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Tomica - Week 5.pdf

GBA 334 Application Assignment 5 Instructions

Application assignments require solving problems from the textbook. Most of the problems require that you use Excel OM. Some chapters will require you to use POM OM for Windows or TreePlan. The answers must be submitted to the Dropbox in a Microsoft Word or Microsoft Excel file.

You must state your answers within a complete sentence so that your understanding of applying the results of the computations can be observed. You should also include the work for your computation; this will assist in applying partial credit if your answers are not correct.

Do not submit OM for Windows files as server security policies do not allow many of these files to be passed in the system. If you need to show the OM work, either save as an Excel file (a function within aM) or paste a screen capture of the OM Entry Screen before solving AND the OM result screen(s).

NOTE: OM files should not be sent through the online system. If using OM for your solution, run the file in OM and then copy and paste the solution into a MS Excel file (within OM there is an option tab at bottom of the screen to save as MS Excel.) If you cannot do this, with the OM solution file open on your screen, select alt-print screen and then paste the image into a MS Excel file.

If you need any assistance, please do not hesitate to contact your instructor. He or she will be happy to assist.

For this module, you will complete the following problems from the textbook: Chapter 6, pages 280-282, Problems 20,22,30, and 35 using Excel OM/POM OM. NOTE: For Problem 30, there is no need to solve the problem using linear programming methods. Instead, you should focus on solving using the project management capabilities within Excel OM/POM OM. Linear programming will be covered in Module 7.

Submit Application Assignment 5 to the Dropbox no later than Sunday 11:59 EST/EDT of Module 5. Remember, the required formats are Microsoft Word and Microsoft Excel.

------------- PROJECT MANAGEMENT

(a) Determine the expected times and variances for each acti vity.

(b) Construct a project network for this problem. (c) Determine the EST, EFT, LST, LFT, and slack

for each activity. Also determine the critical path and project completion time.

(a) Determine the expected times and variances for

each activity. (b) Construct a project network for this problem. (c) Determine the EST, EFT, LST, LFT, and slack

for each activity. Also determine the critical path and project completion time.

(d) What is the probability that the project will be finished in less than 57 days?

(e) What is the probability that the project will need at least 50 days?

21 LeBron Woods is responsible for developing a lead- ership training program for his organization. The following table describes the relationships between the activities that need to be completed.

20 A series of activities must be completed in a coor- dinated fashion to complete a landscaping overhaul. The following table shows the activities; their opti- mistic, most likely, and pessimistic durations; and their immediate predecessors.

DAYS IMMEDIATE

ACTIVITY a m b PREDECESSORS

A 4 8 12

B 4 10 13 A

C 7 14 18 B

D 9 16 20 B

E 6 9 12 B

F 2 4 6 D,E

G 4 7 13 C,F

H 3 5 7 G

1 2 3 4 G.H

PERCENTAGE ACTUAL

ACTIVITY COMPLETED COST

A 100 $20,000

B 100 $36.000

C 100 $26.000

D 100 $44,000

E 55 $29,000

F 55 $12,000

G 10 $5.000

H 13 $1,800-\~~J'

25 Fred Ridgeway has been given the responsibility;:: of managing a training and development program''.\Ot He knows the EST and LST (both in months), and:}: the total costs for each activity. This information iS~ given in the table at the top of the next page.::., (a) Using ESTs, determine Fred's total monthlY}-

budget. .,~\ (b) Using LSTs, determine Fred's total monthl~.'.

budget. '

(d) What is the probability that the project will be finished in less than 49 days?

(e) What is the probability that the project will need at least 54 days?

22 The expected project completion time for the con- struction of a pleasure yacht is 21 months, and the project variance is 6. What is the probability that the

project will (a) require at least 17 months? (b) be completed within 20 months? (c) require at least 23 months? (d) be completed within 25 months?

