# Operations Management

```Operations Management
Lecture 2
1
Review of Lecture 1
Inputs
Make/create
Move
Sell
Outputs
Move
2
Review of Lecture 1
3
Review of Lecture 1
High
Innovation
Quality
Improvement
Low
Low
Productivity
High
4
Airline Industry – Continued
“Southwest says that if its
boarding times increased by
10 minutes per flight, it would
need 40 more planes at a cost
of \$40 million each to run the
same number of flights it does
currently.” - textbook
5
Learning Objectives

Process Analysis: Understand the concepts
»
»
»
»
»
»

Flow time
Capacity (rate)
Throughput rate (output rate)
Utilization
Cycle time
Bottlenecks
Toolbox: Process Analysis
– Process mapping
– Capacity analysis (also called bottleneck analysis)
6
Paper Airplane “Factory”
With those seated next to you form a group of 5.
 Manufacture as many planes as you can in 200
seconds. (1 paper at a time)
 At most 2 “Tasks” per group member (includes
bringing papers to group).
 Write down times to preform task.

7
8
Basic Process Measures
Utilization (ρ)
Ratio of time a resource is used relative to the
time it is available (dimensionless quantity).
Examples
Commercial Call Center:
90%
Car Factory Robot: 80%
Emergency Call Center: 30%
9
Basic Process Measures
Capacity (rate)
Dictionary definition: “the maximum amount that something can contain”.
 The amount of output that a system is capable of
achieving over a period of time.
 The maximum possible output or service rate.
Examples
Bank:
Car Factory:
200 customers/day
10,000 cars/month
10
Process Flows:
Single Stage, Single Machine/Server
Input rate
[units/hr]
Output rate
[units/hr]
...
Flow Time [hr]
• Capacity = 1 / FlowTime [units/hr]
 Assuming resources are available (all input except
demand), Only for single stage, single machine/server.
 The maximum possible output rate that can be achieved.
• Output rate = min{Input Rate, Capacity}
 In the long run. Also called the throughput rate.
• Utilization = Throughput Rate / Capacity
= min{Input Rate, Capacity} / Capacity
= min{Input Rate / Capacity, 1}
11
Process Flows:
Single Stage, Single Machine/Server
Input rate
[units/hr]
...
Inventory [units]
... ...
Output rate
[units/hr]
... ...
Flow Time [hr]
12
Example
In SingleTeller bank, it takes the teller 15 minutes
to serve a customer. Every 30 minutes a customer
goes to the teller.
–
–
–
–
What is flow unit?
What is the capacity?
At what rate the process generates output?
What is the utilization of the teller?
13
The physics of process flows

Identify “flow units”: Unit of analysis. Flow through the
process, starting as input and later leaving the process as
output.
– What is my product? e.g. cars, noodle bowls, customers

Identify Rates
– Input rate: Rate at which units are arriving to the system
– Output rate (throughput, flow rate): Rate at which units are
leaving the system
– Capacity: Maximum rate at which units can leave the system

Flow Times (Time spent in process)
– How long does it take me to produce one product?

Stocks (Inventory build-up)
– What parts of the process do units spend more time at? e.g.
parking lot full of finished cars, warehouse full of raw materials,
queue of customers waiting.
14
Basic Process Measures in
Production and Service Operations
Production process
Service process
Flow unit
Materials
Customers
Input rate
Raw material releasing
rate (e.g., iron ore)
Customer arrival rate
Output rate
Finished goods output
rate
Customers departure rate
(service completion rate)
Flow time
Time required to turn
materials into a product
Time that a customer is
being served
Theoretical
Flow Time
Total time a product
spends in different
activities
Total time a customer
spends in different
activities
Inventory
Amount of work-inprocess
Number of customers
being served
Capacity
(rate)
Maximum output rate
Maximum service
completion rate
15
Some Basics

What is the output rate of a process?
– Capacity rate = maximum possible output rate
– Throughput rate = actual output rate

What is the input rate of a process?
– Depends on the process and flow units
– It could be demand rate (e.g., arrivals into a
restaurant, bank, etc.)
– It could be a planned arrival rate (e.g., raw material
arrival into a factory)
16
Some Basics

Is input rate always equal to output rate?

What is the difference between the short-run and
the long-run?

In the short-run:
 What happens if input rate is greater than output rate?
 What happens if input rate is less than output rate?

In the long-run:
 What happens if input rate is greater than output rate?
 What happens if input rate is less than output rate?
