Assignment Capacity

Key Problem 2

MamossaAssaf Inc. fabricates garage doors. Roofs are punched in a roof punching press (

15

minutes per roof) and then formed in a roof forming press ( 8 base punching press (

3

base forming press (

10

are welded together ( each station.

minutes per roof). Bases are punched in a

10

minutes per base) and then formed in a minutes per base), and the formed base is welded in a base welding machine (

12

minutes per base). The base sub-assembly and the roof then go to final assembly where they minutes per garage) on an assembly welding machine to complete the garage. Assume one operator at Roof Base

R Punch 15 B-Punch 3 R-Form 8 B-Form 10 Weld 12 Assembly 10

Door

Capacity- Basics Ardavan Asef-Vaziri March, 2015 2

Key Problem 2: Flow Time

Roof

R Punch 15 R-Form 8 Assembly

Base (a)

B-Punch 3 B-Form 10 Weld 12 10

What is the Theoretical Flow Time? (The minimum time required to produce a garage from start to finish.) Roof Path: 15+8 = 23 Base Path: 3+10+12 = 25

Max = 25 + 10 = 35 Critical Path = Max(33,35) = 35 Theoretical Flow Time = 35

Door

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Key Problem 2: Capacity

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

Roof

R Punch 15 R-Form 8 Assembly

Door Base

B-Punch B-Form Weld 10 12 Process Capacity is 4 per hour

R-Form:1/8 per min. or 7.5 per hr.

B-Punch:1/3 per min. or 20 per hr.

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

(c) If you want to increase the process capacity, what is the activity process that you would put some additional resource? Welding: 1/12 per min. or 5 per hr.

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

R-Punch

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Key Problem 2: Capacity

(d) Compute utilization of al the resources at the full process capacity. In other words, assume that the throughput is equal to process capacity. Throughput = 4

In reality, utilization of

R-Punch Utilization = 4 /4 = 100%.

all the resources will be

R-Form Utilization = 4 /7.5 = 53.33%.

less than what we have

B-Punch Utilization = 4 /20 = 20%.

computed.

B-Form Utilization = 4 / 6 = 66.67%.

This process can never

Welding Utilization = 4 /5 = 80%.

produce 4 flow units per

Assembly Utilization = 4 /6 = 66.67%

hour continually. No Process can work at 100% capacity. Impossible.

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Key Problem 2: Bottleneck Shift

(e) Suppose we double the capacity of the bottleneck by adding the same capital and human resources. What is the new capacity of the system.

R Punch

Roof

R-Form R Punch 15 8 Assembly

Door Base

B-Punch B-Form Weld 10 12 3 10

R-Punch: 2/15 per min. or 8 per hr.

R-Form:1/8 per min. or 7.5 per hr.

B-Punch:1/3 per min. or 20 per hr.

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

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

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

Process Capacity is 5 per hour

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Key Problem 2: Diminishing Marginal Return

(f) We doubled the capacity of the bottleneck but the capacity of the system increased by only 25%. This situation is an example of what managerial experiment?

1) 2) Bottleneck shifts from R-Punch to Welding Diminishing Marginal Return

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Key Problem 2: Pooling and Cross Training

g) Now suppose we return back to the original situation where we have a single machine and a single operator at each operation. However, also suppose that we pool R-Punch and B Punch machines and we cross-train their operations and form a new resource pool named Punch where both R-Punch and B Punch operations can be done in this resource pool. What is the new capacity of the system?

R-Form R-Form 8 Assembly Assembly B-Form B-Form 10 Weld Weld 12 10

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Key Problem 2: Pooling and Cross Training

R&B-Punch R-Form R-Form Punch 8 Assembly Assembly Punch 15 , 3 B-Form B-Form Weld Weld 10 10

Punch: 2/18 per min. or 6.67 per hr.

R-Form:1/8 per min. or 7.5 per hr.

12

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

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

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

Process Capacity is 5 per hour

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Key Problem 2: Productivity Improvement -Method, Training, Technology, Management

h) This situation is an example of what managerial experiment?