23 The Coogan Construction Company has determined that the expected completion time for its most popu- lar model home follows the normal probability dis- tribution with a mean of 25 weeks and a standard deviation of 4 weeks. (a) What is the probability that the next home will

be completed within 30 weeks? (b) What is the probability that the next home will

be completed within 22 weeks? (c) Find the number of weeks within which Coogan

is 99% sure the next home will be completed. (d) Find the number of weeks within which Coogan

is 85% sure the next home will be completed. 24 The General Foundry air pollution project discussed

in this chapter has progressed over the past several weeks, and it is now the end of week 8. Lester Harky would like to know the value of the work completed, the amount of any cost overruns or underruns for the project, and the extent to which the project is ahead of schedule or behind schedule by developing a ta- ble like the one in Table 7. The current project status is shown in the following table.

A,B

C E

F D

F,H G,l

IMMEDIATE PREDECESSORS

DAYS

ACTIVITY a m b

A 3 7 14

B 5 10 15

C 3 5 10

D 5 12 13

E 2 5 8

F 2 5 14

G 5 8 11

H 6 10 14

3 4 8

4 7 10

PROJECT MANAGEMENT

PERCENTAGE ACTUAL

ACTIVITY COMPLETED

COST

A 100

$1,900

B 100

$5,300

C 100

$6,150

D 40

$1,800

E 60

$1,755

F 0

$ a

29 General Foundry's project crashing data are shown in Table 10. Crash this project by hand to 10 weeks. What are the final times for each activ- ity after crashing, and what is the total cost associ- ated with reducing the duration of this project from

15 to 10 weeks? 30 Bowman Builders manufactures steel storage sheds

for commercial use. Joe Bowman, president of Bow- man Builders, is contemplating producing sheds for home use. The activities necessary to build an ex- perimental model and related data are given in the table on the next page. The project completion time

using standard times is 14 weeks. Set up and solve an LP model using Excel to

crash this project to 10 weeks. How much does it cost to reduce the duration of this project from 14 to

10 weeks? 31 The table on the next page describes the variouS ac-

tivities of a construction project in a chemical plant. (a) Set up and solve an LP model using Excel to

crash this project to 22 dayS. What is the total

crashing cost? (b) Assuming each activity can only be crashed in

whole days, what is the earliest completion of this project? What is the total associated crash

cost? . 32 A new order filling system needs tO,be installed as

soon as possible. The table on the next page lists the project'S activities and their predecessors. Also pro- vided is the cost information to reduce the standard

activity times.Set up and solve an LP model using Excel to crash this project to 24 days. What is the total crash-

ing cost?

(a) Develop a weekly budget for this project, using

the earliest start times. (b) Develop a weekly budget for this project, using

the latest start times. 28 Susan Roger's project (see Problem 27) has pro-

gressed over the past several weeks, and it is now the end of week 8. Susan would like to know the cur- rent status of the project with regard to schedule and budget by developing an appropriate table. Assume that all activities follow their earliest time schedules. The relevant data are shown in the following table.

PERCENTAGE

ACTIVITY COMPLETED

ACTUAL COST

A 100

$13,000

B 100

$12,000

C 100

$6,000

D 100

$6,000

E 60

$9,000

F 10

$800

G 80

$3,600

H 15

$375

Assume that activities not shown in the table have not yet started and have incurred no cost to date. All activities follow their earliest time schedules.

27 Susan Roger needs to coordinate the opening of a new office for her company in the city of Denver. The activity time and relationships for this project, as well as the total budgeted cost for each activity,

are shown in the following table.

