编程代考 Operations Management

Operations Management
Lecture 2 Process Analysis
After-class slides only contains the
new material and does not include

the review of the previous class
which we do in class

Learning Objectives
! Process Analysis: Understand the concepts » Utilization
» Capacity (rate)
» Flow time
» Throughput rate (output rate) » Cycle time
» Bottlenecks
! Toolbox: Process Analysis
– Process mapping
– Capacity analysis (also called bottleneck analysis)

Basic Process Measures: Utilization
Utilization (ρ)
Ratio of time a resource is used relative to the time it is available (dimensionless quantity).
⇢ = How often the resource is being used . total availability time
Commercial Call Center: 90%
Car Factory Robot: 80% Emergency Call Center:

Basic Process Measures
Capacity (rate)
Dictionary definition: “the maximum amount that something can contain”. General Business Definition
Ø The amount of output that a system is capable of achieving over a period of time.
Ø The maximum possible output or service rate.
Bank: 200 customers/day Car Factory: 10,000 cars/month

In SingleTeller bank, it takes the teller 15 minutes to serve a customer. Every 30 minutes a customer goes to the teller.
– What is the flow unit?
– What is the capacity? 1/15 customer/minute= 4 customer/hour
– At what rate the process generates output? 1/30 customers/minute=2 customers/hour
– What is the utilization of the teller? (1/30)/(1/15)=1/2 =50%

Capacity, Input Rate, Output Rate

Process Flows:
Single Stage, Single Machine/Server
Input rate
[units/hr]
Output rate
[units/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 (flow rate).
Utilization = Throughput Rate / Capacity
= min{Input Rate, Capacity} / Capacity
Flow Time [hr]
= min{Input Rate / Capacity, 1}

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:
ØWhat happens if input rate is greater than capacity?
Inventory builds up
ØWhat happens if input rate is less than capacity?
– In the long-run:
ØWhat happens if input rate is greater than capacity? The system becomes unstable, overflow of input, loss of input
ØWhat happens if input rate is less than capacity?

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)

Long Run Analysis
• In the long run, the input rate must be no larger than the capacity rate (otherwise, we will have input lost)
What goes in the process, must come out of the process. Input rate must be less than or equal to the capacity rate; Otherwise the system will overflow (input lost).

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.

Basic Process Measures in Production and Service Operations
Production process
Service process
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)
Time required to turn materials into a product
Time that a customer is being served
Amount of work-in-process
Number of customers being served
Capacity (rate)
Maximum output rate
Maximum service completion rate

Key Steps in Process Analysis
! Step 1: Determine the purpose of the analysis
! Step 2: Process Mapping (Define the process)
– Determinetheflowunits
– Determinethetasks(sub-processes),andthesequenceofthetasks – Determinethetimeforeachtask
– Determinewhichresourcesareusedineachtask
– Determinewhereinventoryiskeptintheprocess
– Recordthisthroughaprocessflowdiagram » Linear flow chart
» Swim-lane (deployment) flowchart
» Gantt chart
! Step 3: Capacity Analysis (also called Bottleneck Analysis) – Determinethecapacityofeachresourceandoftheprocess
Further analysis will be covered later during the course.

‘s / J Suppose we order a Hot Breakfast Sandwich (490
Cal, 31g Fat):
! Purpose of the analysis:
– To determine the capacity (rate) of the ’s
make-to-order (“Made-just-for-you”) system.
! 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).

Hot Breakfast Sandwich Steps
Recall from process mapping:
We observed the following steps:
– Determine the flow units
– Determine the tasks (sub-processes),
– and the sequence of the tasks
– Determine the time for each task 2.
– Determine which resources are used in each task
– Determine where inventory is kept in the process 3.
– Record this through a process flow diagram
» Linear flow chart
» Swim-lane (deployment) flowchart » Gantt chart
1. Cashiers takes the order (8s)
Worker1 toasts buns (it takes the toaster 10s)
Worker2 adds dressing (8s)
4. Worker3 adds meat patties (6s)
5. Worker4 wraps it (2s)
6. Worker5 delivers (2s).

