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Constraint ManagementConstraint Management7

7 – 1Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

For For Operations Management, 9eOperations Management, 9e by by Krajewski/Ritzman/Malhotra Krajewski/Ritzman/Malhotra © 2010 Pearson Education© 2010 Pearson Education

PowerPoint Slides PowerPoint Slides by Jeff Heylby Jeff Heyl

Managing ConstraintsManaging Constraints

Constraints are factors that limit performanceperformanceCapacity is the maximum rate of outputThree types of constraintsA bottleneck is any resource whose capacity limits the organization’s ability to

f


meet volume, mix, or fluctuating demand requirements

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Theory of ConstraintsTheory of Constraints

TOC is a systematic management approach that focuses on actively managing those

t i t th t i d fi ’constraints that impede a firm’s progress toward its goal of maximizing profits and effectively using its resourcesIt outlines a deliberate process for identifying and overcoming constraintsTOC methods increase the firm’s profits by


TOC methods increase the firm’s profits by focusing on materials flow through the entire system


TABLE 7.1 | HOW THE FIRM’S OPERATIONAL MEASURES RELATE TO ITS| FINANCIAL MEASURES

O ti l TOC Vi R l ti hi t Fi i lOperational Measures

TOC View Relationship to Financial Measures

Inventory (I) All the money invested in a system in purchasing things that it intends to sell

A decrease in I leads to anincrease in net profit, ROI,and cash flow.

Throughput (T) Rate at which a system generates money through sales

An increase in T leads to anincrease in net profit, ROI,and cash flows.

Operating Expense (OE)

All the money a system spends to turn inventory into throughput

A decrease in OE leads to anincrease in net profit, ROI,and cash flows


and cash flows.Utilization (U) The degree to which equipment, space,

or workforce is currently being used,and is measured as the ratio of averageoutput rate to maximum capacity,expressed as a percentage

An increase in U at thebottleneck leads to anincrease in net profit, ROI,and cash flows.

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Theory of ConstraintsTheory of ConstraintsTABLE 7.2 | SEVEN KEY PRINCIPLES OF THE THEORY OF CONSTRAINTS1. The focus should be on balancing flow, not on balancing capacity.2. Maximizing the output and efficiency of every resource may not maximize the

throughput of the entire system.g p y3. An hour lost at a bottleneck or a constrained resource is an hour lost for the whole

system. In contrast, an hour saved at a nonbottleneck resource is a mirage because it does not make the whole system more productive.

4. Inventory is needed only in front of the bottlenecks in order to prevent them from sitting idle, and in front of assembly and shipping points in order to protect customer schedules. Building inventories elsewhere should be avoided.

5. Work, which can be materials, information to be processed, documents, or customers, should be released into the system only as frequently as the bottlenecks need it. Bottleneck flows should be equal to the market demand. Pacing everything t th l t i i i i t d ti


to the slowest resource minimizes inventory and operating expenses.6. Activating a nonbottleneck resource (using it for improved efficiency that does not

increase throughput) is not the same as utilizing a bottleneck resource (that does lead to increased throughput). Activation of nonbottleneck resources cannot increase throughput, nor promote better performance on financial measures outlined in Table 7.1.

7. Every capital investment must be viewed from the perspective of its global impact on overall throughput (T), inventory (I), and operating expense (OE).


TOC involves the implementation of these five stepsfive steps

1. Identify the System Bottleneck(s)2. Exploit the Bottleneck(s)3. Subordinate All Other Decisions to Step 24. Elevate the Bottleneck(s)


5. Do Not Let Inertia Set In

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Bottlenecks can both be internal or external to the firm and are typically a process or step with the lowest capacitylowest capacityThroughput time is the total elapsed time from the start to the finish of a job or a customer being processed at one or more workcentersA bottleneck can be identified in several different ways

1 If it h th hi h t t t l ti it d


1. If it has the highest total time per unit processed2. If it has the highest average utilization and total

workload3. If a reduction of processing time would reduce the

average throughput time for the entire process

Identifying the BottleneckIdentifying the Bottleneck

EXAMPLE 7.1Managers at the First Community Bank are attempting to shorten the time it takes customers with approved loan ppapplications to get their paperwork processed. The flowchart for this process, consisting of several different activities, each performed by a different bank employee, is shown in Figure 7.1. Approved loan applications first arrive at activity or step 1, where they are checked for completeness and put in order. At step 2, the loans are categorized into different classes according to the loan amount and whether they are being requested for personal or commercial reasons. While credit

h ki t t 3 l li ti d t


checking commences at step 3, loan application data are entered in parallel into the information system for record-keeping purposes at step 4. Finally, all paperwork for setting up the new loan is finished at step 5. The time taken in minutes is given in parentheses.