1) 2) Cross training and pooling can increase the capacity Usually cost of cross training and pooling is lower than the cost of adding the second resource unit. i) Now suppose by investing in improved jigs and fixtures (

technology

), and also by implementing a better

method

of doing the job, and also

training

, we can reduce the welding time from 12 minutes to 10 minutes. What is the new capacity of the system ?

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Key Problem 2: More Than One Bottleneck

R&B-Punch R-Form R-Form Process Capacity is 6 per hour Punch 8 Assembly Assembly Punch 15 , 3 B-Form B-Form Weld Weld 10 10 10

j) Why it is impossible to work at 100% of capacity? There are 3 bottlenecks. This is a risky situation. Any of the bottlenecks could cause the throughput of the system to fall below 6 per hour. The more bottlenecks in the system, the higher the probability of not meeting the capacity. Suppose punch fail to provide input to B-Form for 1 hour, or B-Form fails to provide Weld, or Weld fails to provide Assembly- That hour of capacity perishes.

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Key Problem 2: Critical Chain

R-Punch Punch 15 R-Form R-Form 8 Assembly Assembly B-Punch Punch B-Form B-Form 3 10

Not only the system has two bottlenecks, but one bottleneck feeds the second. Furthermore. Both paths to the last bottleneck are critical. They can both increase the flow time.

Capacity- Basics

Weld Weld 10 Path 1 23 Path 2 23

Ardavan Asef-Vaziri March, 2015

10 Assembly Assembly 10

12

Lessons Learned

1. When we relax a Bottleneck Resource, the Bottleneck shifts to another resource 2. By doubling the bottleneck resource, the capacity usually does not double. This could be interpreted as diminishing marginal return situation. 3. One other way to increase capacity is cross training (for human resources ) and pooling (for Capital Resources).

4. Usually cost of cross training and pooling is lower than the cost of adding the second resource unit.

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Lessons Learned

5. One other way to increase capacity in to reduce unit load. This is done by better management, (a) better methods, (b) training, (c) replacing human resources by capital resources (more advanced technology), and (d) better management. 6. Processes cannot work at 100% capacity. Capacity is perishable it is lost if input is not ready. The more the bottleneck recourses the lower the utilization. 7. Convergence points are important in managing the flow time. The more convergence points the high the probability of the flow time exceed the average flow time.

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Problem 3: Problem 5.2 book

You May STOP Here

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Key Problem1: Flow Chart

A flowchart customers, information, or equipment through the various steps of a process is a diagram that traces the flow of materials, C E A B D B C F   Capacity Metrics: Capacity, Time to Perform the Activity (Unit Load; Tp), Cycle Time Flow Time Metrics: Theoretical Flow Time; Flow Time

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Key Problem1: Single-Stage and Two-Stage Process

    Cycle time = Capacity = 1 min 1/1 per min, 60 per hour Theoretical Flow Time = Ip = 1 That is Max Ip indeed 1 min Activity A     Cycle time = 10 min Tp =10 min Capacity = 1/10 per min, 6 per hour Theoretical Flow Time = 18 min Ip = 1.8

That is Max Ip indeed ActA  

IpA = IpB =

1 0.8

That is Max Ip indeed ActB 0 18 Activity A Tp =1 min Activity B Tp =8 min CT 28 CT 38 CT 48

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Key Problem1: Two-Stage Process

  Cycle time = Capacity = 10 min 6 per hr   Theoretical Flow Time = 15 min Ip = 1.5

ActA 

IpA =

0.5



IpB =

1 ActB Activity A Tp =5 min Activity B Tp =10 min CT CT CT 0 15 25 35    The Resource in charge of Activity A is Specialized and Fast The Resource in charge of Activity B is Specialized and Fast Process Capacity 6 per hour

Capacity- Basics Ardavan Asef-Vaziri March, 2015

45

18

Key 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, now it takes 16 to complete a flow unit Cycle time = 8 min ActivityAB1  Capacity = 7.5 per hr  60(2/16) per hr Theoretical Flow Time = 16 Activity AB2 16 Capacity increased from 6 to 7.5. Therefore,

throughput pooling and cross-training can increase

. We will latter show that

flow time

will also go

down

. ActAB1 ActAB2 0 16 CT 24 CT 32 CT 40

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Problem 3: Problem 5.2 book

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

Her

roommate tray in it.

