Introduction to Production & Operations
Management
3 Basic Functions of Business Organizations
Ensure and
allocate financial
resources
Produce goods or
services
Assess consumer
needs, and sell /
promote goods or
services
What is Production / Operations Management?
Production is the creation of goods OR services
Operations Management (OM) is the set of activities that
creates value in the form of goods or services through the
transformation process.
Operations: A Transformation Process
Feedback
Inputs
Valueadded
Workers
Managers
Performance
Equipment
Operations
and
processes
Facility
Materials
Outputs
Goods
Services
Land
Energy
Information
Feedbacks are evaluated to determine whether a control is needed or not
Operations functions: to add value
Value-added: The term used to describe the difference between
the cost of inputs and the value or price of outputs.
In non-profit organization, the value of output is their value to
society.
In profit organization, the value of outputs is measured by
products’ price.
Value-added and Nonvalue-added Activity
Value-added activity
Nonvalue-added activity
Example: Food Processor
Inputs
Raw Vegetables
Metal Sheets
Water
Energy
Labor
Building
Equipment
Processing
Cleaning
Making cans
Cutting
Cooking
Packing
Labeling
Consumer Feedback
Outputs
Canned vegetables
Example: Hospital
Processing
Outputs
Doctors, nurses
Examination
Healthy
Hospital
Surgery
patients
Medical Supplies
Monitoring
Equipment
Medication
Laboratories
Therapy
Inputs
Improvement of patients health condition
& Survey…
More
Psychological
Example: MAN 5502
Inputs
Processing
Outputs
Knowledge
Lecturing
Future
• Text Book
Tutoring
operations
• Lecture Notes
Assignment
managers
• Handouts
Exam
• Course CD
• ……
Teaching Evaluation
Goods or Service?
What is difference???
Feedback
Inputs
Outputs
•Are customers directly involved in the
transformation process?
•No: → Goods
•Yes: → service
Characteristics of Goods
Tangible product
Consistent product
definition
Production usually
separate from
consumption
Can be inventoried
Low customer
interaction
Characteristics of Service
Intangible product
Produced and consumed
at same time
Often unique
High customer interaction
Inconsistent product
definition
Often knowledge-based
Goods-Service Continuum
Figure 1.5
Steel production
Home
Auto Repair
Maid Service
Automobile
remodeling
Appliance
Manual car
Teaching
fabrication
Retail sales
repair
wash
Banking
High percentage goods
Low percentage goods
Low percentage service
High percentage service
Manufacturing and Service Employment
Employment (millions)
120 –
100 –
80 –
Service
60 –
40 –
20 –
0–
Manufacturing
|
|
|
|
|
|
|
1950
1970
1990 2010 (est)
1960
1980
2000
Organizations in Each Sector
The Dilemma of Almost Every Firm: Supply Does Not Match Demand
• Inventory results from a mismatch between supply and demand
Mismatch can take one of the following two forms
Demand waits for supply
(inventory=waiting customers)
Supply waits for demand
(inventory=goods or resources)
•Analyzing processes helps us to create a better match
• Supply would always be able to meet demand
▪ if processes were instantaneous (Flow Time=0)
▪ and had unlimited capacity (Flow Rate=infinity)
Example of Supply – Demand Mismatches
Retailing
ER
Air Travel
Supply
Consumer electronics
Medical service
Seats on specific flight
Demand
Consumers buying a
new video game
Urgent need for medical
service
Travel for specific time
and destination
Supply
exceeds
Demand
High demand costs;
few inventory turns
Doctors, nurses, and
infrastructure are
underutilized
Empty seat
Demand
exceeds
Supply
Forgone profit
opportunity; consumer
dissatisfaction
Crowding and delays in
the ER; potential
diversion of ambulances
Overbooking; customer
has to take different
flight (profit loss)
Actions to
match
S&D
Forecasting; quick
response
Staffing to predicted
demand; priorities
Dynamic pricing;
booking polices
Managerial
importance
Per-unit inventory
costs for consumer
electronics retailing all
too often exceed net
profits
Delays in treatment or
transfer have been linked
to death
About 30% of all seats
fly empty; a 1-2%
increase in seat
utilization makes the
difference between
profits and losses
How Much Inventory is in the world?
No one keeps track so we do not know for sure.
But we are interested because it helps us
understand how efficient the world is at turning
inventory into economic output.
An estimate of Worldwide Inventory
In 2012 there was about $70 trillion worth of economic output globally.
The U.S. represents about 22% of the overall output. So if the rest of the world were as efficient as the
U.S. that would mean that about $10 trillion existed in worldwide inventory.
However, we know that rest of the world is not as efficient. China for example has twice the logistic
cost of the us as a percentage of economic activity or GDP.
SO the BRIC countries have a combined GDP almost as large as the U.S. economy. And if the other
BRIC countries have about the efficiency of China that would add about $2 trillion to the overall global
business inventory.
This estimate likely understates true global inventories since it does not account for relative
inefficiencies in other emerging markets and does not account for government owned inventories.
However based on this we can see that the number of inventory turns per year globally is probably in
the ballpark of 6 (70/12).
AND if we could be just a little more efficient (say reduce inventory but just 10%) we would free up $1.2
trillion in capital that could be invested in growth activities that could benefit companies, countries and
ultimately people.
Types of Inventories
Raw materials & purchased parts
Partially completed goods, i.e. Work in progress
Finished-goods inventories (manufacturing firms)
or merchandise (retail stores)
Tools, & supplies
Maintenance and repairs (MRO) inventory
Goods-in-transit to warehouses or customers
Functions of Inventory
Anticipation stock : to meet anticipated demand
Seasonal inventories
▪
Firms that experience high seasonal demand build up in a preseason.
Decoupling stock:
▪
To keep continuity of production from some accident (i.e.
equipment breakdown)
▪
One important use of inventories in manufacturing is to decouple
operations through the use of work in process inventories
Functions of Inventory
Safety stock: t0 protect against stock-outs
Hedging inventory …
▪
to help hedge against price increases…to take advantage of
quantity discounts
Pipeline inventory (WIP) → Little’s Law
▪
Production operations take a certain amount of time → WIP.
Productivity
Operations: A Transformation Process
Feedback
Inputs
Value-dded
Outputs
Workers
Managers
Equipment
Facility
Materials
Land
Energy
Information
Performance
Goods
Services
Productivity
Productivity is a measure of the effective use of resources,
usually expressed as the ratio of output to input.
Outputs
Productivity =
Inputs
Input: labor, material, energy, and others.
Output: goods and services.
Productivity
Productivity is a measure of the effective use of resources,
usually expressed as the ratio of output to input.
