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Capacity and Constraint Management

PowerPoint presentation to accompany

Heizer and Render

Operations Management, Eleventh Edition

Principles of Operations Management, Ninth Edition

PowerPoint slides by Jeff Heyl

SUPPLEMENT

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Outline

Capacity

Bottleneck Analysis and the Theory of Constraints

Break-Even Analysis

Reducing Risk with Incremental Changes

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Outline - Continued

Applying Expected Monetary Value (EMV) to Capacity Decisions

Applying Investment Analysis to Strategy-Driven Investments

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Learning Objectives

When you complete this supplement you should be able to :

Define capacity
Determine design capacity, effective capacity, and utilization
Perform bottleneck analysis
Compute break-even

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Learning Objectives

When you complete this supplement you should be able to :

Determine the expected monetary value of a capacity decision
Compute net present value

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Capacity

The throughput, or the number of units a facility can hold, receive, store, or produce in a period of time
Determines
fixed costs
Determines if
demand will
be satisfied
Three time horizons

This slide provides some reasons that capacity is an issue. The following slides guide a discussion of capacity.

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Planning Over a Time Horizon

Figure S7.1

Modify capacity

Use capacity

Intermediate-range planning (aggregate planning)

Subcontract Add personnel

Add equipment Build or use inventory

Add shifts

Short-range planning (scheduling)

Schedule jobs

Schedule personnel

Allocate machinery

Long-range planning

Add facilities

Add long lead time equipment

* Difficult to adjust capacity as limited options exist

Options for Adjusting Capacity

Time Horizon

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Design and Effective Capacity

Design capacity is the maximum theoretical output of a system
Normally expressed as a rate
Effective capacity is the capacity a firm expects to achieve given current operating constraints
Often lower than design capacity

This slide can be used to frame a discussion of capacity.

Points to be made might include:

- capacity definition and measurement is necessary if we are to develop a production schedule

- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.

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Utilization and Efficiency

Utilization is the percent of design capacity actually achieved

Efficiency is the percent of effective capacity actually achieved

Utilization = Actual output/Design capacity

Efficiency = Actual output/Effective capacity

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Bakery Example

Actual production last week = 148,000 rolls

Effective capacity = 175,000 rolls

Design capacity = 1,200 rolls per hour

Bakery operates 7 days/week, 3 - 8 hour shifts

Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls

It might be useful at this point to discuss typical equipment utilization rates for different process strategies if you have not done so before.

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Bakery Example

Actual production last week = 148,000 rolls

Effective capacity = 175,000 rolls

Design capacity = 1,200 rolls per hour

Bakery operates 7 days/week, 3 - 8 hour shifts

Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls

It might be useful at this point to discuss typical equipment utilization rates for different process strategies if you have not done so before.

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Bakery Example

Actual production last week = 148,000 rolls

Effective capacity = 175,000 rolls

Design capacity = 1,200 rolls per hour

Bakery operates 7 days/week, 3 - 8 hour shifts

Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls

Utilization = 148,000/201,600 = 73.4%

It might be useful at this point to discuss typical equipment utilization rates for different process strategies if you have not done so before.

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Bakery Example

Actual production last week = 148,000 rolls

Effective capacity = 175,000 rolls

Design capacity = 1,200 rolls per hour

Bakery operates 7 days/week, 3 - 8 hour shifts

Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls

Utilization = 148,000/201,600 = 73.4%

Efficiency = 148,000/175,000 = 84.6%

It might be useful at this point to discuss typical equipment utilization rates for different process strategies if you have not done so before.

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Bakery Example

Actual production last week = 148,000 rolls

Effective capacity = 175,000 rolls

Design capacity = 1,200 rolls per hour

Bakery operates 7 days/week, 3 - 8 hour shifts

Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls

Utilization = 148,000/201,600 = 73.4%

Efficiency = 148,000/175,000 = 84.6%

It might be useful at this point to discuss typical equipment utilization rates for different process strategies if you have not done so before.

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Bakery Example

Actual production last week = 148,000 rolls

Effective capacity = 175,000 rolls

Design capacity = 1,200 rolls per hour

Bakery operates 7 days/week, 3 - 8 hour shifts

Efficiency = 84.6%

Efficiency of new line = 75%

Expected Output = (Effective Capacity)(Efficiency)

= (175,000)(.75) = 131,250 rolls

It might be useful at this point to discuss typical equipment utilization rates for different process strategies if you have not done so before.

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Bakery Example

Actual production last week = 148,000 rolls

Effective capacity = 175,000 rolls

Design capacity = 1,200 rolls per hour

Bakery operates 7 days/week, 3 - 8 hour shifts

Efficiency = 84.6%

Efficiency of new line = 75%

Expected Output = (Effective Capacity)(Efficiency)

= (175,000)(.75) = 131,250 rolls

It might be useful at this point to discuss typical equipment utilization rates for different process strategies if you have not done so before.

