One of the tools used to manage large projects is known as the critical path method (CPM).

ne of the tools used to manage large projects is known as the critical path method (CPM). In CPM the manager builds a network of all phases of a project and then evaluates the network to determine critical aspects of the project. In a CPM network, each vertex is an event. such as the start or completion of a task. The arcs comrecting the vertices represent the duration of the activity. Unlike the examples in the text. they also store the name of the activity. To better understand the concept, let's look at a possible CPM plan to build a house. The network for this project is shown in Figure. A. Prepare plans {10} F. Electrical {4} K. Palnt Inside [4} B. Building permits [5] G. Root {3} L. Fixturestcaroet {3} G. Select contractor {2} H. Plumbing [E] M. Landscape [7} D. Foundation {3} I. Drywall {4] P. Final inspection {2} E. 1lI'It'allls {5} J. Paint outside {F} In the plan we see that it will take 1i]I days to prepare the building plan {A} and 5 days to get it approved (B). Furthermore, we can't start building until we have selected the contractor (C). We could construct the shortest pad'r from the start to the end for our plan, but it would be of little value. Du the other hand, ifwe determined the maximum paththat is, the path with the greatest sum of the weightswe would know which steps in our plan are critical. If a critical step slips even one day. we slip our end date. We can slip noncritical dates, however, without slipping our end date, so long as the slip does not change the critical path for the project. l'lrlodifj,F Algorithm, \"Minimum Spanning Tree of a Graph,\" to determine the maximum path through the graph. Then provide a menu that allows the project manager to answer the following questions: i. What is the shortest possible completion time [SPCTJ'E' The SPCT is the longest path through the graph from beginning to end. ii. What is the earliest start time (EST) for each activity? The EST is the sum of the weights in the maximum spanning tree up to the activity. iii. What is the latest start time {LEI} for each activity? The LST is the SPCT for the whole project minus the SPCT for the rest of the project (starting from the current activity}