UIC
BUSINESS
Process Analysis and Little’s
Law
IDS 532
Instructor: Selva Nadarajah
Discussion Plan
•
•
•
•
•
UIC
BUSINESS
Process analysis notation
Guidelines to analyze a process (in-class exercises)
Little’s law
Measures of utilization
Retail and supply chain performance measures related to Little’s law
(Text book chapters: 2 & 3)
Selva Nadarajah
2
UIC
BUSINESS
Process View of an Organization
• A process is a set of activities that accepts inputs and produces outputs.
Inputs
Transformation
Process
Raw material,
Customers
Outputs
Goods,
Services
Resources
Labor & Capital
• Why can’t business processes transform inputs into outputs instantaneously?
• What stops these processes from creating more supply?
Selva Nadarajah
3
UIC
BUSINESS
Examples of Processes
• Call center
Automated
routing
Agent
Wait
• Iron production
Ore
Preheater
First
Iron smelter
reactor
………
Briquetting
Goods
• In general, a process can have multiple inputs and outputs.
Selva Nadarajah
4
UIC
BUSINESS
Basic Performance Metrics
Input rate
[units/hr]
Inventory [units]
Flow rate
[units/hr]
Flow Time [hrs]
• Capacity is defined as the maximum possible flow rate.
• Cycle time (= 1/flow rate) is the average time between completion of successive units.
**This animation is a graphical illustration but not a process flow diagram
Selva Nadarajah
5
UIC
BUSINESS
Fundamentals of Process Flow Notation
Activity/Task
Buffer
Flow
Typically not represented graphically
Resource
**When an activity has a single resource, the term activity and resource are used interchangeably
Selva Nadarajah
6
UIC
BUSINESS
Diploma Production Process
• In a fictitious business school named OM, diploma production involves three main steps
 Stamp “OM MBA” on diploma
 Verify and stamp name
 Punch a hole to insert the diploma in a fancy folder
• What is the flow unit in this process? diplomas
• What is the process flow diagram?
OM MBA
Selva Nadarajah
Name
Hole Punch
7
UIC
BUSINESS
Diploma Production
OM MBA
Processing rate
(dipl/min)
12
Name
7.5
Hole Punch
??
24
• How much time does “OM MBA” take to process a diploma? 1/12 mins/dipl. = 5 sec/dipl.
• In which buffer is there an inventory build up? The one between “OM MBA” and “Name”
• What is the rate at which inventory builds up in this process? 4.5 dipl/min
• Is this imbalance sustainable?
Perhaps for diploma production but not possible for a long time
Selva Nadarajah
8
UIC
BUSINESS
Diploma Production
OM MBA
Name
Hole Punch
Processing rate
(dipl/min)
12
??
7.5
?? 24
Processing Time
(sec/dipl)
5
8
2.5
• Can you guess how to compute the capacity of the entire process?
Minimum of activity capacities: 7.5 dipl/min
Selva Nadarajah
9
UIC
BUSINESS
Bottleneck and Process Capacity
Bottleneck
Bottleneck is the activity with
the smallest capacity, that is,
this activity determines the
process capacity
Selva Nadarajah
10
UIC
BUSINESS
Process Flow Rate
Bottleneck
Input
Capacity constrained
Is the process capacity always
equal to the process flow rate?
No, because the process
may be constrained by
demand
Bottleneck
Input
Demand constrained
Selva Nadarajah
11
Analyzing Processes: Guidelines
UIC
BUSINESS
1. Setup
 Select process scope (define the cycle)
 Define flow unit
 Draw process flow diagram
2. Rule #1: Break process down to individual activities
3. Rule #2: Work with repetitive cycles in each step
4. Rule #3: Put it back together at the process level
Selva Nadarajah
12
Example 1: Diploma Production
UIC
BUSINESS
Base case
OM MBA
Name
Flow Rate
12 dipl./min
7.5 dipl./min
24 dipl./min
Cycle Time
5 sec./dipl
8 sec./dipl.
2.5 sec. dipl
Hole Punch
• What is the bottleneck activity? Name
• What is the process capacity?
Selva Nadarajah
7.5 dipl./min
13
UIC
BUSINESS
Unbalanced System
• First two stages unbalanced
• Scenario1: “OM MBA” works for 30 min, then takes break
Processing
Rate
OM MBA
Name
12 dipl./min
7.5 dipl./min
• Question: How long can the break last without slowing down the process?
