Computation Section
Project Management
 - Project Network

The Project Network describes the project in an ordered way necessary for critical path analysis. There are two ways to construct a network for the analysis, activity on arc and activity on node. The activity on arc representation is the preferred method for most introductory textbooks because it often results in smaller networks and is simpler for hand calculations. The activity on node representation is more convenient for computer implementations, however, and we use it for the Project Management add-in.

The project network is shown below for the example. The rectangular boxes are the nodes that represent the activities. Activity names are shown in the boxes. The number with a name is the index of the node in the project network. The arcs connecting the nodes describe the precedence relations. The graph, which is constructed by the add-in, also shows the nodes and arcs on the critical path.



When the Solve button is clicked, the add-in creates a new worksheet with the network construction. The node information is placed on the left side of the worksheet beginning in column A. There is a node for each activity. It is important that the nodes be indexed so that if node i precedes j in the project, then i < j. If the indices of the activities do not have this order, the activities are sorted before they are assigned to nodes. The sorted order of the activities is shown in column B. This column is colored green because it is computed by an algorithm rather than a formula. The network is not dynamic, and every time the structure of the project changes a new network must be constructed by clicking the Solve button. Since the original definition of the activities were ordered correctly in the example, column B has an increasing sequence of integers. Column C holds the names of the activities, transferred by formula from the Project worksheet.

Columns D and E are used for the graphical display. The Level for some node i is the number of arcs traversed on the longest path (in number of arcs) from the start node to node i. We see for the example that there are 7 arcs on the longest path from node 1 to node 16. These numbers determine the horizontal placement of the nodes on the graph with the smallest numbers nearer the left margin of the worksheet. The Depth determines the vertical placement on the nodes on the graph with the smallest numbers near the top of the worksheet. The add-in uses a fairly arbitrary method for setting the depth that assures that no two nodes have the same position on the graph. The project network display at the top of the page was constructed with the levels and depths of columns D and E.


Sometimes the arcs describing two precedence relations overlap with the default locations and the user may wish to change the level and/or depth numbers in columns D or E to get a more pleasing graph. We decide to change the locations of activities C, F and G to clarify the arc display. The changed node display is below. To create the new project network choose the Graph button on the project page. In the Network Graph dialog, leave the Compute Level/Depth box unchecked. This constructs the graph directly from the data entered in columns D and E. Checking the box, recomputes the default level and depth values.

  The modified network is below.



The arcs on the project network describe the precedence relations. For each arc, the To Index, in column I, is the index of a node and the From Node, in column J, is the index of a predecessor of the node. Activities with no predecessors in the data are given arcs coming from the start node. Activities with no successors are given arcs going to the end node. When the arcs are sorted first by the From Index and second by the To Index, the arcs appear as at the right. The From indices are increasing from top to bottom. For a given From node, the To indices are increasing from top to bottom. This is accomplished automatically by the computer. The From and To names, in columns K and L, are provided to relate the arcs to the activities. The cells colored red in column M indicate arcs on the critical path. The critical arcs are colored by an algorithm initiated through the Show Critical button on the project worksheet.



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Operations Management / Industrial Engineering
by Paul A. Jensen
Copyright 2004 - All rights reserved