17
Short Run Analysis: Funnel Analogy
• In the short run, the input rate
can be larger than the capacity
rate for a period of time
 A properly sized buffer is needed
to store units waiting to be
processed (build-up inventory)
Buffer
18
Long Run Analysis
• In the long run, the input rate
must be no larger than the
capacity rate
What goes in the
process, must come out
of the process.
Input rate must be less
than or equal to the
output rate;
Otherwise the system
will overflow.
19
Key Steps in Process Analysis
Step 1: Determine the Purpose of the analysis
Step 2: Process mapping (Define the process)
•
•
•
•
•
•
Determine the flow units
Determine the time for each task
Determine which resources are used in each task
Determine where inventory is kept in the process
Record this through a process flow diagram
(Linear flow chart, Swim-lane (deployment) flow chart, Gantt chart)
Step 3: Capacity Analysis (also called Bottleneck Analysis)
• Determine the capacity of each resource, and of the process
Further analysis will be covered later during the course
20
Process Flow Diagram Elements
Buffers: Queues or inventories
Decision points
Flow of materials
Raw
Material
Making
Finished
Packing
Packed
Note: If different types of breads, the bread-making and packing activities may differ for each
21
Tim Horton's / Burger King 
Suppose we order a Hot Breakfast Sandwich (490
Cal, 31g Fat):
 Purpose of the analysis:
– To determine the capacity (rate) of the Tim Horton’s

Given this purpose, the process map does
not need to consider the following:
– Queued customers (i.e., customers in line)
– The baked meat cooking processes (we assume
cooked meat is always available when needed during
the make-to-order process).
22
Hot Breakfast Sandwich Steps
Recall from process mapping:
– Determine the flow units
– Determine the tasks (subprocesses), and the
– Determine the time for
– Determine which resources
– Determine where inventory
is kept in the process
– Record this through a
process flow diagram
» Linear flow chart
» Swim-lane (deployment)
flowchart
» Gantt chart
We observed the following steps:
1. Cashiers takes the order
(8s)
2. Worker1 toasts buns (it
takes the toaster 10s)
(8s)
patties (6s)
5. Worker4 wraps it (2s)
6. Worker5 delivers (2s).
23
Linear Flow Chart
• Flow unit: An order (each order = one burger)
• Flow time of each task
Place an
order
8s
Toast
buns
10s
dressings
8s
patties
Package
6s
2s
Deliver
2s
• Determine which resources are used in each task
• Could indicate resources along each task
• Swim-lane diagram or Gantt chart may be better
24
Swim-Lane (Deployment) Flowchart
RESOURCES
Cashier
Worker1
Toaster
Worker 2
Worker 3
Worker 4
Worker 5
ACTIVITIES
Place an
order
Toast
buns
dressings
patties
Package
Deliver
25
Swim-Lane Flowchart: Modified
RESOURCES
Cashier
Worker1
Toaster
Worker 2
ACTIVITIES
Place an
order
Toast
buns
dressings
patties
Package
Worker 3
Worker 4
Worker 5
Deliver
26
Gantt Chart
RESOURCES
ACTIVITIES
Cashier
Place an order
Worker1
Toaster
Toast buns
Worker 2
Worker 3
patties
Worker 4
Package
Worker 5
Deliver
Time Span
8s
10s
8s
6s
2s
2s
Time
Process Mapping: Some Notes
• There is no one way to draw a process map
• Get feedback from all the people involved in the
process to validate the process map
– Do not map the process as you think it works
– Map it as it actually works
• Process maps are surprisingly informative
– Common response: “I never knew we did it that way!”
• Starting point for process analysis, and a great
tool for brainstorming process improvements
28
Basic Process Analysis
Single Stage Process
Toast buns
Toaster
Worker 1
Flow Time
(Time that buns spend in the toaster)
10 sec
Capacity Rate
6 orders/min,???
or 360 orders/hr
29
Basic Process Analysis
Multiple Stage Process
Place an
order
Toast
buns
dressings
patties
Package
Deliver
Cashier
Worker 1
Toaster
Worker 2
Worker 3
Worker 4
Worker 5
8 sec
10 sec
8 sec
6 sec
2 sec
2 sec
450/hr
360/hr
450/hr
600/hr
1800/hr
1800/hr
Theoretical
ofwhole
the whole
process:
FlowFlow
TimeTime
of the
process:
??? 36 sec
Note: The theoretical
flow time ignores the
possibility of waiting;
so it is the lowest
possible flow time
Capacity
rate of
theofwhole
process:
360 orders/hr
Capacity
rate
the whole
process:
???