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Check for credit rating (15 min)

Complete paperwork for new loan

(10 min)

Enter loan application into the system

(12 min)

Categorize loans (20 min)

Check loan documents and put them order

(15 min)


Figure 7.1 – Processing Credit Loan Applications at First Community Bank

Which single step is the bottleneck? The management is also interested in knowing the maximum number of approved loans this system can process in a 5-hour work day.


SOLUTIONWe define the bottleneck as step 2, where a single-minute reduction in its time reduces the average throughput time of thereduction in its time reduces the average throughput time of the entire loan approval process. The throughput time to complete an approved loan application is 15 + 20 + max(15, 12) + 10 = 60 minutes. Although we assume no waiting time in front of any step, in practice such a smooth process flow is not always the case. So the actual time taken for completing an approved loan will be longer than 60 minutes due to nonuniform arrival of applications, variations in actual processing times, and the related factors.


The capacity for loan completions is derived by translating the “minutes per customer” at the bottleneck step to “customer per hour.” At First Community Bank, it is 3 customers per hour because the bottleneck step 2 can process only 1 customer every 20 minutes (60/3).

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Services may not have simple line flows and demand may vary considerablyand demand may vary considerablyBottlenecks can be identified by using average utilizationVariability creates floating bottlenecksVariability increases complexity


Application 7.1Application 7.1

Two types of customers enter Barbara’s Boutique shop for customized dress alterations. After T1, Type A customers proceed to step T2 and then to any of the three workstations at T3 f ll d b t T4 d T7 Aft t T1 T BT3, followed by steps T4 and T7. After step T1,Type B customers proceed to step T5 and then steps T6 and T7. The numbers in the parentheses are the minutes it takes that activity to process a customer.

a. What is the capacity per hour of Type A customers?b. If 30 percent of the customers are Type A customers and 70

percent are Type B customers, what is the average capacity?


p yp , g p yc. When would Type A customers experience waiting lines,

assuming there are no Type B customers in the shop? Where would Type B customers have to wait, assuming no Type A customers?

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T3-a(14)

T1(12)

T7(10)

T4(18)

T3-c(11)

T3-b(10)

TypeA or B?

Type A

Type B

T2(13)

T6(22)

T5(15)


a. For Type A customers, step T2 can process (60/13) = 4.62 customers per hour. T3 has three work stations and a capacity of (60/14) + (60/10) + (60/11) = 15.74 customer per hour. Step T4 can process (60/18) = 3.33 customers per hour. The bottleneck for type A customers is the step with the highest processing time per customer, T4.


T3-a(14)

T1(12)

T7(10)

T4(18)

T3-c(11)

T3-b(10)

TypeA or B?

Type A

Type B

T2(13)

T6(22)

T5(15)


b. The bottleneck for Type B customers is T6 since it has the longest processing time per customer. The capacity for Type B customers is (60/22) = 2.73 customers per hour. Thus the average capacity is 0.3(3.33) + 0.7(2.73) = 2.9 customers per hour

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T3-a(14)

T1(12)

T7(10)

T4(18)

T3-c(11)

T3-b(10)

TypeA or B?

Type A

Type B

T2(13)

T6(22)

T5(15)


before T2 and T4 because the activities immediately preceding them have a higher rate of output.

c. Type A customers would wait

before steps T5 and T6 for the same reason. This assumes there are always new customers entering the shop.

Type B customers would wait


EXAMPLE 7.2Diablo Electronics manufactures four unique products (A, B, C, and D) that are fabricated and assembled in five differentand D) that are fabricated and assembled in five different workstations (V, W, X, Y, and Z) using a small batch process. Each workstation is staffed by a worker who is dedicated to work a single shift per day at an assigned workstation. Batch setup times have been reduced to such an extent that they can be considered negligible. Figure 7.2 is a flowchart of the manufacturing process. Diablo can make and sell up to the limit of its demand per week, and no penalties are incurred for not being able to meet all the demand.


Which of the five workstations (V, W, X, Y, or Z) has the highest utilization, and thus serves as the bottleneck for Diablo Electronics?

