LGT 3105 OM Toys City Inc.

Hong Kong Polytechnic UniversityLGT3105 Operation Management

2011-12 Semester 2

Individual Assignment

Company: Toys City Inc.

Student Name :Cheung Ho Yi, HollyStudent ID :10548046DGroup :2061Component :LTL001Teaching Staff :Jiang LiDue Date :8th February, 2012

Question 1

If you were Mr. Lam, would you have accommodated David Cheung's vacation request? Why? What

is the maximum time you would be comfortable giving David Cheung off if his only responsibility was

the auditing of liquid assets

Table 1

Activity Description Duration Immediate Predecessors

01 Pre-audit preparation 28 ---

02 Observation of inventory 25 1

03 General audit procedures 22 2

04 Audit of liquid assets 35 2

05 Inventory pricing 145 2

06 Audit of fixed assets 22 3

07 Audit of liabilities 93 5

08 Audit of COGs 25 5

09 Miscellaneous audit 11 4, 8

10 Lawyer’s letter 1 7

11 Management’s letter 1 6, 9

12 Subsequent review 18 6, 9

13 Preparation of financial statements 15 10, 11

14 Preparation of tax returns 12 10, 12

15 Partner/manager review 6 13, 14

Table 2

Activity Name Early Start Early Finish Late Start Late Finish Slack

01. Pre-audit preparation 0 28 0 28 0

02. Observation of inventory 28 53 28 53 0

03. General audit procedures 53 75 233 255 180

04. Audit of liquid assets 53 88 231 266 178

05. Inventory pricing 53 198 53 198 0

06. Audit of fixed assets 75 97 255 277 180

07. Audit of liabilities 198 291 198 291 0

08. Audit of COGs 198 223 241 266 43

09. Miscellaneous audit 223 234 266 277 43

10. Lawyer’s letter 291 292 191 292 0

11. Management’s letter 234 235 291 292 57

12. Subsequent review 234 252 277 295 43

13. Preparation of financial statements 292 307 292 307 0

14. Preparation of tax returns 292 304 295 307 2

15. Partner/manager review 307 313 307 313 0

If I were Mr. Lam, I would have accommodated David Cheung’s vacation request. As we can see in table

2, Audit of liquid asset (Activity 4) is not a critical activity that the early start is not equal to late start and

the early finish is not equal to the late finish.

There is a slack time of 178 hours, so it is possible to give David a vacation if he promises to come back

before the 231st hour of the project which is the latest start time of audit of liquid asset. As a week involve

40 audit hours, the maximum time for David Cheung’s off is 178/40 = 4.45 weeks.

Question 2 – Part 1

Assume that for the first 106 duration hours all the activities were processed exactly on schedule.

Recommend an accelerating plan that would meet the accelerated deadline (60 hours earlier than

originally agreed) at minimum additional cost.

As it is assumed that the activities were processed exactly on schedule for the first 106 duration hours, the

desired project completion time of the remaining part should be 313 – 106 – 60 = 147hours. Therefore, the

desired project completion time of the whole project is 147 + 106 = 253hours.

In this question, we have to use the Time-Cost Model to reach the desired project completion time with

minimal cost. In table 3, Exhibit 5 is converted into a new format with “Possible Time Saved”, “Extra Cost”

and “Cost/ Time Unit”.

Table 3

Activity

Normal Acceleration Possible

Time Saved

(a) – (c)

Extra

Cost

(d) – (b)

Extra Cost/

Time SavedTime

(a)

Cost

(b)

Time

(c)

Cost

(d)

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 --

First, we have to draw network diagram with the early start/finish and late start/finish times and identify

the critical path(s).

Network Diagram 1

After drawing the first network diagram, we find out there is a critical path which is (01) Pre-audit

Preparation (02) Observation of Inventory (05) Inventory Pricing (07) Audit of liabilities (10)

Lawyer’s letter (13) Preparation of Financial Statement (15) Partner/Manager Review

Table 4 Identify the 1st task to crash

ActivityNormal

Time

Critical

Task?

Crash Time

(hours)

Possible Time

Saved

Crash Cost/

hourBest Option

3. General audit procedures 22 -- -- 0 --

4. Audit of liquid asset 35 -- -- 0 --

5. Inventory pricing 92 Y 56 36 42.92

6. Audit of fixed assets 22 -- -- 0 --

7. Audit of liabilities 93 Y 48 45 18.67 Y

8. Audit of COGS 25 -- -- 0 --

9. Miscellaneous audit 11 -- 9 2 10

10. Lawyer’s letter 1 Y -- 0 --

11. Management’s letter 1 -- -- 0 --

12. Subsequent review 18 -- 3 15 50

13. Preparation of financial

statements15 Y 10 5 120

14. Preparation of tax returns 12 -- 2 10 50

15. Partner/manager review 6 Y -- 0 --

Second, we have to determine which activities to crash. Since Activity 7 (Audit of Liabilities) is the

activity on the critical path with the lowest crash cost, it is the best option to crash.

