Chapter 3: Strategic Capacity Management
We will discuss …What is capacity?The concept of process capacityCapacity utilizationEconomies and diseconomies of scaleCapacity balanceLittle's law
Relating inventory, flow time, and flow rateBatch sizes and capacityDecision Trees
Strategic Capacity Planning
Capacitythe ability to hold, receive, store, or
accommodate.measures can (as opposed to does)
Strategic capacity planningapproach for determining the overall capacity
level of capital intensive resources, including facilities, equipment, and overall labor force size.Examples??
Two Ways to Improve a Process
Reduce excess capacity at some step in the processLower the cost for the same output
Use the capacity at an underutilized process step to increase the capacity at a bottleneckIncrease the output at the same cost
A bottleneck is the weakest linkProcess capacity = minimum {Res 1 capacity,. Res 2 capacity, …)
Capacity Utilization
Capacity used rate of output actually achieved
Best operating level capacity for which the process was designed
Capacity utilization rate = Capacity used / Best operating level
UnderutilizationBest OperatingLevel
Avgunit costof output
Volume
Overutilization
Example of Capacity Utilization
During one week of production, a plant produced 83 units of a product. Its historic highest or best utilization recorded was 120 units per week. What is this plant’s capacity utilization rate?
Answer: Capacity utilization rate = Capacity used
. Best operating
level = 83/120 =0.69 or 69%
Economies & Diseconomies of Scale
100-unitplant
200-unitplant 300-unit
plant400-unit
plant
Volume
Averageunit costof output
Economies of Scale and the Experience Curve working
Diseconomies of Scale start working
Other IssuesCapacity FocusThe concept of the
focused factory holds that production facilities work best when they focus on a fairly limited set of production objectives Plants Within Plants (PWP) Extend focus concept
to operating level
Capacity FlexibilityFlexible processesFlexible workers Flexible plants
Capacity Planning: Balance
Stage 1 Stage 2 Stage 3Unitsper
month
6,000 7,000 5,000
Unbalanced stages of production
Stage 1 Stage 2 Stage 3Unitsper
month
6,000 6,000 6,000
Balanced stages of production
Maintaining System Balance: Output of one stage is the exact input requirements for the next stage
What it is: Inventory (I) = Flow Rate (R) * Flow Time (T)
Implications:• Out of the three performance measures (I,R,T), two can be chosen by management, the other is GIVEN by nature• Hold throughput (flow rate) constant: Reducing inventory = reducing flow time
Little’s Law
7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00
11
10
9
8
7
6
5
4
3
2
1
0
Flow Time
Inventory
Inventory=Cumulative Inflow – Cumulative Outflow
Cumulative Inflow
Cumulative Outflow
Time
Patients
Can be used in analyzing capacity issues!
Examples Suppose that from 12 to 1 p.m.
200 students per hour enter the GQ and each student is in the system for an average of 45 minutes. What is the average number of students in the GQ? Inventory = Flow Rate * Flow Time = 200 per hour * 45 minutes (=
0.75 hours) = 150 students
If ten students on average are waiting in line for sandwiches and each is in line for five minutes, on average, how many students are arrive each hour for sandwiches? Flow Rate = Inventory / Flow Time
= 10 Students / 5 minutes = 0.083 hour
= 120 students per hour
Airline check-in data indicate from 9 to 10 a.m. 255 passengers checked in. Moreover, based on the number waiting in line, airport management found that on average, 35 people were waiting to check in. How long did the average passenger have to wait?
Flow Time = Inventory / Flow Rate = 35 passengers / 255 passengers per hour = 0.137 hours
= 8.24 minutes
Batch of 12
Batch of 60
Batch of 120
Batch of 300
Time [minutes]60 120 180 240 300
Set-up from Part A to Part B
Set-up from Part B to Part A
Produce Part A (1 box corresponds to 24 units = 12 scooters)
Produce Part B (1 box corresponds to 12 units = 12 scooters)
Production cycle
Production cycle
The Impact of Batch Size on Capacity
Number Produced in 720 MinBatch Size Part A Part B
12 60 6060 180 180
120 240 240300 300 300
• Capacity calculation:
• Note: Capacity increases with batch size:
• Note further: … and so does inventory
Batch SizeSet-up time + Batch-size*Time per unit
Capacity given Batch Size=(in units/time)
Capacity 1/p
00.050.1
0.150.2
0.250.3
0.350.4
0.450.5
10 50 90 130
170
210
250
290
330
370
410
450
490
530
570
610
650 Batch Size
Capacity Analysis with Batching
Data about set-up times and batching
Set-up time, S
Process 1 Assembly process
120 minutes -
Per unit time, p 2 minutes/unit 3 minutes/unit
Capacity (B=12) 0.0833 units/min 0.33 units/minuteCapacity (B=300) 0.4166 units/min 0.33 units/minute
Batch size = 12 Batch size = 300Setup 120 0 120 0Batch size 12 12 300 300Per unit 2 3 2 3Capacity (per min) 0.083 0.333 0.417 0.333Capacity (per hour) 5 20 25 20Process Capacity (per hour) 5 20
Figure : Choosing a “good” batch size
Batch size is too small, process capacity could be increased (set-up step is at the bottleneck)
Batch size is too large, could be reduced with no negative impact on process capacity (set-up is not at the bottleneck)
Capacity
1/p
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
10 50 90 130
170
210
250
290
330
370
410
450
490
530
570
610
650 Batch Size
Capacity of sloweststep other than the onerequiring set-up
B/[S+B*p] = k implies that B = S*k / (1 – p*k)
Problem
Part a: What is the capacity for a batch size = 50?
