Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Understanding Critical Path Method: Determining Longest Path and Event Slack, Exams of Creative Thinking

University of Notre Dame Australia (UNDA)Creative Thinking

The concept of the Critical Path Method, which is used to determine the longest path in a system of activities and events, and how to calculate slack time for each event. The method helps prioritize activities and ensure projects are completed on time.

Typology: Exams

2021/2022

Uploaded on 07/05/2022

carol_78
carol_78 ๐Ÿ‡ฆ๐Ÿ‡บ

4.8

(59)

1K documents

1 / 10

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
The$Critical$Path:$What$It$Is$and$How$To$Utilize$It$
$
Introduction$
$ A$company$is$planning$on$making$tables$that$consist$of$a$drawer,$four$legs,$and$the$
tabletop.$$The$legs$take$11$hours$to$build,$the$top$takes$3$hours$to$build,$and$the$drawer$
takes$10$hours.$$After$each$part$is$built$it$is$painted.$The$legs$take$2$hours,$top$takes$1$
hours,$and$the$drawer$3$hours.$$The$drawer$is$then$attached$to$the$top$(1$hours).$$After$the$
top$and$drawer$are$attached,$the$four$legs$are$attached$(1$hours).$$Your$supervisor$puts$
you$in$charge$of$making$the$decisions$of$what$activities$are$going$to$take$priority$over$
others.$$
To$solve$this$problem,$the$critical$path$must$be$used$to$determine$what$series$of$
events$in$the$most$timeKconsuming.$$This$system$is$made$up$of$many$activities$that$are$
assigned$with$a$time,$and$these$activities$also$must$go$in$a$specific$order.$$After$mapping$
out$all$of$the$activities$in$the$system,$the$critical$path$can$be$determined.$$The$critical$path$
will$be$the$most$timeKconsuming$path$within$the$system,$and$this$will$help$determine$what$
activities$must$take$priority$over$other$activities$to$stay$on$a$time$schedule.$This$concept$is$
extremely$important$when$it$comes$to$cutting$cost$within$a$company$and$keeping$
downtime$to$a$minimum$to$maximize$profit.$
This$document$will$provide$everything$that$is$needed$to$solve$critical$path$
problems.$$It$will$first$go$through$each$component$of$the$critical$path.$$After$that,$it$will$
assist$with$creating$the$diagram$and$calculations$from$an$example$to$solve$for$the$critical$
path.$$Finally,$it$will$take$you$through$stepKbyKstep$instructions$on$how$to$solve$for$the$
critical$path$in$the$chair$manufacturing$company$above.$
$ $
Components/of/a/Critical/Path$
To$begin$work$with$the$critical$path,$it$is$important$to$understand$each$part$or$concept$that$
applies$when$creating$a$chart.$
$
โ— The$critical/path$is$the$
entire$path$through$the$
diagram$that$will$take$the$
longest$amount$of$time$to$
complete.$This$sets$the$
precedent$of$what$time$the$
whole$process$needs$to$be$
completed$by$and$gives$
other$shorter$activities$
some$slack$time.$
$
Figure/1/
pf3
pf4
pf5
pf8
pf9
pfa

Partial preview of the text

Download Understanding Critical Path Method: Determining Longest Path and Event Slack and more Exams Creative Thinking in PDF only on Docsity!

The Critical Path: What It Is and How To Utilize It Introduction A company is planning on making tables that consist of a drawer, four legs, and the tabletop. The legs take 11 hours to build, the top takes 3 hours to build, and the drawer takes 10 hours. After each part is built it is painted. The legs take 2 hours, top takes 1 hours, and the drawer 3 hours. The drawer is then attached to the top (1 hours). After the top and drawer are attached, the four legs are attached (1 hours). Your supervisor puts you in charge of making the decisions of what activities are going to take priority over others. To solve this problem, the critical path must be used to determine what series of events in the most time-ยญโ€consuming. This system is made up of many activities that are assigned with a time, and these activities also must go in a specific order. After mapping out all of the activities in the system, the critical path can be determined. The critical path will be the most time-ยญโ€consuming path within the system, and this will help determine what activities must take priority over other activities to stay on a time schedule. This concept is extremely important when it comes to cutting cost within a company and keeping downtime to a minimum to maximize profit. This document will provide everything that is needed to solve critical path problems. It will first go through each component of the critical path. After that, it will assist with creating the diagram and calculations from an example to solve for the critical path. Finally, it will take you through step-ยญโ€by-ยญโ€step instructions on how to solve for the critical path in the chair manufacturing company above. Components of a Critical Path To begin work with the critical path, it is important to understand each part or concept that applies when creating a chart. โ— The critical path is the entire path through the diagram that will take the longest amount of time to complete. This sets the precedent of what time the whole process needs to be completed by and gives other shorter activities some slack time. Figure 1