• Answer:




Cycle = produce for 30 min, break for X min
Total time = 30 + X min
Total work = 30 min * (12 dipl./min) = 360 diplomas
360/ (30 + X) = 7.5 ⟹ X = 18 min
Selva Nadarajah
14
UIC
BUSINESS
Inventory Buildup
• Question: If we do that, what is the average inventory b/w these stages
• Answer:
Flow Rate
OM MBA
Name
12 dipl./min
7.5 dipl./min
• Flow rate difference between “OM MBA” and “Name” is 4.5 dipl./min
Inventory
Focus on one cycle: Produce for 30 mins, break for 18 mins
time
Selva Nadarajah
15
UIC
BUSINESS
Inventory buildup contd…
Inventory
time
total inventory in a cycle area of triangle 0.5×48×135 135
• Avg. inventory =
=
=
=
48
2
duration of a cycle
triangle base
• Avg. inventory =
Selva Nadarajah
maximum inventory 135
=
2
2
16
UIC
BUSINESS
Resource Downtime
• Scenario 2: Every 120 diplomas, the hole punch needs to be emptied. Takes an
average of 1 min to empty
OM MBA
Name
Hole Punch
Flow Rate
12 dipl./min
7.5 dipl./min
Capacity?
Cycle Time
5 sec./dipl
8 sec./dipl.
Cycle time?
• Answer:




Cycle: 120 diplomas followed by clean out
Total time = 120*2.5 sec + 60 sec = 360 sec = 6 min
Total work = 120 diplomas
New capacity= 120 dipl. / 6 min. = 20 dipl./min.
Selva Nadarajah
Hole Punch processing
rate is 24 dipl/min and
its processing time is
2.5 sec./dipl.
17
UIC
BUSINESS
Imperfect Yield
• Scenario 3: “Name” activity produces defects 3% of the time
OM MBA
Name
Hole Punch
Flow Rate
12 dipl./min
Capacity?
24 dipl./min
Cycle Time
5 sec./dipl.
Cycle time?
2.5 sec./dipl.
• Answer:




Cycle: 100 diplomas attempted
Total time = (100 dipl.) * (8 sec./dipl.) = 800 sec = 13.33 min
Total work = 97 diplomas
Capacity = 97 dipl. / 13.33 min. = 7.28 dipl./min.
Selva Nadarajah
Name processing rate
is 7.5 dipl/min and its
processing time is 8
sec./dipl.
18
UIC
BUSINESS
Little’s Law
• Little’s law relates the averages of basic performance metrics over time
• I = Inventory = how many flow units are in the process
• R = Flow Rate = rate at which flow units leave the process
• T = Flow Time = total time a flow unit is in the process
• Little’s Law:
Inventory = Flow Rate x Flow Time
or
I=RxT
• Practical implication: Given any two metrics the third can be found
Selva Nadarajah
19
Insurance Company Example
UIC
BUSINESS
• An insurance company processes 10,000 claims per year. The average processing time
is 3 weeks. How many claims are in the system on average? (Assuming 50 weeks in a
year)
R= 200 claims / week, T = 3 Weeks, I = R x T = 600 claims
• Now, the company reduces its processing time by 80%. How many claims are in the
system on average?
R= 200 claims / week, T = 0.6 Weeks, I = R x T =120 claims
Selva Nadarajah
20
Potbelly’s Promise
UIC
BUSINESS
• When you enter Potbelly, you see the overhead sign saying “FAST: 8 minutes through
the line max” and you notice that 24 people are waiting (including you). For Potbelly
to delivery that promise, how many customers should be leaving the check-out counter
every minute?
T = 8 min, I = 24 customers, R = I / T = 3 customers / min
Selva Nadarajah
21
UIC
BUSINESS
Utilization
• Measure that quantifies actual processing rate relative to how much could be
processed if operating at capacity
Utilization =
Flow rate
Capacity
• Can be applied to an individual resource, activity, or the entire process
• The bottleneck activity has the highest utilization
• Utilization is at most 100% but can be less because (?)
1. Demand is less than capacity
2. Input is less than capacity
3. Downtime or setups in the process
Selva Nadarajah
22
Illustration of Utilization
UIC
BUSINESS
• There are four steps in the manufacturing process of a stuffed toy: cutting, stuffing,
sealing, and packaging. There are two employees each for cutting and stuffing but
one each for sealing and packaging. The processing times of cutting, stuffing, sealing,
and packaging are 8, 5, 3, and 2 seconds per toy. What is the utilization at the
"packaging" resource if demand is unlimited?