Linear Flow Chart
Activities
Material Flows
Inventory buffers
Work in Process

Linear Flow Chart
! Flow unit: an order
– Assume each order contains only one burger
! Tasks and sequences
! Flow time of each task
Cashier Worker 1 Worker 2 Worker 3 Worker 4
8s 10s 8s 6s 2s 2s
Determine which resources are used in each task – Could indicate resources along each task
– To do this, Swim-lane diagram or Gantt chart are better
Place an order
Toast buns
Add dressings
Add meat patties

Swim-lane (deployment) flowchart
Worker 1 Toaster
Place an order
Activities
Toast buns
Add dressings
Add meat patties

Swim-lane (deployment) flowchart
Worker 1 Toaster
Activities
Place an order
Toast buns
Add dressings
Add meat patties

Worker 1,Toaster Worker 2
Activities
Place an order Toast buns
Add dressings Add meat patties Package

Capacity Analysis: Single Stage Process
Add Patties
! Flow Time (time customers spend): we refer to this as activity time.
! Capacity Rate (assume sufficient demand rate)? 600 orders / hour

Pipes with Different Capacities

Capacity Analysis: Multiple Stage Process
Place an order
Toast buns
Add dressings
Cashier Toaster Worker 2 Worker 3 Worker 4 Worker 5 Worker 1
8s 10s 8s 6s 2s 2s 450/hr 360/hr 450/hr 600/hr 1800/hr 1800/hr
Flow time of the whole process: __________ s
≠ 1/FlowTime
Capacity rate of the whole process: __________ orders / hr Throughput rate of the whole process: ___3_6_0_____ orders / hr Utilization (ρ) of each worker?
Add meat patties
Package Deliver

Place an order
Toast buns
Toaster Worker 1
10s 360/hr
Add dressings
Add meat patties
The Bottleneck
Worker 2 Worker 3 Worker 4 Worker 5
8s 6s 2s 2s 450/hr 600/hr 1800/hr 1800/hr
! The slowest resource in a process is called the bottleneck (i.e., it is the slowest link).
! The bottleneck process determines the capacity rate of the entire system.

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/(output rate)

Multiple Stage Process Revisited
Package Deliver
Cashier Toaster Worker 2 Worker 3 Worker 4 Worker 5 Worker 1
8s 10s 8s 6s 2s 2s 450/hr 360/hr 450/hr 600/hr 1800/hr 1800/hr
Place an order
Toast buns
Flow time of the whole process: __________ s
Add dressings
Capacity rate of the whole process: __________ orders / hr Throughput rate of the whole process: ___3_6_0_____ orders / hr Cycle time of the whole process: _______10s___ s
Add meat patties

Parallel Pipes

What if we add a cashier?
Place an order
Toast buns
Add dressings
900/hr 360/hr 450/hr 600/hr 1800/hr (2 x 450/hr)
Flow time of the whole process: __________ sec
Capacity rate of the whole process: __________ orders / hr
Throughput rate of the whole process: __________ orders / hr
Utilization of each worker? Cashier1: 40%, cashier 2:40%, toaster,w1:100%, w2:80%, w3:60%, w4: 20%,w5:20%
Add meat patties
Package Deliver
Place an order
Cashier 1 Toaster Worker 2 Worker 3 Worker 4 Worker 5 Worker 1
8s 10s 8s 6s 2s 2s

Toast buns
Toaster Worker 1
10s 360/hr
Place an order
Add dressings
Add meat patties
Package Deliver
The Bottleneck Revisited
Worker 2 Worker 3 Worker 4 Worker 5
8s 6s 2s 2s 450/hr 600/hr 1800/hr 1800/hr
! The slowest resource in a process is called the bottleneck (i.e., it is the slowest link).
! The bottleneck process determines the capacity rate of the entire system.
! Capacity increase of non-bottleneck processes do not increase the capacity rate of the entire system

