PROJECT SCHEDULING
Download as PPT, PDF0 likes817 views
The document summarizes the key steps in project scheduling including identifying activities, determining precedence relationships, calculating earliest and latest start/finish times, determining slack times, identifying the critical path, and considering probabilistic approaches using PERT analysis. Specifically, it provides an example of scheduling a project for a computer manufacturing company, identifying 10 activities, calculating their earliest/latest times, determining the critical path, and finding the mean and variance of activity times and the overall project using three-point estimates.
![KLONE COMPUTERS –
Finding activities’ mean and variance
µA =[76+4(86)+120]/6 = 90
σΑ = (120 - 76)/6 = 7.33 σA
2
= (7.33)2
= 53.78
36
Activity µ σ
A 90 7.33 53.78
B 15 1.00 1.00
C 5 0.33 0.11
D 20 3.00 9.00
E 21 1.00 1.00
F 25 2.33 5.44
G 14 2.00 4.00
H 28 1.33 1.78
I 30 4.67 21.78
J 45 3.67 13.44
σ2](https://image.slidesharecdn.com/pdpe-10-4014-3616-09-181006164421/85/PROJECT-SCHEDULING-36-320.jpg)
PROJECT SCHEDULING
- 1. PROJECT SCHEDULING Prepared by Shahrukh Vahora (160113105009) Subject: Plant Design & Project Engineering Department of chemical engineering G H Patel College of Engineering & Technology V.V.Nagar 1
- 2. CONTENT • Introduction • Task Designate • Identifying the Activities of a Project • Exmaple • The PERT/CPM Approach for Project Scheduling 2
- 3. Introduction • A project is a collection of tasks that must be completed in minimum time or at minimal cost. • Objectives of Project Scheduling • Completing the project as early as possible by determining the earliest start and finish of each activity. • Calculating the likelihood a project will be completed within a certain time period. • Finding the minimum cost schedule needed to complete the project by a certain date. 3
- 4. • A project is a collection of tasks that must be completed in minimum time or at minimal cost. • Objectives of Project Scheduling 4 – Investigating the results of possible delays in activity’sInvestigating the results of possible delays in activity’s completion time.completion time. – Progress control.Progress control. – Smoothing out resource allocation over the duration ofSmoothing out resource allocation over the duration of the project.the project.
- 5. Task Designate • Tasks are called “activities.” • Estimated completion time (and sometimes costs) are associated with each activity. • Activity completion time is related to the amount of resources committed to it. • The degree of activity details depends on the application and the level of specificity of data. 5
- 6. Identifying the Activities of a Project • To determine optimal schedules we need to • Identify all the project’s activities. • Determine the precedence relations among activities. • Based on this information we can develop managerial tools for project control. 6
- 7. Identifying Activities, Example KLONE COMPUTERS, INC. • KLONE Computers manufactures personal computers. • It is about to design, manufacture, and market the Klonepalm 2000 palmbook computer. 7
- 8. EXMAPLE OF KLONE COMPUTERS 8 • There are three major tasks to perform:There are three major tasks to perform: – Manufacture the new computer.Manufacture the new computer. – Train staff and vendor representatives.Train staff and vendor representatives. – Advertise the new computer.Advertise the new computer. • KLONE needs to develop a precedence relationsKLONE needs to develop a precedence relations chart.chart. • The chart gives a concise set of tasks and theirThe chart gives a concise set of tasks and their immediate predecessors.immediate predecessors.