•
•
•
•
•
Answer:
Capacity of packaging = ½ toys per second.
Process capacity = Min(2/8, 2/5, 1/3, 1/2) = ¼ toys per second.
Flow rate = Min(Demand, Process capacity) = ¼ toys per second. Why?
Utilization = Flow rate/Capacity = 0.25/0.5 = 50%.
Selva Nadarajah
23
UIC
BUSINESS
Implied Utilization
• Measures mismatch between what could flow through the resource (demand/work
load) and what the resource can provide (capacity)
Implied utilization =
Demand
Capacity
• Can be applied to an individual resource, activity, or the entire process
• Implied utilization of multiple resources can be greater than 100%
 Activities with implied utilization greater than 100% are candidates for capacity
expansion
• The bottleneck activity has the highest implied utilization
Selva Nadarajah
24
Illustration of Implied Utilization
UIC
BUSINESS
• There are four steps in the manufacturing process of a stuffed toy: cutting,
stuffing, sealing, and packaging. There are two employees each for cutting and
stuffing but one each for sealing and packaging. The processing times of cutting,
stuffing, sealing, and packaging are 8, 5, 3, and 2 seconds per toy. What is the
implied utilization at the "packaging" resource if demand is 1 toy per second?
•
•
•
•
•
Answer:
Capacity of packaging = ½ toys per second.
Process capacity = Min(2/8, 2/5, 1/3, 1/2) = ¼ toys per second.
Implied utilization = Demand/Capacity = 1/0.5 = 200%.
What would be implied utilization if demand was unlimited?
Selva Nadarajah
25
Retail and Supply Chain Benchmarks
UIC
BUSINESS
• Little’s law can be leveraged to compute two commonly used benchmarks in the retail
and supply chain areas
1. Days of supply: Number of days an average item spends in the store (or supply
chain)
2. Inventory turns: Number of times a store (or supply chain) turns over its inventory
• Low turnover is a sign of low sales and hence excess inventory
• High turnover signals strong sales and is typically seen as a positive sign
Annual Inventory turns =
Selva Nadarajah
365
Days of supply
26
Using Little’s Law to Compute Days of Supply
UIC
BUSINESS
• Consider a retail firm with multiple products
• How can inventory be measured?
 Physical units: Not appropriate
 Monetary unit: OK
• Little’s law with flow unit as the “individual dollar bill”
 Inventory is expressed in dollars
 What is the flow rate? Cost of goods sold (COGS)
Days of supply (Flow time) =
Selva Nadarajah
Inventory
Flow rate (COGS)
27
UIC
BUSINESS
Per-unit Inventory Cost
• Inventory holding costs are typically substantially higher than financial holding costs




Inventory may become obsolete or be perishable
Theft
Storage costs and overhead
Impact on waiting times (discussion in session 5) and quality (discussed in session 6)
Per-unit inventory costs =
Selva Nadarajah
Annual inventory costs
Annual inventory turns
28
UIC
BUSINESS
Walmart Vs Kohls
(numbers in millions)
Kohl’s
Walmart
Cost of goods sold (COGS)
$ 11,359
$ 307,646
Inventory (Inv)
$ 3,036
$ 36,318
2011 Data
Calculations
Days of supply (Inv/COGS x 360)
Inventory turns (COGS/Inv)
97 days
43 days
3.74 turns/yr
8.47 turns/yr
• What do these numbers tell us about Kohls and Walmart?
 Walmart turns over its inventory at a substantially higher rate
 This is a positive sign for Walmart for reasons already discussed
Selva Nadarajah
29
Walmart Vs Kohls
UIC
BUSINESS
• Suppose inventory costs are 20% per year of COGS
• Question: What is the per-unit inventory cost?
• Answer:
 Kohl’s: 20%/3.74 = 5.35%
 Walmart: 20% / 8.47 = 2.36%
Selva Nadarajah
30
UIC
BUSINESS
Net Profit Margin
• Source: Stern, NYU
Retail segment
Net margin % (Jan 2014) Net margin % (Jan 2020)
Automotive
2.94
3.55
Building supply
5.56
6.45
Distributors
3.53
4.51
General
2.90
2.44
Grocery and food
0.75
1.44
Internet
3.37
4.57
Special lines
3.88
3.31
• The two percent inventory cost difference between Kohl’s and Walmart in our analysis
is significant!
Selva Nadarajah
31