Productivity measures are useful for
Tracking an operating unit’s performance over time
Judging the performance of an entire industry or country
Computing Productivity
Partial
measures
Output
Labor
Output Output
Machine Capital
Output
Energy
Multifactor
measures
Output
Labor + Machine
Total
measure
Goods or Services Produced
All inputs used to produce them
Output
Labor + Capital + Energy
Business, Industry, Country
The unit of measure must be the same for all
factors in the denominator
Productivity Calculations
Labor Productivity
Units produced
Productivity =
Labor-hours used
1,000
=
= 4 units/labor-hour
250
One resource input  single-factor productivity
Multi-Factor Productivity
Output
Productivity =
Labor + Material + Energy
+ Capital + Miscellaneous
Also known as total factor productivity
Output and inputs are often expressed in dollars
Multiple resource inputs  multi-factor productivity
Example
Output = 10,000 units x $10/unit
Labor = 500 hr x $9/hr
10,000 Units Produced
Sold for $10/unit
500 labor hours
Labor rate: $9/hr
Cost of raw material: $5,000
Cost of part material: $25,000
What is the
labor productivity?
Solutions to Example
Output : 10,000 x $10/item = $100,000
Input : 500 hours x $9 /hr = $4500
Labor productivity= 100,000 / 4500 = 22.22
MFP (multi factor productivity)
= output / (labor + materials)
100,000 / {4,500 + 25,000 + 5,000}
MFP = 2.90
10,000 Units Produced
Sold for $10/unit
500 labor hours
Labor rate: $9/hr
Cost of raw material: $5,000
Cost of Part material: $25,000
Productivity Calculation Example
Units produced:
5,000
Standard price:
$30/unit
Labor input:
500 hours
Cost of labor:
$25/hour
Cost of materials:
$5,000
Cost of overhead: 2x labor cost
Output = 5,000 x 30 = $150,000
Labor = 500 x 25 = $12,500
Material= 5,000 = $5,000
Overhead = 12,500 x 2 = $25,000
What is the multifactor productivity?
Solution
M ultifactor Productivity=
Output
Labor +M aterial+Overhead
=
5,000 units  $30/unit
(500 hours  $25/hour) + $5,000 + (2(500 hours  $25/hour))
=
$150,000
$42,500
= 3.5294
Productivity Growth
The increase in productivity from one period to the
next relative to the productivity in the preceding
period
Current productivity- Previous productivity
Productivity Growth=
100%
Previous productivity
Previous Productivity = 80
Current Productivity = 84
Growth = 84 – 80  100 = 5%
80
Before:
After:
Output: 60 units/hr x $31/unit = $1860 /hr
Output: 60 units/hr *1.25 x* $31/unit = $1860 /hr*1.25
Input:
Input:
Labor: 5 * $12/hr = $60 /hr
Labor: (5+1) * $12/hr = $72 /hr
Material= $16/unit*60/hr = $960/hr
Material= $(16-6)/unit*60*1.25/hr = $10*75/hr=750
Overhead = 1.6*Labor=1.6*60/hr = 96/hr
Overhead = 1.6*Labor=1.6*72/hr = 115.2/hr
Output/TC=1860/(60+960+96) = 1860/1116
Output/TC=2325/(72+750+115.2) = 2325/937.2
= 1.667
= 2.481
Service Sector Productivity
Service sector productivity is difficult to measure
and manage because
It involves intellectual activities
It has a high degree of variability
Service Sector Productivity
A useful measure related to productivity is process yield
Where products are involved
ratio of output of good product to the quantity of raw material
input.
Where services are involved, process yield measurement
is often dependent on the particular process:
ratio of cars rented to cars available for a given day
ratio of student acceptances to the total number of students
approved for admission.
Measurement Problems
Quality may change while the quantity of inputs
and outputs remains constant
External elements may cause an increase or
decrease in productivity
Precise units of measure may be lacking
Improving Productivity at Starbucks
A team of 10 analysts
continually look for ways
to shave time. Some
improvements:
Stop requiring signatures on
credit card purchases under $25
Saved 8 seconds per
transaction
Change the size of the ice scoop
Saved 14 seconds per drink
New espresso machines
Saved 12 seconds per shot
Operations improvements have helped Starbucks increase yearly
revenue per outlet by $200,000 to $940,000 in six years.
Productivity has improved by 27%, or about 4.5% per year.
Process Selection and
Facility Layout
Process Selection
Deciding on the way how production of goods
or services will be organized
It has major implication for
Capacity planning, Layout of Facilities,
Equipment, Design of work system
Occurs
When new products or services are being planned
Periodically due to technological changes, competitive pressures
Key Aspects of Process Selection.
How much variety will the system need to handle?
(Standard/Customized)
What degree of equipment flexibility is needed?
(Rapidly changing/not)
What is the expected volume of output?
(High/Low)
Process Types
Job shop, Batch, Repetitive, Continuous, Project
Job shop: a tool and die shop, Auto shop…
Small scale, low volume of high-variety , High flexibility,
skilled workers.
Batch: Bakery
Moderate volume and variety
Process Types
Assembly line/Repetitive (V): automobile, carwash
high volume of standardized items, limited variety
Please watch the video clip
Because of the copyright, I cannot upload the following.
https://www.youtube.com/watch?v=vlptoTkE25Q
Please watch this video clip.
You can find the link in the below.
Process Types
Assembly line/Repetitive (V): automobile, carwash
high volume of standardized items, limited variety
https://www.youtube.com/watch?v=vlptoTkE25Q
Process Types
Assembly line/Repetitive (V): automobile, carwash
high volume of standardized items, limited variety
Continuous (Video): Petroleum product, steel, …
Very high volume of non-discrete and very low variety
Project :
Used for work that is non-routine, with a unique set of
objective to be accomplished in a limited time frame.