, IMMEDIATE TIME TOTAL

ACTIVITY PREDECESSORS

(WEEKS) COST

A 2 $2,200

B A

3 $5,100

C A

4 $6,000

D B,C

2 $3,600

E C

3 $2,700

F D,E

3 $1,800

26 Fred Ridgeway's project (see Problem 25) has progressed over the past several months, and it is now the end of month 16. Fred would like to know the current status of the project with regard to sched- ule and budget by developing an appropriate table. The relevant data are shown in the following table.

nthly

ll.thly

ility ram. and

on is

PROJECT MANAGEMENT

Table for Problem 30

ACTIVITY

F G

IMMEDIATE PREDECESSORS

C D,E

STANDARD STANDARD CRASH TIME CRASH

TIME (WEEKS) COST (WEEKS) COST

3 $1.000 2 $1.600

2 $2,000 1 $2,700

1 $300 1 $300

7 $1,300 3 $1.600

6 $850 3 $1.000

2 $4,000 1 $5,000

4 $1,500 2 $2,000

Table for Problem 31 IMMEDIATE STANDARD

STANDARD CRASH TIME CRASH

ACTIVITY PREDECESSORS TIME (DAYS) COST

(DAYS) COST

A 4 $2,000

2 $2,600

B A 6 $3,500

5 $4,300

C A 8 $3,300

6 $3,900

D B 5 $1,200

4 $1,800

E C,D 3 $1,700

2 $2,200

F E 7 $2,200 5

$3,600

G E 5 $ 900 4

$1,550 i,

H F.G 4 $1.200 3

$1,700

The first step that this team performs is general sys- tems design. The optimistic, mosllikely, and pessi- mistic times are 3, 4, and 5 weeks. Following this, a number of activities can begin. Activity 2 is involved with procedures design. Optimistic, most likely. and pessimistic times for completing this activity are 4,. 5, and 12 weeks. Activity 3 is developing detail~d report designs. Optimistic, most likely, and pessim~S';, tic time estimates are 6, 8, and 10 weeks. ActiVIty.. 4, detailed forms design, has optimistic, most likely:> and pessimistic time estimates of 2,5, and 5 weekS.

Table for Problem 32 IMMEDIATE STANDARD

STANDARD CRASH TIME CRASH

ACTIVITY PREDECESSORS TIME (DAYS) COST

(DAYS) COST

A 7 $2.000

5 $ 3.500

B A 10 $3.000

8 $ 4,700

C A 8 $3,400 7

$ 3.700

D C 6 $1.600

4 $ 2.600

E C 7 $1.900

4 $ 4.000 ,.~

F D.E 5 $1.200

3 $ 2,800

G B,C 11 $8.200 8 $10.900

H F.G 4 $2.600 3 $ 3.800

33 Software Development Specialists (SDS) is in- volved with developing software for customers in the banking industry. SDS breaks a large program- ming project into teams that perform the necessary steps. Team A is responsible for going from general systems design all the way through to actual systems testing. This involves 18 separate activities. Team B is then responsible for the final installation.

To determine cost and time factors, optimistic, most likely, and pessimistic time estimates have been made for all of the 18 activities involved for team A.

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Tomica - Week 6.pdf

GBA 334 Application Assignment 6 Instructions

Application assignments require solving problems from the textbook. Most of the problems require that you use Excel QM. Some chapters will require you to use POM QM for Windows or TreePlan. The answers must be submitted to the Dropbox in a Microsoft Word or Microsoft Excel file.

Do not submit QM for Windows files as server security policies do not allow many of these files to be passed in the system. If you need to show the QM work, either save as an Excel file (a function within QM) or paste a screen capture of the QM Entry Screen before solving AND the QM result screen(s).

NOTE: QM files should not be sent through the online system. If using QM for your solution, run the file in QM and then copy and paste the solution into a MS Excel file (within QM there is an option tab at bottom of the screen to save as MS Excel.) If you cannot do this, with the QM solution file open on your screen, select alt-print screen and then paste the image into a MS Excel file.

If you need any assistance, please do not hesitate to contact your instructor. He or she will be happy to assist.

