## All Weeks Introduction to Operations Management Coursera Quiz Answers

### Introduction to Operations Management Week 2 Quiz Answers

#### Quiz 1: Homework Assignment: Module 2 – Process Analysis

Q1. **Posh Nails**

Katie Posh runs an upscale nail salon. The service process includes five activities that are conducted in the sequence described below. (The time required for each activity is shown in parentheses):

- Activity 1: Welcome a guest. (1 minute)
- Activity 2: Clip and file nails. (3 minutes)
- Activity 3: Paint. (5 minutes)
- Activity 4: Dry. (10 minutes)
- Activity 5: Check out the customer. (4 minutes)

Three servers (S1, S2, and S3) offer the services in a worker-paced line. The assignment of tasks to servers is the following: S1 does Activity 1. S2 does Activities 2 and 3. S3 does Activities 4 and 5. The drying process does not require server 3’s constant attention; she/he needs to only escort the customer to the salon’s drying chair (equipped with fans for drying). The time to do this is negligible. There exists only one drying chair in the salon.

*Which resource is the bottleneck of the process?*

- S1
- S3
**S2**- Dryer chair

Q2. **Posh Nails**

Katie Posh runs an upscale nail salon. The service process includes five activities that are conducted in the sequence described below. (The time required for each activity is shown in parentheses):

- Activity 1: Welcome a guest. (1 minute)
- Activity 2: Clip and file nails. (3 minutes)
- Activity 3: Paint. (5 minutes)
- Activity 4: Dry. (10 minutes)
- Activity 5: Check out the customer. (4 minutes)

Three servers (S1, S2, and S3) offer the services in a worker-paced line. The assignment of tasks to servers is the following: S1 does Activity 1. S2 does Activities 2 and 3. S3 does Activities 4 and 5. The drying process does not require server 3’s constant attention; she/he needs to only escort the customer to the salon’s drying chair (equipped with fans for drying). The time to do this is negligible. There exists only one drying chair in the salon.

*What is the utilization of server 2 (in decimal form)? Assume that there is unlimited demand and that the process only admits customers at the rate of the bottleneck.*

**S2 does Activities 2 and 3. S3 does Activities 4 and 5. The drying process does not require server 3’s constant attention; she/he needs to only escort the customer to the salon’s drying chair**.

Q3. **Posh Nails**

Katie Posh runs an upscale nail salon. The service process includes five activities that are conducted in the sequence described below. (The time required for each activity is shown in parentheses):

- Activity 1: Welcome a guest. (1 minute)
- Activity 2: Clip and file nails. (3 minutes)
- Activity 3: Paint. (5 minutes)
- Activity 4: Dry. (10 minutes)
- Activity 5: Check out the customer. (4 minutes)

Three servers (S1, S2, and S3) offer the services in a worker-paced line. The assignment of tasks to servers is the following: S1 does Activity 1. S2 does Activities 2 and 3. S3 does Activities 4 and 5. The drying process does not require server 3’s constant attention; she/he needs to only escort the customer to the salon’s drying chair (equipped with fans for drying). The time to do this is negligible. There exists only one drying chair in the salon.

*What is the average labor utilization of the servers (in decimal form)? Assume that there is unlimited demand and that the process only admits customers at the rate of the bottleneck.*

**S2 does Activities 2 and 3. S3 does Activities 4 and 5. The drying process does not require server 3’s constant attention; she/he needs to only escort the customer to the salon’s drying chair**.

Q4. **Posh Nails**

- Activity 1: Welcome a guest. (1 minute)
- Activity 2: Clip and file nails. (3 minutes)
- Activity 3: Paint. (5 minutes)
- Activity 4: Dry. (10 minutes)
- Activity 5: Check out the customer. (4 minutes)

*Assume a wage rate of $12 per hour. What are the direct labor costs for one customer (in dollars)?*

**S2 does Activities 2 and 3. S3 does Activities 4 and 5. The drying process does not require server 3’s constant attention; she/he needs to only escort the customer to the salon’s drying chair**.

Q5. BN1. Butternut is a ski resort in Massachusetts. One of their triple chair lifts unloads 1296 skiers per hour at the top of the slope. (A triple chair lift can carry three passengers per chair. Note that each lift contains multiple chairs.) The ride from the bottom to the top takes 5 minutes. On average, how many skiers are riding on the lift at any one time?

Q6. Tech Company is a medium-sized consumer electronics retailer. The company reported $155,000,000 in revenues for 2007 and $110,050,000 in Costs of Goods Sold (COGS). In the same year, Tech Co. held an average of $20,000,000 in inventory.

*How many times did Tech Co. turn its inventory in 2007?*

Q7. Tech Company is a medium-sized consumer electronics retailer. The company reported $155,000,000 in revenues for 2007 and $110,050,000 in Costs of Goods Sold (COGS). In the same year, Tech Co. held an average of $20,000,000 in inventory.

*Inventory cost at Tech Co. is 35 percent per year. What is the per unit inventory cost (in dollars) for an MP3 player sold at $50? Assume that the margin corresponds to the retailer’s average margin.*

Q8. The Gamer Company is a video game production company that specializes in educational video games for kids. The company’s R&D department is always looking for great ideas for new games. On average, the R&D department generates about 25 new ideas a week. To go from idea to approved product, the idea must pass through the following stages: paper screening (a 1-page document describing the idea and giving a rough sketch of the design), prototype development, testing, and a focus group. At the end of each stage, successful ideas enter the next stage. All other ideas are dropped. The following chart depicts this process, and the probability of succeeding at each stage.

