# Critical Path

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• Published : April 6, 2013

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LGT3105 Operations Management
Semester 2, 2012/13

Individual Written Assignment
(Case 1 Toys City)

Name: LUON Shuk Yan
Student Id: 11280338d
LEC001
SEM 005
Class Instructor: Johnny Wan

Question (1)

I would have accommodated David Cheung’s vacation request.

According to the network diagram above

The critical path of the project is:

Activity 1 Activity 2 Activity 5 Activity 7 Activity 10 Activity 13 Activity 15

As audit of liquid assets (activity 4) is not on the critical path, it is not a critical activity. This slack job has a slack time of 178 hours for which slack time= late start time – early start time (231-53) = late finish time – early finish time (266-88).

The project duration will not be affected even if David takes his one week vacation as the slack time is as long as 178 hours.

The maximum time I would be comfortable giving David Cheung off is 143 hours. (Slack time – duration of his activity = 178 -35). As the latest start time for audit of liquid assets is the 231st hour, the duration of the project will not be affected if David will be back to his work before the 231st hour.

Question (2)

As all the activities were processed exactly on schedule for the first 106 duration hours, the network diagram after the first 106 duration hours is as follow:

The critical path is:
Activity5 Activity7 Activity10 Activity13 Activity15

The remaining duration is 207 hours (= 313 – 106).

We should first calculate the per-unit cost for each hour saved in each activity.

The cost per time unit = Cost to reduce to the minimum Maximum number of time unit reduced

| | Normal| Acceleration| | | |
Activity| Description| Time| Cost(\$)| Time| Cost(\$)| Possible time saved| Extra cost| Cost per time unit (\$)| 3| General audit procedures| 22| 1200| 22| 1200| 0| 0| -| 4| Audit of liquid asset| 35| 1890| 35| 1890| 0| 0| -| 5| Inventory pricing| 92| 3055| 56| 4600| 36| 1545| 42.92| 6| Audit of fixed assets| 22| 1050| 22| 1050| 0| 0| -| 7| Audit of liabilities| 93| 3880| 48| 4720| 45| 840| 18.67| 8| Audit of COGS| 25| 1310| 25| 1310| 0| 0| -|

9| Miscellaneous audit| 11| 640| 9| 660| 2| 20| 10| 10| Lawyer’s letter| 1| 40| 1| 40| 0| 0| -|
11| Management’s letter| 1| 40| 1| 40| 0| 0| -|
12| Subsequent review| 18| 920| 3| 1670| 15| 750| 50| 13| Preparation of financial statements| 15| 480| 10| 1080| 5| 600| 120| 14| Preparation of tax returns| 12| 480| 2| 980| 10| 500| 50| 15| Partner/manager review| 6| 360| 6| 360| 0| 0| -|

According to CPM, we should crash the activities until we reach the desired project duration. For this project, the desired duration is 147 hours. (207 – 60)

In the case with only one critical path, we should crash the activities on the critical path with the lowest per-unit crash cost and crash only one activity one time.

With accordance to the above table, we can see activity 7 is the best activity to be crashed as the crash cost of activity 7 is the lowest and it is on the critical path. We crash activity 7 until we create new critical path(s). It means that we should crash activity 7 by 43 hours. New critical paths are created.

The existing critical paths are:

[ I ]: Activity 5 Activity 7 Activity10 Activity13 Activity15

[ II ]: Activity5 Activity8 Activity9 Activity12 Activity14 Activity15

For the case of two critical paths, we should find 1 or 2 activities that can reduce both critical paths simultaneously and for which the combination of activities are with the lowest combined crash costs. The best option is crashing activities 7 and 9 as the combined costs of them are lowest (\$18.67). Activity 7 and activity 9 should be crashed by 2 hours as we reach the crash limit of activity 7 (45 hours) and activity 9 (2 hours).

After that, we should crash Activity 5, since...