Types of Processing
Job shop
Batch
Repetitive/
Assembly
Continuous
Description
Customized
Goods or
Services
SemiStandardized
Goods or
Services
Standardized
Goods or
Services
Highly
Standardized
Goods or
Services
Advantage
Able to handle Flexibility
a wide variety
of work
Low unit cost,
high volume,
efficient
Very efficient,
very high
volume
Disadvantage
Slow, high
cost per unit,
complex
planning and
scheduling
Low
flexibility,
high cost of
downtime
Very rigid,
lack of variety,
costly to
change, very
high cost of
downtime
Moderate cost
per unit,
moderate
scheduling
and
complexity
Product Process Matrix
Job shop
Variety
Batch
Assembly
Line/Repetitive
Continuous
Volume
Product Process Matrix
Emergency
Room
Variety
Commercial
Bakery
Automobile
Carwash
Petroleum
Refinery
Volume
Facilities Layout
Layout
the configuration of departments, work centers, and
equipment, with particular emphasis on movement of work
(customers or materials) through the system
Facilities layout decisions arise when:
Designing new facilities
Re-designing existing facilities
The basic Objective
To facilitate a smooth flow of work, material, and
information through the system
Basic Layout Types
Product Layouts most conducive to repetitive
processing
Assembly Line and Continuous (processing selection)
Process Layouts used for intermittent processing
Batch and job shop
Fixed-Position Layouts used when projects require
layout
Combination layouts
Repetitive Processing: Product Layouts
Product layout
Layout that uses standardized processing operations to
achieve smooth, rapid, high-volume flow
Production/Assembly Line
Raw materials
or customer
Station
1
Station
2
Station
3
Station
4
Material
Material
Material
Material
Labor
Labor
Labor
Labor
Finished
item
Cafeteria Line
Tray/
Silver
Salad
Main
Course
Potato
Veggie
Bread
Roll
Dessert Cashier
Non-repetitive Processing: Process Layouts
Process layouts
Designed to process items or provide services that
involve a variety of processing requirements
Requires frequently adjustment to equipment.
(discontinuous work flow)
Dept. A
Dept. C
Dept. E
Dept. B
Dept. D
Dept. F
Used for Intermittent processing
Job Shop or Batch
Comparison of Process and Product Layout
Figure 6.7
Fixed Position Layouts
Fixed Position layout (video)
Layout in which the product or project remains
stationary, and workers, materials, and equipment are
moved as needed
https://www.youtube.com/watch?v=r8p5iSHmSBY
Combination Layouts
Small jobs
Continuous Production
Customization
Standardization
…continuum…
Less Efficient
More Efficient
Higher Unit $
Lower Unit $
Product Layout
Process Layout
combine product, process, & fixed position layouts
Combination Layouts
Some operational environments use a combination of
the three basic layout types:
Hospitals
Supermarket
Some organizations are moving away from process
layouts in an effort to capture the benefits of product
layouts
Cellular manufacturing
Cellular Layouts
Cellular Production: A type of layout in which
machines are grouped into a cell that processes
items with similar processing requirements
Miniature product layouts
Conveyor systems possible
Only minor variations to routes (skipping an operations)
Process Analysis
Process
Process:
any part of an organization that takes inputs
and transforms them into outputs
Process Analysis
Why do we need to analyze the process?
-
To identify inefficient tasks
-
To spot possible effectiveness improvement tasks
-
To understand where value can be added
What are the relevant performance measures?
Inventory, Flow time and Flow rate
The Process Flow Diagram (Production System)
Inventories
Raw Material
flow
Activities
Activity 1/
Shaping
Pass Inspection
Assembly
Staining/
finishing
Finished Units
into warehouse
Rework
Fail Inspection

What (interesting) questions can we ask about a process?

Inventory: number of flow units contained within the process

In a production setting: Work-in-Process: WIP

Flow Time (cycle time): time it takes for 1 flow unit to get through the process

Flow (throughput) Rate: flow units/unit time
The Process Flow Diagram (Production System)
Inventories
Raw Material
flow
Activities
Activity 1/
Shaping
Pass Inspection
Assembly
Staining/
finishing
Finished Units
into warehouse
Rework
Fail Inspection

What (interesting) questions can we ask about a process?

Inventory: number of flow units contained within the process

In a production setting: Work-in-Process: WIP

Flow Time (cycle time): time it takes for 1 flow unit to get through the process

Flow (throughput) Rate: flow units/unit time
Cycle time = 15 seconds
Process Flow Diagram
Activities: Add value, may or may not
carry inventory, have capacity
Arrows indicate Flow
Inventory Buffer: Do NOT have a
capacity (but may have a max volume)
Flow Diagram (A Three-Station Assembly Line)
The company is a scooter manufacturing company.
The assembly line consists of three workstations,
each performing a single step and requiring one
worker. The processing times of the workstations
A, B, and C are 13, 11, and 8 minutes per unit.
Multiple Types of Flow Units
There is an example involving multiple product or customer types.
An employment verification agency receives resumes from consulting & law firms
with the request to validate information provided by their job candidates.
Three customer types (Internship, Staff and Consulting/Lawyer Positions) share
the first step (filing) and the last step (sending confirmation letter) in the process
They differ with respect to other steps
For internship positions, (a) the agency provides education information (Education
Analysis)
For staff positions, (b) the agency contacts previous employers & analyze the
recommendation letter (Contact employer with rec. letter)
For consulting/lawyer positions, (c) the agency contact former supervisors/colleagues
(Contact person) & (b) previous employers + analyze the recommendation letter
resumes
Contact person
Consulting
Staff
Internship
Filing
Verified
Applications
Contact
employer with
rec. letter
Education
analysis
Confirm
letter
Bagel Store
Consider a bagel store selling three types of bagels: Grilled
Veggie, Veggie and Cream Cheese
The different processes are required, based on the types of
bagels (Before each process, some buffers are required)
Grilled Veggie: (i) cut, (ii) put grilled stuff on bagel, and (iii) veggie
on bagel and (iv) wrap
Veggie: (i) cut, (ii) veggie on bagel, and (iii) wrap
Cream Cheese: (i) cut, (ii) cream cheese, and (iii) wrap
Diagram
Raw
Bagels
Put Grilled
Stuff on Bagel
Grilled Veggie
Veggie
Cream Cheese
Finished
Bagels
Cut
Veggies
on Bagel
Cream
Cheese
Wrap
How to draw a process flow diagram
Process: Getting an X-ray at a hospital
Unit of Job is defined as a patient
Entry point is defined as point at which the patient leaves the
physician's office for the X-ray lab.
Exit point defined as the point at which the patient enters the
physician’s office with the completed X-ray film.
Description
Activity
Description
1
Patient leaves the physician’s office
2
Patient walks to the X-ray lab
3
The receptionist receives the patient information
4
An X-ray technician fills out a standard form
5
Patient undresses in preparation for X-ray
6
A lab technician takes X-ray
7
A darkroom technician develops X-ray
8
The X-ray technician checks X-ray for clarity:
9
If X-ray is not satisfactory, repeat the previous steps.
Otherwise, patient puts on clothes and get ready to leave lab
10
Patient walks back to the physician’s office
11
The X-rays are transferred to the physician by a messenger
12
Patient and X-rays arrive at the Physician’s office
Process Diagram
Leave office
Walk to lab
1
Info. Process
2
X-Ray form
3
Prepping
4
5
Walk to office
10
12
Patient
AND xray back
to office
Check X-ray
Messenger
Take X-ray
7
6
YES
9
11
Develop X-ray
8
NO
Capacity, Bottleneck, Flow Rate
Assume a process is in place.