The paper screening for each idea takes 2 hours of a staff member’s time. After that, there is a stage of designing and producing a prototype. A designer spends 4 hours designing the game in a computer-aided-design (CAD) package. The actual creation of the mock-up is outsourced to one of many suppliers with essentially limitless capacity. It takes 4 days to get the prototype programmed, and multiple prototypes can be created simultaneously. A staff member of the testing team needs 2 days to test an idea. Running the focus group takes 2 hours of a staff member’s time per idea, and only one game is tested in each focus group. Finally, the management team meets for 3 hours per idea to decide if the game should go into production.

Available working hours for each staff member are 8 hours per day, 5 days a week. The current staffing plan is as follows:

A. Paper screening: 3 staff members.

B. Design and Production: 4 staff members.

C. Testing: 6 staff members.

D. Focus Group: 1 staff member.

E. Final Decision: 1 management team

*How many new ideas would Gamer Co. approve for production per week if it had unlimited capacity (staff) in its R&D process?*

Q9. The Gamer Company is a video game production company that specializes in educational video games for kids. The company’s R&D department is always looking for great ideas for new games. On average, the R&D department generates about 25 new ideas a week. To go from idea to approved product, the idea must pass through the following stages: paper screening (a 1-page document describing the idea and giving a rough sketch of the design), prototype development, testing, and a focus group. At the end of each stage, successful ideas enter the next stage. All other ideas are dropped. The following chart depicts this process, and the probability of succeeding at each stage.

The paper screening for each idea takes 2 hours of a staff member’s time. After that, there is a stage of designing and producing a prototype. A designer spends 4 hours designing the game in a computer-aided-design (CAD) package. The actual creation of the mock-up is outsourced to one of many suppliers with essentially limitless capacity. It takes 4 days to get the prototype programmed, and multiple prototypes can be created simultaneously. A staff member of the testing team needs 2 days to test an idea. Running the focus group takes 2 hours of a staff member’s time per idea, and only one game is tested in each focus group. Finally, the management team meets for 3 hours per idea to decide if the game should go into production.

Available working hours for each staff member are 8 hours per day, 5 days a week. The current staffing plan is as follows:

A. Paper screening: 3 staff members.

B. Design and Production: 4 staff members.

C. Testing: 6 staff members.

D. Focus Group: 1 staff member.

E. Final Decision: 1 management team

*Which stage is the bottleneck according to the current staffing plan?*

- Testing
- Focus group
**Design and production**- Paper screening
- Final decision

Q10. The Gamer Company is a video game production company that specializes in educational video games for kids. The company’s R&D department is always looking for great ideas for new games. On average, the R&D department generates about 25 new ideas a week. To go from idea to approved product, the idea must pass through the following stages: paper screening (a 1-page document describing the idea and giving a rough sketch of the design), prototype development, testing, and a focus group. At the end of each stage, successful ideas enter the next stage. All other ideas are dropped. The following chart depicts this process, and the probability of succeeding at each stage.

The paper screening for each idea takes 2 hours of a staff member’s time. After that, there is a stage of designing and producing a prototype. A designer spends 4 hours designing the game in a computer-aided-design (CAD) package. The actual creation of the mock-up is outsourced to one of many suppliers with essentially limitless capacity. It takes 4 days to get the prototype programmed, and multiple prototypes can be created simultaneously. A staff member of the testing team needs 2 days to test an idea. Running the focus group takes 2 hours of a staff member’s time per idea, and only one game is tested in each focus group. Finally, the management team meets for 3 hours per idea to decide if the game should go into production.

Available working hours for each staff member are 8 hours per day, 5 days a week. The current staffing plan is as follows:

A. Paper screening: 3 staff members.

B. Design and Production: 4 staff members.

C. Testing: 6 staff members.

D. Focus Group: 1 staff member.

E. Final Decision: 1 management team

*With the current staffing plan, how many new ideas will be put into production per week?*

#### Quiz 2: Final Exam – Module 2

Q1. **Smooth Chin Device Company**

The Smooth Chin Device Company is a manufacturer of high-end electric razors. These razors are produced using a machine-paced process. For each razor, a tray with components enters the process at the beginning of a conveyor belt. The tray then passes through the six steps (consisting of various tasks) explained in the table below. Workers perform the assembly operations on the moving tray. The last step consists of an inspection of the then fully assembled razor. The activity times of the process are as follows:

There are six workers, one at each of the six stations (A-F). They begin their workday at 8:00 a.m. and work steadily until 4:00 pm. (They are replaced with other workers for breaks and lunches, but the production is not slowed or stopped during these times.) Their hourly wage rate is $25 per hour. You can assume unlimited demand.

*Which station is the bottleneck of the process?*

- F
- E
- A
**D**- C
- B

Q2. **Smooth Chin Device Company**

The Smooth Chin Device Company is a manufacturer of high-end electric razors. These razors are produced using a machine-paced process. For each razor, a tray with components enters the process at the beginning of a conveyor belt. The tray then passes through the six steps (consisting of various tasks) explained in the table below. Workers perform the assembly operations on the moving tray. The last step consists of an inspection of the then fully assembled razor. The activity times of the process are as follows:

There are six workers, one at each of the six stations (A-F). They begin their workday at 8:00 a.m. and work steadily until 4:00 pm. (They are replaced with other workers for breaks and lunches, but the production is not slowed or stopped during these times.) Their hourly wage rate is $25 per hour. You can assume unlimited demand.