- 9. KLONE COMPUTERS, INC 9 Activity Description A Prototype model design B Purchase of materials Manufacturing C Manufacture of prototype model activities D Revision of design E Initial production run Activity Description A Prototype model design B Purchase of materials Manufacturing C Manufacture of prototype model activities D Revision of design E Initial production run F Staff training Training activities G Staff input on prototype models H Sales training F Staff training Training activities G Staff input on prototype models H Sales training Advertising activities I Pre-production advertising campaign J Post-redesign advertising campaign Advertising activities I Pre-production advertising campaign J Post-redesign advertising campaign
- 10. KLONE COMPUTERS, INC From the activity description chart, we can determine immediate predecessors for each activity. 10 Activity A is an immediate predecessor of activity B, because it must be competed just prior to the commencement of B. A B
- 11. KLONE COMPUTERS, INC 11 Immediate Estimated Activity Predecessor Completion Time A None 90 B A 15 C B 5 D G 20 E D 21 F A 25 G C,F 14 H D 28 I A 30 J D,I 45 Precedence Relationships Chart
- 12. The PERT/CPM Approach for Project Scheduling • The PERT/CPM approach to project scheduling uses network presentation of the project to • Reflect activity precedence relations • Activity completion time • PERT/CPM is used for scheduling activities such that the project’s completion time is minimized. 12
- 13. KLONE COMPUTERS, INC. - Continued • Management at KLONE would like to schedule the activities so that the project is completed in minimal time. • Management wishes to know: • The earliest and latest start times for each activity which will not alter the earliest completion time of the project. • The earliest finish times for each activity which will not alter this date. • Activities with rigid schedule and activities that have slack in their schedules. 13
- 14. Earliest Start Time / Earliest Finish Time • Make a forward pass through the network as follows: • Evaluate all the activities which have no immediate predecessors. • The earliest start for such an activity is zero ES = 0. • The earliest finish is the activity duration EF = Activity duration. • Evaluate the ES of all the nodes for which EF of all the immediate predecessor has been determined. • ES = Max EF of all its immediate predecessors. • EF = ES + Activity duration. • Repeat this process until all nodes have been evaluated • EF of the finish node is the earliest finish time of the project. 14
- 15. Earliest Start / Earliest Finish – Forward Pass 15 A 90 B 15 C 5 F 25 I 30 G 14 D 20 E 21 H 28 J 45 90,105 90,115 90,120 105,110 110,124 115,129 129,149 149,170 149,177 120,165 149,194 170 194 A 0,90 B I F C G D E H J 177 194 EARLIEST FINISH
- 16. Latest start time / Latest finish time • Make a backward pass through the network as follows: • Evaluate all the activities that immediately precede the finish node. • The latest finish for such an activity is LF = minimal project completion time. • The latest start for such an activity is LS = LF - activity duration. • Evaluate the LF of all the nodes for which LS of all the immediate successors has been determined. • LF = Min LS of all its immediate successors. • LS = LF - Activity duration. • Repeat this process backward until all nodes have been evaluated. 16
- 17. Latest Start / Latest Finish – Backward Pass 17 B F C A I E DG H H 28 166,194 J J 45 149,194 E 21 173,194 90,105 90,115 90,120 105,110 115,129 129,149 149,170 149,177 149,194 153,173 146,166 194 129,149 0,90 129,149 D 20 129,149 129,149 129,149 129,149 129,149 129,149 129,149 G 14 115,129 I 30 119,149 29,119 C 5 110,115B 1595,110 5,95 F 25 90, 115 0,90A 90
- 18. Slack Times • Activity start time and completion time may be delayed by planned reasons as well as by unforeseen reasons. • Some of these delays may affect the overall completion date. • To learn about the effects of these delays, we calculate the slack time, and form the critical path. 18
- 19. Slack Times • Slack time is the amount of time an activity can be delayed without delaying the project completion date, assuming no other delays are taking place in the project. 19 Slack Time = LS - ES = LF - EF
- 20. 20 Critical activities must be rigidly scheduled Critical activities must be rigidly scheduled Activity LS - ES Slack A 0 -0 0 B 95 - 90 5 C 110 - 105 5 D 119 - 119 0 E 173 - 149 24 F 90 - 90 0 G 115 - 115 0 H 166 - 149 17 I 119 - 90 29 J 149 - 149 0 Slack time in the Klonepalm 2000 Project