Task 1
Task 2
Task 3
• What is its capacity? How many units per unit time go
through each task? The process as a whole?
• What is the bottleneck? Which production step limits the
process capacity?
• What is the Flow rate? How many units can the process
produce over a time?
Process Capacity = minimum(Cap of R1, Cap of R2…)
Capacity of a task is the physical limitation in terms of
“how much can be processed at this task”
The capacity of the process is:
Process Capacity = minimum(Cap of R1, Cap of R2…)
What is the capacity of this process?
3 units/hr
Task 1
5 units/hr
2 units/hr
Task 2
Task 3
What is a bottleneck?
An operation in a sequence of operation whose capacity
is lower than that of the other operations
What is a bottleneck?
An operation in a sequence of operation whose capacity
is lower than that of the other operations
Which task is the bottleneck? Task 3
3 units/hr
Task 1
5 units/hr
2 units/hr
Task 2
Task 3
Flow Rate
Flow Rate or Throughput Rate: flow units/unit time
Flow Rate = minimum(Available unit, Demand, Proc. Cap.)
The combination of available unit, demand and process
capacity yields the rate at which our flow unit actually
flows through the process.
Cycle Time
• Cycle Time: Average time for completion of a unit at
a production step or process. Measured as time/unit
1
Cycle Time
=
Flow rate
Cost of direct labor (per unit of time)
= Total wage / Flow rate
Ave. Labor Utilization = Labor content / (Labor Content + Total idle time)
Idle time for a single worker
= Cycle time – Processing time of the single worker
Utilization vs Implied Utilization
•
Utilization: a measure of
how much the process actually produces (Flow rate) relative to
how much it could produce (Capacity)
•
Implied Utilization: the mismatch between
what could flow through the resource (Demand) and
what the resource can provide (Capacity)
Capacity
Demand
Flow Rate
100 tons/hr
75 tons/hr
75 tons/hr
100 tons/hr
100 tons/hr
100 tons/hr
100 tons/hr
125 tons/hr
100 tons/hr
Utilization
Implied Utilization
Utilization vs Implied Utilization
•
Utilization: a measure of
how much the process actually produces (Flow rate) relative to
how much it could produce (Capacity)
•
Implied Utilization: the mismatch between
what could flow through the resource (Demand) and
what the resource can provide (Capacity)
Capacity
Demand
Flow Rate
Utilization
Implied Utilization
100 tons/hr
75 tons/hr
75 tons/hr
75/100
75/100
100 tons/hr
100 tons/hr
100 tons/hr
100/100
100/100
100 tons/hr
125 tons/hr
100 tons/hr
100/100
125/100
A Three-Station Assembly Line
The company is a scooter manufacturing company
and operates 35 hours per week. The assembly line
consists of three workstations, each performing a
single step and requiring one worker. Note that
the wage rate is $12 per hour. The processing times
of the workstations A, B, and C are 13, 11, and 8
minutes per unit. From the data, we know that the
weekly demand is 125 scooters.
A
B
C
13 min/unit
11 min/unit
8 min/unit
A Three-Station Assembly Line (Scooters)
▪
▪
Description (given information)
✓
Demand = 125 scooters per week
✓
Assume that the process operates 35 hours per week
✓
Each activity requires one worker (3x$12/h)
Question
✓
How many units can each station produce for one hour?
✓
Cost of direct labor (per unit of time)
✓
Average Labor Utilization
A
B
C
13 min/unit
11 min/unit
8 min/unit
60/13 = 4.61 units/hr
60/11 = 5.45 units/hr
60/8 = 7.5 units/hr
A Three-Station Assembly Line (Scooters)
▪
Description (given information)
✓
Demand = 125 scooters per week
✓
Assume that the process operates 35 hours per week
✓
Each activity requires one worker (3x$12/h)
Demand = 125 units/week = 125 units/35 hours = 3.57 units/hour
Total wage = 3 worker x $ 12 per hour x 35 hours per week = $1,260 per week
A
B
C
13 min/unit
11 min/unit
8 min/unit
60/13 = 4.61 units/hr
60/11 = 5.45 units/hr
60/8 = 7.5 units/hr
1
Flow rate =
Flow Rate vs Cycle Time
Cycle Time
Flow rate = minimum (input, cap, demand)
= min (inf, 4.61, 3.57) = 3.57 units/hr or 125 units/week
Demand = 125 scooters per week = 125/35 = 3.57 units/hr
Cycle time: How long does it take to produce one unit?
In order to produce 3.57 units, we need 1 hour.
1/3.57 hours/unit → (0.28 hours/unit) x (60 mins/1hours)= 16.8 mins/unit
A
B
C
13 min/unit
11 min/unit
8 min/unit
60/13 = 4.61 units/hr
60/11 = 5.45 units/hr
60/8 = 7.5 units/hr
Cost of direct labor
Cost of direct labor (per unit of time)
= Total wage / Flow rate
= ($1260/week)/(125 unit/week) = $10.08/unit
Assume that the process operates 35 hours per week
Total wage
Each activity requires one worker (3x$12/h)
= 3 x 12 x 35
Demand = 125 scooters per week
= $1,260/wk
A
B
C
13 min/unit
11 min/unit
8 min/unit
60/13 = 4.61 units/hr
60/11 = 5.45 units/hr
60/8 = 7.5 units/hr
1
Average Labor Utilization
Flow rate =
Cycle Time
Ave. Labor Utilization = Labor content / (Labor Content + Total idle time)
Labor content : Sum of the processing time.
Labor content = (13 + 11 + 8) minutes/unit = 32 minutes/unit
Idle time for a single worker
= Cycle time – Processing time of the single worker
Cycle time = 1/Flow rate = 1/3.57 hours/unit = 16.8 minutes/unit
A
B
C
13 min/unit
11 min/unit
8 min/unit
16.8-11 = 5.8
16.8-8 = 8.8
Idle time 16.8-13 = 3.8
Average Labor Utilization
Labor content : Sum of the processing time.