*What is the process capacity (you can ignore any start-up or empty system effects), in razors/hour?*

**For each razor, a tray with components enters the process at the beginning of a conveyor belt. The tray then passes through the six steps (consisting of various tasks) explained in the table below. Workers perform the assembly operations on the moving tray.**

Q3. **Smooth Chin Device Company**

The Smooth Chin Device Company is a manufacturer of high-end electric razors. These razors are produced using a machine-paced process. For each razor, a tray with components enters the process at the beginning of a conveyor belt. The tray then passes through the six steps (consisting of various tasks) explained in the table below. Workers perform the assembly operations on the moving tray. The last step consists of an inspection of the then fully assembled razor. The activity times of the process are as follows:

There are six workers, one at each of the six stations (A-F). They begin their workday at 8:00 a.m. and work steadily until 4:00 pm. (They are replaced with other workers for breaks and lunches, but the production is not slowed or stopped during these times.) Their hourly wage rate is $25 per hour. You can assume unlimited demand.

*What are the direct labor costs (you can ignore any start-up or empty system effects)associated with producing one razor, in dollars?*

**For each razor, a tray with components enters the process at the beginning of a conveyor belt. The tray then passes through the six steps (consisting of various tasks) explained in the table below. Workers perform the assembly operations on the moving tray.**

Q4. **Smooth Chin Device Company**

*What is the average labor utilization (you can ignore any start-up or empty system effects)of the six workers? Please give your answer in decimal form (e.g. 0.5 for 50% utilization).*

**For each razor, a tray with components enters the process at the beginning of a conveyor belt. The tray then passes through the six steps (consisting of various tasks) explained in the table below. Workers perform the assembly operations on the moving tray.**

Q5. Strohrmann, a large-scale bakery in Pennsylvania, is laying out a new production process for their packaged bread, which they sell to several grocery chains. It takes 12 minutes to bake the bread.

*How large an oven is required so that the company is able to produce 4,000 units of bread per hour (give your answer in terms of the number of units that can be baked simultaneously)?*

Q6. The following table shows financial data (year 2009) for two US retailers: Save-A-Lot Retailers and Wally’s Mart.

Assume that both companies have an average annual holding cost rate of 20% (i.e. it costs both retailers $2 to hold an item for one entire year that they procured for $10).

*How many days, on average, does a product stay in Save-A-Lot’s inventory before it is sold? Assume that stores operate 365 days a year.*

The following table shows financial data (year 2009) for two US retailers: Save-A-Lot Retailers and Wally’s Mart.

Assume that both companies have an average annual holding cost rate of 20% (i.e. it costs both retailers $2 to hold an item for one entire year that they procured for $10).

*How much lower, on average, is the inventory cost for Save-A-Lot compared to Wally’s Mart of a household cleaner valued at $50 COGS? Give your answer in terms of dollars. Assume that the unit cost of the household cleaner is the same for both companies and that the price and the inventory turns of an item are independent.*

Q8. **Great Valley Income Tax Advice**

GV is a small accounting firm supporting wealthy individuals in their preparation of annual income tax statements. Every December, GV sends out a short survey to their customers, asking for the information required for preparing the tax statements. Based on 50 years of experience, GV categorizes their cases into the following groups:

- Group 1 (new customers, easy): 15 percent of cases
- Group 2 (new customers, complex): 5 percent of cases
- Group 3 (repeat customers, easy): 50 percent of cases
- Group 4 (repeat customers, complex): 30 percent of cases

Here, “easy” versus “complex” refers to the complexity of the customer’s earning situation.

In order to prepare the income tax statement, GV needs to complete the following set of activities. Processing times (and even which activities need to be carried out) depend on which group a tax statement falls into. All of the following processing times are expressed in minutes per income tax statement.

The activities are carried out by the following three people:

- Administrative support person: filing and writing.
- Senior accountant (who is also the owner): initial meeting, review by senior accountant.
- Junior accountant: preparation.

Assume that all three people work eight hours per day and 20 days a month. For the following questions, assume the product mix as described above. Assume that there are 50 income tax statements arriving each month.

*Which person is the bottleneck?*

b. Senior accountant

**a. Administrator**

c. Junior accountant

Q9. **Great Valley Income Tax Advice**

GV is a small accounting firm supporting wealthy individuals in their preparation of annual income tax statements. Every December, GV sends out a short survey to their customers, asking for the information required for preparing the tax statements. Based on 50 years of experience, GV categorizes their cases into the following groups:

- Group 1 (new customers, easy): 15 percent of cases
- Group 2 (new customers, complex): 5 percent of cases
- Group 3 (repeat customers, easy): 50 percent of cases
- Group 4 (repeat customers, complex): 30 percent of cases

Here, “easy” versus “complex” refers to the complexity of the customer’s earning situation.

In order to prepare the income tax statement, GV needs to complete the following set of activities. Processing times (and even which activities need to be carried out) depend on which group a tax statement falls into. All of the following processing times are expressed in minutes per income tax statement.

The activities are carried out by the following three people:

- Administrative support person: filing and writing.
- Senior accountant (who is also the owner): initial meeting, review by senior accountant.
- Junior accountant: preparation.

Assume that all three people work eight hours per day and 20 days a month. For the following questions, assume the product mix as described above. Assume that there are 50 income tax statements arriving each month.