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Identifying the BottleneckIdentifying the BottleneckProduct A

Raw materials

Product: APrice: $75/unitDemand: 60 units/wk

Step 1 at workstation V

(30 min)

Finish with step 3at workstation X

(10 min)

Step 2 atworkstation Y

(10 min)

$5

$5 Purchased parts

Product CProduct: CPrice: $45/unitDemand: 80 units/wk

Finish with step 4at workstation Y

(5 min)

Step 2 atworkstation Z

(5 min)

Step 3 atworkstation X

(5 min)

Step 1 atworkstation W

(5 min)

$2

Product B

Raw materialsPurchased parts

Product: BPrice: $72/unitDemand: 80 units/wk

Finish with step 2at workstation X

(20 min)


(10 min)

$3

$2


Raw materialsPurchased parts$3

Product D

Raw materialsPurchased parts

Product: DPrice: $38/unitDemand: 100 units/wk

$4 Step 2 atworkstation Z

(10 min)

Finish with step 3at workstation Y

(5 min)


(15 min)

$6

Figure 7.2 Flowchart for Products A, B, C, and D


SOLUTIONBecause the denominator in the utilization ratio is the same for every workstation, with one worker per machine at each step inevery workstation, with one worker per machine at each step in the process, we can simply identify the bottleneck by computing aggregate workloads at each workstation.

The firm wants to satisfy as much of the product demand in a week as it can. Each week consists of 2,400 minutes of available production time. Multiplying the processing time at each station for a given product with the number of units demanded per week yields the workload represented by that


y yproduct. These loads are summed across all products going through a workstation to arrive at the total load for the workstation, which is then compared with the others and the existing capacity of 2,400 minutes.

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Workstation Load from Product A

Load from Product B

Load from Product C

Load from Product D

Total Load (min)

V


V

W

X

Y

Z



60 30 1800 0 0 0 1 800

Workstation Load from Product A

Load from Product B

Load from Product C

Load from Product D

Total Load (min)

V

These calculations show that workstation X is the bottleneck, b th t k l d t X d th il bl

60 × 30 = 1800 0 0 0 1,800

0 0 80 × 5 = 400 100 × 15 = 1,500 1,900

60 × 10 = 600 80 × 20 = 1,600 80 × 5 = 400 0 2,600

60 × 10 = 600 80 × 10 = 800 80 × 5 = 400 100 × 5 = 500 2,300

0 0 80 × 5 = 400 100 × 10 = 1,000 1,400

V

W

X

Y

Z


because the aggregate work load at X exceeds the available capacity of 2,400 minutes per week.

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O’Neill Enterprises manufactures three unique products (A, B, C) that are fabricated and assembled in four different workstations (W, X, Y, Z) using a small batch process. Each of th d t i it f th f k t ti th hthe products visits every one of the four workstations, though not necessarily in the same order. Batch setup times are negligible. A flowchart of the manufacturing process is shown below. O’Neill can make and sell up to the limit of its demand per week, and there are no penalties for not being able to meet all the demand. Each workstation is staffed by a worker dedicated to work on that workstation alone, and is paid $12 per hour. Variable overhead costs are $8000/week. The plant operates one 8-hour shift per day or 40 hours/week


operates one 8-hour shift per day, or 40 hours/week. Which of the four workstations W, X, Y, or Z has the highest total workload, and thus serves as the bottleneck for O’Neill Enterprises?


Product A

Fi i h i h 4S 2 S 3S 1

Flowchart for Products A, B, and C

Product B

Raw materialsPurchased part

Product: BPrice: $85/unitDemand: 70 units/wk

Finish with step 4at workstation Z

(13 min)


(10 min)


(10 min)


(12 min)

$9

$5


Product: APrice: $90/unitDemand: 65 units/wk


(16 min)


(15 min)


(9 min)


(10 min)

$7

$6


Product C


Product: CPrice: $80/unitDemand: 80 units/wk


(10 min)


(10 min)


(12 min)


(5 min)

$10

$5

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SOLUTIONIdentify the bottleneck by computing total workload at each workstation. The firm wants to satisfy as much of the productworkstation. The firm wants to satisfy as much of the product demand in a week as it can. Each week consists of 2400 minutes of available production time. Multiplying the processing time at each station for a given product with the number of units demanded per week yields the capacity load. These loads are summed across all products going through that workstation and then compared with the existing capacity of 2400 minutes.


Work Station

Load from Product A

Load from Product B

Load from Product C

Total Load (minutes)


W

X

Y

Z


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Work Station

Load from Product A

Load from Product B

Load from Product C

Total Load (minutes)

Th l l ti h th t k t ti Z i th b ttl k

(65x10)= 650 (70×10)= 700 (80×12)= 960 2310

(65×9)= 585 (70×12)= 840 (80×10)= 800 2225

(65×15)= 975 (70x10)= 700 (80x5)= 400 2075

(65×16)= 1040 (70×13)= 910 (80×10)= 800 2750

W

X

Y

Z


These calculations show that workstation Z is the bottleneck, because the aggregate work load at Z exceeds the available capacity of 2400 minutes per week.