Labor content = (13 + 11 + 8) minutes/unit = 32 minutes/unit
Total Idle time = 3.8+5.8+8.8 = 18.4
Average Labor Utilization = Labor content / (Labor Content + Total idle time)
= 32/ (32+18.4) = 63.5%
Efficiency
Number of workstation x Cycle time
A
B
C
13 min/unit
11 min/unit
8 min/unit
16.8-11 = 5.8
16.8-8 = 8.8
Idle time 16.8-13 = 3.8
(Implied) Utilization
Utilization = Flow rate / Capacity = 3.57 / 4.61 = 77.4%
Implied Utilization = Demand / Capacity = 3.57 / 4.61 = 77.4%
Demand = 125 scooters per week/35 hours = 3.57 units/hr
Capacity = 4.61 units/hr
A
B
C
13 min/unit
11 min/unit
8 min/unit
3.57/4.61 = 77.4%
3.57/5.45 = 65.6%
3.57/7.5 = 47.6%
Parallel Processes
Two identical sandwich lines
two workers at three operations
All completed sandwiches are wrapped
Order
30 sec/sandwich
Bread
Fill
Toast
15 sec/sandwich
20 sec/sandwich
40 sec/sandwich
Bread
Fill
Toast
15 sec/sandwich
20 sec/sandwich
40 sec/sandwich
Wrap
37.5 sec/sandwich
Capacity Analysis
Toast workstation has the longest processing time – 40
seconds, which leads to 1.5 sandwiches per minute.
The two lines deliver two sandwiches every 40 seconds,
which leads to 3 sandwiches per minute.
At 37.5 seconds, wrapping and delivery has the longest
processing time and is the bottleneck (60/37.5 per minute)
Capacity per hour is 3,600 seconds/37.5 seconds/sandwich
= 96 sandwiches per hour
Processing time is 30 + 15 + 20 + 40 + 37.5 = 142.5 seconds
Simultaneous Process
Standard process for cleaning teeth
Cleaning and examining X-rays can happen simultaneously
Cleaning
Check in
Takes
X-ray
Develops
X-ray
24 min/unit
2 min/unit
2 min/unit
4 min/unit
X-ray
exam
5 min/unit
Dentist
Check
out
8 min/unit
6 min/unit
Capacity Analysis
All possible paths must be compared
Cleaning path is 2 + 2 + 4 + 24 + 8 + 6 = 46 minutes
X-ray exam path is 2 + 2 + 4 + 5 + 8 + 6 = 27 minutes
Longest path involves the hygienist cleaning the teeth
Bottleneck is the hygienist at 24 minutes
Hourly capacity is 60/24 = 2.5 patients
Patient should be completed in 46 minutes
Line Balancing
https://youtu.be/HZ5HrkN52j8
Flow rate = min (input, demand, capacity)
If input is sufficiently high,
Flow rate = min (demand, capacity)
Cycle time = 1/Flow rate
If input and demand are sufficiently high,
Flow rate = capacity
Cycle time = 1/Flow rate = 1/Capacity = Processing time
Cycle time is a longest processing time.
In the next two slides, we assume that input and demand are sufficiently
large so that cycle time is equal to a longest processing time.
5 workers vs 1 worker
(Assume that demand and input are sufficiently large )
0.1 min.
0.7 min.
1.0 min.
0.5 min.
0.2 min.
With 5 workstations, Cycle Time = 1.0 minute.
With 1 workstation, Cycle Time =
0.1 min.
0.7 min.
1.0 min.
2.5 minutes.
0.5 min.
0.2 min.
3 workers vs 3 workers
(Assume that demand and input are sufficiently large )
With 3 workstations, CT = 1.0 minute.
0.1 min.
0.7 min.
Workstation 1
1.0 min.
0.5 min.
Workstation 2
0.2 min.
Workstation 3
With 3 workstations, CT = 1.8 minute.
0.1 min.
0.7 min.
Workstation 1
1.0 min.
0.5 min.
Workstation 2
0.2 min.
Workstation 3
Line Balancing
Line balancing
The process of assigning tasks to workstations in such a
way that the workstations have approximately equal
time requirements
Why is line balancing important?
1.
It allows us to use labor and equipment more efficiently.
2.
To avoid fairness issues that arise when one workstation must
work harder than another.
Example (One Physician)
The pre-induction physical examination given by the US Army involves the
following seven activities. These activities can be performed in any order,
with two exceptions: the medical history must be taken first and the exit
medical evaluation is the final step. At present there is one physician on duty
during each shift.
Example (One Physicians & three paramedics)
The pre-induction physical examination given by the US Army involves the
following seven activities. These activities can be performed in any order,
with two exceptions: the medical history must be taken first and the exit
medical evaluation is the final step. At present there are three paramedics
and one physicians on duty during each shift. Only a physician can perform
the exit evaluation and conduct the psychological interview. Other activities
can be carried out by either physicians or paramedics
Example
These activities can be performed in any order, with two exceptions:
▪
the medical history must be taken first
▪
the exit medical evaluation is the final step.
Medical
history
Medical
Evaluation
Example
At present there are three paramedics and one physicians
▪
Only a physician can perform the exit evaluation and conduct the psychological interview.
▪
Other activities can be carried out by either physicians or paramedics
Activity
Time (min)
Remark
Medical history
12
physicians or paramedics
Blood Test
6
physicians or paramedics
Eye Exam
10
physicians or paramedics
Measurements (weight, height, etc)
8
physicians or paramedics
Medical Exam
16
physicians or paramedics
Psychological interview
10
Physician only
Exit Medical eval
10
Physician only
Psy Inter+
Medical
Evaluation
Example
At present there are three paramedics and one physicians
▪
Only a physician can perform the exit evaluation and conduct the psychological interview.
▪
Other activities can be carried out by either physicians or paramedics
Medical
history
Psy.
interview
Medical
Evaluation
physician
Three paramedics
Example (Layout 1)
At present there are three paramedics and one physicians
▪
Only a physician can perform the exit evaluation and conduct the psychological interview.
▪
Other activities can be carried out by either physicians or paramedics
18
Medical
history +
Blood test
18
Eye Exam
+ Measure
Three paramedics
20
16
Medical
Exam
Psy.
interview
Medical
Evaluation
physician
Layout I
Three paramedics
18
18
Medical
history +
Blood test
Eye Exam
+ Measure
60/18 = 3.33
60/18 = 3.33
physician
20
16
Medical
Exam
60/16 = 3.75
Psy.
interview
Medical
Evaluation
60/20 = 3
How many people can be processed per hour? What activity is the bottleneck?
Bottleneck: Physician
What is the average labor utilization of workers?
Assume the process operates at it capacity (i.e., cycle time = 20 mins).
In other words, demand and input is sufficently large.
Labor content = 18+18+16+20 = 72
Total idle time = (20-18)+(20-18)+(20-16)+(20-20) = 8
72/(72+8) = 0.9
Layout I
Three paramedics
18
18
Medical
history +
Blood test
Eye Exam
+ Measure
60/18 = 3.33
60/18 = 3.33
physician
20
16
Medical
Exam
60/16 = 3.75
Psy.
interview
Medical
Evaluation
60/20 = 3
Assume that a wage rate of $21 per hour. What are the direct labor costs
for one patient?