30
Beyond Basics
Resource
(sec/unit)
Capacity Rate
(unit/min)
Capacity rate
(unit/hr)
Cashier
8
7.5
450
Toaster
10
6
360
Worker 1
10
6
360
Worker 2
8
7.5
450
Worker 3
6
10
600
Worker 4
2
30
1800
Worker 5
2
30
1800
Unit Load: Total amount of time the resource works to process each flow unit
31
What information do unit loads give us?
is organized
for Each
Resource
for Each
Resource
Labor Skills
Low
High
Equipment
Specialization
High
Low
Process Type
Flow Shop
Job Shop
32
Gantt Chart: Multiple Stage Process
RESOURCES
ACTIVITIES
Cashier
Place an order
Worker1
Toaster
Toast buns
Worker 2
Worker 3
patties
Worker 4
Package
Worker 5
Deliver
Time Span
8s
8s
10s
10s
8s
8s
6s
6s
2s
2s
2s
Time
2s
The Bottleneck
• The resource with the lowest capacity rate
– The “slowest” resource (or the resource with the
– Unit load: Total amount of time the resource works to
process each flow unit
• Determines the capacity rate of the entire
process
• Increasing the capacity of non-bottleneck
resources does not increase the capacity rate of
the process
34
Pipes with Different Capacities
35
Increasing the capacity rate of a process
What if we add a cashier?
Place an
order
Place an
order
Toast
buns
dressings
patties
Package
Deliver
Cashiers
Worker 1
Toaster
Worker 2
Worker 3
Worker 4
Worker 5
8 sec
10 sec
8 sec
6 sec
2 sec
2 sec
900/hr
(2 * 450/hr)
360/hr
450/hr
600/hr
1800/hr
1800/hr
Theoretical
Flow
Time
sec
Theoretical
Flow
Timeofofthe
thewhole
wholeprocess:
process:36
???
Capacity
rate of
theofwhole
process:
360 orders/hr
Capacity
rate
the whole
process:
???
36
Increasing the capacity rate of a process
What if we add a toaster?
Place an
order
Toast buns
Toast buns
dressings
patties
Package
Deliver
Cashier
Worker 1
Toasters
Worker 2
Worker 3
Worker 4
Worker 5
8 sec
10 sec
8 sec
6 sec
2 sec
2 sec
450/hr
720/hr
(2 * 360/hr)
450/hr
600/hr
1800/hr
1800/hr
Theoretical
Time
sec
TheoreticalFlow
Flow
Timeofofthe
thewhole
wholeprocess:
process:36
???
Capacity
rate of
theofwhole
process:
450 orders/hr
Capacity
rate
the whole
process:
???
37
Cycle Time
Cycle time is the time between completed units
 Flow time is the time to complete each unit
 For a multi-stage process, the cycle time and the
flow time are not the same


Cycle time=1/(capacity rate)
38
Gantt Chart (Visualize Cycle Time)
Resources Activities
Cashier
Place order
Time Span
8s
Worker 1 Toast buns
Worker 4 Package
8s
10s
8s
10s
10s
8s
8s
8s
6s
6s
2s
Worker 5 Deliver
2s
6s
2s
2s
10s 2s
10s 2s
Time
39
RESOURCES
ACTIVITIES
Cashier
Place an order
Worker1
Toaster 1
Toast buns
Worker1
Toaster 2
Toast buns
Worker 2
Worker 3
patties
Worker 4
Package
Worker 5
Deliver
Time Span
8s
8s
10s
10s
8s
Worker 1 is not busy all
the time, and can take
care of 2 toasters
8s
6s
6s
2s
2s
2s
Time
8s 2s
Main Insights

To increase the capacity rate of the entire system,
increase the capacity of the bottleneck process.

The bottleneck may change when capacity is added (i.e.,
a new bottleneck process may now appear).
– Important when we are justifying additional capacity

Questions
– What does increasing the capacity of the bottleneck process do
to the utilization of the bottleneck station?
» Flow time? Cycle time?
– If we double the bottleneck capacity, does the capacity of the
entire system also double?
41
What if we further add one cashier and
relocate one worker?