For this module, you will complete the following problems from the textbook: • Chapter 7, pages 309 and 311, Problems 9, 11, and 19 using Excel QM/POM

QM) • Chapter 8, pages 353-354, Problem 34 using Excel QM (to get to the queuing

models in Excel QM, click on the Excel QM tab ~ Alphabetical ~ Waiting Lines)

Submit Application Assignment 6 to the Dropbox no later than Sunday 11 :59 EST/EDT of Module 6. Remember, the required formats are Microsoft Word and Microsoft Excel.

NETWORK MODELS

Rroblems* . . • 9 Bechtold Construction is in the process of mstalhng

Q. power lines to a large housing development. Ste.ve Bechtold wants to minimize the total length of WIre used, which will minimize his costs. The housing development is shown as a network in Figure 21. Each house has been numbered, and the distances between houses are given in hundreds of feet. What do you recommend? The city of New Berlin is considering making sev- eral of its streets one-way. What is the maximum number of cars per hour that can travel from east to west? The network is shown in Figure 22. Transworld Moving has been hired to move the of- fice furniture and equipment of Cohen Properties to their new headquarters. What route do you rec- ommend? The network of roads is shown in Figure 23. Because of a sluggish economy, Bechtold Construc- tion has been forced to modify its plans for the hous- ing development in Problem 9. The result is that the path from node 6 to 7 now has a distance of 7. What impact does this have on the total length of wire needed to install the power lines?

go1J

Q: 14

Due to increased property taxes and an aggressive road development plan, the city of New Berlin has been able to increase the road capacity of two of its roads (see Problem 10). The capacity along the road repre- sented by the path from node I-node 2 has been in- creased from 2 to 5. In addition, the capacity from node I-node 4 has been increased from 1 to 3. What impact do these changes have on the number of cars per hour that can travel from east to west? The director of security wants to connect security video cameras to the main control site from five potential trouble locations. Ordinarily, cable would simply be run from each location to the main control site. However, because the environment is poten- tially explosive, the cable must be run in a special conduit that is continually air purged. This conduit is very expensive but large enough to handle five cables (the maximum that might be needed). Use the minimal-spanning tree technique to find a minimum distance route for the conduit between the locations noted in Figure 24. (Note that it makes no difference which one is the main control site.) One of our best customers has had a major plant breakdown and wants us to make as many widgets

! i' ",

'Note: g means the problem may be solved with QM for Windows.

FIGURE 21 Network for Problem 9

FIGURE 22 Network for Problem 10

309

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II !I~:-, ! I I

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NETWORK MODELS

FIGURE 26 Network for Problem 17

Q: 19 The road system around the hotel complex on Inter- national Drive (node I) to Disney World (node 11) in Orlando, Florida, is shown in the network of Figure 27. The numbers by the nodes represent the traffic flow in hundreds of cars per hour. What is the maximum flow of cars from the hotel complex to Disney World?

Q: 20 A road construction project would increase the road capacity around the outside roads from International Drive to Disney World by 200 cars per hour (see Problem 19). The two paths affected would be 1-2-6-9-11 and 1-5-8-10- What impact would this have on the total flow of cars? Would the total flow of cars increase by 400 cars per hour?

Q: 21 Refer to Problem 19 and model this problem using linear programming. Solve it with any software.

FIGURE 27 Network for Problem 19

Q: 22 In Problem 21, a linear program was developed for the road system at Disney World. Modify this linear program to make the changes detailed in Problem 20. Solve this problem and compare it to the solution without the changes.

Q: 23 Solve the maximal-flow problem presented in the net- work of Figure 28 below. The numbers in the network represent thousands of gallons per hour as they flow through a chemical processing plant.

Q: 24 Two terminals in the chemical processing plant, rep- resented by nodes 6 and 7, require emergency repair (see Problem 23). No material can flow into or out of these nodes. What impact does this have on the capacity of the network?

