Draw the network diagram and what is the critical path -

Question

Question 1. The R&D department is planning to bid on a large project for the development of a new communication system for commercial planes. The accompanying table: shows the activities. Times, and sequences requited:

Activity	Immediate Predecessor	Time
A	-	3
B	A	2
C	A	4
D	A	4
E	B	6
F	C, D	6
G	D.F	2
H	D	3
I	E,G,H	3

a. Draw the network diagram.

b. What is the critical path?

c. Suppose you want to shorten the completion time as much as possible; and you have the option of shortening any or all of B, C, a and G each one week.

d. What is the new ethical path and earliest completion time?

Question 2. A construction project is broken into the following 10 activities:

Activity	Immediate Predecessor	Time
1	-	4
2	1	2
3	1	4
4	1	3
5	2,3	5
6	3	6
7	4	2
8	5	3
9	6,7	5
10	8,9	7

a. Draw the network diagram.

b. find the critical path.

c. If activities 1 and 10 cannot be shortened, but activities 2 through 9 can be shortened to a minimum of one week each at a cost of 10,000 per week, which activities would you shorten to cut the project by four weeks?

Question 3. The following represents a project that should be scheduled using CPM:

		Time (Days)
Activity	Immediate Predecessor	a	m	b
A	-	1	3	5
B	-	1	2	3
C	A	1	2	3
D	A	2	3	4
E	B	3	4	11
F	C,D	3	4	5
G	D,E	1	4	6
H	F,G	2	4	5

a. Draw the network diagram.

b. find the critical path?

c. What is the expected project completion time?

d. What is the probability of completing this project within 16 days?

Question 4. Here is a CPM network with activity times in weeks:

a. Determine the critical path.

b. How many weeks the project take to complete?

c. Suppose could be shortened by two weeks and D by one week. How would this affect the completion date?

Question 5. The following table represents a plan for a project

		Time (Days)
Job No.	Predecessor Job(s)	a	m	b
1	-	2	3	4
2	1	1	2	3
3	1	4	5	12
4	1	3	4	11
5	2	1	3	5
6	3	1	2	3
7	4	1	8	9
8	5,6	2	4	6
9	8	2	4	12
10	7	3	4	5
11	9,10	5	7	8

a. Construct the appropriate network diagram.

b. Indicate the critical path.

c. What is the expected completion time for the project?

d. You can accomplish any one of the following at an additional cost of $1500:
(1) Reduce job 5 by two days.
(2) Reduce job 3 by two days.
(3) Reduce job 7 by two days.
If you will save $1000 for each day that the earliest completion time is reduced, which action, if any, would you choose?

e. What is the probability that the project will take more than 30 days to complete?

Question 6. The National State Bank is trying to make sure that they have enough tellers to handle the Friday afternoon rush of workers wanting to cash their paychecks. They are only concerned with the last hour of the day from 4:00 to 5:00 PM. It takes 5 minutes per customers to be processed by the tellers. The average customers arrivals are shown in the table below.

Time	Cutomer Arriving
4:00-4:05	2
4:05-4:10	5
4:10-4:15	6
4:15-4:20	8
4:20-4:25	10
4:25-4:30	12
4:30-4:35	10
4:30-4:35	12
4:40-4:45	10
4:45-4:50	6
4:50-4:55	4
4:55-5:05	2
5:05-5:10	0
Total	90

The bank currently has 8 teller stations and all are staffed during the Friday afternoon rush hour.

a. What is the current maximum output at the bank during rush hour?

b. Can the bank Process all customers by 5:00 P.M.?

c. What is the maximum waiting time for customers and what time period does it occur in?

Question 7. The home office billing department of a chain of department stores prepares monthly inventory reports for use by the stores purchasing agents. Given the following information, use the critical path method to determine

a. How long the total process will take.

b. Which jobs can be delayed without delaying the early start of any subsequent activity.

	Job and description	Immidiate Predcessors	Time(Hours)
a	Start	-	0
b	Get computer printout of cutomer purchase	a	10
c	Get stock records for the month	a	20
d	Reconcile purchase printouts and stocks records	b, c	30
e	Total stock records by departement	b, c	20
f	Determine records quantities for coming period	e	40
g	Repare stock reports for purchaing agents	d. f	20
h	Fhish	g

Question 8. The following CPM network has estimates of the normal time in weeks listed fir the activities.

a. Identify the critical path

b. What is the length of time to complete the project

c. Which activities have slack, and how much?

d. Here is a table or normal and crash times and costs, Which activities would you shorten to cut two weeks from the schedule in a rational fashion? What would be the incremental cost? Is the critical path changed?