โ— Events take place at the nodes, the circles with numbers in them identifying which event is taking place at that time. โ— Activities are the paths represented by arrows connecting each node to each other. The arrows point from the event that just took place to the event(s) that can now start because the event leading to it/them has finished. Each path is accompanied by a time. This is the time that it takes to complete the activity. โ— The earliest start time is just what it says, the soonest time that an event can begin. This is calculated by starting from the beginning of the diagram and moving forward through it, adding up the activity times needing to be completed before it. โ— The latest start time is the latest time that an activity can start to keep the whole system still on track to finish with the critical path (longest path through the system). This is calculated by working from the end of the diagram with the total time and subtracting the activity time(s) from that. โ— Slack event time is the free time that an event has to stay on itโ€™s necessary time track. It is calculated by subtracting the earliest event time from the latest event time. All events that are involved in the critical path will have a slack time of 0 because there is no extra time available for that event. โ— Slack activity time is similar to slack event time yet viewed in terms of the activities instead of the event nodes. All activities involved in the critical path will have a slack activity time of 0. These concepts will be easier to apply when seen in an example situation accompanied by calculations. Figure 2 Figure 3

  1. The paths that are not part of the critical path will have a numerator smaller than the denominator. This difference between the numerator and denominator is your slack time to start each event or node. Remember that there is no slack time for any event or node on the critical path. The following problem has been solved already, but it is good practice to try it for yourself. All the information you need is in the table and the visual representation is below that. Now there is also the Earliest Event Time (๐ธ๐ธ๐‘‡), Latest Event Time ๐ฟ๐ธ๐‘‡ , Slack Event Time (๐‘†๐ธ๐‘‡), and Slack Activity Time (๐‘†๐ด๐‘‡) to consider. These values are relatively easy to calculate once you have created the pictorial diagram such as the one below. Key: x 1 /y 1 = Node 1 0/0 Table 1 ๐‘ฌ๐‘บ๐‘ป(๐‘๐‘œ๐‘‘๐‘’ 1 ) = Earliest time an event can start at node 1, the numerator (x 1 ) ๐‘ฌ๐’‚๐’“๐’๐’Š๐’†๐’”๐’• ๐‘บ๐’•๐’‚๐’“๐’• ๐‘ป๐’Š๐’Ž๐’† ๐ธ๐‘†๐‘‡ = ๐‘†๐‘ก๐‘Ž๐‘Ÿ๐‘ก ๐‘‡๐‘–๐‘š๐‘’ ๐‘“๐‘–๐‘Ÿ๐‘ ๐‘ก ๐‘›๐‘œ๐‘‘๐‘’ + ๐ด๐‘๐‘ก๐‘–๐‘ฃ๐‘–๐‘ก๐‘ฆ ๐‘ก๐‘–๐‘š๐‘’ ๐‘๐‘’๐‘ก๐‘ค๐‘’๐‘’๐‘› ๐‘›๐‘œ๐‘‘๐‘’๐‘  ๐‘ณ๐‘ฌ๐‘ป(๐‘๐‘œ๐‘‘๐‘’ 1 ) = Latest time an event can start at node 1 but not delay the critical path (y 1 ) Latest Start Time = Earliest Start Time of the Next node -ยญโ€ Activity Time between ๐‘บ๐‘ฌ๐‘ป(๐‘๐‘œ๐‘‘๐‘’ 1 ) = The Slack event time at node 1. This should be 0 because the first node is part of the critical path. ๐‘บ๐‘ฌ๐‘ป( 1 ) = ๐ฟ๐ธ๐‘‡( 1 ) โˆ’ ๐ธ๐ธ๐‘‡( 1 ) ๐‘บ๐‘จ๐‘ป(๐‘๐‘œ๐‘‘๐‘’ 1 ) = The slack activity time at node 1. This should be 0 because the first node is part of the critical path. ๐‘บ๐’๐’‚๐’„๐’Œ ๐‘จ๐’„๐’•๐’Š๐’—๐’Š๐’•๐’š ๐‘ป๐’Š๐’Ž๐’† = ๐ฟ๐‘†๐‘‡ ๐‘’๐‘›๐‘‘ ๐‘›๐‘œ๐‘‘๐‘’ โˆ’ ๐ธ๐‘†๐‘‡ ๐‘๐‘’๐‘”๐‘–๐‘›๐‘›๐‘–๐‘›๐‘” ๐‘›๐‘œ๐‘‘๐‘’ โˆ’ ๐ด๐‘๐‘ก๐‘–๐‘ฃ๐‘–๐‘ก๐‘ฆ ๐‘ก๐‘–๐‘š๐‘’ ๐‘๐‘’๐‘ก๐‘ค๐‘’๐‘’๐‘› ๐‘กโ„Ž๐‘’ ๐‘›๐‘œ๐‘‘๐‘’ ๐‘  As we see above, The Slack Event times for all nodes on the critical path are 0. These figures relate to the individual node instead of the movement from one node to the next (Slack Activity Time). Activity Start Node End Node Activity Time Slack Activity Time A 1 2 12 0 B 1 3 8 3 C 1 4 4 6 D 2 5 6 0 E 3 5 7 3 F 4 5 8 6 G 4 6 6 6 H 4 7 6 6 I 5 8 10 0 J 6 8 4 14 K 7 8 5 13 Node Number Earliest Event Time Latest Event time Slack Event Time 1 0 0 0 2 12 12 0 3 8 11 3 4 4 10 6 5 18 18 0 6 10 24 14 7 10 23 13 8 28 28 0 Table 2

