Assignment Capacity

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Assignment Capacity. What is a Process.

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### AssignmentCapacity

What is a Process

A process is any activity or group of activities. Process analysis is the detailed understanding and documentation of how work is performed and how it can be redesigned and improved. Tools for documenting a process: Flowchart, service blueprint, process chart,

Identify opportunity

1

Definescope

2

Documentprocess

3

Implement changes

6

Redesignprocess

5

Evaluateperformance

4

Flow Chart

A flowchart is a diagram that traces the flow of materials, customers, information, or equipment through the various steps of a process

E

C

B

A

D

B

C

F

• Capacity-related metrics: Capacity, time to perform the process
• Quality-related metrics: Defective rate, customer satisfaction rate
• Efficiency-related metrics: Cost, productivity, utilization
• Flexibility-related metrics: Time to change the process from one type of product to another
Problem1: Single-Stage and Two-Stage Process
• Cycle time =
• Capacity =
• Theoretical Flow Time =
• Ip=

1 min

Operation A

1/1 per min, 60 per hour

Tp =1 min

1 min

1

Operation B

Operation A

• Cycle time =
• Capacity =
• Theoretical Flow Time =
• Ip=
• IpA =
• IpB =

10 min

Tp =8 min

Tp =10 min

1/10 per min, 6 per hour

OprA

18 min

1.8

OprB

1

CT

CT

CT

0.8

0

28

38

48

18

Problem1: Two-Stage Process
• Cycle time =
• Capacity =
• Theoretical Flow Time =
• Ip=
• IpA =
• IpB =

10 min

6 per hr

15 min

1.5

Operation B

Operation A

0.5

Tp =10 min

Tp =5 min

1

OprA

OprB

• Operation A is Specialized and Fast
• Operation B is Specialized and Fast
• Process Capacity 6 per hour

CT

CT

CT

0

17

23

29

11

Problem1d: Single-Stage Process
• Lets cross train them and reduce set up time of the operation.
• They are not fast anymore. Instead of 5+10=15 it takes 16 to complete a part

Operation AB1

8 min

• Cycle time =
• Capacity =
• Theoretical Flow Time =

60(2/16) per hr

Operation AB2

7.5 per hr

16

16

OprAB1

Due to pooling and cross-training, capacity increased from 6 to 7.5. Therefore, throughput can go up. We will show that flow time will also go down.

OprAB2

CT

CT

CT

0

16

48

64

32

Problem 2. Problem 5.3 in the book

Three hairstylists and a receptionist. On average it takes 10 minutes to shampoo, 15 minutes to style the hair and 5 minutes to bill a customer. The customer first checks in with the receptionist. This takes only 3 minutes. One of the three stylists then takes charge and performs all the three activities—shampooing, styling and billing—consecutively.

Receptionist

Hair Stylist

Sh-Sty-Bill

Check-in

3 minutes

10+15+5=30

a) How many customers can be serviced per hour in this salon?

The capacity of each stylists is 60 /30 = 2 customers/ hour.

Capacity of the stylist pool is 3(2) =6 customers/ hour.

Capacity of the stylist pool is 3/30 per min or 6 customers/ hour.

Capacity of the receptionist is 1/3(60) = 20 customers per hour.

Problem 2. Problem 5.3 in the book

The capacity of the process is min (6, 20) = customers per hour.

The bottleneck is the stylist pool.

Receptionist

Hair Stylist

Sh-Sty

ChinBill

3+5 =8

10+15=25

b) What would be the impact on the theoretical capacity if the billing operation is transferred to the receptionist?

• The capacity of the three stylists is 1/25 = per min or 2.4 per hr.
• Capacity of the stylist pool is 3/25 per min or 7.2 per hr.
• Capacity of the receptionist is (1/8)(60) = 7.5 customers per hour.
• The capacity is min (7.2, 7.5) = 7.2 customers per hour.
• The bottleneck is still the stylist pool.
Problem 3

Eastern Coffee follows the flow chart below to serve its customers. It takes a worker two minutes to take order and receive payment, two minutes to prepare coffee, and three minutes to clean equipment.

Clean Equipment

Prepare Coffee

Eastern Coffee has two workers: worker A takes order and prepares coffee, while worker B handles the cleaning. Order processing takes 2 min., preparing the coffee takes 2 min., Cleaning takes 3 min.

a) How many customers can Eastern Coffee serve per hour?