Acitivity	Normal Time	Crash Time	Normal Cost	Crash Cost	Possible Number Of weeks	Cost/Week
A	7	6	7,000	8000
B	2	1	5000	7000
C	4	3	9000	10200
D	5	4	3000	4500
E	2	1	2000	3000
F	4	2	4000	7000
G	5	4	5000	8,000

Question 9. Hungry Henry's is building a new restaurant. In order complete the project the following activities, along with their time estimates, are given below.

	Time Estimate (wk)
Activity	a	m	b	Immidiate Predcessors
A	2	4	7	-
B	1	4	9	A
C	3	6	9	A
D	2	3	5	B, C
E	1	3	9	B
F	2	4	5	C, D
G	3	8	10	E
H	1	2	3	F, E
I	3	5	7	G.,H

a. Calculate the expected time and the Variance for each activity.

b. Draw the critical path diagram. Show the early start, early finish times and late start, late finish times.

c. Show the critical path.

d. What is the probability that the project can be completed in 26 weeks? What is the probability it will take longer than 2O weeks?

e. Are there any other paths that can interfere with completing this project?

Question 10. Bragg's bakery is building a new automated bakery in downtown Sandusky. Here are the activities that need to be completed to get the new bakery built and the equipment installed.

Acitivity	Predcessors	Normal Time (Weeks)	Crashe Time (weeks )	Expediting Cost/week
A	_	9	6	3000
B	A	8	5	3500
C	A	15	10	4000
D	B,C	5	3	2000
E	C	10	6	2500
F	D,E	2	1	5000

a. Draw the project diagram.

b. What is the normal project length?

c. What is the project length is all activities are crashed to their minimum?

d. Bragg's loss $3500 in profit take is we are willing to pay crashing cost as long as it is less than $3500?

Question 11. A processor makes two components, A and B. which are that packaged together as the final product. (each product sold contains one A and one B), The processor can do only one component at a time: either it can make As or it can make Ds. Then is a setup time when switching from A to B.

Current plans are to make 100 units of component A, then 100 units of component B, then 100 units of comment A, then 100 units of component B, and so forth, what the setup and run times for each component are given below.

Component	Setup/ChageCover Time	Run Time/Unit
A	5 minutes	0,2 minute
B	10 minutes	0,1 minute

Assume the packaging of the tow components is totally automated and takes only two seconds per unit of the final product. This packaging time is small enough that you can ignore it. What is the make hourly output, in terms of the number of units of packaged product (which includes one component A. and one component B)?

Question 12. An enterprising student has set up an internship cleaninghouse for business students. Each student that uses the services fills out a font and lists up to 10 companies that he or she would like to ham contacted. The clearinghouse has a choice of two methods to use for processing the forms. The traditional method requires about 20 minutes reviewing the form and arranging the information in the proper order for processing. The other alternative we use an optical scan system, which takes only a minute to prepare but requires five minutes per company for completing the processing. If it costs about the same amount per minute for processing with either of the two methods when should each be used?

Question 13. Rockneas Recycling refurbishes rundown business students. The process uses a moving bet which carries each student through the five steps of the process in sequence. The five steps are as follows:

Step	Description	Time required Per student
1	Unpack and place on belt	10 minute
2	Strip off bad habits	15 minute
3	Scrub and clean mind	08 minute
4	Insert modern methods	10 minute
5	Polish and pack	12 minute

One faculty member is assigned to each of these steps. Faculty members work a 40-hourweek and rotate jobs each week. Mr. Rockness has been working on a contract from General Eclectric, which requires delivery of 2000 refurbished students per week. A representative of the human resource department has just called complaining that the company hasn't been receiving the agreed-upon number of students. A check of finished goods inventory by Mr. Rackness reveleves that there is no stock left. What is going on?

Question 14. The bathtub theory of operations management is being promoted as the next breakthrough for global competitiveness. The factory is a bathtub with 50 gallons of capacity. The drain is the outlet to the market and can output three gallons per hour when wide open. The faucet is the raw material input and can let material in a rate of four gallons per hour. Now to test, your comprehension of the intricacies of operations (assume the bathtub is empty to begin with):

a. Draw a diagram of the factory and determine the maximum rate at which the market can be served if all valves are set to maximum. What happens to the system over time?

b. Suppose that instead of a faucet, a five-gallon container issued for filling the bathtub (assume a full container is next to the tub to begin with); it takes two ban hours to refill the container and return it to due bathtub. What happens to the system over time?