Part b: For a batch size of 10, what is the bottleneck
STEP 1 STEP 2 STEP 3Act Time in min/part 1 2 1.5Setup Time in min 20 0 0
part b
Batch is: 10Capacity of Resource (parts/min) 0.333 0.500 0.667
Step 1 is bottleneck
part aBatch is: 50
Capacity of Resource (parts/min) 0.714 0.500 0.667parts/hour 42.9 30.0 40.0(minutes/part) 1.4 2 1.5
Capacity is 0.5 parts/min or 30 parts/hour
What batch size should be chosen to smooth the flow?
Process Utilization and Capacity Utilization Process Utilization = Flow Rate / Process Capacity
Example: Tom can process 100 forms per day and he actually processes 70 forms.
Process utilization = ?? Utilization of resource = Flow rate / Capacity of
resource Process 400 items per hour Capacities of resources (items/hour):
Resource 1: 500 implies utilization of 80% Resource 2: 450 implies utilization of 89% Resource 3: 600 implies utilization of 67%
Bottleneck is the resource with the lowest capacity and the highest utilization
Bottleneck is ??
Decision Trees Used to structure
complex decision problems
Use expected return criteria
Consider probabilities of occurrence of events
Use: chance nodes (denoted by
circles ) decision (or choice) nodes
(denoted by squares) Use a concept of “folding
back” to arrive at the best policy
Example of a Decision Tree Problem
A glass factory specializing in crystal is experiencing a substantial backlog, and the firm's management is considering three courses of action:
A) Arrange for subcontractingB) Construct new facilitiesC) Do nothing (no change)
The correct choice depends largely upon demand, which may be low, medium, or high. By consensus, management estimates the respective demand probabilities as 0.1, 0.5, and 0.4.
Example of a Decision Tree Problem (Continued): The Payoff Table
The management also estimates the profits when choosing from the three alternatives (A, B, and C) under the differing probable levels of demand. These profits, in thousands of dollars are presented in the table below:
0.1 0.5 0.4Low Medium High
A 10 50 90B -120 25 200C 20 40 60
Example of a Decision Tree Problem (Continued): Step 1. We start by drawing
the three decisions
AB
C
Example of Decision Tree Problem (Continued): Step 2. Add our possible states of nature, probabilities, and
payoffs
AB
C
High demand (0.4)Medium demand (0.5)Low demand (0.1)
$90k$50k$10k
High demand (0.4)Medium demand (0.5)Low demand (0.1)
$200k$25k
-$120k
High demand (0.4)Medium demand (0.5)Low demand (0.1)
$60k$40k$20k
Example of Decision Tree Problem (Continued): Step 3. Determine the
expected value of each decision
High demand (0.4)
Medium demand (0.5)
Low demand (0.1)
A
$90k$50k$10k
EVA=0.4(90)+0.5(50)+0.1(10)=$62k
$62k
Example of Decision Tree Problem (Continued): Step 4. Make decision
High demand (0.4)Medium demand (0.5)Low demand (0.1)
High demand (0.4)Medium demand (0.5)Low demand (0.1)
AB
CHigh demand (0.4)Medium demand (0.5)Low demand (0.1)
$90k$50k$10k
$200k$25k
-$120k
$60k$40k$20k
$62k
$80.5k
$46k
Alternative B generates the greatest expected profit, so our choice is B or to construct a new facility
Problem 2 Owner of a small firm
wants to purchase a PC for billing, payroll, client records
Need small systems now -- larger maybe later
Alternatives:Small: No expansion
capabilities @ $4000Small: expansion
@6000Larger system @ $9000
After 3 years small systems canbe traded in for a
larger one @ $7500Expanded @ $4000Future demand is
Likelihood of needing larger system later is 0.80
What system should he buy?
Problem 2L: .8 9,000
9,000 S: .2 9,000
10,000 Large 10,000 Exp
Need large Trade-in 13,500 9,000 Exp L: .8
S: .2 6,000 9,200
Small 11,500 Trade-in 11,500
Need largeL: .8S: .2 4,000
10,000