Q: 25 Solve the shortest-route problem presented in the network of Figure 29 below, going from node 1 to

FIGURE 28 Network for Problem 23

FIGURE 29 Network for Problem 25

311

QUEUING MODELS

clerk is not busy with customers, he can fill his time with filing or processing mailed-in requests for ser- vice. On a typical day, dri vers come into the DMV according to the following pattern:

AITivals follow a Poisson distribution. Service times follow an exponential distribution, with an aver- age of 10 minutes per customer. How many clerks should be on duty during each period to maintain the desired level of service? You may use Excel's Goal Seek procedure to find the answer.

22 Julian Argo is a computer technician in a large in- surance company. He responds to a variety of complaints from agents regarding their computers' performance. He receives an average of one com- puter per hour to repair, according to a Poisson dis- tribution. It takes Julian an average of 50 minutes to repair any agent's computer. Service times are exponentially distributed. (a) Determine the operating characteristics of the

computer repair facility. What is the probability that there will be more than two computers wait- ing to be repaired?

(b) Julian believes that adding a second repair tech- nician would significantly improve his office's efficiency. He estimates that adding an assistant, but still keeping the department running as a single-server system, would double the capacity of the office from 1.2 computers per hour to 2.4 computers per hour. Analyze the effect on the waiting times for such a change and compare the results with those found in part (a).

(c) Insurance agents earn $30 for the company per hour, on average, while computer techni- cians earn $18 per hour. An insurance agent who does not have access to his computer is unable to generate revenue for the company. What would be the hourly savings to the firm associated with employing two technicians in- stead of one?

23 Julian is considering putting the second technician in another office on the other end of the building, so that access to a computer technician is more con- venient for the agents. Assume that the other agent will also have the ability to repair a computer in 50 minutes and that each faulty computer will go to the next available technician. Is this approach more cost-effective than the two approaches considered in Problem 22?

i j

24 Bru-Thru is a chain of drive-through beer and wine outlets where customers arrive, on average, every five minutes. Management has a goal that customers will be able to complete their transaction, on aver- age, in six minutes with a single server. Assume that this system can be described as an MIM/l configura- tion. What is the average service time that is neces- sary to meet this goal?

25 Recreational boats arrive at a single gasoline pump located at the dock at Trident Marina at an average rate of 10 per hour on Saturday mornings. The fill- up time for a boat is normally distributed, with an average of 5 minutes and a standard deviation of 1.5 minutes. Assume that the arrival rate follows the Poisson distribution. (a) What is the probability that the pump is vacant? (b) On average, how long does a boat wait before

the pump is available? (c) How many boats, on average, are waiting for the

pump?

26 A chemical plant stores spare parts for maintenance in a large warehouse. Throughout the working day, maintenance personnel go to the warehouse to pick up supplies needed for their jobs. The warehouse receives a request for supplies, on average, every 2 minutes. The average request requires 1.7 minutes to fill. Maintenance employees are paid $20 per hour, and warehouse employees are paid $12 per hour. The warehouse is open 8 hours each day. Assuming that this system follows the MIM/s requirements, what is the optimal number of warehouse employees to hire?

27 During peak times the entry gate at a large amuse- ment park experiences an average arrival of 500 customers per minute, according to a Poisson dis- tribution. The average customer requires four sec- onds to be processed through the entry gate. The park's goal is to keep the waiting time less than five seconds. How many entry gates are necessary to meet this goal?

28 Customers arrive at Valdez's Real Estate at an aver- age rate of one per hour. Arrivals can be assumed to follow the Poisson distribution. Juan Valdez, the agent, estimates that he spends an average of 30 minutes with each customer. The standard deviation of service time is 15 minutes, and the service time distribution is arbitrary. (a) Calculate the operating characteristics of the

queuing system at Valdez's agency. (b) What is the probability that an arriving customer

will have to wait for service?

29 If Valdez wants to ensure that his customers wait an average of around 10 minutes, what should be his average service time? Assume that the standard deviation of service time remains at J 5 minutes.

40 25

ARRIV AL RATE (CUSTOMERS/HOUR)

8 A.M.-IO A.M.

10 A.M.-2 P.M.

2 p.M.-5 P.M.