Cookies are that holds one dozen cookies (

2 minutes

). then takes

1 minute to set the oven and place the

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.

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Problem 3: Problem 5.2: Flow unit = 1 order of 1 dozen.

Take Order Wash Mix 6 Spoon 2 load Set 1 Bake 9 Un load Cool 5 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 = 1/8 = per min = 7.5 orders per hour.

Roommate = 1/4 per min = 15 orders/hour. Oven = 1/10 =per min = 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. Pack 2 Pay 1

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Problem 3: Problem 5.2

d) Compute utilization at full capacity operation (if possible).

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. Oven = 2/10 per min = 12 orders/hour min Capacity = min {

7.5

, 15 , 12 } =

7.5

orders of 1 dozen/hr.

The bottleneck shifts to Kristen.

Doubling the capacity of oven does not double the process capacity. The process capacity is only increased to 7.5 orders per hour. That is 25% improvement. This is an example of (1) shift in the bottleneck, (2) diminishing marginal return.

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Problem 3: Problem 5.2

f) Lets go back to one oven case. What is the impact of cross training of Kristen and RM? Cross training pools Kristen and RM into a single resource pool (Workers). The unit load of Worker Resource Pool is Capacity = min { 6 + Two Ovens

10

 ,

6

} =

6

capacity is 6 dozen per hour. g) Now suppose we have two ovens. With two ovens, capacity = min {

10

,

2*6

7.5, 6 + Cross Train  8+4 = 12 2/12 per min. = 10 orders of 1 dozen/hr. orders of 1 dozen/hr. } =

10

min. per unit.

The capacity of Workers Resource Pool is increased to With one oven, cross training does not affect the theoretical process capacity. The Oven remains the bottleneck. The per hr. The bottleneck shifted to the Workers Resource Pool.

6, 6 + Two Ovens + Cross Train  10.

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Problem 6. 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 contribution margins (P-V) 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) = $26 64.29(26) = $1671.5 per day

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Problem 7

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?

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

AA BC

B 75 A 60 C 45 D 100 E 90

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Problem 7

If the system can work at the process capacity, which of the following is NOT true?

A) The utilization of machine A is at least 75% B) The utilization of machine B at least about 53% C) The utilization of machine B is at most 60% D) The utilization of machine D is 90% E) All 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) We produce at least 45 AA: 45/60 = 75% B) We produce at least 40 BC: 40/75 = 53.33% C) 45/75 = 60% D) 90/100 = 90%

AA BC

B 75 A 60 C 45 D 100

Capacity- Basics Ardavan Asef-Vaziri March, 2015

E 90

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Problem 8

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 machines are marked in the graph on the right. Which machine is the bottleneck?

A) A B) B C) C D) D E) J 50 units per week . The capacities (units/week) of the

X Y

A 50 C 70 J 90 B 60 D 80

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Problem 8

Which of the following is true?

A) The utilization of machine A is at least 80% B) The utilization of machine B at least about 66% C) The utilization of machine D is at least 50% D) The utilization of machine C is at most about 72% E) All 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

X

A) We produce at least 40 X: 40/50 = 80% B) We produce at least 40 X: 40/60 = 66.67% C) 40/80 = 50% D) 50/70 = 71.43%

Y

A 50 C 70 J 90 B 60 D 80

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What is a Process

Process analysis and improved. is the detailed understanding and documentation of how work is performed and how it can be redesigned Identify opportunity 1 Implement changes 6 Define scope 2 Redesign process 5 Document process 3 Evaluate performance 4     Capacity Metrics: Capacity, Time to perform the process (Unit Load; Tp) Quality Metrics: Defective rate, Customer satisfaction rate Efficiency Metrics: Cost, Productivity, Utilization Flexibility Metrics: Setup time, Cross Training

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