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Capacity and Strategy

Capacity decisions impact all 10 decisions of operations management as well as other functional areas of the organization
Capacity decisions must be integrated into the organization’s mission and strategy

You might point out to students that this slide links capacity to work measurement (standard times).

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Capacity Considerations

Forecast demand accurately

Match technology increments and sales volume

Find the optimum operating size
(volume)

Build for change

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Economies and Diseconomies of Scale

Figure S7.2

Economies of scale

Diseconomies of scale

1,300 sq ft store

2,600 sq ft store

8,000 sq ft store

Number of square feet in store

1,300

2,600

8,000

Average unit cost

(sales per square foot)

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Managing Demand

Demand exceeds capacity
Curtail demand by raising prices, scheduling longer lead time
Long term solution is to increase capacity
Capacity exceeds demand
Stimulate market
Product changes
Adjusting to seasonal demands
Produce products with complementary demand patterns

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Complementary Demand Patterns

Figure S7.3

4,000 –

3,000 –

2,000 –

1,000 –

J F M A M J J A S O N D J F M A M J J A S O N D J

Sales in units

Time (months)

Combining the two demand patterns reduces the variation

Snowmobile motor sales

Jet ski engine sales

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Tactics for Matching Capacity to Demand

Making staffing changes
Adjusting equipment
Purchasing additional machinery
Selling or leasing out existing equipment
Improving processes to increase throughput
Redesigning products to facilitate more throughput
Adding process flexibility to meet changing product preferences
Closing facilities

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Service-Sector Demand and Capacity Management

Demand management

Appointment, reservations, FCFS rule

Capacity
management

Full time,
temporary,
part-time
staff

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Bottleneck Analysis and the Theory of Constraints

Each work area can have its own unique capacity

Capacity analysis determines the throughput capacity of workstations in a system

A bottleneck is a limiting factor or constraint

A bottleneck has the lowest effective capacity in a system

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Bottleneck Analysis and the Theory of Constraints

The bottleneck time is the time of the slowest workstation (the one that takes the longest) in a production system

The throughput time is the time it takes a unit to go through production from start to end

Figure S7.4

2 min/unit

4 min/unit

3 min/unit

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Capacity Analysis

Two identical sandwich lines

Lines have two workers and three operations

All completed sandwiches are wrapped

Wrap/

Deliver

37.5 sec/sandwich

Order

30 sec/sandwich

Bread

Fill

15 sec/sandwich

20 sec/sandwich

Bread

Fill

Toaster

15 sec/sandwich

20 sec/sandwich

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Capacity Analysis

The two lines each deliver a sandwich every 20 seconds

At 37.5 seconds, wrapping and delivery has the longest processing time and is the bottleneck

Capacity per hour is 3,600 seconds/37.5 seconds/sandwich = 96 sandwiches per hour

Throughput time is 30 + 15 + 20 + 20 + 37.5 = 122.5 seconds

Wrap/

Deliver

37.5 sec

Order

30 sec

Bread

Fill

15 sec

20 sec

Bread

Fill

Toaster

15 sec

20 sec

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Capacity Analysis

Standard process for cleaning teeth

Cleaning and examining X-rays can happen simultaneously

Check
out

6 min/unit

Check in

2 min/unit

Develops
X-ray

4 min/unit

8 min/unit

Dentist

Takes
X-ray

2 min/unit

5 min/unit

X-ray
exam

Cleaning

24 min/unit

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Capacity Analysis

All possible paths must be compared

Bottleneck is the hygienist at 24 minutes

Hourly capacity is 60/24 = 2.5 patients

X-ray exam path is 2 + 2 + 4 + 5 + 8 + 6 = 27 minutes

Cleaning path is 2 + 2 + 4 + 24 + 8 + 6 = 46 minutes

Longest path involves the hygienist cleaning the teeth, patient should complete in 46 minutes

Check
out

6 min/unit

Check
in

2 min/unit

Develops
X-ray

4 min/unit

8 min/unit

Dentist

Takes
X-ray

2 min/unit

5 min/unit

X-ray
exam

Cleaning

24 min/unit

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Theory of Constraints

Five-step process for recognizing and managing limitations

Step 1: Identify the constraints

Step 2: Develop a plan for overcoming the constraints

Step 3: Focus resources on accomplishing Step 2

Step 4: Reduce the effects of constraints by offloading work or expanding capability

Step 5: Once overcome, go back to Step 1 and find new constraints

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Bottleneck Management

Release work orders to the system at the pace of set by the bottleneck

Drum, Buffer, Rope

Lost time at the bottleneck represents lost time for the whole system

Increasing the capacity of a non-bottleneck station is a mirage

Increasing the capacity of a bottleneck increases the capacity of the whole system

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Break-Even Analysis

Technique for evaluating process and equipment alternatives
Objective is to find the point in dollars and units at which cost equals revenue
Requires estimation of fixed costs, variable costs, and revenue

This chart introduces breakeven analysis and the breakeven or crossover chart. As you discuss the assumptions upon which this techniques is based, it might be a good time to introduce the more general topic of the limitations of and use of models. Certainly one does not know all information with certainty, money does have a time value, and the hypothesized linear relationships hold only within a range of production volumes. What impact does this have on our use of the models?

