Introduction to operations and supply chain management 3e bozarth chapter 06

 Apply a wide variety of analytical tools to capacity decisions, including expected value and break-even analysis, decision trees, learning curves, the Theory of Constraints, waiting li

Managing Capacity

Chapter 6

Chapter Objectives

Be able to:

 Explain what capacity is, how firms measure capacity, and the difference between theoretical and rated capacity

 Describe the pros and cons associated with three different

capacity strategies: lead, lag, and match

 Apply a wide variety of analytical tools to capacity decisions, including expected value and break-even analysis, decision trees, learning curves, the Theory of Constraints, waiting line theory, and Little’s Law.

 Capacity – The capability of a worker, a

machine, a workcenter, a plant, or an

organization to produce output in a time period.

 Capacity decisions –

 How is it measured?

 Which factors affect capacity?

 The impact of the supply chain on the organization’s effective capacity.

© 2010 APICS Dictionary

Measures of Capacity

 Theoretical capacity – The maximum output capability, allowing for no adjustments for preventive maintenance, unplanned

downtime, or the like.

 Rated capacity – The long-term, expected

output capability of a resource or system.

© 2010 APICS Dictionary

Examples of Capacity

Table 6.1

Indifference Point Examples

Capacity for a PC Assembly Plant

(800 units per line per shift)×(# of lines)×(# of shifts) Controllable Factors Uncontrollable Factors

1 or 2 shifts?

2 or 3 lines? Employee

training?

Supplier problems? 98% or 100% good? Late or on time?

Three Common Capacity Strategies

capacity is added in anticipation of demand.

capacity is added only after demand has

materialized.

strikes a balance between the lead and lag capacity strategies by avoiding period of high under or

overutilization.

Comparing Strategies

Figure 6.1

Evaluating Capacity Alternatives

Cost Comparison

TC = FC + VC * X

TC = Total Cost

FC = Fixed Cost

VC = Variable cost per unit of business activity

X = amount of business activity

Cost Comparison - Example 6.1

Figure 6.2

Table 6.2

Cost Comparison - Example 6.1

Total cost of common carrier option = Total cost of contract carrier option

Find the indifference point – the output level at which

the two alternatives generate equal costs

Expected Value

 Expected value – A calculation that

summarizes the expected costs, revenues, or profits of a capacity alternative, based on

several demand levels with different

probabilities.

Expected Value – Example 6.2

Expected Value – Example 6.2

C(low demand) = $5,000 + $300(30) = $14,000 C(medium demand) = $5,000 + $300(50) = $20,000 C(high demand) = $5,000 + $300(80) = $29,000

Decision Trees

use to evaluate capacity decisions to enable users to see the interrelationships between decisions and

possible outcomes.

Decision Tree Rules

decision point or an outcome point and develop

branches from there.

results for each of the smaller branches and move backward by calculating weighted averages for the branches based on their probabilities.

Decision Trees – Example 6.3

Original Expected

Value Example

Figure 6.4

Break-Even Analysis

 Break-even point – The volume level for a business at which total revenues cover total costs.

Where:

BEP = break-even point

FC = fixed costs

VC = variable cost per unit of business activity

R = revenue per unit of business activity

Break-Even Analysis – Example 6.4

Suppose the firm makes $1,000 profit on each shipment before transportation costs are considered What is the

break-even point for each shipping option?

Contracting: BEP = $5,000 / $700 = 7.1 or 8 shipments

Common: BEP = $0 / $250 = 0 shipments Leasing: BEP = $21,000 / $950 = 22.1 or 23 shipments

Learning Curves

 Learning curve theory – A theory that

suggests that productivity levels can improve

at a predictable rate as people and even

systems “learn” to do tasks more efficiently.

For every doubling of cumulative output, there

is a set percentage reduction in the amount

of inputs required

Learning Curves

Learning Curve – Example 6.5

What is the learning percentage?

4/5 = 80% or 80

Learning Curve – Example 6.5

How long will it take to answer the 25 th call?

Figure 6.6

Other Capacity Considerations

 The strategic importance of an activity to a firm.

 The desired degree of managerial control.

 The need for flexibility.

The Theory of Constraints

and managing capacity which recognizes that nearly all products and services are created through a

series of linked processes, and in every case, there

is at least one process step that limits throughput for the entire chain.

Figure 6.7

The Theory of Constraints

 Identify the constraint

 Exploit the constraint

 Keep it busy!

 Subordinate everything to the constraint

 Make supporting it the overall priority

 Elevate the constraint

 Try to increase its capacity — more hours, screen out defective parts from previous step.

 Find the new constraint and repeat

 As one step is removed as a constraint, a new one will emerge

Theory of Constraints – Example 6.6

Where is the Bottleneck? Cut and Style

Table 6.5

Theory of Constraints – Example 6.6

Current

Process

Figure 6.9

Theory of Constraints – Example 6.6

Adding a

Second Stylist

Figure 6.10

Theory of Constraints – Example 6.6

Waiting Line Theory

 Waiting Line Theory – A theory that helps

managers evaluate the relationship between capacity decisions and important

performance issues such as waiting times and line lengths.

Figure 6.12

Waiting Line Theory

 Waiting Line Concerns:

 What percentage of the time will the server be busy?

 On average, how long will a customer have to wait in line? How long will the customer be in the system?

 On average, how may customers will be in line?

 How will those averages be affected by the arrival rate of customers and the service rate of the workers?

Waiting Lines – Example 6.7

The probability of arrivals in a time period =

Example: Customers arrive at a drive-up window at a rate of 3

per minute If the number of arrivals follows a Poisson distribution, what is the probability that two or fewer

customers would arrive in a minute?

P(< 2) = P(0) + P(1) + P(2) = 050 + 149 + 224 = 423 or 42.3%

Waiting Lines – Example 6.7

The average utilization of the system:

Example: Suppose that customers arrive at a rate of four per minute and that the worker at the window is able to handle on

average 5 customers per minute The average utilization of the

system is:

Waiting Lines – Example 6.8

The average number of customers waiting in the system (CW) =

The average number of customers in the system (CS) =

Example: Given an arrival rate of four customers per minute

and a service rate of five customers per minute:

Average number of customers waiting:

Average number in the system:

Waiting Lines – Example 6.9

The average time spent waiting (TW) =

The average time spent in the system (TS) =

Example: Given an arrival rate of four customers per minute

and a service rate of five customers per minute:

Average time spent waiting:

Average time spent in the system:

Little’s Law

Little’s Law is a law that holds for any system

that has reached a steady state that enables us

to understand the relationship between

inventory, arrival time, and throughput time.

I = RT

Little’s Law - Example 6.11

Figure 6.14

Little’s Law - Example 6.11

Average Throughput Time =

T = I/R = (25 orders) / (100 orders per day)

= 25 days in order processing

Average time an order spends in workcenter A =

T = I/R = (14 orders)/(70 orders per day)

= 2 days in workcenter A

Amount of time the average A order spends in the plant =

Order processing time + workcenter A time

= 25 days + 2 days = 45 days

Amount of time the average B order spends in the plant =

Order processing time + workcenter B time

= 25 days + 05 days = 30 days

Little’s Law - Example 6.11

Average time an order spends in the plant =

70% x 45 days + 30% *.30 days

= 405 days

Estimate average throughout time for the entire system =

T = I/R = (40.5 orders)/(100 orders per day)

= 405 days for the average order

Managing Capacity

Case Study

Forster’s Market

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