Direct labor costs = Total wage/flow rate = 21*4/3 = $28
Example (Layout 2)
At present there are three paramedics and one physicians
▪
Only a physician can perform the exit evaluation and conduct the psychological interview.
▪
Other activities can be carried out by either physicians or paramedics
12
24
Medical
history
Blood test
+ Eye Exam
+ Measure
Three paramedics
20
16
Medical
Exam
Psy.
interview
Medical
Evaluation
physician
Layout 2
Three paramedics
12
24
Medical
history
Blood test
+ Eye Exam
+ Measure
60/12 = 5
60/24 = 2.5
physician
20
16
Medical
Exam
60/16 = 3.75
Psy.
interview
Medical
Evaluation
60/20 = 3
How many people can be processed per hour? What activity is the bottleneck?
Bottleneck: Paramedic #2
What is the average labor utilization of workers?
Assume the process operates at it capacity (cycle time = 24 mins).
Labor content = 12+24+16+20 = 72
Total idle time = (24-12)+(24-24)+(24-16)+(24-20) = 24
72/(72+24) =0.75
Layout 2
Three paramedics
12
24
Medical
history
Blood test
+ Eye Exam
+ Measure
60/12 = 5
60/24 = 2.5
physician
16
Medical
Exam
60/16 = 3.75
Psy.
interview
Medical
Evaluation
60/20 = 3
Assume that a wage rate of $21 per hour. What are the direct labor costs
for one patient?
Direct labor costs = Total wage/flow rate = 21*4/2.5 = $33.6
Example (Layout 3)
At present there are three paramedics and one physicians
▪
Only a physician can perform the exit evaluation and conduct the psychological interview.
▪
Other activities can be carried out by either physicians or paramedics
20
Medical
history
+ Measure
16
Blood test
+ Eye Exam
Three paramedics
20
16
Medical
Exam
Psy.
interview
Medical
Evaluation
physician
Layout 3
Three paramedics
20
16
Medical
history
+ Measure
Blood test
+ Eye Exam
60/20 = 3
60/16 = 3.75
physician
20
16
Medical
Exam
60/16 = 3.75
Psy.
interview
Medical
Evaluation
60/20 = 3
How many people can be processed per hour? What activity is the bottleneck?
What is the average labor utilization of workers?
Assume the process operates at it capacity (cycle time = 20 mins).
Labor content = 20+16+16+20 = 72
Total idle time = (20-20)+(20-16)+(20-16)+(20-20) = 8
72/(72+8) = 0.9
Layout 3
Three paramedics
20
16
Medical
history
+ Measure
Blood test
+ Eye Exam
60/20 = 3
60/16 = 3.75
physician
20
16
Medical
Exam
60/16 = 3.75
Psy.
interview
Medical
Evaluation
60/20 = 3
Assume that a wage rate of $21 per hour. What are the direct labor costs
for one patient?
Direct labor costs = Total wage/flow rate = 21*4/3 = $28
Extension (three paramedics & two physicians)
Medical
history
Psy.
interview
Medical
Evaluation
Extension (three paramedics & two physician)
Three paramedics
18
18
Two physicians
16
Medical
history +
Blood test
Eye Exam
+ Measure
60/18 = 3.33
60/18 = 3.33
60/16 = 3.75
18
18
16
Medical
Exam
Medical
history +
Blood test
Eye Exam
+ Measure
Medical
Exam
60/18 = 3.33
60/18 = 3.33
60/16 = 3.75
10
10
Psy.
interview
Medical
Evaluation
60/10 = 6
60/10 = 6
2*(60/20) = 6
Extension (three paramedics & two physician)
20
Psy.
interview
Medical
history
Physician 1
Medical
Evaluation
Physician 2
Psy.
interview
Medical
Evaluation
Extension (three paramedics & two physician)
Three paramedics
52
20
Medical
history +
Blood test
Eye Exam
+ Measure
Medical
Exam
Medical
history +
Blood test
Eye Exam
+ Measure
Medical
Exam
Psy.
interview
Eye Exam
+ Measure
Medical
Evaluation
Physician 2
Psy.
interview
Medical
history +
Blood test
Physician 1
Medical
Evaluation
Medical
Exam
3*(60/(20+16+16)) = 3*(60/52) = 3.46
(60/20) x 2= 6
For your information
Worker-paced line vs Machine-paced line
Worker-paced line (different speed)
4min
3min
2min
Machine-paced line (same speed)
4min
4min
4min
Time to process a Quantity x starting with an Empty process
Worker-paced line
Each worker is free to work at his or her own pace. Ex) Q4.7
If the first worker finishes earlier than the next worker,
The first worker puts the completed work in the inventory.
time through empty process = Sum of the processing times
Machine-paced line,
All of the steps must work at the same rate. Ex) Q4.4
time through empty process = Cycle time x the number of stations
Time to finish X units
= time through empty process + (X-1 unit) x cycle time
Q4.7 (Worker-paced line)
Toy bicycle manufacturing company.
The assembly line consists of seven work stations
Five workers
Worker 1: Step 1 (30sec.) + Step 2 (20 sec.)
Worker 2: Step 3 (35sec.) + Step 4 (25 sec.)
Worker 3: Step 5 (30sec.)
Worker 4: Step 6 (45sec.)
Worker 5: Step 7 (40sec.)
W1
W2
W3
W4
W5
50 sec/unit
60 sec/unit
30 sec/unit
45 sec/unit
40 sec/unit
Q4.7 (Worker-paced line)
How long would it take to produce 100 units, starting with an
empty system?
Each worker is free to work at his or her own pace.
time through empty process
= Sum of the processing times
Time to finish X units
= time through empty process + (X-1 unit) x cycle time
=(50+60+30+45+40) + (100-1)x60
W1
W2
W3
W4
W5
50 sec/unit
60 sec/unit
30 sec/unit
45 sec/unit
40 sec/unit
Q4.7 (Worker-paced line)
What is the average labor utilization, ignoring the
production of the first and last units?
Average Labor Utilization
= Labor content / (Labor Content + Total idle time)
W1
W2
W3
W4
W5
50 sec/unit
60 sec/unit
30 sec/unit
45 sec/unit
40 sec/unit
Q4.7 (Worker-paced line)
What is the cost of direct labor for the bicycle?