- 21. The Critical Path • The critical path is a set of activities that have no slack, connecting the START node with the FINISH node. • The critical activities (activities with 0 slack) form at least one critical path in the network. • A critical path is the longest path in the network. • The sum of the completion times for the activities on the critical path is the minimal completion time of the project. 21
- 22. The Critical Path 22 B F C A I E DG H H 28 166,194 J J 45 149,194 E 21 173,194 90,105 90,115 90,120 105,110 115,129 129,149 149,170 149,177 149,194 D 20 0,90 129,149 G 14 115,129 I 30 119,149 A 90 C 5 110,115B 15 95,110 F 25 90, 1150,90
- 23. Possible Delays • We observe two different types of delays: • Single delays. • Multiple delays. • Under certain conditions the overall project completion time will be delayed. • The conditions that specify each case are presented next. 23
- 24. Single delays • A delay of a certain amount in a critical activity, causes the entire project to be delayed by the same amount. • A delay of a certain amount in a non-critical activity will delay the project by the amount the delay exceeds the slack time. When the delay is less than the slack, the entire project is not delayed. 24
- 25. Gantt Charts • Gantt charts are used as a tool to monitor and control the project progress. • A Gantt Chart is a graphical presentation that displays activities as follows: • Time is measured on the horizontal axis. A horizontal bar is drawn proportionately to an activity’ s expected completion time. • Each activity is listed on the vertical axis. • In an earliest time Gantt chart each bar begins and ends at the earliest start/finish the activity can take place. 25
- 26. Gantt Charts- Monitoring Project Progress • Gantt chart can be used as a visual aid for tracking the progress of project activities. • Appropriate percentage of a bar is shaded to document the completed work. • The manager can easily see if the project is progressing on schedule (with respect to the earliest possible completion times). 26
- 27. Gantt Charts – Advantages and Disadvantages • Advantages. • Easy to construct • Gives earliest completion date. • Provides a schedule of earliest possible start and finish times of activities. • Disadvantages • Gives only one possible schedule (earliest). • Does not show whether the project is behind schedule. • Does not demonstrate the effects of delays in any one activity on the start of another activity, thus on the project completion time. 27
- 28. The Probability Approach to Project Scheduling • Activity completion times are seldom known with 100% accuracy. • PERT is a technique that treats activity completion times as random variables. • Completion time estimates are obtained by the Three Time Estimate approach 28
- 29. The Probability Approach – Three Time Estimates 29 • The TThe Three Time Estimatehree Time Estimate approachapproach providesprovides completion time estimate for each activity.completion time estimate for each activity. • We use the notation:We use the notation: a = an optimistic time to perform the activity.a = an optimistic time to perform the activity. m = the most likely time to perform the activity.m = the most likely time to perform the activity. b = a pessimistic time to perform the activity.b = a pessimistic time to perform the activity.
- 30. 30 µ σ = the mean completion time = a + 4m+ b 6 = the standard deviation = b -a 6 Approximations for the mean and the standardApproximations for the mean and the standard deviation of activity completion time are based on thedeviation of activity completion time are based on the BetaBeta distribution.distribution. The Distribution, Mean, and StandardThe Distribution, Mean, and Standard Deviation of an ActivityDeviation of an Activity
- 31. The Project Completion Time Distribution - Assumptions 31 To calculate the mean and standard deviation of the project completion time we make some simplifying assumptions.
- 32. The Project Completion Time Distribution - Assumptions • Assumption 2 • The time to complete one activity is independent of the time to complete any other activity. • Assumption 3 • There are enough activities on the critical path so that the distribution of the overall project completion time can be approximated by the normal distribution. 32 • Assumption 1Assumption 1 – A critical path can be determined by using the meanA critical path can be determined by using the mean completion times for the activities.completion times for the activities. – The project mean completion time is determined solely by theThe project mean completion time is determined solely by the completion time of the activities on the critical path.completion time of the activities on the critical path.