Problem 3

TpA = 2+2=4, TpB = 3

Capacity of worker A: 60/4 = 15 customers/hour

Capacity of worker B: 60/3 = 20 customers/hour

Capacity of the bottleneck is 15 customers/hour

Western Coffee follows the same flow chart above, and each activity takes the same amount of time as Eastern. Western Coffee also has two workers: worker C only takes order and payment, while worker D handles the coffee preparation and cleaning.

b) How many customers can Eastern Coffee serve per hour?

TpC = 2, TpD = 2+3=5

Capacity of worker C: 60/2 = 30 customers/hour

Capacity of worker D: 60/5 = 12 customers/hour

Capacity of the bottleneck is 12 customers/hour

Problem 4

Angels Inc. fabricates garage doors. Roofs are punched in a roof punching press (10 minutes per roof) and then formed in a roof forming press (5 minutes per roof). Bases are punched in a base punching press (10 minutes per base) and then formed in a base forming press (15 minutes per base), and the formed base is welded in a base welding machine (5 minutes per base). The base sub-assembly and the roof then go to final assembly where they are welded together (10 minutes per garage) on an assembly welding machine to complete the garage. Assume one operator at each station.

• Draw a flowchart of the process.
• What is the minimum time required to produce a garage (from starting an order to finishing it)?
• What is the capacity of the factory in terms of garages per hour?
• If you want to increase the capacity, what is the stage that you would put some additional resource?
Flow Chart

R-Punch

R-Form

R-Form

R-Punch

10

5

Assembly

Assembly

10

Weld

B-Punch

B-Form

Weld

B-Form

B-Punch

10

5

15

Flow Chart

Punch

Form

R-Form

R-Punch

10

5

Assembly

Assembly

10

Weld

Punch

Form

Weld

B-Form

B-Punch

10

5

15

Problem 4
• What is the Theoretical Flow Time? (The minimum time (the required to produce a garage from start to finish.)

Roof: 10+5+10 =25

Base: 10+15+5+10 = 40

 Max(25, 40) = 40 min

(b) What is the capacity of the factory in terms of garages per hour?

R-Punch:1/10 per min. or 6 per hr

R-Form:1/5 per min. or 12 per hr

B-Punch:1/10 per min. or 6 per hr

B-Form:1/15 per min. or 4 per hr

Welding: 1/5 per min. or 12 per hr

Assembly: 1/10 per min. or 6 per hr

Capacity is 4 per hour

(c) If you want to increase the capacity, what is the stage that you would put some additional resource?

B-Form

Problem 4

(d) Suppose the machines and operations of B-Punch and R-Bunch can do both Base-punching and Roof-punching. Also suppose there will be no change in the activity times. Further, make the same assumption regarding Forming operations.

Punch

Form

R-Form

R-Punch

R-Punch

R-Form

10

5

R-Form

R-Punch

Assembly

10

5

Assembly

Assembly

10

Assembly

10

Weld

Punch

Form

Weld

B-Form

B-Punch

Weld

B-Punch

B-Form

10

5

15

Weld

B-Form

B-Punch

10

5

15

Problem 4

Punching (R+B) = 10+10=20

Forming (R+B) = 5+ 15 = 20

Punching Capacity = 2/20 = 1/10 per min = 6 per hour

Forming Capacity = 2/20 = 1/10 per min = 6 per hour

Welding: 1/5 per min. or 12 per hour

Assembly: 1/10 per min. or 6 per hour

Capacity is 6 per hour

(c) If you want to increase the capacity, what is the stage that you would put some additional resource?

All the three departments except Welding.

Problem 5. Problem 5.4 in the book

A company makes two products, A and B, using a single resource pool. The resource is available for 900 min per day. The profit margins for A and B are \$20 and \$35 per unit respectively. The total unit loads are 10 and 20 minutes.

a) The company wishes to produce a mix of 60% As and 40% Bs. What is the effective capacity (units per day)?

An aggregate product will need

0.6(10) + 0.4(20) = 14 minutes

• Capacity is 1/14 per minute or 900(1/14) = 64.29 per day
• b) What is the financial throughput per day? Financial throughput is the rate at which a firm is generating money.
• An aggregate product will generate 0.6(20) + 0.4(35) = \$28
• 64.29(28) = \$1671.5 per day
Problem 6

The following graph shows a production process for two products AA and BC. Station D and E are flexible and can handle either product. No matter the type of the product, station D can finish 100 units per day and station E can finish 90 units per day. Station A works only for Product A and have a capacity of 60 units per day. Station B and C are only for Product BC and have capacity of 75 and 45 units per day, respectively. The demands for each product is 50 units per day.

