishTime = proposedEarliestFinishTime;
}
}
edge.Content.EarliestFinishTime = earliestFinishTime;
completedEdgeIds.Add(edgeId);
remainingEdgeIds.Remove(edgeId);
// Note we are making progress.
progress = true;
}
}
// If we have not made any progress then a cycle must exist in
// the graph and we will not be able to calculate the earliest
// finish times.
if (!progress)
{
throw new InvalidOperationException(Properties.Resources.CannotCalculateEarliestFinishTimesDueToCyclicDependency);
}
}
// Now complete the End nodes
foreach (Node <T, TActivity> node in vertexGraphBuilder.EndNodes)
{
var nodeIncomingEdgeIds = new HashSet <T>(node.IncomingEdges);
if (!nodeIncomingEdgeIds.IsSubsetOf(completedEdgeIds))
{
throw new InvalidOperationException($@"Cannot calculate EST for activity {node.Id} as not all dependency events have EFT values.");
}
if (!node.Content.EarliestStartTime.HasValue)
{
int earliestStartTime = nodeIncomingEdgeIds
.Select(vertexGraphBuilder.Edge)
.Max(x => x.Content.EarliestFinishTime.Value);
if (node.Content.MinimumEarliestStartTime.HasValue)
{
int proposedEarliestStartTime = node.Content.MinimumEarliestStartTime.Value;
// Augment the earliest start time artificially (if required).
if (proposedEarliestStartTime > earliestStartTime)
{
earliestStartTime = proposedEarliestStartTime;
}
}
if (node.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestStartTime = node.Content.MaximumLatestFinishTime.Value - node.Content.Duration;
// Diminish the earliest start time artificially (if required).
if (proposedLatestStartTime < earliestStartTime)
{
earliestStartTime = proposedLatestStartTime;
}
}
node.Content.EarliestStartTime = earliestStartTime;
}
if (!node.Content.LatestFinishTime.HasValue)
{
int latestFinishTime = node.Content.EarliestFinishTime.Value;
if (node.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestFinishTime = node.Content.MaximumLatestFinishTime.Value;
// Diminish the latest finish time artificially (if required).
if (proposedLatestFinishTime < latestFinishTime)
{
latestFinishTime = proposedLatestFinishTime;
}
}
else if (node.Content.MinimumFreeSlack.HasValue)
{
int proposedLatestFinishTime = latestFinishTime + node.Content.MinimumFreeSlack.Value;
// Augment the latest finish time artificially (if required).
if (proposedLatestFinishTime > latestFinishTime)
{
latestFinishTime = proposedLatestFinishTime;
}
}
node.Content.LatestFinishTime = latestFinishTime;
}
}
return(true);
}
internal static bool CalculateCriticalPathBackwardFlow <T, TResourceId, TActivity, TEvent>
(this VertexGraphBuilderBase <T, TResourceId, TActivity, TEvent> vertexGraphBuilder)
where TActivity : IActivity <T, TResourceId>
where TEvent : IEvent <T>
where T : struct, IComparable <T>, IEquatable <T>
where TResourceId : struct, IComparable <TResourceId>, IEquatable <TResourceId>
{
if (vertexGraphBuilder is null)
{
throw new ArgumentNullException(nameof(vertexGraphBuilder));
}
if (!vertexGraphBuilder.AllDependenciesSatisfied)
{
return(false);
}
if (vertexGraphBuilder.FindInvalidConstraints().Any())
{
return(false);
}
// Only perform if all events a have earliest finish times.
if (!vertexGraphBuilder.Events.All(x => x.EarliestFinishTime.HasValue))
{
return(false);
}
// Only perform if all activities a have earliest finish times.
if (!vertexGraphBuilder.Activities.All(x => x.EarliestFinishTime.HasValue))
{
return(false);
}
// Only perform if all end nodes a have latest finish times.
if (!vertexGraphBuilder.EndNodes.All(x => x.Content.LatestFinishTime.HasValue))
{
return(false);
}
// We can assume at this point that all the activity constraints are valid.
var completedEdgeIds = new HashSet <T>();
var remainingEdgeIds = new HashSet <T>(vertexGraphBuilder.EdgeIds);
int endNodesEndTime = vertexGraphBuilder.EndNodes.Select(x => x.Content.LatestFinishTime.Value).DefaultIfEmpty().Max();
int isolatedNodesEndTime = vertexGraphBuilder.IsolatedNodes.Select(x => x.Content.LatestFinishTime.Value).DefaultIfEmpty().Max();
int endTime = Math.Max(endNodesEndTime, isolatedNodesEndTime);
// Complete the End nodes first to ensure the completed edge IDs
// contains something.
foreach (Node <T, TActivity> node in vertexGraphBuilder.EndNodes)
{
{
// Latest Finish Time.
int latestFinishTime = endTime;
if (node.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestFinishTime = node.Content.MaximumLatestFinishTime.Value;
// Diminish the latest finish time artificially (if required).
if (proposedLatestFinishTime < latestFinishTime)
{
latestFinishTime = proposedLatestFinishTime;
}
}
node.Content.LatestFinishTime = latestFinishTime;
}
// Free float/slack calculations.
node.Content.FreeSlack = node.Content.LatestFinishTime - node.Content.EarliestFinishTime;
foreach (T incomingEdgeId in node.IncomingEdges)
{
Edge <T, TEvent> incomingEdge = vertexGraphBuilder.Edge(incomingEdgeId);
int?latestFinishTime = node.Content.LatestStartTime;
if (node.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestFinishTime = node.Content.MaximumLatestFinishTime.Value;
// Diminish the latest finish time artificially (if required).