For the example problem above, the critical path is โ€œA-ยญโ€D-ยญโ€Iโ€ since this path takes the longest time. The diagram below shows a pictorial way of representing the data. The red arrows are the critical path. Interpretation of a Critical Path Diagram A critical path diagram can be applied to a wide variety of events or activities. For example a critical path diagram could be used for a city evacuation plan. The way to interpret these diagrams is to think of the critical path as the most important to follow. Each activity in the critical path must be done in that order and all the other activities can be done during an activity on the critical path. This is what slack time is. Slack time describes how an event doesnโ€™t need to be completed immediately after the previous event. An example being during an evacuation of a city, the critical path might be moving the people on the highway towards safety (A-ยญโ€D-ยญโ€I). While at the same time, people in the suburbs need to be evacuated but since it does not take as long to move them, that event has slack time. From the above diagram, this would be like taking the path C-ยญโ€H-ยญโ€K. Essentially you can start each activity later. The interpretation of these diagrams is a good way to convert real life situations into a mathematical approach to solve them. Application of Critical Path In many different situations there is a need to determine the critical path, and using the methods explained above it can be found. The activity time for each activity is obtained using a time study. A time study is a method used to obtain information about a process. It consists of measuring the time and rating of the worker to determine an accurate time for each activity. Many large manufacturers will have an employee that is responsible for completing time studies on all the steps of their manufacturing processes. Example Application A real life example of finding the critical path is as follows: A furniture making company builds tables that consist of a drawer, four legs, and the top of the table. Building legs takes 11 hours, building the top takes 3 hours, and building the drawer takes 10 hours. After each part is built, each part is painted. The legs take 2 hours, top 1 hour, and the drawer 3 hours. The drawer is then attached to the tabletop (1 hour). After the top and drawer are attached, the four legs can be attached (1 hour). Find the critical Path. The solution to this problem is as follows:

  1. Calculate Earliest Start Time for each node. Be sure to start at the first node, and the earliest start time is zero. (Hint: For nodes with two activities going into it, the later of the two start times will be used.) ๐ธ๐‘Ž๐‘Ÿ๐‘™๐‘–๐‘’๐‘ ๐‘ก ๐‘†๐‘ก๐‘Ž๐‘Ÿ๐‘ก ๐‘‡๐‘–๐‘š๐‘’ (๐ธ๐‘†๐‘‡) = ๐‘†๐‘ก๐‘Ž๐‘Ÿ๐‘ก ๐‘‡๐‘–๐‘š๐‘’ ๐‘“๐‘–๐‘Ÿ๐‘ ๐‘ก ๐‘›๐‘œ๐‘‘๐‘’ + ๐ด๐‘๐‘ก๐‘–๐‘ฃ๐‘–๐‘ก๐‘ฆ ๐‘ก๐‘–๐‘š๐‘’ ๐‘๐‘’๐‘ก๐‘ค๐‘’๐‘’๐‘› ๐‘›๐‘œ๐‘‘๐‘’๐‘  For example for Node 5: ๐ธ๐‘Ž๐‘Ÿ๐‘™๐‘–๐‘’๐‘ ๐‘ก ๐‘†๐‘ก๐‘Ž๐‘Ÿ๐‘ก ๐‘‡๐‘–๐‘š๐‘’ (๐ธ๐‘†๐‘‡) = 13 + 1 = 14 Figure 7 Node Earliest Event Time Latest Event Time Slack Event Time 1 0 2 11 3 3 4 10 5 13 6 14 7 15 Figure 6 Table 5
  1. Calculate the latest event start time by starting at the last node and going backwards. Latest Start Time = Earliest Start Time -ยญโ€ Activity Time For Example, Node 5. Latest Event Time = 15 -ยญโ€ 1 = 14 Figure 9 Node Earliest Event Time Latest Event Time Slack Event Time 1 0 0 2 11 12 3 3 12 4 10 10 5 13 13 6 14 14 7 15 15 Table 6 Figure 8

Glossary Term Definition Critical Path The most time consuming path within a system of events. Nodes Places on a critical path diagram indicating where events begin. Paths The arrows in a critical path diagram to show the movement of activities throughout the system. Earliest Event Time The time at which an event can first begin. Latest Event Time The time at which an event can start while still meeting the time criteria set by the critical path. Slack time The flexible time that an event has between its earliest event time and latest event time. Time Studies Systematic timings of activities, events, and process to create standardized timings for each of those.