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Break-Even Analysis

Fixed costs are costs that continue even if no units are produced
Depreciation, taxes, debt, mortgage payments
Variable costs are costs that vary with the volume of units produced
Labor, materials, portion of utilities
Contribution is the difference between selling price and variable cost

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Break-Even Analysis

Revenue function begins at the origin and proceeds upward to the right, increasing by the selling price of each unit
Where the revenue function crosses the total cost line is the break-even point

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Break-Even Analysis

Figure S7.5

Profit corridor

Loss corridor

Total revenue line

Total cost line

Variable cost

Fixed cost

Break-even point

Total cost = Total revenue

–

900 –

800 –

700 –

600 –

500 –

400 –

300 –

200 –

100 –

–

| | | | | | | | | | | |

0 100 200 300 400 500 600 700 800 900 1000 1100

Cost in dollars

Volume (units per period)

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Break-Even Analysis

Costs and revenue are linear functions
Generally not the case in the real world
We actually know these costs
Very difficult to verify
Time value of money is often ignored

Assumptions

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Break-Even Analysis

TR = TC

Px = F + Vx

Break-even point occurs when

BEPx = break-even point in units

BEP$ = break-even point in dollars

P = price per unit (after all discounts)

x = number of units produced

TR = total revenue = Px

F = fixed costs

V = variable cost per unit

TC = total costs = F + Vx

BEPx =

P – V

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Break-Even Analysis

Profit = TR - TC

= Px – (F + Vx)

= Px – F – Vx

= (P - V)x – F

BEPx = break-even point in units

BEP$ = break-even point in dollars

P = price per unit (after all discounts)

x = number of units produced

TR = total revenue = Px

F = fixed costs

V = variable cost per unit

TC = total costs = F + Vx

(P – V)/P

P – V

1 – V/P

BEP$ = BEPx P = P

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Break-Even Example

Fixed costs = $10,000 Material = $.75/unit

Direct labor = $1.50/unit Selling price = $4.00 per unit

1 – (V/P)

$10,000

1 – [(1.50 + .75)/(4.00)]

BEP$ = =

$10,000

.4375

= = $22,857.14

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Break-Even Example

Fixed costs = $10,000 Material = $.75/unit

Direct labor = $1.50/unit Selling price = $4.00 per unit

1 – (V/P)

$10,000

1 – [(1.50 + .75)/(4.00)]

BEP$ = =

$10,000

.4375

= = $22,857.14

P – V

$10,000

4.00 – (1.50 + .75)

BEPx = = = 5,714

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Break-Even Example

50,000 –

40,000 –

30,000 –

20,000 –

10,000 –

–

| | | | | |

0 2,000 4,000 6,000 8,000 10,000

Dollars

Units

Fixed costs

Total costs

Revenue

Break-even point

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Break-Even Example

Multiproduct Case

where V = variable cost per unit

P = price per unit

F = fixed costs

W = percent each product is of total dollar sales
expressed as a decimal

i = each product

Break-even point in dollars (BEP$)

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Multiproduct Example

Fixed costs = $3,000 per month

ITEM	PRICE	COST	ANNUAL FORECASTED SALES UNITS
Sandwich	$5.00	$3.00	9,000
Drink	1.50	.50	9,000
Baked potato	2.00	1.00	7,000

1	2	3	4	5	6	7	8
ITEM (i)	SELLING PRICE (P)	VARIABLE COST (V)	(V/P)	1 - (V/P)	ANNUAL FORECASTED SALES $	% OF SALES	WEIGHTED CONTRIBUTION (COL 5 X COL 7)
Sandwich	$5.00	$3.00	.60	.40	$45,000	.621	.248
Drinks	1.50	0.50	.33	.67	13,500	.186	.125
Baked potato	2.00	1.00	.50	.50	14,000	.193	.097
$72,500	1.000	.470

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Multiproduct Example

Fixed costs = $3,000 per month

ITEM	PRICE	COST	ANNUAL FORECASTED SALES UNITS
Sandwich	$5.00	$3.00	9,000
Drink	1.50	.50	9,000
Baked potato	2.00	1.00	7,000