if (proposedLatestFinishTime < latestFinishTime.GetValueOrDefault())
{
latestFinishTime = proposedLatestFinishTime;
}
}
incomingEdge.Content.LatestFinishTime = latestFinishTime;
completedEdgeIds.Add(incomingEdgeId);
remainingEdgeIds.Remove(incomingEdgeId);
}
}
// Backward flow algorithm.
while (remainingEdgeIds.Any())
{
bool progress = false;
foreach (T edgeId in remainingEdgeIds.ToList())
{
Edge <T, TEvent> edge = vertexGraphBuilder.Edge(edgeId);
// Get the successor node and its outgoing edges IDs.
var successorNode = vertexGraphBuilder.EdgeHeadNode(edgeId);
var successorNodeOutgoingEdgeIds = new HashSet <T>(successorNode.OutgoingEdges);
// If calculations for all the successor edges have been completed, then use them
// to complete the calculations for this edge.
if (successorNodeOutgoingEdgeIds.IsSubsetOf(completedEdgeIds))
{
if (!successorNode.Content.LatestFinishTime.HasValue)
{
int latestFinishTime = successorNodeOutgoingEdgeIds
.Select(vertexGraphBuilder.Edge)
.Min(x => x.Content.LatestFinishTime.Value);
if (successorNode.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestFinishTime = successorNode.Content.MaximumLatestFinishTime.Value;
// Diminish the latest finish time artificially (if required).
if (proposedLatestFinishTime < latestFinishTime)
{
latestFinishTime = proposedLatestFinishTime;
}
}
successorNode.Content.LatestFinishTime = latestFinishTime;
}
if (!successorNode.Content.FreeSlack.HasValue)
{
int latestFinishTime = successorNodeOutgoingEdgeIds
.Select(vertexGraphBuilder.EdgeHeadNode)
.Min(x => x.Content.EarliestStartTime.Value);
if (successorNode.Content.LatestFinishTime.HasValue)
{
int proposedLatestFinishTime = successorNode.Content.LatestFinishTime.Value;
// Diminish the latest finish time artificially (if required).
if (proposedLatestFinishTime < latestFinishTime)
{
latestFinishTime = proposedLatestFinishTime;
}
}
if (successorNode.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestFinishTime = successorNode.Content.MaximumLatestFinishTime.Value;
// Diminish the latest finish time artificially (if required).
if (proposedLatestFinishTime < latestFinishTime)
{
latestFinishTime = proposedLatestFinishTime;
}
}
successorNode.Content.FreeSlack = latestFinishTime - successorNode.Content.EarliestStartTime - successorNode.Content.Duration;
}
edge.Content.LatestFinishTime = successorNode.Content.LatestStartTime;
completedEdgeIds.Add(edgeId);
remainingEdgeIds.Remove(edgeId);
// Note we are making progress.
progress = true;
}
}
// If we have not made any progress then a cycle must exist in
// the graph and we will not be able to calculate the latest
// finish times.
if (!progress)
{
throw new InvalidOperationException(Properties.Resources.CannotCalculateLatestFinishTimesDueToCyclicDependency);
}
}
// Now complete the Start nodes.
foreach (Node <T, TActivity> node in vertexGraphBuilder.StartNodes)
{
var nodeOutgoingEdgeIds = new HashSet <T>(node.OutgoingEdges);
if (!nodeOutgoingEdgeIds.IsSubsetOf(completedEdgeIds))
{
throw new InvalidOperationException($@"Cannot calculate LFT for activity {node.Id} as not all dependency events have LFT values.");
}
if (!node.Content.LatestFinishTime.HasValue)
{
int latestFinishTime = nodeOutgoingEdgeIds
.Select(vertexGraphBuilder.Edge)
.Min(x => x.Content.LatestFinishTime.Value);
if (node.Content.LatestFinishTime.HasValue)
{
int proposedLatestFinishTime = node.Content.LatestFinishTime.Value;
// Diminish the latest finish time artificially (if required).
if (proposedLatestFinishTime < latestFinishTime)
{
latestFinishTime = proposedLatestFinishTime;
}
}
if (node.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestFinishTime = node.Content.MaximumLatestFinishTime.Value;
// Diminish the latest finish time artificially (if required).
if (proposedLatestFinishTime < latestFinishTime)
{
latestFinishTime = proposedLatestFinishTime;
}
}
node.Content.LatestFinishTime = latestFinishTime;
}
if (!node.Content.FreeSlack.HasValue)
{
int latestFinishTime = nodeOutgoingEdgeIds
.Select(vertexGraphBuilder.EdgeHeadNode)
.Min(x => x.Content.EarliestStartTime.Value);
if (node.Content.LatestFinishTime.HasValue)
{
int proposedLatestFinishTime = node.Content.LatestFinishTime.Value;
// Diminish the latest finish time artificially (if required).
if (proposedLatestFinishTime < latestFinishTime)
{
latestFinishTime = proposedLatestFinishTime;
}
}
if (node.Content.MaximumLatestFinishTime.HasValue)
{
int proposedLatestFinishTime = node.Content.MaximumLatestFinishTime.Value;
// Diminish the latest finish time artificially (if required).
if (proposedLatestFinishTime < latestFinishTime)
{
latestFinishTime = proposedLatestFinishTime;
}
}
node.Content.FreeSlack = latestFinishTime - node.Content.EarliestStartTime - node.Content.Duration;
}
}
return(true);
}