Cashier 2
Place an
order
Place an
order
Cashier 1
8s
Toaster 2
Toast
buns
Toast
buns
Toaster 1
Worker 1
10s
900/hr
720/hr
2 x 450/hr
2 x 360/hr
Worker 4
dressings
dressings
patties
Worker 2
8s
900/hr
Package
and deliver
Worker 3
6s
600/hr
Worker 5
4s
900/hr
2 x 450/hr
Flow time of the whole process: _________ sec
Which task is the bottleneck? __________________________
Capacity rate of the entire process: ________ orders / hr
Cycle time of the entire process: ________ seconds/ order
42
Adding one cashier and relocating one
worker: Gantt chart
Resources Activities
Cashier 1
Place an order
Cashier 2
Place an order
Time Span
8s
Wkr 1,Toaster 1 Toast buns
Wkr 1,Toaster 2 Toast buns
Worker 2
Worker 4
Worker 3
Worker 5
Package and Deliver
We assume worker 1
is not busy all the
time and can take
care of two toasters.
8s
10s
10s
8s
8s
6s
6s
2s 2s 2s 2s
6s
Time
43
Another Example
Place an
order
Toast
buns
dressings
patties
Package
Deliver
Cashier
Worker 1
Toaster
Worker 2
Worker 3
Worker 3
Worker 3
8 sec
10 sec
8 sec
6 sec
2 sec
2 sec
Theoretical Flow Time of the whole process: 36 sec
Note: The theoretical
flow time ignores the
possibility of waiting;
so it is the lowest
possible flow time
Capacity
rate of
theofwhole
process:
360 orders/hr
Capacity
rate
the whole
process:
???
44
Thinking in terms of “Unit Loads”
Resource
(sec/unit)
Capacity Rate
(unit/min)
Capacity rate
(unit/hr)
Cashier
8
7.5
450
Toaster
10
6
360
Worker 1
10
6
360
Worker 2
8
7.5
450
Worker 3
10
6
360
Unit Load: Total amount of time the resource works to process each flow unit
45
Increasing Capacity (1)
Increase the Size of the “Resource Pool”
• One Toaster
Capacity rate: 360/hr
• Two Toasters
Working in Parallel
Capacity rate: 720/hr
10 sec
Toast buns
Toast buns
10 sec
Toast buns
10 sec
46
Increasing Capacity (2)
• This Toaster
Capacity rate: 360/hr
• Faster Toaster
Works twice as fast
Capacity rate: 720/hr
Toast buns
Toast buns
10 sec
5 sec
47
Increasing the Capacity Rate of a Process
• Increase the capacity rate of the bottleneck
• Some other resources may become a
– Important when we justify additional capacity
48
Increasing the capacity rate of a process
Expand the resource pool at the bottleneck
Place an
order
Toast buns
Toast buns
dressings
patties
Package
Deliver
Cashier
Worker 1
Toasters
Worker 2
Worker 3
Worker 4
Worker 5
8 sec
10 sec
8 sec
6 sec
2 sec
2 sec
450/hr
720/hr
(2 * 360/hr)
450/hr
600/hr
1800/hr
1800/hr
Theoretical Flow Time of the whole process: 36 sec
Capacity rate of the whole process: 450 orders/hr
49
Increasing the capacity rate of a process
Reduce Unit Load at the Bottleneck
Place an
order
Toast
buns
dressings
patties
Package
Cashier
Worker 1
Toaster
Worker 2
Worker 3
Worker 4
Worker 5
Old Flow
Time
8 sec
10 sec
8 sec
6 sec
2 sec
2 sec
Old Capacity
Rate
450/hr
360/hr
450/hr
600/hr
1800/hr
1800/hr
New Flow
Time
8 sec
5 sec
8 sec
6 sec
2 sec
2 sec
New
Capacity
Rate
450/hr
720/hr
450/hr
600/hr
1800/hr
1800/hr
Theoretical Flow Time : ???
Deliver
Capacity rate of the process: ???
50
Any operational benefit of reducing unit
Place an
order
Toast
buns
dressings
patties
Package
Cashier
Worker 1
Toaster
Worker 2
Worker 3
Worker 4
Worker 5
Old Flow
Time
8 sec
10 sec
8 sec
6 sec
2 sec
2 sec
Old Capacity
Rate
450/hr
360/hr
450/hr
600/hr
1800/hr
1800/hr
New Flow
Time
4 sec
10 sec
6 sec
4 sec
1 sec
1 sec
New
Capacity
Rate
900/hr
360/hr
600/hr
900/hr
3600/hr
3600/hr
Theoretical Flow Time : ???
Deliver
Capacity rate of the process: ???