Assume the workers are paid $15 per hour
Cost of direct labor (per unit of time)
= Total wage per hour / Flow rate
= 5 person x $15 per hour per person/ 60unit per hour
= $1.25 / unit
W1
W2
W3
W4
W5
50 sec/unit
60 sec/unit
30 sec/unit
45 sec/unit
40 sec/unit
Little’s Law
• Cycle Time: Average time for completion of a unit at
a production step or process. Measured as time/unit
• Throughput Rate (R): Average number of units processed over a
time interval. Measured as units/time
1
Throughput rate =
Cycle Time
Little’s Law
•
Throughput Time (T): Average time that a unit takes to go through
the entire process. Measured as time
•
Inventory (I or WIP): Average number of units in system over a
time interval. Measured as units
Key
relationship
WIP = Throughput rate x Throughput time
(Little’s Law)
Example
U.S.
Immigration
Champagne
Industry
MBA
Program
Large PC
Manufacturer
Flow Unit
Application for
Immigration
Benefit
Bottle of
Champagne
MBA
Student
Computer
Flow rate,
Throughput
Approved or
Rejected visa
cases:
6.3 million/yr
260 million
bottles per yr
600
students
per yr
5000 units/day
Flow time
Ave. processing
time: 0.63 yr
Ave. time in
cellar: 3.46 yrs
2 yrs
10 days
Inventory
Pending cases:
4.0 million cases
900 million
bottles
1200
students
50000
computers
Little’s law
Inventory (I) = Throughput Rate (R) * Throughput Time (T)
Throughput, Throughput Rate, Flow Rate
Throughput Time, Cycle Time, Flow Time
Theoretical Cycle Time is
the longest total time for a job to traverse the individual activities
in the process without any waiting.
Process Cycle Time
the longest total time for a job to traverse the individual activities
in the process with any waiting.
Pictures from Burger King, Dell
Service Application (Hospital)
Ideal Scenario for a patient (first patient, no waiting times)
11 patients/day
=1 patient/hour
11 hours
11 patients/day
=1 patient/hour
7 patients arrive
5 patients leave
2 patients are at hospital.
11 patients/day
=1 patient/hour
7 patients arrive
Every 5 minutes, compute inventory,
5 patients leave
2 patients are at hospital.
Average Inventory 2.076 patients
11 patients/day
=1 patient/hour
For Patient 7, Tarrvial = 11:05 Tdeparture = 13:15
Average Inventory 2.076 patients
11 patients/day
=1 patient/hour
For Patient 7, Tarrvial = 11:05 Tdeparture = 13:15
Average Inventory 2.076 patients
Average flow time : 2.076 hours
11 patients/day
=1 patient/hour
Little’s law
Inventory (I) = Throughput Rate (R) * Throughput Time (T)
2.076
=
1
* 2.076
Service Application
Inflow (t):
# of jobs (patients) flowing into the system at time t
Clinical Process (i.e. x-ray, doctor visit, testing, etc.)
Outflow (t) :
# of completed jobs (patients) flowing out of the system at time t
Throughput (Flow rate)
Both the inflow and outflow rate fluctuate over time
However, in a stable environment,
the average inflow rate = the average outflow rate
there is no change of storage in the system over some
length of time
This AVERAGE flow (inflow=outflow) rate is referred to as
THROUGHPUT or Flow Rate
Measured as the average number of jobs (patients) per
unit time through the system
Cycle (Flow) Time, CT
The Cycle (flow) Time is
the time spent by a job (patient) in the process
from the time he/she enters the process to the time
he/she leaves the process
Obviously, this time varies among jobs (patients).
Define CT as the AVERAGE cycle time for a “job”
(patient)
averaged over all patients
Little’s law
Inventory (I) = Throughput Rate (R) * Throughput Time (T)
Throughput, Throughput Rate, Flow Rate
Throughput Time, Cycle Time, Flow Time
Pictures from Burger King, Dell
Using Little’s Law to Determine Throughput
Assume that it takes an average customer 2.25 hours to obtain a x-ray
On average, there are 24 customers waiting at several stages, to obtain
an X-ray.
What would be the estimated average number of patients that can be
processed through the system in a typical day?
In this case, T = 2.25 hr; and I = 24 customers which implies:
Throughput rate = 24/2.25 = 10.67 customers/hr
the average throughput of the process is 10.67 customers per hour
Assume 8 hr per days → 10.67 units/hour * 8 hours/day = 85.36 units/day
Using Little’s Law to Estimate Material T
A Wendy's processes:
an average of 5,000 lb. of hamburger per week.
The typical inventory of raw meat is 2,500 lb.
In this case, throughput(R) = 5,000 lb/week; and I = 2,500 lb.
T= 2500/5000 = 0.5 weeks
Using Little’s Law to Estimate in-process inventory
A branch of Travelers Insurance Company
processes 10,000 claims per year.
The average processing time is 3 weeks.
Assuming 50 working weeks in a year
Throughput rate = 10,000 jobs/year, T = 3/50 year
I = 10,000*3/50 = 600 jobs
On average there should be 600 claims scattered across the various
processing stages
Estimating
Process Cycle
Time
Process Cycle Time
Process Cycle Time is defined as the total time a “job” spends in a
process. We will now illustrate how the cycle time for the X-Ray
process can be determined
This analysis assumes that we are able to characterize an existing
process in terms of discrete activities and that we have historical
data on the amount of time a “job” spends at each activity/stage
in the process.
Example, Process Cycle Time
Process: Getting an X-ray at a hospital
Unit of Job is defined as a patient
Entry point is defined as point at which the patient leaves the
physician's office for the X-ray lab.
Exit point defined as the point at which the patient enters the
physician’s office with the completed X-ray film.
Description
Activity
Description
1
Patient leaves the physician’s office
2
Patient walks to the X-ray lab
3
The receptionist receives the patient information
4
An X-ray technician fills out a standard form
5
Patient undresses in preparation for X-ray
6
A lab technician takes X-ray
7
A darkroom technician develops X-ray
8
The X-ray technician checks X-ray for clarity:
9
If X-ray is not satisfactory, repeat the previous steps.
Otherwise, patient puts on clothes and get ready to leave lab
10
Patient walks back to the physician’s office
11
The X-rays are transferred to the physician by a messenger
12
Patient and X-rays arrive at the Physician’s office
Process Diagram
Leave office
Walk to lab
1
Info. Process
2
X-Ray form
3
Prepping
4
5
Walk to office
10
12
Patient
AND xray back
to office
Check X-ray
Messenger
Take X-ray
7
6
YES
9
11
Develop X-ray
8
NO
Activity Cycle Time
Activity
Code
Activity
Time
(min)
Typical
Waiting
Time(min)
1
0
0
2
7
0
3
6
5
4
5
7
5
3
0
6
5
9
7
12
3
8
3
0
9
0
0
10
7
0
11
20
40
12
0
0
Based on the example, we can see
that activity cycle time is defined as
the time for a patient to undergo
each activity as well as the waiting
time.
