Question

You are the manager of a project to improve a billing process at your firm. The table below contains the data you will need to conduct a cost analysis of the project Indirect costs are $1,600 per week, and penalty costs are $600 per week after week 12 Immediate Normal Cost Crash Cost Predecessor(s) Normal Time (weeks) Crash Time (weeks) ($) ($) Activity A 4 5,500 7,500 В 5 3 8,000 9,500 A 1 1 3,500 3,500 В 6 3 6,000 11,500 В, С 7 4,000 7,500 6,500 F 7 3,500 a. What is the minimum-cost schedule for this project? The minimum-cost schedule is 13 weeks. (Enter your response as an integer.) b. What is the difference in total project costs between the earliest completion time of the project using "normal" times and the minimum-cost schedule you derived in part (a)? less than using the "normal" times. (Enter your response as an integer.) The minimum-cost schedule costs $

Answer 1

Step 1: - Drawing Network Diagram

E 716) - Dummy 6/ 3 ESTILST) Critical Path NT(CT)

Step 2. Statement Showing activity cost slope

Activity	Normal Cost ($)	Crash Cost ($)	Difference in cost	Normal Time (weeks)	Crash Time (Weeks)	Difference in Time	Cost Slope = Difference in cost/ Difference in Time
A (1-2)	5500	7500	2000	4	1	3	666.67
B (1-3)	8000	9500	1500	5	3	2	750.00
C (2-4)	3500	3500	0	1	1	0	0.00
D (3-5)	6000	11500	5500	6	3	3	1833.33
E (4-6)	4000	7500	3500	7	6	1	3500.00
F (5-6)	3500	6500	3000	7	6	1	3000.00
Sub Total	$30,500

.

Step 3:-

Critical path of the project is 1 - 3 - 5 - 6 having normal duration of completion of 18 Weeks.

Normal Cost of Project is $30500 (i.e. 5500+8000+3500+6000+4000+3500)

.

Step 4:- Various Paths and their progress

Various Paths	Crash Time	Normal Time	Crashing Progress
1 - 2 - 4 - 6	1+1+6 = 8	4+1+7 = 12	12
1 - 3 - 4 - 6	3+0+6 = 9	5+0+7 = 12	12/11/10
1 - 3 - 5 - 6	3+3+6 = 12	5+6+7 = 18	18/17/16/15/14/13/12

We crash least cost activities on the critical paths Crashing Activity

Therefore,

First we crash Activity B (1 - 3) by 2 Weeks,

Second we crash Activity D (3-5) by 3 Weeks,

Finally, We crash Activity F(5-6) By 1 Weeks.

Step 5 :- Statement showing Associated cost of Project on each week.

Project Length (Weeks)	Activity Crashed (each Week)	Crashing Cost (Each Week)	Cumulative Crashing Cost	Normal Cost	Indirect Cost	Penalty Cost	Total Cost of Project
				Sum of Normal Cost	($1600 x No. Of Weeks)	[($600 x No. of Weeks - 12 Weeks)]
18	-	0	0	30500	28800	3600	62900
17	B (1-3)	750	750	30500	27200	3000	61450
16	B (1-3)	750	1500	30500	25600	2400	60000
15	D (3-5)	1833.33	3333.33	30500	24000	1800	59633.33
14	D (3-5)	1833.33	5166.66	30500	22400	1200	59266.66
13	D (3-5)	1833.33	6999.99	30500	20800	600	58899.99
12	F (5-6)	3000	9999.99	30500	19200	0	59699.99

Step 6 : - Final Answer

a) The Minimum-Cost Schedule for the Project is 13 Weeks.

b) The Minimum cost Schedule cost is $ 4000 (i.e. 62900 - 58900) Less than Cost using Normal Times