YEAR 12 FURTHER MATHS UNIT 4 MODULE 2 NETWORKS AND DECISION MATHEMATICS CRITICAL PATH ANALYSIS

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YEAR 12 FURTHER MATHS UNIT 4 MODULE 2 NETWORKS AND DECISION MATHEMATICS CRITICAL PATH ANALYSIS Directed graphs or digraphs can be used to model situations where an order or direction is implied.

1 YEAR 12 FURTHER MATHS UNIT 4 MODULE 2 NETWORKS AND DECISION MATHEMATICS CRITICAL PATH ANALYSIS Directed graphs or digraphs can be used to model situations where an order or direction is implied. For example, in the construction of a building the foundations must be laid before the walls can be erected. Often many activities cannot be started until other activities are completed. Any large scale project consists of many phases. The success of the project depends very much on the quality of the planning, scheduling and controlling of these phases. Example: Drawing Activity Networks from Precedence Tables Activity Immediate (EDGE) predecessor A - B - C D E F G A B B C, D E, F Solution: A and B do not have any predecessors so they form the start and can be done at the same time. Check the precedence table and draw edges for each activity from its predecessor. NOTE: G is not an immediate predecessor of any activity so it is the final edge. Do Ex 15C Page 533 Questions 1 a, b, c

2 Dummy Activities Why have a dummy activity? 1.To avoid multiple arcs between two nodes. Sometimes a list of activities and their predecessors leads to multiple arcs between two particular nodes. It is best to avoid this happening so that you can identify different paths through the network. The solution is to create a dummy or invented activity, used solely to keep the precedence structure and allow unique paths to be seen. Eg. If a project has two activities A and B from the start node that are both predecessors of activity C. The diagram on the left is what we would have with multiple arcs; the diagram on the right is the way it is drawn with a dummy activity. It can be drawn before A or before B. Note: a dummy activity is drawn as a dashed arc and still should have a direction. 2. To avoid logical difficulties. Eg. An activity X, has U and V as predecessors. Another activity Y, has only V as a predecessor. A dummy activity is used to keep the correct logical structure as shown in the diagram below right. Draw X after U, draw Y after V, and to ensure that X cannot start until V has been finished, draw a dotted arrow, indicating a dummy activity, from the end of V to the start of.

3 Do Exercise 15C Page 533 Q1d onwards

4 The Critical path Some activities are more critical than others in the completion of a project. Activities can be delayed if they are not critical. A critical activity is any task that if delayed will also delay the entire project. The critical path is the path that gives the largest total of the weighting. These events must occur on time if the project is not to be held up. It is along the critical path that time on the overall project may be saved. Example: Identify the critical path in this project. Solution: Identify all the paths through the network. The float time (or slack). For each activity that is not on the critical path there will be some slack. Eg. Some activities may be able to start a little later and still not affect the finishing time. Float (or Slack) Time is the amount by which the latest finish time is greater than its earliest start time. Float = LST - EST To find the earliest time of an event occurring. (EST) Add the numbers along the path from the first event. Beside each event a double box is drawn. In the left hand box, enter the earliest event time. Always take the largest value. To find the latest time of an event occurring. (LST) Work backward from the earliest time for the final event, by subtracting the number on the edge. Do Exercise 15D Page 543 All questions

5 Crashing In large projects, once the critical path has been identified, it may be possible to put in extra resources (at extra cost) to reduce the duration of one or more of the critical activities. This will have the effect of reducing the overall project duration, which may result in sufficient cost savings to make the extra resource allocation and cost worthwhile. Reducing the length of (some) critical activities is called crashing. It is along the critical path that reductions in activities reduce the length of the project. The minimum possible time to complete an activity (using maximum resources) is called the crash time. The costs associated with crash time for an activity are called crash costs. NOTE: Sometimes reducing activities along a critical path can produce another new critical path that was not critical before. A simple crashing example: Text Book Page 546

6 Example: a. What is the critical path for this project and the minimum completion time? Also complete the table showing EST and LST. Activity EST LST A B C D E F G H I J

Chapter 6: Activity Planning Part 2

Chapter 6: Activity Planning Part 2 NET481: Project Management Afnan Albahli " Representing Lagged Activities Lag activities: are two activities that will be undertaken in parallel but there is a lag between