TIME

:353

QUEUING MODELS

354

30 Customers arrive at an automated coffee vend- ing machine at a rate of 4 per minute, following a Poisson distribution. The coffee machine dispenses a cup of coffee at a constant rate of 10 seconds. (a) What is the average number of people waiting

in line? (b) What is the average number of people in the

system? (c) How long does the average person wait in line

before receiving service? 31 Chuck's convenience store has only one gas pump.

Cars pull up to the pump at a rate of one car every eight minutes. Depending on the speed at which the customer works, the pumping time varies. Chuck estimates that the pump is occupied for an average of five minutes, with a standard deviation of one minute. Calculate Chuck's operating characteristics. Comment on the values obtained. What, if anything, would you recommend Chuck should do?

32 Get Connected, Inc., operates several Internet kiosks in Atlanta, Georgia. Customers can access the Web at these kiosks, paying $2 for 30 minutes or a fraction thereof. The kiosks are typically open for 10 hours each day and are always full. Due to the rough usage these PCs receive, they break down fre- quently. Get Connected has a central repair facility to fix these PCs. PCs arrive at the facility at an aver- age rate of 0.9 per day. Repair times take an average of 1 day, with a standard deviation of 0.5 days.

Calculate the operating characteristics of this queuing system. How much is it worth to Get Con- nected to increase the average service rate to 1.25 PCs per day?

33 A construction company owns six backhoes, which each break down, on average, once every 10 work- ing days, according to a Poisson distribution. The mechanic assigned to keeping the backhoes running is able to restore a backhoe to sound running order in 1 day, according to an exponential distribution. (a) How many backhoes are waiting for service, on

average? (b) How many are currently being served? (c) How many are in running order, on average? (d) What is the average waiting time in the queue? (e) What is the average wait in the system?

34 A technician monitors a group of five computers in an automated manufacturing facility. It takes an average of 15 minutes, exponentially distributed, to adjust any computer that develops a problem. The computers run for an average of 85 minutes, Poisson distributed, without requiring adjustments. Compute the fo11owing measures: (a) average number of computers waiting for

adjustment (b) average number of computers not in working

order

35 A copier repair person is responsible for servic- ing the copying machines for seven companies in a local area. Repair cal1s come in at an average of one call every other day. The arrival rate follows the Poisson distribution. Average service time per call, including travel time, is exponentially distributed, with a mean of two hours. The repair person works an eight-hour day. (a) On average, how many hours per day is the

repair person involved with service calls? (b) How many hours, on average, does a customer

wait for the repair person to arrive after making a call?

36 The Johnson Manufacturing Company oper- ates six identical machines that are serviced by a single technician when they break down. Break- downs occur according to the Poisson distribu- tion and average 0.03 breakdowns per machine operating hour. Average repair time for a ma- chine is five hours and follows the exponential distribution. (a) What percentage of the technician's time is spent

repairing machines? (b) On average, how long is a machine out of

service because of a breakdown? (c) On average, how many machines are out of

service? (d) Johnson wants to investigate the economic feasi-

bility of adding a second technician. Each tech- nician costs the company $18 per hour. Each hour of machine downtime costs $120. Should a second technician be added?

37 A typical subway station in Washington, DC, has six turnstiles, each of which can be controlled by the station manager to be used for either entrance or exit control-but never for both. The manager must decide at different times of the day how many turn- stiles to use for entering passengers and how many to use to allow passengers to exit.

At the Washington College Station, passengers enter the station at a rate of about 84 per minute be- tween the hours of 7 and 9 A.M. Passengers exiting trains at the stop reach the exit turnstile area at a rate of about 48 per minute during the same morning rush hour. Each turnstile can allow an average of 30 passengers per minute to enter or exit. Arrival and service times have been thought to follow Poisson and exponential distTibutions, respectively. Assume that riders form a common queue at both entry and exit turnstile areas and proceed to the first empty turnstile.

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