What if we add a toaster?
Toast buns
Place an order
Cashier Toaster 1 Worker 2 Worker 3 Worker 4 Worker 5 Worker 1
8s 10s 8s 6s 2s 2s
450/hr 720/hr 450/hr 600/hr (2 x 360/hr)
1800/hr 1800/hr
What if we add
a third toaster?
Capacity of the whole process
will not change
Flow time of the whole process: _________ sec
Which task is now the bottleneck?
Capacity rate of the whole process: ________ orders / hr
Cycle time of the whole process : ________ s
Add dressings
Add meat patties
Package Deliver
Toast buns

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?
! How to improve a process?
! Add capacity to the bottleneck. This is an improvement if the value of the extra capacity exceeds
the cost of the extra capacity.
! Improve balance by moving work from the bottleneck activity to a non bottleneck activity.
! Determine the best span of control for a worker.
! If a process is demand rather than capacity constrained, stimulate demand by offering additional value to the customer, e.g. higher quality more product variety or shorter lead time.

Are there any operational benefits of reducing flow time at non-bottlenecks?
Place an order
Toast buns
Add dressings
Old Flow time:
8s 10s 8s 6s 2s 2s
Old Capacity rate:
450/hr 360/hr 450/hr 600/hr 1800/hr 1800/hr
4s 10s 6s 4s 1s 1s rate:
900/hr 360/hr 600/hr 900/hr 3600/hr 3600/hr
Shorter flow time will make it easier to rapidly respond to customers and it may result in higher prices (better service). Assuming that the business is capacity constrained, i.e., there is sufficient demand that you could sell any additional output you make.
Add meat patties

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
– The length of time a unit spends in the system
! Cycle time
– The Inverse of the output 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!

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.

Readings & More…
! For a better grasp of the key concepts, the following readings are only recommended:
Chapter 3 of the tailored book.
! For next class, please:
– Take a good look materials posted on Quercus. – Please finalize your groups for the case studies.
! Next Class: Little’s Law and Inventory Build-up

Upcoming Deadlines and Reminders
! Assignement 1: January 30th , 11:59PM sharp. Post on
utorsubmit:https://submit.utm.utoronto.ca/utorsu bmit/
– Please follow the instructions given on the assignment carefully.
! Please try to form groups of upto 4 and submit your group list(Due January 30th , 11:59 PM). Mahsa posted the instructions Quercus.
! Midterm Exam: Feb. 18th, 7 PM- 9 PM on quercus. –
Please let me know if you have an academic conflict with the
midterm (let me know by Jan 30
the latest)

(Visualize Cycle Time)
Resources Activities
Cashier Worker 1 Worker 2 Worker 3 Worker 4 Worker 5
Place order Toast buns
Add dressings Add meat patties Package
2s 2s 2s 2s 10s 2s 10s 2s

Appendix: Adding a toaster:
Activities
Place an order
We assume worker 1 is not busy all the time and can take care of two toasters.
Wkr 1,Toaster 1Toast buns
Wkr 1,Toaster 2
Toast buns Add dressings
Add meat patties Package
Worker 2 Worker 3 Worker 4 Worker 5
2s 2s 8s2s

Appendix: Example: Adding one cashier and relocating one worker: Gantt chart
Wkr 1,Toaster 1
Wkr 1,Toaster 2
Activities
Place an order
Place an order
Toast buns
Toast buns
Add dressings
Add dressings
Add meat patties Package and Deliver
We assume worker 1 is not busy all the time and can take care of two toasters.

Appendix: Example: What if we further add one cashier and relocate one worker?
Cashier 2 Toaster 2
Place an order
Toast buns
Add dressings
Add meat patties
Package and deliver
Place an order
Toast buns
Add dressings
Cashier 1 Toaster 1 Worker 2 Worker 3 Worker 5 Worker 1
8s 10s 8s 6s 4s 900/hr 720/hr 900/hr 600/hr 900/hr
2 x 450/hr 2 x 360/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: ____6____ seconds/ order
Add meat patties station

Appendix: Self-Test: Question 1
What is the difference between (a) and (b)? (a) Two parallel 10-sec toasters:
Toast Toast
(b) One faster 5-sec toaster:
Same capacity
however the second process has shorter response time

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