Now let us proceed to evaluating the
process cycle time and the cycle
time efficiency (average Labor Utilization).
Historic Data
Activity
Code
Activity
Time
(min)
Typical
Waiting
Time(min)
Activity Cycle
Time
(min)
Ave. #
Of Visits
per Patient
Revised
Activity
Time (min)
Revised
Waiting
Time(min)
Revised
Act. Cycle
Time(min)
1
0
0
0
1
0x1
0x1
0x1
2
7
0
7
1
7x1
0x1
7x1
3
6
5
11
1
6x1
5x1
11x1
4
5
7
12
1
5x1
7x1
12x1
5
3
0
3
1
3x1
0x1
3x1
6
5
9
14
1.25
5x1.25
9x1.25
14x1.25
7
12
3
15
1.25
12x1.25
3x1.25
15x1.25
8
3
0
3
1.25
3x1.25
0x1.25
3x1.25
9
0
0
0
0
0x1
0x1
0x1
10
7
0
7
1
7x1
0x1
7x1
11
20
40
60
1
20x1
40x1
60x1
12
0
0
0
1
0x1
0x1
0x1
Process Cycle Time
Process Cycle time is the sum of individual activity cycle
times if there is only one path in the entire process flow
diagram
If some operations are carried out in parallel, then we need
to be concerned with the process critical path.
In a process, the “longest” path is referred to as the critical
path.
Process Cycle Time – for X-ray example
Path 1: 1-2-3-4-5-6-7-8-11-12
Path 2:1-2-3-4-5-6-7-8-10-12
Identifying the Critical Path
Process Cycle time for each path
(note the scaling of 6, 7, and 8 to denote the average time
per patient)
Path 1: 1-2-3-4-5-6-7-8-11-12
= 0+7+11+12+3+[1.25*(14+15+3)]+60+0
= 133 min
Path 2:1-2-3-4-5-6-7-8-10-12
= 0+7+11+12+3+[1.25*(14+15+3)]+7+0
= 80 min
Process cycle time
The longest path is path 1. This is then the critical path.
133 min > 80min
We can interpret this time as being the AVERAGE amount of
time a job (patient) has to spend in the process
Cycle Time Efficiency
CT efficiency is defined as:
CT efficiency = (Theoretical Cycle Time)/(Process Cycle time)*100
Theoretical Cycle Time is
the longest total time for a job to traverse the individual activities
in the process without any waiting.
Process Cycle Time
the longest total time for a job
to traverse the individual activities
in the process with any waiting.
Cycle Time Efficiency
CT efficiency
=
Theoretical CT
∗ 100
Process CT
=
Theoretical CT
∗ 100
Theoretical CT+ Waiting Time
Theoretical Cycle Time
Theoretical CT for each path
Path 1: 1-2-3-4-5-6-7-8-11-12
= 0+7+6+5+3+[1.25*(5+12+3)]+20+0 = 66 min
Path 2:1-2-3-4-5-6-7-8-10-12
= 0+7+6+5+3+[1.25*(5+12+3)]+7+0
= 53 min
Thus the theoretical CT is 66 min
Cycle Time Efficiency for the X-ray example
CT efficiency
= (Theoretical CT)/(Process Cycle Time)*100
CT efficiency = (66/133)*100 = 49.62%
Estimating
Capacity
Why is Capacity management important?
Demand > Capacity
Opportunity losses
Capacity > demand
Wasted resources, excessive fixed cost
Tools to help the capacity decision
Forecasting
Understanding uncertainty and considering the decision making
process (Spreadsheet modeling)
Breakeven analysis
Capacity Analysis
Capacity is always concerned with resources that are
allocated to perform activities.
Essentially, resources are utilized to perform activities,
i.e., they are not consumed.
Resources can be used by multiple activities and similarly,
an activity can require the use of multiple resources.
Historic Data: X – ray example
Activity
Code
Activity
Time
1
0
None
1
2
7
None
1
3
6
Receptionist
1
4
5
X-Ray Technician
1
5
3
Changing Room
1
6
5
X-Ray tech, X-Ray Lab
1.25
7
12
Dark Room Tech, Dark Room
1.25
8
3
X-Ray tech, X-Ray Lab
1.25
10
7
None
1
11
20
None
1
12
0
None
1
Resources Required
Average Number of
Visits per Patient
Resources Available/Linkages
Number of Units Available
Activity
Receptionist
1
3
X-Ray Technician
4
4,6, and 8
X-Ray Lab
2
6 and 8
Dark Room Tech
3
7
Dark Room
2
7
Changing Room
2
5
Resources Required
Activity/Resources Linkages
Resource
Receptionist
X-Ray
Technician
X-Ray
Lab
Dark Room
Tech
Dark
Room
Changing
Room
Activity
Unit Load
(m/job)
3
6
4, 6, 8
5+
1.25(5+3)
6, 8
1.25(5+3)
7
7
5
1.25(12)
1.25(12)
Activity
Code
Activity
Time
1
0
2
7
3
6
4
5
5
3
6
5
7
12
8
3
10
7
11
20
12
0
3
Activity/Resources Linkages
Resource
Receptionist
X-Ray
Technician
X-Ray
Lab
Dark Room
Tech
Activity
Unit Load
(m/job)
Activity
Unit
Cap.
Code
(job/min)
1
0
1/6
2
60/6=10
7
3
6
3
6
4, 6, 8
5+
1.25(5+3)
1/15
6, 8
1.25(5+3)
1/10
4
5
6
7
1.25(12)
7
1/15
8
Dark
Room
Changing
Room
7
5
1.25(12)
3
Activity
Cap.
Time
(jobs/hr)
60/15=4
5
3
60/10=6
Units
Available
Pool Cap.
(jobs/hr)
1
1 x 10 = 10
4
4 x 4 = 16
2
2 x 6 = 12
3
3 x 4 = 12
2
2x4=8
2
2 x 20 = 40
5
12
60/15=4
3
1/15
10
60/15=4
7
11
20
1/3
60/3=20
12
0
Bottleneck Resource
The Dark Room pool has the lowest
Resource
Pool Cap.
(jobs/hr)
Receptionist
1 x 10 = 10
X-Ray
Technician
4 x 4 = 16
X-Ray
Lab
2 x 6 = 12
Dark Room
Tech
3 x 4 = 12
capacity and is therefore the bottleneck
The theoretical capacity of a process
equals the bottleneck resource pool
capacity
Thus, the theoretical process capacity is
dictated by this resource and is 8
patients/hour
Dark
Room
Changing
Room
2x4=8
2 x 20 = 40