*What is the (implied) utilization of the senior accountant?*

Q10. **Great Valley Income Tax Advice**

GV is a small accounting firm supporting wealthy individuals in their preparation of annual income tax statements. Every December, GV sends out a short survey to their customers, asking for the information required for preparing the tax statements. Based on 50 years of experience, GV categorizes their cases into the following groups:

- Group 1 (new customers, easy): 15 percent of cases
- Group 2 (new customers, complex): 5 percent of cases
- Group 3 (repeat customers, easy): 50 percent of cases
- Group 4 (repeat customers, complex): 30 percent of cases

Here, “easy” versus “complex” refers to the complexity of the customer’s earning situation.

In order to prepare the income tax statement, GV needs to complete the following set of activities. Processing times (and even which activities need to be carried out) depend on which group a tax statement falls into. All of the following processing times are expressed in minutes per income tax statement.

The activities are carried out by the following three people:

- Administrative support person: filing and writing.
- Senior accountant (who is also the owner): initial meeting, review by senior accountant.
- Junior accountant: preparation.

Assume that all three people work eight hours per day and 20 days a month. For the following questions, assume the product mix as described above. Assume that there are 50 income tax statements arriving each month.

*What is the (implied) utilization of the junior accountant?*

Q11. **Great Valley Income Tax Advice**

- Group 1 (new customers, easy): 15 percent of cases
- Group 2 (new customers, complex): 5 percent of cases
- Group 3 (repeat customers, easy): 50 percent of cases
- Group 4 (repeat customers, complex): 30 percent of cases

Here, “easy” versus “complex” refers to the complexity of the customer’s earning situation.

The activities are carried out by the following three people:

- Administrative support person: filing and writing.
- Senior accountant (who is also the owner): initial meeting, review by senior accountant.
- Junior accountant: preparation.

*What is the (implied) utilization of the administrative support person?*

### Introduction to Operations Management Week 3 Quiz Answers

#### Quiz 1: Homework Assignment: Module 3 – Productivity

Q1. **Chiemsee Knee Replacement Clinic**

The Chiemsee Knee Replacement Clinic (CKRC) is a sports clinic located at the northern edge of the German Alps. It specializes in knee replacements for skiers who come to CKRC from Germany, Austria, Switzerland, and Italy. The clinic currently has one operating room (OR). However, since the clinic has dramatically more demand than capacity, the management team contemplates investing in a second OR. A lean consulting firm, however, suggests that before going ahead with installing new capacity, the clinic should first look at how it uses its existing capacity. The data collected by the consulting firm reveal that:

- The OR is available for 12 hours a day; the hospital has decided to not perform any procedures between 7pm and 7am. This time is equally divided across three surgeons.
- The standard procedure time for the knee surgery done at the clinic is 1h.
- The cleaning and housekeeping that needs to happen after each procedure takes 20 minutes. Almost all of this time could be saved if the cleaning crew were notified earlier on.
- 10 minutes are spent on patient preparation / anesthesia work before each procedure. (Note: this is not part of the 60-minute procedure time). Proposals have been evaluated to move these 10 minutes to outside the OR, and there exists no medical reason that would prohibit doing this.)
- A surgeon only starts a case if all of the work associated with the case (preparation, procedure, and cleaning) can be completed in the 4h allotted to each surgeon. Surgeons never start BEFORE their allotted time.
- Though the clinic aims to operate 7 days a week, holidays, vacation, and construction time lead to an average of one day a week that the OR cannot be used at all.

*How many cases are going through the OR per day on the days when the OR is in use?*

**A lean consulting firm, however, suggests that before going ahead with installing new capacity, the clinic should first look at how it uses its existing capacity. The data collected by the consulting firm**

Q2. **Chiemsee Knee Replacement Clinic**

The Chiemsee Knee Replacement Clinic (CKRC) is a sports clinic located at the northern edge of the German Alps. It specializes in knee replacements for skiers who come to CKRC from Germany, Austria, Switzerland, and Italy. The clinic currently has one operating room (OR). However, since the clinic has dramatically more demand than capacity, the management team contemplates investing in a second OR. A lean consulting firm, however, suggests that before going ahead with installing new capacity, the clinic should first look at how it uses its existing capacity. The data collected by the consulting firm reveal that:

- The OR is available for 12 hours a day; the hospital has decided to not perform any procedures between 7pm and 7am. This time is equally divided across three surgeons.
- The standard procedure time for the knee surgery done at the clinic is 1h.
- The cleaning and housekeeping that needs to happen after each procedure takes 20 minutes. Almost all of this time could be saved if the cleaning crew were notified earlier on.
- 10 minutes are spent on patient preparation / anesthesia work before each procedure. (Note: this is not part of the 60-minute procedure time). Proposals have been evaluated to move these 10 minutes to outside the OR, and there exists no medical reason that would prohibit doing this.)
- A surgeon only starts a case if all of the work associated with the case (preparation, procedure, and cleaning) can be completed in the 4h allotted to each surgeon. Surgeons never start BEFORE their allotted time.
- Though the clinic aims to operate 7 days a week, holidays, vacation, and construction time lead to an average of one day a week that the OR cannot be used at all.

*What is the OEE of the operating room? Assume a 12h window in which the OR could be used.*

**A lean consulting firm, however, suggests that before going ahead with installing new capacity, the clinic should first look at how it uses its existing capacity. The data collected by the consulting firm**

Q3. **Parsa Real Estate**

Parsa Real Estate is a company that buys and rents real estate. The company is looking into buying an office building for $1M. The building has 10,000 square feet of rentable office space.

The company analysts predict that they can rent the office space for $6 per square foot per month, but demand is a function of price in the following way:

% Occupied = 2 – 0.2*Rent (Rent is in dollars per square foot per month. Also, at $6.00, Oscar thinks he can fill about 80% of the office space.)