Determining the Product MixDetermining the Product Mix

EXAMPLE 7.3The senior management at Diablo Electronics (see Exercise 7.2)

t t i fit bilit b ti th i ht t fwants to improve profitability by accepting the right set of orders, and so collected some additional financial data. Variable overhead costs are $8,500 per week. Each worker is paid $18 per hour and is paid for an entire week, regardless of how much the worker is used. Consequently, labor costs are fixed expenses. The plant operates one 8-hour shift per day, or 40 hours each week. Currently, decisions are made using the traditional method, which is to accept as much of the highest contribution margin product as possible (up to the limit of its


contribution margin product as possible (up to the limit of its demand), followed by the next highest contribution margin product, and so on until no more capacity is available.

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Pedro Rodriguez, the newly hired production supervisor, is knowledgeable about the theory of constraints and bottleneck-based scheduling. He believes that profitability can indeed be i d if b ttl k l it d t d t iimproved if bottleneck resources were exploited to determine the product mix. What is the change in profits if, instead of the traditional method used by Diablo Electronics, the bottleneck method advocated by Pedro is used to select the product mix?

SOLUTIONDecision Rule 1: Traditional Method


Select the best product mix according to the highest overall contribution margin of each product.


Step 1: Calculate the contribution margin per unit of each product as shown here.

A B C D

Price

Raw material and purchased parts

= Contribution margin


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Step 1: Calculate the contribution margin per unit of each product as shown here.

When ordered from highest to lowest, the

$75.00 $72.00 $45.00 $38.00

–10.00 –5.00 –5.00 –10.00

$65.00 $67.00 $40.00 $28.00

A B C D

Price

Raw material and purchased parts

= Contribution margin


g ,contribution margin per unit sequence of these products is B, A, C, D.


Step 2: Allocate resources V, W, X, Y, and Z to the products in the order decided in step 1. Satisfy each demand until the bottleneck resource (workstation X) is encountered. S bt t i t f 2 400 i t il bl fSubtract minutes away from 2,400 minutes available for each week at each stage.

Work Center

Minutes at the Start

Minutes Left After Making 80 B

Minutes Left After Making 60 A

Can Only Make 40 C

Can Only Make 100 D

VWX


Y

Z

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2,400 2,400 600 600 6002,400 2,400 2,400 2,200 7002,400 800 200 0 0

Work Center




Can Only Make 40 C

Can Only Make 100 D

VWX


The best product mix according to this traditional approach is then 60 A, 80 B, 40 C, and 100 D.

2,400 1,600 1,000 800 3002,400 2,400 2,400 2,200 1,200

Y

Z


Step 3: Compute profitability for the selected product mix.

ProfitsProfits

Revenue

Materials

Labor

Overhead

Profit


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Profits

(60 × $75) + (80 × $72) + (40 × $45) + (100 × $38) = $15,860

Profits

Revenue

Materials

Labor

Overhead

Profit

(60 × $10) + (80 × $5) + (40 × $5) + (100 × $10) = –$2,200

(5 workers) × (8 hours/day) × (5 days/week) × ($18/hour) = –$3,600

= –$8,500

= $1,560


Manufacturing the product mix of 60 A, 80 B, 40 C, and 100 D will yield a profit of $1,560 per week.


Decision Rule 2: Bottleneck MethodSelect the best product mix according to the dollar contribution margin per minute of processing time at the bottleneckmargin per minute of processing time at the bottleneck workstation X. This method would take advantage of the principles outlined in the theory of constraints and get the most dollar benefit from the bottleneck.

Step 1: Calculate the contribution margin/minute of processing time at bottleneck workstation X:


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Product A Product B Product C Product D

Contribution marging

Time at bottleneck

Contribution margin per minute



$65.00 $67.00 $40.00 $28.00

Product A Product B Product C Product D

Contribution margin

When ordered from highest to lowest contribution margin/ minute at the bottleneck, the manufacturing sequence of these products is D, C, A, B, which is reverse of the earlier order. Product D is scheduled first because it does not consume any

$ $ $ $

10 minutes 20 minutes 5 minutes 0 minutes

$6.50 $3.35 $8.00 Not defined

g

Time at bottleneck

Contribution margin per minute


Product D is scheduled first because it does not consume any resources at the bottleneck.

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Work Center




Can Only Make 40 C

Can Only Make 100 D

V

W

X


Y

Z



2,400 2,400 2,400 600 600

2,400 900 500 500 500

2,400 2,400 2,000 1,400 0

Work Center




Can Only Make 40 C

Can Only Make 100 D

V

W

X


The best product mix according to this bottleneck based approach is then 60 A, 70 B, 80 C, and 100 D.