Which station(s) is the bottleneck?

• Stations A and C
• Station B and C
• Stations C and D
• Stations D and E
• Station C and E

A: 60

D: 100

E: 90

B: 75

C: 45

Problem 6
• Which of the following is NOT true?
• The utilization of machine A is at least 75%
• The utilization of machine B at least about 53%
• The utilization of machine B is at most 60%
• The utilization of machine D is 90%
• None of the above.
• E  We can produce at most 90 AA and BC.
• C  We can produce at most 45 BC
• We may produce all combinations from 50AA and 40 BC to 45AA and 45 BC

A: 60

D: 100

E: 90

• We produce at least 45 AA: 45/60 = 75%
• We produce at least 40 BC: 40/75 = 53.33%
• 45/75 = 60%
• 90/100 = 90%

B: 75

C: 45

Problem 7
• A company has five machines and two products. Product X will be processed on Machine A, then J, then B. Product Y will be processed on Machine C, then J, then D. The demands for both products are 50 units per week. The capacities (units/week) of the machines are marked in the graph on the right. Which machine is the bottleneck?
• A
• B
• C
• D
• J
Problem 7
• Which of the following is NOT true?
• The utilization of machine A is at least 80%
• The utilization of machine B at least about 66%
• The utilization of machine D is at least 50%
• The utilization of machine C is at most about 72%
• None of the above.
• We can produce at most 90 X and Y. We may produce all combinations from 50 X and 40 Y to 40 X and 50Y
• We produce at least 40 X: 40/50 = 80%
• We produce at least 40 X: 40/60 = 66.67%
• 40/80 = 50%
• 50/70 = 71.43%
Problem 8. Multiple Choice
• Which of the following 2 statements is true?
• I. A process can have more than 1 bottleneck resource.
• II. Having flexible equipment can increase utilization.
• Only I
• Only II
• Both I and II
• Neither I nor II
• Cannot be determined
• Which of the following statement is false?
• Throughput rate is always smaller than or equal to the capacity
• Customers may wait even if the utilization rate of the service process is smaller than 100%
• Bottleneck resource(s) always has 100% utilization rate
• Increasing WIP may increase utilization rate
• None of the above
Problem 8. Multiple Choice
• To improve the utilization rate, we can
• I. Cross-train the workers
• III. Shift from MTS systems to MTO system
• Choose the most appropriate.
• I
• II
• III
• I and II
• I, II, and III
Problem 9. Problem 5.2 book

Reconsider Kristen’s cookie-baking enterprise from Exercise 4.2. 4.2 - Kristen and her roommate are in the business of baking custom cookies. As soon as she receives an order by phone, Kristen washes the bowl and mixes dough according to the customer\'s order - activities that take a total of 6 minutes. She then spoons the dough onto a tray that holds one dozen cookies (2 minutes). Her roommate then takes 1 minute to set the oven and place the tray in it. Cookies are baked in the oven for 9 minutes and allowed to cool outside for 5 minutes. The roommate then boxes the cookies (2 minutes) and collects payment from the customer (1 minute). Determine the unit load on the three resources in the process – Kristen, her roommate and the oven. Assuming that all three resources are available 8 hours a day 100% of the time.

Problem 9. Problem 5.2: Flow unit = 1 order of 1 dozen.

Take

order

wash

mix

spoon

& set

bake

a) Compute the unit load of each resource

Kristen = 6+ 2 = 8 min/unit;

Roommate = 1+ 2+1 = 4 min/unit;

Oven = 1+9 = 10 min/unit

b) Compute the capacity of each resources.

Kristen = 60/8 = 7.5 orders/hour;

RM = 60/4 = 15 orders/hour;

Oven = 60/10 = 6 orders/hour min.

c) Compute the process capacity.

Capacity = min {7.5, 15, 6} = 6 orders of 1 dozen/hr.