Question 15. A local market research flan has just won a contract for several thousand small projects Involving data gathering and statistical analysis. In the past the firm has assigned each project to a single member of its highly trained professional staff. This person would both gather and analyze the data Using this approach an experienced person can complete an average of 10 such projects in an eight-hour day.

The firm's management is thinking of signing two people to melt project in older to allow them to specialize and become more efficient. The process would require the data gathere to fill out a Matrix on the computer. check it, and transmit it to the statistical analysis program for the analyst to complete. Data can he gathered on one project while the analysis is being completed on another, but the analysis must be complete before the statistical analysis program can accept the new data. After some practice, the new process can he completed with a standard time of 20 minutes for the data gathering and 30 minutes for the analysis.

a. What is the production (output pr how) for each alternative? What is the productivity (output per labor how)?

b. How long would it take to compete 1000 projects with each alternative? What would be the labor contact (total number of labor hours ) for 1,000 projects for each alternative.

Question 16. The following activities are part of a project to be scheduled using CPM:

ACTIVITY	IMMEDIEATE PREDECESSOR	TIME(weeks)
A	_	6
B	A	3
C	A	7
D	C	2
E	B,D	4
F	D	3
G	E,F	7

a. Draw the network.
b. What is the critical path?
c. How many weeks will it take to complete the project?

d. How much slack does activity B have?

Question 17. Schedule the following activities using CPM

ACTIVITY	IMMEDIEATE PREDECESSOR	TIME(weeks)
A	_	1
B	A	4
C	A	3
D	B	2
E	C,D	5
F	D	2
G	F	2
H	E,G	3

a. Draw the network.
b. What is the critical path?
c. How many weeks will it take to complete the project?

d. Which activities have slack, and how much?

Question 18. Here is a network with the activity times shown in days:

a. Find the critical path.

b. The following table shows the normal times and tha crash times, along with the associated costs for each activity.

ACTIVITY	NORMAL TIME	CRASH TIME	NORMAL COST	CRASH COST
A	7	6	$7,000	$8,000
B	3	2	5000	7000
C	4	3	9000	10200
D	5	4	3000	4500
E	2	1	2000	3000
F	4	2	4000	7000
G	5	4	5000	8000

If the project is to be shortened by four days, show which activities, in order of reduction , would be shortened and the resulting cost.

Question 19. FOR THE NETWORK SHOWN :

a. Determine the critical path and the early completion time in weeks for the project.

For the data shown, reduce the project completion time bye three weeks. Assume a linear cost per week shortened, and show, step by step , hoe you arrived at your schedule.

ACTIVITY	NORMAL TIME	NORMAL COST	CRASH TIME	CRASH COST
A	5	$7,000	$3	$13,000
B	10	12000	7	18000
C	8	5000	7	7000
D	6	4000	5	5000
E	7	3000	6	6000
F	4	6000	3	7000
G	4	7000	3	9000

Question 20. A project has been defined to contain the following activities, along with their time estimates for cmpletion.

ACTIVITY	TIME ESTIMATES(WK)			IMMEDIATE PREDECESSOR
A	2	5	8	_
B	1	5	9	_
C	4	6	9	A
D	2	2	2	B
E	1	2	9	A
F	2	4	5	C,D
G	3	8	10	C,E
H	1	2	3	F,G

a. Calculate the expected time and the variance for each activity.

b. Draw the critical path diagram. Shoe the early start, early finish times and late start, late finish times.

c. Show the critical path.

d. What is the probability that the project can be comp;eted in 19 weeks.

Question 21. Assume the network and data that follow:

ACTIVITY	NORMAL TIME	NORMAL COST	CRASH TIME(weeks)	CRASH COST	IMMEDIATE PREDECESSORS
A	2	60	1	70	_
B	4	80	2	160	A
C	8	70	4	110	A
D	6	60	5	90	A
E	7	100	6	130	B
F	4	40	3	100	D
G	5	100	4	150	E,F

a. Construct the network diagram.

b. Indicate the critical path when normal activity times are used.

c. Compute the minimum total direct cost for each project duration based on the cost associated with each activity. Consider durations of 13, 14, 15, 16, 17, and 18 weeks.

d. If the indirect costs for each project duration are $100 ( 18 weeks), $350(17 weeks), $300(16 weeks), $250(15 weeks), $200(14 weeks), and $150(13weeks), what is the total project cost for each duration ? Indicate the minimum total cost duration.