1	2	3	4	5	6	7	8
ITEM (i)	SELLING PRICE (P)	VARIABLE COST (V)	(V/P)	1 - (V/P)	ANNUAL FORECASTED SALES $	% OF SALES	WEIGHTED CONTRIBUTION (COL 5 X COL 7)
Sandwich	$5.00	$3.00	.60	.40	$45,000	.621	.248
Drinks	1.50	0.50	.33	.67	13,500	.186	.125
Baked potato	2.00	1.00	.50	.50	14,000	.193	.097
$72,500	1.000	.470

= = $76,596

$3,000 x 12

.47

$76,596

312 days

= = $245.50

Daily sales

.621 x $245.50

$5.00

= 30.5  31

Sandwiches

each day

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Reducing Risk with Incremental Changes

Figure S7.6

(a) Leading demand with incremental expansion

Demand

Expected demand

New capacity

Demand

(d) Attempts to have an average capacity with incremental expansion

New capacity

Expected demand

Demand

New capacity

Expected demand

(b) Leading demand with a one-step expansion

Demand

Expected demand

New capacity

This slide probably requires some discussion or explanation. Perhaps the best place to start is the left hand column where capacity either leads or lags demand incrementally. As you continue to explain the options, ask students to suggest advantages or disadvantages of each.

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Reducing Risk with Incremental Changes

(a) Leading demand with incremental expansion

Figure S7.6

Expected demand

New capacity

Demand

Time (years)

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Reducing Risk with Incremental Changes

(b) Leading demand with a one-step expansion

Figure S7.6

Expected demand

New capacity

Demand

Time (years)

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Reducing Risk with Incremental Changes

Figure S7.6

Expected demand

Time (years)

Demand

New capacity

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Reducing Risk with Incremental Changes

(d) Attempts to have an average capacity with incremental expansion

Figure S7.6

Expected demand

New capacity

Demand

Time (years)

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Applying Expected Monetary Value (EMV) and Capacity Decisions

Determine states of nature

Future demand

Market favorability

Assign probability values to states of nature to determine expected value

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EMV Applied to Capacity Decision

Southern Hospital Supplies capacity expansion

EMV (large plant) = (.4)($100,000) + (.6)(–$90,000)

= –$14,000

EMV (medium plant) = (.4)($60,000) + (.6)(–$10,000)

= +$18,000

EMV (small plant) = (.4)($40,000) + (.6)(–$5,000)

= +$13,000

EMV (do nothing) = $0

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Strategy-Driven Investment

Operations managers may have to decide among various financial options
Analyzing capacity alternatives should include capital investment, variable cost, cash flows, and net present value

This slide suggests that the process selection decision should be considered in light of the larger strategic initiative

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Net Present Value (NPV)

where F = future value

P = present value

i = interest rate

N = number of years

F = P(1 + i)N

In general:

Solving for P:

(1 + i)N

P =

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Net Present Value (NPV)

where F = future value

P = present value

i = interest rate

N = number of years

F = P(1 + i)N

In general:

Solving for P:

While this works fine, it is cumbersome for larger values of N

(1 + i)N

P =

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NPV Using Factors

where X = a factor from Table S7.1 defined as = 1/(1 + i)N and F = future value

Portion of Table S7.1

TABLE S7.1	Present Value of $1
YEAR	6%	8%	10%	12%	14%
1	.943	.926	.909	.893	.877
2	.890	.857	.826	.797	.769
3	.840	.794	.751	.712	.675
4	.792	.735	.683	.636	.592
5	.747	.681	.621	.567	.519

(1 + i)N

P = = FX

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Present Value of an Annuity

An annuity is an investment which generates uniform equal payments

S = RX

where X = factor from Table S7.2

S = present value of a series of uniform
annual receipts

R = receipts that are received every year
of the life of the investment

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Present Value of an Annuity

Portion of Table S7.2

TABLE S7.2	Present Value of and Annuity of $1
YEAR	6%	8%	10%	12%	14%
1	.943	.926	.909	.893	.877
2	1.833	1.783	1.736	1.690	1.647
3	2.676	2.577	2.487	2.402	2.322
4	3.465	3.312	3.170	3.037	2.914
5	4.212	3.993	3.791	3.605	3.433

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Present Value of an Annuity

River Road Medical Clinic equipment investment

$7,000 in receipts per for 5 years

Interest rate = 6%

From Table S7.2

X = 4.212

S = RX

S = $7,000(4.212) = $29,484

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Limitations

Investments with the same NPV may have different projected lives and salvage values

Investments with the same NPV may have different cash flows

Assumes we know future interest rates

Payments are not always made at the end of a period

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All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher.

Printed in the United States of America.

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