51
Processes may be unbalanced
Place an Order
Toast buns
Flow Time
8 sec
10 sec
Capacity Rate
450/hour
360/hour
Process is “Blocked”
• When the next stage is busy, the order cannot be
sent to the next stage after finishing the current
stage, unless an inventory buffer is introduced
52
Another example
Flow Time
8 sec
6 sec
Capacity Rate
450/hour
600/hour
Process is “starved”
53
Bottleneck Characteristics
• The bottleneck is fully utilized while other
resources are not utilized
• If a buffer is provided at some upstream stage to
the bottleneck, inventory may build up at the
buffer
• Inventory will not build up at the (immediately)
downstream stages to the bottleneck even if
buffers are provided
• Shortening non-bottleneck tasks decreases flow
time but does not affect capacity rate
– Reducing flow time improves response time
54
Process Analysis: Multiple Flow Units
Resource
Product A
Product B
Product C
1
2.5
2.5
2.5
2
1.5
2
2.5
3
12
0
0
4
0
3
3
5
3
3
3
• If you produce only Product A, what is capacity rate of the
process (per hour)? Which resource is the bottleneck?
• If your product mix is 1 unit of A, 2 units of B and 2 units of
C, what is your capacity rate? Bottleneck?
55
Process Analysis: Multiple Flow Units
Resource
Product A
Product B
Product C 1A+2B+2C
1
2.5
2.5
2.5
12.5
2
1.5
2
2.5
10.5
3
12
0
0
12
4
0
3
3
12
5
3
3
3
15
• When multiple flow units go through a process,
the “product mix” needs to be considered while
determining the unit load and the capacity
• The bottleneck depends on the product mix
56
Process Analysis: Multiple Flow Units
• Flow diagrams are not easy to draw
• How to identify bottleneck?
– Count the total amount of work per resource (also
• When multiple flow units go through a process, a
“product mix” needs to be considered while
determining capacity
• The bottleneck depends on the product mix
• The bottlenecks can move as the product mix
changes
57
Theoretical versus Effective Capacity
• Some capacity is lost due to machine maintenance,
machine set-ups, etc.
• Example. Changing over from one product type to
another may require adjustments to the machine,
tools, etc (“set-ups”)
58
Try to do it for yourself again at home

Consider four consecutive stages A, B, C, and D with the following
capacity rates: 12 units/hr, 15 units/hr, 11 units/hr, and 14 units/hr,
respectively. Assume that the demand on the system is 13 units/hr
(Short run).
– Where you would add buffers to the system (minimum number of buffer)?
– What if stage C had a variable capacity rate of 13+-1 units/hr, instead of the
original given 11 units/hr. Would you add or remove any buffer from the system
compared to the previous part of the question.
61
Summary: Process terminology

Capacity rate
– The maximum rate at which units can flow through a process

Bottleneck Process
– The resource with the lowest capacity rate in a process
– It determines the capacity rate of the entire system

Flow Time or Throughput Time
– The length of time a unit spends in the system

Cycle time
– The Inverse of the capacity rate (i.e., the average time between
completion of successive units)
Confusingly, in practice many firms use the terms flow time and cycle
time interchangeably: always clarify what is being referred to!
62
Summary: Capacity Analysis

The bottleneck is fully utilized (ρ=1) while other resources
are not fully utilized (ρ≤1).

To increase the capacity rate of the system, focus on
increasing the capacity of the bottleneck process.

The bottleneck can change when capacity is added to it
– important when we are justifying additional capacity.

Shortening non-bottleneck tasks decreases flow time
– This improves response time (which is still important), but it does
not affect capacity rate of the process.
63

Interesting Articles:
– Deep Change: How operational innovation can
transform your company, by Michael Hammer, Harvard
– BPMS Watch: Analyzing and Optimizing Process
Performance
(http://www.bpminstitute.org/articles/article/article/bpmswatch-analyzing-and-optimizing-processperformance.html)
– Shining examples, The Economist, June 17, 2006.
– One Word: Logistics: The unheralded key to the New
Economy, By Daniel Gross, Slate, Jan. 20, 2006.
(http://www.slate.com/id/2134513/)
64

– Take a good look at the Quercus site for the course.

Next Class: Forecasting
65
Self-Test: Question 1

What is the difference between (a) and (b)?
(a) Two parallel 10-sec toasters:
10 s
Toast
Toast
10 s
(b) One faster 5-sec toaster:
Toast
5s
66
Self-Test Question 2

What if both Worker 1(toast buns) and worker
3(add meat patties) need to share the toaster
(one toaster is available and toasting buns takes
10 seconds on toaster and toasting patties takes
6 seconds)?
67
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