The building needs to be maintained (security, insurance, maintenance, etc.), which costs $10,000 per month regardless of occupancy. Also, there is a variable cost of $2 per month for each square foot occupied.

Define the return on invested capital as the ratio of the profits (PER YEAR) and the invested capital. You can draw an ROIC tree in the same way that we drew a KPI tree in class. Simply have the ROIC as “the root” of the tree instead of profits. Then answer the following question.

*What is the ROIC? (Please give your answer in decimal form. For example, 0.25 for 25%)*

**A lean consulting firm, however, suggests that before going ahead with installing new capacity, the clinic should first look at how it uses its existing capacity. The data collected by the consulting firm**

Q4**. Parsa Real Estate**

Parsa Real Estate is a company that buys and rents real estate. The company is looking into buying an office building for $1M. The building has 10,000 square feet of rentable office space.

The company analysts predict that they can rent the office space for $6 per square foot per month, but demand is a function of price in the following way:

% Occupied = 2 – 0.2*Rent (Rent is in dollars per square foot per month. Also, at $6.00, Oscar thinks he can fill about 80% of the office space.)

The building needs to be maintained (security, insurance, maintenance, etc.), which costs $10,000 per month regardless of occupancy. Also, there is a variable cost of $2 per month for each square foot occupied.

Define the return on invested capital as the ratio of the profits (PER YEAR) and the invested capital. You can draw an ROIC tree in the same way that we drew a KPI tree in class. Simply have the ROIC as “the root” of the tree instead of profits. Then answer the following question.

*What would be the new ROIC be if Parsa Real Estate decides to charge rent of $8.00 per square foot per month? (Please give your answer in decimal form. For example, 0.25 for 25%)*

Q5. **12 Tasks to 4 Workers**

Consider the following tasks that must be assigned to four workers on a conveyor-paced assembly line (i.e., a machine-paced line flow). Each worker must perform at least one task. There exists unlimited demand unless stated otherwise.

Time to Complete Task (seconds):

- Task 1: 30
- Task 2: 25
- Task 3: 15
- Task 4: 20
- Task 5: 15
- Task 6: 20
- Task 7: 50
- Task 8: 15
- Task 9: 20
- Task 10: 25
- Task 11: 15
- Task 12: 20

The current conveyor-paced assembly-line configuration assigns the workers in the following way:

• Worker 1: Tasks 1, 2, 3

• Worker 2: Tasks 4, 5, 6

• Worker 3: Tasks 7, 8, 9

• Worker 4: Tasks 10, 11, 12

*What is the capacity of the current line (in units per hour)?*

Q6. **12 Tasks to 4 Workers**

Consider the following tasks that must be assigned to four workers on a conveyor-paced assembly line (i.e., a machine-paced line flow). Each worker must perform at least one task. There exists unlimited demand unless stated otherwise.

Time to Complete Task (seconds):

- Task 1: 30
- Task 2: 25
- Task 3: 15
- Task 4: 20
- Task 5: 15
- Task 6: 20
- Task 7: 50
- Task 8: 15
- Task 9: 20
- Task 10: 25
- Task 11: 15
- Task 12: 20

The current conveyor-paced assembly-line configuration assigns the workers in the following way:

• Worker 1: Tasks 1, 2, 3

• Worker 2: Tasks 4, 5, 6

• Worker 3: Tasks 7, 8, 9

• Worker 4: Tasks 10, 11, 12

*What is the direct labor content (in seconds per unit)?*

Q7. **12 Tasks to 4 Workers**

Consider the following tasks that must be assigned to four workers on a conveyor-paced assembly line (i.e., a machine-paced line flow). Each worker must perform at least one task. There exists unlimited demand unless stated otherwise.

Time to Complete Task (seconds):

- Task 1: 30
- Task 2: 25
- Task 3: 15
- Task 4: 20
- Task 5: 15
- Task 6: 20
- Task 7: 50
- Task 8: 15
- Task 9: 20
- Task 10: 25
- Task 11: 15
- Task 12: 20

The current conveyor-paced assembly-line configuration assigns the workers in the following way:

• Worker 1: Tasks 1, 2, 3

• Worker 2: Tasks 4, 5, 6

• Worker 3: Tasks 7, 8, 9

• Worker 4: Tasks 10, 11, 12

*Assume a demand rate of 20 units per minute. What would be the takt time of the process (in seconds per unit)?*

Q8. **12 Tasks to 4 Workers**

Time to Complete Task (seconds):

- Task 1: 30
- Task 2: 25
- Task 3: 15
- Task 4: 20
- Task 5: 15
- Task 6: 20
- Task 7: 50
- Task 8: 15
- Task 9: 20
- Task 10: 25
- Task 11: 15
- Task 12: 20

The current conveyor-paced assembly-line configuration assigns the workers in the following way:

• Worker 1: Tasks 1, 2, 3

• Worker 2: Tasks 4, 5, 6

• Worker 3: Tasks 7, 8, 9

• Worker 4: Tasks 10, 11, 12

*Assume a demand rate of 20 units per minute. What would be the target manpower?*

#### Quiz 2: Final Exam – Module 3

**Q1. Wind Tunnel Testing – Carbon Bike Frames**

As an equipment provider for several Olympic cyclists, Carbon Bike Frames (CBF) operates a very expensive wind tunnel facility near San Diego, CA. The wind tunnel is used to find the best compromise between ergonomics and aerodynamics for the cyclist. Presently, more and more cyclists are interested in CBF’s services, so the company considers building a second facility. However, given the enormous costs of the wind tunnel, they also want to explore a more effective use of the current facility. An initial data collection reveals that:

- The standard fitting time for a cyclist is 2h. On average, the wind tunnel is used for 7 fitting procedures a day (new customers or customers who want a refit). The wind tunnel is available 24 hours a day.
- CBF offers a free second session should the customer not be entirely satisfied with their bike fit (internally also known as “rework sessions”). About 2 out of 5 customers come back for such a “refit,” which takes the same amount of time as the initial fit.
- 20 minutes of the each fitting procedure is spent on setting up the bike on a stationary trainer and getting the athlete ready. Almost all of this could happen outside the wind tunnel, i.e. while another fitting procedure is still going on.
- About one day out of 10, the wind tunnel is down for maintenance or repair.