The oven is the theoretical bottleneck.

cool

pack

get

pay

Problem 5.2

• d) Compute utilization at full capacity
• Kristen = 6/7.5 = 80%; RM = 6/15 = 40%; Oven = 6/6 = 100%.
• e) What is the impact of buying another Oven?
• Doubles the oven resources pool capacity to 12 orders per hour.
• The process capacity, however, is only increased to 7.5 orders per hour as the bottleneck shifts to Kristen.
• f) What is the impact of cross training?
• Cross training pools Kristen and RM into a single resource pool (Workers).
• The unit load is 8+4 = 12 minutes per unit.
• The capacity of this resource pool (workers) is increased to
• (60)(2)/12 = 10 orders of 1 dozen/hr.

Problem 9. Problem 5.2

• With one oven, cross training does not affect the process capacity (since the Oven remains the bottleneck). The capacity is 6 dozen per hour.
• With two ovens, however, the bottleneck shifted to Kristen before cross training as determined earlier. The capacity is 7.5 dozen per hour.
• Diminishing Marginal Return. Doubling the capacity of oven does not double production. The bottleneck shifts to another recourse.
• Cross training increases the process capacity to 10 orders per hour. The human resource is the bottleneck.

Problem 10

A local grocery store has 2 cashier stations, and 1 experienced cashier and 1 novice cashier. During a typical working day (8 hours), 120 customers will show up. The novice cashier will serve 48 customers and the experienced cashier will serve 72 customers. On average it takes 6 minutes for the novice cashier to serve one customer and 3 minutes for the experienced cashier to serve one customer.

Problem 10

a) During the rush hours, approximate 25 customers will show up in an hour. Does the store have enough capacity for the rush hour?

• Yes, the capacity of the store is 25 customers per hour.
• Yes, the capacity of the store is 30 customers per hour.
• No, the capacity of the store is 10 customers per hour.
• No, the capacity of the store is 20 customers per hour.
• None of the above.

On average it takes 6 minutes for the novice cashier to serve a customer  60/6 = 10 customers/hr

• On average it takes 3 minutes for the experienced cashier to serve a customer  60/3 = 20 customers/hr
• Capacity = 10+20 = 30

Problem 10

b) During the day, both cashier stations on average have 2 customers waiting. On average, how long does a customer stay in the novice cashier’s waiting line?

• 8 minutes
• 11 minutes
• 16 minutes
• 20 minutes
• None of the above
• The novice cashier will serve 48/8 = 6 customers/hr
• R = 6 /hr
• TiNR = IiN
• 6TiN = 2
• TiN = 1/3 hr or 20 min

Problem 10

c) On average, how long does a customer stay in the experienced cashier’s line?

• 7 minutes
• 9.4 minutes
• 13.3 minutes
• 15 minutes
• None of the above
• On the same token
• the novice cashier will serve 72/8 = 9 customers/hr
• R = 9 /hr
• TR = I  9TiE = 2  TiE=2/9 hr or 13.33 min

Problem 10

d) On average, how long does a customer spend in the store?

The novice and experienced cashier serve 6, and 9 customersper hour, respectively.

Customers served by Novice: 6 min service time, 20 min waiting time. T = 26 min for 6/15 customers.

Customers served by Experienced: 3 min service time, 13.33 min waiting time. T = 16.33 for 9/15 customers.

(6/15)(26) + (9/15)(16.33) = 20.2

Problem 10

To shorten the waiting time, the manager does a detailed study and finds that half of the customers purchase 5 items or less, and half of the customers purchase more than 5 items. The manager decides to let the novice cashier only serve the customers that purchase 5 items or less. After the change, it turns out that both cashier stations have 1.75 customers waiting on average. Assume that the novice cashier serves all of the customers purchasing 5 items or less and the experienced cashier serves all of the customers purchasing more than 5 items.

Problem 10

e) What is the average waiting time in the novice cashier’s line?

• 13 minutes
• 14 minutes
• 17 minutes
• 19 minutes
• None of the above
• Each of the two cashiers will serve 120/2 = 60 customers per day or 60/8 =7.5 customers/hr
• TiNR = IiN
• 7.5TiN = 1.75
• TiN = 1.75/7.5 = 0.2333 hr or 14 min

Problem 10

f) What is the average waiting time in the experienced cashier’s line?

• 9 minutes
• 11 minutes
• 12 minutes
• 14 minutes
• None of the above
• R and I are the same for Naïve and Experience
• Therefore, T is the same; 14 min