- 33. The Project Completion Time Distribution The three assumptions imply that the overall project completion time is normally distributed, the following parameters: 33 Mean = Sum of mean completion times along the critical path. Variance = Sum of completion time variances along the critical path. Standard deviation = √Variance
- 34. The Probability Approach – KLONE COMPUTERS 34 Activity Optimistic Most Likely Pessimistic A 76 86 120 B 12 15 18 C 4 5 6 D 15 18 33 E 18 21 24 F 16 26 30 G 10 13 22 H 24 18 32 I 22 27 50 J 38 43 60
- 35. The Probability Approach – KLONE COMPUTERS • Management at KLONE is interested in information regarding the completion time of the project. • The probabilistic nature of the completion time must be considered. 35
- 36. KLONE COMPUTERS – Finding activities’ mean and variance µA =[76+4(86)+120]/6 = 90 σΑ = (120 - 76)/6 = 7.33 σA 2 = (7.33)2 = 53.78 36 Activity µ σ A 90 7.33 53.78 B 15 1.00 1.00 C 5 0.33 0.11 D 20 3.00 9.00 E 21 1.00 1.00 F 25 2.33 5.44 G 14 2.00 4.00 H 28 1.33 1.78 I 30 4.67 21.78 J 45 3.67 13.44 σ2
- 37. KLONE COMPUTERS – Finding mean and variance for the critical path • The mean times are the same as in the CPM problem, previously solved for KLONE. • Thus, the critical path is A - F- G - D – J. • Expected completion time =µA +µF +µG +µD +µJ=194. • The project variance =σA 2 +σF 2 +σG 2 +σD 2 +σJ 2 = 85.66 • The standard deviation = = 9.255 37 σ2
- 38. The Probability Approach – Critical path spreadsheet 38 MEAN 194 STANDARD DEVIATION* 9.255629 * Assumes all critical activities are on one critical path VARIANCE* 85.66667 If not, enter in gold box, the variance on one critical path of interest. PROBABILITY COMPLETE BEFORE 180 = 0.065192 Acitivty Node Critical µ σ σ2 ES EF LS LF Slack Design A * 90 7.333333 53.77778 0 90 0 90 0 Materials B 15 1 1 90 105 95 110 5 Manufacture C 5 0.333333 0.111111 105 110 110 115 5 Design Revision D * 20 3 9 129 149 129 149 0 Production Run E 21 1 1 149 170 173 194 24 Staff Training F * 25 2.333333 5.444444 90 115 90 115 0 Staff Input G * 14 2 4 115 129 115 129 0 Sales Training H 28 1.333333 1.777778 149 177 166 194 17 Preprod. Advertise I 30 4.666667 21.77778 90 120 119 149 29 Post. Advertise J * 45 3.666667 13.44444 149 194 149 194 0 CRITICAL PATH ANALYSIS
- 39. Cost Analyses Using The Critical Path Method (CPM) • The critical path method (CPM) is a deterministic approach to project planning. • Completion time depends only on the amount of money allocated to activities. • Reducing an activity’s completion time is called “crashing.” 39
- 40. Crash time/Crash cost • There are two crucial completion times to consider for each activity. • Normal completion time (TN). • Crash completion time (TC), the minimum possible completion time. 40 • The cost spent on an activity varies between – Normal cost (CN). The activity is completed in TN. – Crash cost (CC). The activity is completed in TC.
- 41. Crash time/Crash cost – The Linearity Assumption • The maximum crashing of activity completion time is TC– TN. • This can be achieved when spending CN – CC. • Any percentage of the maximum extra cost (CN – CC)spent to crash an activity, yields the same percentage reduction of the maximum time savings (TC– TN). 41
- 42. REFERENCES • PLANT DESIGN AND ECONOMICS FOR CHEMICAL ENGINEER- 4TH EDITION , CHAPTER-11, BY- MAX S PETER, KLAUS D TIMMERHAUS 42
- 43. •THANK YOU 43