2,400 1,900 1,500 900 200

2,400 1,400 1,000 1,000 1,000

Y

Z

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Profits

Revenue

Materials

Labor

Overhead

Profit




Profits

(60 × $75) + (70 × $72) + (80 × $45) + (100 × $38) = $16,940

(60 × $10) + (70 × $5) + (80 × $5) + (100 × $10) = –$2,350

(5 workers) × (8 hours/day) × (5 days/week) × ($18/hour) = –$3,600

Revenue

Materials

Labor

Overhead

Profit

= –$8,500

= $2,490


Manufacturing the product mix of 60 A, 70 B, 80 C, and 100 D will yield a profit of $2,490 per week.

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The senior management at O’Neill Enterprises wants to improve the profitability of the firm by accepting the right set of orders. Currently, decisions are made to accept as much of the highest

t ib ti i d t ibl ( t th li it f itcontribution margin product as possible (up to the limit of its demand), followed by the next highest contribution margin product, and so on until no more capacity is available. Since the firm cannot satisfy all the demand, the product mix must be chosen carefully. Jane Hathaway, the newly hired production supervisor, is knowledgeable about the theory of constraints and bottleneck based scheduling. She believes that profitability can indeed be approved if bottleneck resources were exploited to determine the product mix What is the change in profits if


to determine the product mix. What is the change in profits if instead of the traditional method that O’Neill has used thus far; a bottleneck based approach advocated by Jane is used instead for selecting the product mix?


SOLUTIONDecision rule 1: Traditional method - Select the best product mix according to the highest overall profit margin of eachmix according to the highest overall profit margin of each product.Step 1: Calculate the profit margin per unit of each product as

shown below

A B CPriceRaw Material & Purchased Parts


Labor= Contribution Profit Margin

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SOLUTIONDecision rule 1: Traditional method - Select the best product mix according to the highest overall profit margin of eachmix according to the highest overall profit margin of each product.Step 1: Calculate the profit margin per unit of each product as

shown below

$90.00 $85.00 $80.00

–13.00 –14.00 –15.00

A B CPriceRaw Material & Purchased Parts


When ordering from highest to lowest, the profit margin per unit order of these products is ABC.

Labor= Contribution Profit Margin

–10.00 –9.00 –7.40$67.00 $62.00 $57.60


Step 2: Allocate resources W, X, Y, and Z to the products in the order decided in step 1. Satisfy each demand until the bottleneck resource (workstation Z) is encountered. S f 2400 fSubtract minutes away from 2400 minutes available for each week at each stage.

Work Center Starting After 65 A After 70 B Can Only Make 45 C

W

X

Y


Z

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2400 1750 1050 510

2400 1815 975 525

2400 1425 725 500

Work Center Starting After 65 A After 70 B Can Only Make 45 C

W

X

Y


The best product mix is 65 A, 70 B, and 45 C

2400 1360 450 0Z



ProfitsRevenueMaterialsOverheadLaborProfit


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$15400–$2500–$8000–$1920$2980


Manufacturing the product mix of 65 A, 70 B, and 45 C will yield a profit of $2980.


Decision rule 2: Bottleneck-based approach - Select the best product mix according to the dollar contribution per minute of processing time at the bottleneck workstation Z. This rule

ld t k d t f th i i l tli d i th th fwould take advantage of the principles outlined in the theory of constraints and get the most dollar benefit from the bottleneck.

Step 1: Calculate the contribution/minute of processing time at bottleneck workstation Z:

Product A Product B Product CContribution MarginTime at Bottleneck


Time at Bottleneck Contribution Margin per minute

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Decision rule 2: Bottleneck-based approach - Select the best product mix according to the dollar contribution per minute of processing time at the bottleneck workstation Z. This rule

ld t k d t f th i i l tli d i th th fwould take advantage of the principles outlined in the theory of constraints and get the most dollar benefit from the bottleneck.

Step 1: Calculate the contribution/minute of processing time at bottleneck workstation Z:

$67.00 $62.00 $57.6016 minutes 13 minutes 10 minutes

Product A Product B Product CContribution MarginTime at Bottleneck


When ordering from highest to lowest contribution margin/minute at the bottleneck, the manufacturing sequence of these products is CBA, which is reverse of the traditional method order.

16 minutes 13 minutes 10 minutes

4.19 4.77 5.76Time at Bottleneck

Contribution Margin per minute



Work Center Starting After 80 C After 70 B Can Only Make 43 A

W

X

Y

Z


Z

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2400 1440 740 310

2400 1600 760 373

2400 2000 1300 655

2400 1600 690 2

Work Center Starting After 80 C After 70 B Can Only Make 43 A

W

X

Y

Z


The best product mix is 43A, 70B, and 80C

2400 1600 690 2Z


Step 3: Compute profitability for the selected product mix. The new profitability figures are shown below based on the new production quantities of 43A, 70B, and 80C.