Third, we need to determine how long to crash. As we can see in Table 2, there is a slack of 43 hours in

activity 8 and 9. Then, we decided to reduce 43 hours by crashing Activity 7 (Audit of Liabilities). The new

duration of Activity 7 (Audit of Liabilities) is 50 hours. Therefore, a new critical path is created there is a

crashing cost of 18.67 x 43 = $802.8.

Since a new critical path is created, we have to draw the network diagram again with new early start/finish

and late start/finish to identify the new critical path.

Network Diagram 2

In network diagram 2, the duration of Activity 7 is changed from 93 hours to 50 hours. The new duration of

the whole project is 270, which means we still have to reduce 270 – 253 = 17 hours. Except the critical path

which is identified above, there is a new critical path.

It is (01) Pre-audit Preparation (02) Observation of Inventory (05) Inventory Pricing (08) Audit of

COGS (09) Miscellaneous audit (12) Subsequent review (14) Preparation of tax returns (15)

Partner/Manager Review.

Table 5 Identify the 2nd tasks to crash

ActivityNormal

Time

Critical

Path 1

Critical

Path 2

Crash Time

(hours)

Possible

Time Saved

Crash Cost/

hour

Best

Option

3. General audit

procedures22 -- -- -- 0 --

4. Audit of liquid

asset35 -- -- -- 0 --

5. Inventory 92 Y Y 56 36 42.92

pricing

6. Audit of fixed

assets22 -- -- -- 0 --

7. Audit of

liabilities50 Y -- 48 2 18.67 Y

8. Audit of COGS 25 -- Y -- 0 --

9. Miscellaneous

audit11 -- Y 9 2 10 Y

10. Lawyer’s

letter1 Y -- -- 0 --

11. Management’s

letter1 -- -- -- 0 --

12. Subsequent

review 18 -- Y 3 15 50

13. Preparation of

financial

statements

15 Y -- 10 5 120

14. Preparation of

tax returns12 -- Y 2 10 50

15.

Partner/manager

review

6 Y Y -- 0 --

Now, we have to identify the 2nd tasks to crash. As the table above mentioned, Activity 7 and 9 can reduce

the two critical paths simultaneously and this combination of activities is with the lowest combined crash

costs, we decided to crash activity 7 and 9 at a time.

Since they both have 2 days of possible time saved, we decide to reduce 2 hours by crashing activity 7 and

9. Therefore, the crash limit of both activity 7 and 9 are reached and there is a crashing cost of (18.67 x 2) +

(10 x 2) = $57.34. As 2 days is reduced, we have to draw the network diagram again with new early

start/finish and late start/finish to identify the new critical path.

Network Diagram 3

In network diagram 3, the duration of Activity 7 is changed from 50 hours to 48 hours and duration of

Activity is changed from 11hours to 9 hours. The new duration of the whole project is 268, which means

we still have to reduce 268 – 253 = 15 hours.

Table 6 Identify the 3rd tasks to crash

ActivityNormal

Time

Critical

Path 1

Critical

Path 2

Crash

Time

(hours)

Possible

Time

Saved

Crash

Cost/ hour

Best

Option

3. General audit

procedures22 -- -- 0 --


5. Inventory pricing 92 Y Y 56 36 42.92 Y


7. Audit of liabilities 48 Y -- 0 --

8. Audit of COGS 25 -- Y -- 0 --

9. Miscellaneous audit 9 -- Y -- 0 --



12. Subsequent review 18 -- Y 3 15 50

13. Preparation of

financial statements15 Y 10 5 120

14. Preparation of tax

returns12 -- Y 2 10 50

15. Partner/manager

review6 Y Y -- 0 --

Now, we have to identify the 3rd task to crash. As we can see in table 6, Activity 5 is on the two critical

paths and it is with the lowest crash costs. Hence, we decided to pick Activity 5 as the 3rd task to crash.

As mentioned above, we still have to reduce 15 hours to reach the desired project duration (253hours). We

chose to reduce 15 hours by crashing activity 5.

Network Diagram 4

In network diagram 4 below, we can see that Activity 5’s duration is changed from 145 hours to 130 hours

and a new crashing cost $42.92 x 15 = $643.8 is created.

Duration of the whole project is 253 hours which is the same as the desired completion time. The crashing

cost for the whole project is 802.8 + 57.34 + 643.8 = $1503.94.

Question 2 – Part 2

Would a corporate limit on per-hour reduction cost of $70 an hour ever become a problem if further

reductions were required? Why?

Table 7

ActivityNormal

Time

Critical

Path 1

Critical

Path 2

Crash

Time

(hours)

Possible

Time

Saved

Crash

Cost/

hour

Best

Option

3. General audit



5. Inventory pricing 77 Y Y 56 21 42.92 Y



8. Audit of COGS 25 -- Y -- 0 --





13. Preparation of



returns12 -- Y 2 10 50

15. Partner/manager

review6 Y Y -- 0 --

For this question, we have to identify the largest reduction. We have to first identify the 1st task to crash.