*How many new fits are conducted on a typical day when the wind tunnel is in use (assume the wind tunnel is open that day)?*

**Q2. Wind Tunnel Testing – Carbon Bike Frames**

As an equipment provider for several Olympic cyclists, Carbon Bike Frames (CBF) operates a very expensive wind tunnel facility near San Diego, CA. The wind tunnel is used to find the best compromise between ergonomics and aerodynamics for the cyclist. Presently, more and more cyclists are interested in CBF’s services, so the company considers building a second facility. However, given the enormous costs of the wind tunnel, they also want to explore a more effective use of the current facility. An initial data collection reveals that:

- The standard fitting time for a cyclist is 2h. On average, the wind tunnel is used for 7 fitting procedures a day (new customers or customers who want a refit). The wind tunnel is available 24 hours a day.
- CBF offers a free second session should the customer not be entirely satisfied with their bike fit (internally also known as “rework sessions”). About 2 out of 5 customers come back for such a “refit,” which takes the same amount of time as the initial fit.
- 20 minutes of the each fitting procedure is spent on setting up the bike on a stationary trainer and getting the athlete ready. Almost all of this could happen outside the wind tunnel, i.e. while another fitting procedure is still going on.
- About one day out of 10, the wind tunnel is down for maintenance or repair.

*What is the OEE of the wind tunnel? Recall that the wind tunnel can be used 24h a day.*

**Q3. Tasty Tim’s**

Tasty Tim’s is a specialty taco restaurant. The following tasks are required for the successful assembly of a Tasty taco (times are in seconds per taco):

- Chop and trim meat – 30
- Chop vegetables – 20
- Grill meat – 240
- Grill vegetables – 180
- Prepare toppings

– Lettuce – 10

– Tomato – 15

– Guacamole – 40

- Assemble taco

– Add meat – 5

– Add vegetables – 5

– Add cheese – 5

– Add toppings – 10

- Wrap taco – 20

During the lunch hour, Tasty Tim’s encounters demand for 120 tacos.

*What is the labor content of one of Tasty Tim’s tacos?*

**Q4. Tasty Tim’s**

Tasty Tim’s is a specialty taco restaurant. The following tasks are required for the successful assembly of a Tasty taco (times are in seconds per taco):

- Chop and trim meat – 30
- Chop vegetables – 20
- Grill meat – 240
- Grill vegetables – 180
- Prepare toppings

– Lettuce – 10

– Tomato – 15

– Guacamole – 40

- Assemble taco

– Add meat – 5

– Add vegetables – 5

– Add cheese – 5

– Add toppings – 10

- Wrap taco – 20

During the lunch hour, Tasty Tim’s encounters demand for 120 tacos.

*What is the Takt time (in seconds/unit) takt time for Tasty Tim’s taco shop?*

**Q5. Tasty Tim’s**

Tasty Tim’s is a specialty taco restaurant. The following tasks are required for the successful assembly of a Tasty taco (times are in seconds per taco):

- Chop and trim meat – 30
- Chop vegetables – 20
- Grill meat – 240
- Grill vegetables – 180
- Prepare toppings

– Lettuce – 10

– Tomato – 15

– Guacamole – 40

- Assemble taco

– Add meat – 5

– Add vegetables – 5

– Add cheese – 5

– Add toppings – 10

- Wrap taco – 20

During the lunch hour, Tasty Tim’s encounters demand for 120 tacos.

*In an ideal world, how many workers should Tim hire to make tacos?*

**Q6. Tasty Tim’s**

- Chop and trim meat – 30
- Chop vegetables – 20
- Grill meat – 240
- Grill vegetables – 180
- Prepare toppings

– Lettuce – 10

– Tomato – 15

– Guacamole – 40

- Assemble taco

– Add meat – 5

– Add vegetables – 5

– Add cheese – 5

– Add toppings – 10

- Wrap taco – 20

During the lunch hour, Tasty Tim’s encounters demand for 120 tacos.

*During off-peak afternoon hours, demand at Tasty Tim’s drops to 40 tacos each hour. How many employees should Tim schedule to work during the afternoon? Again, ignore any effects of idle time or inefficiency due to poor line balancing.*

**Q7. FastBus Inc.**

FastBus Inc. offers low-cost bus transportation between Philadelphia and New York City. The company has 2 buses, each bought for $300,000. Each bus can carry 40 passengers per trip and does 7 daily round trips between Philadelphia and New York City. The price of each one-way ticket is $12. The company sells 28 seats on average per one-way trip, so the load factor is 70%.

The annual fixed cost of running the company is $3,000,000. The major variable cost in their line of business is gasoline, which costs $25 per one-way trip. Fast Bus Inc. buses operate 365 days a year.