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Step 3: Compute profitability for the selected product mix. The new profitability figures are shown below based on the new production quantities of 43A, 70B, and 80C.


$16220

–$2739–$8000–$1920$3561


Manufacturing the product mix of 43 A, 70 B, and 80 C will yield a profit of $3561.

DrumDrum--BufferBuffer--Rope SystemsRope Systems

The bottleneck schedule is the drum because it sets the beat or the production

t f th ti l t d i li k d trate for the entire plant and is linked to market demandThe buffer is the time buffer that plans early flows into the bottleneck and thus protects it from disruptionThe rope represents the tying of material


The rope represents the tying of material release to the drum beat, which is the rate at which the bottleneck controls the throughput of the entire plant

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DrumDrum--BufferBuffer--Rope SystemsRope Systems

PROCESS B

CCR (Bottleneck)

Constraint Buffer

Time Buffer

Nonconstraint

PROCESS AM t i l

Buffer DrumRope

Shipping Buffer

Finished Goods

Nonconstraint

PROCESS BCapacity

800 units/wk

Time Buffer Inventory

PROCESS ACapacity

800 units/wk

Material Release

Schedule


MarketDemand

650 units/wkShipping Schedule

Finished Goods InventoryPROCESS C

Capacity700 units/wk

Figure 7.3 – Drum-Buffer-Rope Systems

A Line ProcessA Line Process

Line BalancingA i t f k t t ti i liAssignment of work to stations in a line so as to achieve the desired output rate with the smallest number of workstationsAchieving the goal is similar to the theory of constraints but it differs in how it addresses bottlenecks

P d di AON t k


Precedence diagram – AON network

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Precedence DiagramPrecedence Diagram

EXAMPLE 7.4Green Grass, Inc., a manufacturer of lawn and garden equipment, is designing an assembly line to produce a newequipment, is designing an assembly line to produce a new fertilizer spreader, the Big Broadcaster. Using the following information on the production process, construct a precedence diagram for the Big Broadcaster. Work

Element Description Time (sec)

Immediate Predecessor(s)

A Bolt leg frame to hopper 40 NoneB Insert impeller shaft 30 AC Attach axle 50 AD Attach agitator 40 B


D Attach agitator 40 BE Attach drive wheel 6 BF Attach free wheel 25 CG Mount lower post 15 CH Attach controls 20 D, EI Mount nameplate 18 F, G

Total 244

Precedence DiagramPrecedence Diagram

SOLUTIONFigure 7.4 shows the complete diagram. We begin with work element A, which has no immediate predecessors. Next, we addelement A, which has no immediate predecessors. Next, we add elements B and C, for which element A is the only immediate predecessor. After entering time standards and arrows showing precedence, we add elements D and E, and so on. The diagram simplifies interpretation. Work element F, for example, can be done anywhere on the line after element C is completed.

D

40H

20E

6

B

30


However, element I must await completion of elements F and G.

I

18

F

25

G

15

C

50

6A

40

Figure 7.4 – Precedence Diagram for Assembling the Big Broadcaster

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The desired output rate is matched to the staffing or production planstaffing or production planCycle time is the maximum time allowed for work at each station is

c =1r


wherec = cycle time in hoursr = desired output rate


The theoretical minimum number of stations isstations is

TM =Σtc

where


Σt = total time required to assemble each unit

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Idle time, efficiency, and balance delay

Idle time = nc – Σt

wheren = number of stations

Efficiency (%) = (100)Σt


Efficiency (%) = (100)nc

Balance delay (%) = 100 – Efficiency

Calculating Cycle Time, TM, EfficiencyCalculating Cycle Time, TM, Efficiency

EXAMPLE 7.5Green Grass’s plant manager just received marketing’s latest forecasts of Big Broadcaster sales for the next year. She wantsforecasts of Big Broadcaster sales for the next year. She wants its production line to be designed to make 2,400 spreaders per week for at least the next 3 months. The plant will operate 40 hours per week.

a. What should be the line’s cycle time?b. What is the smallest number of workstations that she could

hope for in designing the line for this cycle time?


c. Suppose that she finds a solution that requires only five stations. What would be the line’s efficiency?