As we can see in table 7, Activity 5 is on the two critical paths and it is with the lowest crash costs. Hence,

we decided to pick Activity 5 as the task for crashing. Since we are finding the largest reduction, we decided

to reduce all possible time saved which is 21hours.

In the network diagram 5 (below), we can see that the duration of Activity 5 is changed from 130 to 109

hours and the crashing limit of Activity 5 is reached. The cost of crashing activity 5 is $42.92 x 21 =

$901.32.

Network Diagram 5

Table 8

ActivityNormal

Time

Critical

Path 1

Critical

Path 2

Crash

Time

(hours)

Possible

Time

Saved

Crash

Cost/

hour

Best

Option

3. General audit



5. Inventory pricing 56 Y Y -- 0 --



8. Audit of COGS 25 -- Y -- 0 --





13. Preparation of


14. Preparation of tax 12 -- Y 2 10 50

returns

15. Partner/manager

review6 Y Y -- 0 --

To further the reduction, we have to identify the second tasks to crash. As the table above mentioned,

Activity 13 and 14 can reduce the two critical paths simultaneously and this combination of activities is with

the lowest combined crash costs, we decided to crash activity 13 and 14 at a time.

Since the maximum possible time saved for Activity 13 is 5 hours, we decide to reduce 5 hours by crashing

activity 13 and 14. Therefore, the crash limit of both activity 13 is reached and there is a crashing cost of

(120 x 5) + (50 x 5) = $850.

Network Diagram 6

Table 9

ActivityNormal

Time

Critical

Path 1

Critical

Path 2

Crash

Time

(hours)

Possible

Time

Saved

Crash

Cost/

hour

Best

Option

3. General audit



5. Inventory pricing 56 Y Y -- 0 --



8. Audit of COGS 25 -- Y -- 0 --





13. Preparation of

financial statements10 Y -- 0 --


returns7 -- Y 2 5 50

15. Partner/manager

review6 Y Y -- 0 --

Since there is no combination of activities can reduce the two critical paths simultaneously (Table 9) and

there is no new critical path (Network Diagram 6), we have already reached the largest reduction. We

reduced the remaining 21 hours by crashing activity 5 and reduce 5 hours by crashing activity 14 and

activity 13 together. The total crashing hours are 21 + 5 = 26 hours.

The total crashing cost is (21 x 42.92) + (5 x 120) + (5 x 50) = 901.32 + 600 + 250 = $1751.32.

The largest possible reduction requires an average cost per hour is $1751.32/26 = $67.36.

Therefore, n the average cost basis, the corporate limit on per-hour reduction cost of $70 an hour will not

become a problem if further reductions were required.

However, if we use marginal cost, the hours which is reduced by crashing Activity 13 an 14 will cost $50 +

$120 = $170 per hour (Table 8). Therefore, the per-hour reduction cost of $70 an hour will not be enough.

Question 3

Assume that the 60-hour acceleration plan was implemented. After 199 duration hours, Mr. Lam

found that the status of the project was as follows:

− Activity 1-6 were 100% completed, and all the activities except 5 had incurred exactly the

budgeted costs, activity 5 costs $480 more than expected.

− Activity 7 was 33.33% completed, and had incurred $1127.5 in costs.

− Activity 8 was 35% completed, and had incurred $655 in costs.

Without further crashing, how long do you expect the project to take now? How much do you expect

the project to cost?

Activity NameBudget (a)

$

Scheduled (b)

%

Completed (c)

%ACWC

BCWS

(a) x (b)

BCWC

(a) x (c)

01. Pre-audit

preparation$1110 100% 100% $1110 $1110 $1110

02. Observation of

inventory$1100 100% 100% $1100 $1100 $1100

03. General audit

procedures$1200 100% 100% $1200 $1200 $1200

04. Audit of liquid assets $1890 74.29% 100% $1890 $1404 $1890

05. Inventory pricing $4850 100% 100% $5330 $4850 $5330

06. Audit of fixed assets $1050 18.18% 100% $1050 $190.91 $1050

07. Audit of liabilities $3880 33.33% 33.33% $1127.5 $1293.33 $1293.33

08. Audit of COGs $1310 64% 35% $655 $838.4 $458.5

Total $13462.5 $11986.64 $13431.8

For the length of the project to take now,

Schedule Variance

= BCWC – BCWS

=$13431.8 - $11986.64

=$1445.16

Schedule Variance/BCWS

=$1445.16/$11986.64

=12.06% Early

The length that we expect the project to take

= 253 x (1-0.1206) hours

=222.4 hours

For the cost,

Cost Variance

= BCWC – ACWC

=$13431.8 - $13462.5

=-30.7

Cost Variance/BCWC

=-30.7/13431.8

=0.2286% Over Budget

The amount we expect the project to cost

=(1+0.002286) x 19350

=19394.2341

LGT 3105 OM Toys City Inc.

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