Define the return on invested capital as the ratio of the profits (PER YEAR) and the invested capital. You can draw an ROIC tree in the same way that we drew a KPI tree in class. Simply have the ROIC as “the root” of the tree instead of profits. Then answer the :

*What is the current number of customers that are served each year? Assume that FastBus operates 365 days per year and that each customer buys only one one-way ticket per person.*

*(Note: please enter your answers in numeric form only. Do NOT use commas or other punctuation in your answer).*

**Q8. FastBus Inc.**

FastBus Inc. offers low-cost bus transportation between Philadelphia and New York City. The company has 2 buses, each bought for $300,000. Each bus can carry 40 passengers per trip and does 7 daily round trips between Philadelphia and New York City. The price of each one-way ticket is $12. The company sells 28 seats on average per one-way trip, so the load factor is 70%.

The annual fixed cost of running the company is $3,000,000. The major variable cost in their line of business is gasoline, which costs $25 per one-way trip. Fast Bus Inc. buses operate 365 days a year.

Define the return on invested capital as the ratio of the profits (PER YEAR) and the invested capital. You can draw an ROIC tree in the same way that we drew a KPI tree in class. Simply have the ROIC as “the root” of the tree instead of profits. Then answer the :

*What is the current ROIC? (Please give your answer in decimal form. For example, 0.25 for 25%)*

**Q9. FastBus Inc.**

FastBus Inc. offers low-cost bus transportation between Philadelphia and New York City. The company has 2 buses, each bought for $300,000. Each bus can carry 40 passengers per trip and does 7 daily round trips between Philadelphia and New York City. The price of each one-way ticket is $12. The company sells 28 seats on average per one-way trip, so the load factor is 70%.

The annual fixed cost of running the company is $3,000,000. The major variable cost in their line of business is gasoline, which costs $25 per one-way trip. Fast Bus Inc. buses operate 365 days a year.

Define the return on invested capital as the ratio of the profits (PER YEAR) and the invested capital. You can draw an ROIC tree in the same way that we drew a KPI tree in class. Simply have the ROIC as “the root” of the tree instead of profits. Then answer the :

*What is the minimum load factor at which the company breaks even? (Please give your answer in decimal form. For example, 0.25 for 25%)*

### Introduction to Operations Management Week 4 Quiz Answers

#### Quiz 1: Homework Assignment: Module 4 – Quality

**Q1. 20-Station Assembly Line**

Consider an assembly line with 20 stations. Each station has a 0.5% probability of making a defect. At the end of the line, an inspection step singles out the defective units. The inspection step catches 80% of all defects. From inspection, units that are deemed to be non-defective are moved to the shipping department.

If a defect is found at inspection, it is sent to the rework department. Rework fixes about 95% of the defective units. Units are directly shipped from the rework department with no further inspection taking place.

*What is the probability that a unit ends up in rework (in decimal form)?*

**In a sample of 100 syringes, the hospital’s quality control officer finds the average dosage to be 0.5mL. The standard deviation of the dosage is 0.02 mL and the distribution of the dosages resembles a normal distribution reasonably closely.**

**Q2. 20-Station Assembly Line**

Consider an assembly line with 20 stations. Each station has a 0.5% probability of making a defect. At the end of the line, an inspection step singles out the defective units. The inspection step catches 80% of all defects. From inspection, units that are deemed to be non-defective are moved to the shipping department.

If a defect is found at inspection, it is sent to the rework department. Rework fixes about 95% of the defective units. Units are directly shipped from the rework department with no further inspection taking place.

*What is the probability that a defective unit is shipped (in decimal form)?*

**In a sample of 100 syringes, the hospital’s quality control officer finds the average dosage to be 0.5mL. The standard deviation of the dosage is 0.02 mL and the distribution of the dosages resembles a normal distribution reasonably closely.**

**Q3. 3-Step Process with Rework**

Consider the following three-step assembly operation with quality problems. All resources are staffed by one employee.

- The first resource has a processing time of 7 minutes per unit.
- The second resource has a processing time of 6 minutes per unit.
- The third resource has a processing time of 5 minutes per unit. With a 40% probability, the flow unit coming out of the third resource has to be reworked. In that case, the operations at the second and third resources are repeated. You can assume that (a) rework always succeeds (i.e. a unit going through the rework loop will always work after the third resource),and (b) the processing times for units in rework are the same as for regular units.

*For every unit of demand, how many units have to flow through the second step in the process?*

**In a sample of 100 syringes, the hospital’s quality control officer finds the average dosage to be 0.5mL. The standard deviation of the dosage is 0.02 mL and the distribution of the dosages resembles a normal distribution reasonably closely.**

**Q4. 3-Step Process with Rework**

Consider the following three-step assembly operation with quality problems. All resources are staffed by one employee.

- The first resource has a processing time of 7 minutes per unit.
- The second resource has a processing time of 6 minutes per unit.
- The third resource has a processing time of 5 minutes per unit. With a 40% probability, the flow unit coming out of the third resource has to be reworked. In that case, the operations at the second and third resources are repeated. You can assume that (a) rework always succeeds (i.e. a unit going through the rework loop will always work after the third resource),and (b) the processing times for units in rework are the same as for regular units.

*Where in the process is the bottleneck?*

- Step 3
- Step 1
**Step 2**

**Q5. Flu Shot Dosage**

A hospital in a developing nation is forced to manually put the flu shot vaccine into syringes. The recommended dosage for the flu shot is 0.5mL. The local health authorities define all syringes that have less than 0.45ml or more than 0.55mL as defective.