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SOLUTIONa. First convert the desired output rate (2,400 units per week) to

an hourly rate by dividing the weekly output rate by 40 hoursan hourly rate by dividing the weekly output rate by 40 hours per week to get units per hour. Then the cycle time is

c = 1/r =

b. Now calculate the theoretical minimum for the number of stations by dividing the total time, Σt, by the cycle time, c = 60 seconds. Assuming perfect balance, we have

1/60 (hr/unit) = 1 minute/unit = 60 seconds/unit


TM =Σtc

244 seconds60 seconds= = 4.067 or 5 stations


c. Now calculate the efficiency of a five-station solution, assuming for now that one can be found:

Efficiency = (100) =Σtnc

2445(60) = 81.3%


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Finding a SolutionFinding a Solution

The goal is to cluster the work elements into workstations so that 1 The number of workstations required is minimized1. The number of workstations required is minimized2. The precedence and cycle-time requirements are not

violated

The work content for each station is equal (or nearly so, but less than) the cycle time for the lineTrial-and-error can be used but commercial software packages are also available


software packages are also availableThe decision rules used by POM for Windows are described in Table 7.3


TABLE 7.3 | HEURISTIC DECISION RULES IN ASSIGNING THE NEXT WORK ELEMENT TO A| WORKSTATION BEING CREATED

Create one station at a time. For the station now being created, identify the unassigned work elements that qualify for assignment: They are candidates ifqualify for assignment: They are candidates if

1. All of their predecessors have been assigned to this station or stations already created.2. Adding them to the workstation being created will not create a workload that exceeds the cycle time.

Decision Rule Logic

Longest work element Picking the candidate with the longest time to complete is an effort to fit in the most difficult elements first, leaving the ones with short times to “fill out” the station.

Shortest work element This rule is the opposite of the longest work element rule because it gives preference in workstation assignments to those work elements that are quicker. It can be tried because no single rule guarantees the best solution. It might provide another solution for the planner to consider


another solution for the planner to consider.

Most followers When picking the next work element to assign to a station being created, choose the element that has the most followers (due to precedence requirements). In Figure 7.4, item C has three followers (F, G, and I) whereas item D has only one follower (H). This rule seeks to maintain flexibility so that good choices remain for creating the last few workstations at the end of the line.

Fewest followers Picking the candidate with the fewest followers is the opposite of the most followers rule.

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The theoretical minimum number of workstations is 5 and the cycle time is 60 seconds, so Figure 7 5 represents an optimal solution to the problem7.5 represents an optimal solution to the problem

D

40H

20

FC

E

6

B

30

A

40


Figure 7.5 – Big Broadcaster Precedence Diagram Solution

I

18

25C

50

40

G

15


A plant manager needs a design for an assembly line to assembly a new product that is being introduced. The time requirements and i di timmediate predecessors for the work elements are as follows:

Work Element Time (sec) Immediate Predecessor

A 12 ―B 60 AC 36 ―D 24 ―E 38 C, DF 72 B, EG 14


G 14 ―H 72 ―I 35 G, HJ 60 IK 12 F, J

Total = 435

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Draw a precedence diagram, complete I, F, J, and K

K

Work Element Time (sec) Immediate

PredecessorA 12 ―B 60 AC 36 ―

D 24 ―

E 38 C, D

F 72 B, E

G 14 ―

H 72 ―

F

J

B

E

A

C

D


I 35 G, H

J 60 I

K 12 F, J

Total = 435

J

IG

H


If the desired output rate is 30 units per hour, what are the cycle time and theoretical minimum?

c = =1r

130 (3600) = 120 sec/unit

TM =Σt

= = 3.6 or 4 stations435120


c 3 6 o stat o s120

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Suppose that we are fortunate enough to find a solution with just four stations. What is the idle time per unit, efficiency, and the balance delay for this solution?the balance delay for this solution?

Idle time = nc – Σt

Efficiency (%) = (100)Σtnc

= 4(120) – 435 = 45 seconds

= (100) = 90.6%435480


Balance delay (%) = 100 – Efficiency = 100 – 90.6 = 9.4%


Using trial and error, one possible solution is shown below.

Station

Work Elements Assigned Cumulative Time

Idle Time(c = 120)

1

2

3

4


4

5

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Using trial and error, one possible solution is shown below.

H, C, A 120 0

B, D, G 98 22

E, F 110 10

I J K 107 13

Station

Work Elements Assigned Cumulative Time

Idle Time(c = 120)

1

2

3

4


I, J, K 107 13

A fifth station is not needed

4

5

Managerial ConsiderationsManagerial Considerations

Pacing is the movement of product from one station to the nextBehavioral factors such as absenteeism, turnover, and grievances can increase after installing production linesThe number of models produced complicates scheduling and necessitates good communication


good communicationCycle times are dependent on the desired output rate

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Solved Problem 1Solved Problem 1

Bill’s Car Wash offers two types of washes: Standard and Deluxe. The process flow for both types of customers is shown in the following chart. Both wash types are first processed th h t A1 d A2 Th St d d h ththrough steps A1 and A2. The Standard wash then goes through steps A3 and A4 while the Deluxe is processed through steps A5, A6, and A7. Both offerings finish at the drying station (A8). The numbers in parentheses indicate the minutes it takes for that activity to process a customer.