*What is the capability score of the manual filling process?*

**Q6. Flu Shot Dosage**

A hospital in a developing nation is forced to manually put the flu shot vaccine into syringes. The recommended dosage for the flu shot is 0.5mL. The local health authorities define all syringes that have less than 0.45ml or more than 0.55mL as defective.

*What percentage of the manually filled syringes will be outside the specification limits provided by the local health authorities? (Please answer in decimal form.)*

**Q7. Flu Shot Dosage**

A hospital in a developing nation is forced to manually put the flu shot vaccine into syringes. The recommended dosage for the flu shot is 0.5mL. The local health authorities define all syringes that have less than 0.45ml or more than 0.55mL as defective.

*To what level would the hospital have to reduce the standard deviation of the operation if his goal were to obtain a capability score of Cp=4/3 (i.e., get 63 defects per million)?*

**Q8. Kanban Cards**

*Which of the following statements about the Kanban System are accurate?*

I. Deploying the Kanban system leads to pulling work through the system instead of pushing work.

II. Deploying the Kanban system leads to pushing work through the system instead of pulling work.

III. The Kanban system controls the work in process inventory.

IV. Kanban requires cross-training all workers.

- I only
- I and IV only
**III and IV only**- I, II and IV
- II only
- I and III only

#### Quiz 2: Final Exam – Module 4

**Q1. 50-Step Assembly Line**

Consider an assembly line with 50 steps that are carried out sequentially. Each of the 50 steps has a defect probability of 1%. The final product produced on the assembly line is defective if any one of the 50 steps made a defect.

At the end of the assembly line there are two operators independently inspecting the product. Each of them is recognizing a defective product with a 90% probability. Assuming that the product is not defective, it is moved to the shipping department. Otherwise, the product is scrapped.

*What is the probability that a defective product is produced (independent of the defect being found or not)?*

**Q2. 50-Step Assembly Line**

Consider an assembly line with 50 steps that are carried out sequentially. Each of the 50 steps has a defect probability of 1%. The final product produced on the assembly line is defective if any one of the 50 steps made a defect.

At the end of the assembly line there are two operators independently inspecting the product. Each of them is recognizing a defective product with a 90% probability. Assuming that the product is not defective, it is moved to the shipping department. Otherwise, the product is scrapped.

Probability that a defective product is produced (independent of the defect being found or not) (in decimal form):

*What is the probability that a defective product is moved to the shipping department?*

**Q3. Process with Scrap**

Consider the following four-step assembly operation with quality problems:

- The first resource has a processing time of 5 minutes per unit and one employee doing the operation.
- The second resource has a processing time of 4 minutes per unit. It also has one employee doing the operation. However, this is a very delicate task and 80% of all products have to be scrapped after this step.
- Two workers are staffed for the third resource. No quality problems occur at this resource and the processing time is 20 minutes per unit.
- At the fourth and final resource, one operator handles the product. No quality problems exist at this step and the processing time is 12 minutes per unit.

*For every unit of demand, how many units have to flow through the second step in the process?*

**Q4. Process with Scrap**

Consider the following four-step assembly operation with quality problems:

- The first resource has a processing time of 5 minutes per unit and one employee doing the operation.
- The second resource has a processing time of 4 minutes per unit. It also has one employee doing the operation. However, this is a very delicate task and 80% of all products have to be scrapped after this step.
- Two workers are staffed for the third resource. No quality problems occur at this resource and the processing time is 20 minutes per unit.
- At the fourth and final resource, one operator handles the product. No quality problems exist at this step and the processing time is 12 minutes per unit.

*Where in the process is the bottleneck?*

- Resource 2
- Resource 1
**Resource 3**- Resource 4

**Q5. Lean Burgers**

The management of a large fast food chain evaluates the supplier of their deep-frozen beef patties. The supplier delivers frozen beef patties that according to the specifications have to weigh between 94.5 grams and 95.5 grams. All other beef patties are rejected.

A random sample of 30 patties that were inspected over the course of the last week revealed that the average weight was 95.0 grams. The standard deviation was 0.25 grams.

*What is the capability score of the supplier?*

**Q6. Lean Burgers**

The management of a large fast food chain evaluates the supplier of their deep-frozen beef patties. The supplier delivers frozen beef patties that according to the specifications have to weigh between 94.5 grams and 95.5 grams. All other beef patties are rejected.

A random sample of 30 patties that were inspected over the course of the last week revealed that the average weight was 95.0 grams. The standard deviation was 0.25 grams.

*What percentage of the deliveries is likely to be outside the specification limits (outside the interval of [94.5, 95.5])?*

**Q7. Lean Burgers**

The management of a large fast food chain evaluates the supplier of their deep-frozen beef patties. The supplier delivers frozen beef patties that according to the specifications have to weigh between 94.5 grams and 95.5 grams. All other beef patties are rejected.

A random sample of 30 patties that were inspected over the course of the last week revealed that the average weight was 95.0 grams. The standard deviation was 0.25 grams.

*To what level would the supplier have to reduce the standard deviation of the operation if his goal were to obtain a capability score of 1 (i.e., get less than or equal to 0.27 percent defective)?*

*(Note: Please enter your answer as a decimal. Fractions are not accepted by the software)*

Q8. TJ1. In the Toyota Production System, “jidoka” refers to

- f. The cross-training of workers for a wide range of skills
- c. The inventory retrieval system where parts are replenished only when they are needed
- e. Continuous line-balancing to maximize utilization
- b. Continuous improvement, where workers organize meetings to discuss ways of improving the production process
- g. None of these
**a. Level production, where different models are produced along side each other on the assembly line**- d. The aggressive reduction of changeover and setup times

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