A4(15)

A3(12)Standard


A8(10)

A7(12)

A6(20)

A5(5)Deluxe

Standard or Deluxe

A2(6)

A1(5)


a. Which step is the bottleneck for the Standard car wash process? For the Deluxe car wash process?

b. What is the capacity (measured as customers served perb. What is the capacity (measured as customers served per hour) of Bill’s Car Wash to process Standard and Deluxe customers? Assume that no customers are waiting at step A1, A2, or A8.

c. If 60 percent of the customers are Standard and 40 percent are Deluxe, what is the average capacity of the car wash in customers per hour?

d. Where would you expect Standard wash customers to i iti li i th t t


experience waiting lines, assuming that new customers are always entering the shop and that no Deluxe customers are in the shop? Where would the Deluxe customers have to wait, assuming no Standard customers?

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SOLUTIONa. Step A4 is the bottleneck for the Standard car wash process,

and Step A6 is the bottleneck for the Deluxe car washand Step A6 is the bottleneck for the Deluxe car wash process, because these steps take the longest time in the flow.

b. The capacity for Standard washes is 4 customers per hour because the bottleneck step A4 can process 1 customer every 15 minutes (60/15). The capacity for Deluxe car washes is 3 customers per hour (60/20). These capacities are derived by translating the “minutes per customer” of each bottleneck activity to “customers per hour ”


bottleneck activity to customers per hour.c. The average capacity of the car wash is

(0.60 × 4) + (0.40 × 3) = 3.6 customers per hour.


d. Standard wash customers would wait before steps A1, A2, A3, and A4 because the activities that immediately precede them have a higher rate of output (i e smaller processingthem have a higher rate of output (i.e., smaller processing times). Deluxe wash customers would experience a wait in front of steps A1, A2, and A6 for the same reasons. A1 is included for both types of washes because the arrival rate of customers could always exceed the capacity of A1.


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A company is setting up an assembly line to produce 192 units per 8-hour shift. The following table identifies the work elements, times, and immediate predecessors:

Work Element Time (sec) Immediate Predecessor(s)

A 40 NoneB 80 AC 30 D, E, FD 25 BE 20 BF 15 B


F 15 BG 120 AH 145 GI 130 HJ 115 C, I

Total 720


a. What is the desired cycle time (in seconds)?b. What is the theoretical minimum number of stations?c. Use trial and error to work out a solution, and show your

solution on a precedence diagram.d. What are the efficiency and balance delay of the solution

found?

SOLUTIONa. Substituting in the cycle-time formula, we get


c = =1r

8 hours192 units (3,600 sec/hr) = 150 sec/unit

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b. The sum of the work-element times is 720 seconds, so

TM =Σtc = = 4.8 or 5 stations

720 sec/unit150 sec/unit-station

which may not be achievable.



c. The precedence diagram is shown in Figure 7.6. Each row in the following table shows work elements assigned to each of the five workstations in the proposed solution.

J

C

30

D

25

E

20

F

B

80

A

Work Element

Immediate Predecessor(s)

A NoneB AC D, E, FD BE BF BG AH G


11515

I

130H

145

G

120

A

40

Figure 7.6 – Precedence Diagram

I HJ C, I

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Solved Problem 2Solved Problem 2J

115

C

30

D

25

E

20

F

15 I

130H

145

B

80

G

120

A

40

Station Candidate(s) Choice Work-Element Time (sec)

Cumulative Time (sec)

Idle Time(c= 150 sec)

S1

S2

145


S3S4

S5

Solved Problem 2Solved Problem 2J

115

C

30

D

25

E

20

F

15 I

130H

145

B

80

G

120

A

40

145

A A 40 40 110

B B 80 120 30D, E, F D 25 145 5

E, F, G G 120 120 30E, F E 20 140 10

Station Candidate(s) Choice Work-Element Time (sec)

Cumulative Time (sec)

Idle Time(c= 150 sec)

S1

S2


E, F E 20 140 10F, H H 145 145 5F, I I 130 130 20F F 15 145 5C C 30 30 120J J 115 145 5

S3S4

S5

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d. Calculating the efficiency, we get

Thus the balance delay is only 4 percent (100 96)

Efficiency (%) = (100)Σtnc =

720 sec/unit5(150 sec/unit)

= 96%


Thus, the balance delay is only 4 percent (100–96).


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