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Assignments and Group Cases
! Assignment 1 (Due Sunday, Jan 30, 11:59 pm – UTORMAT)
! Finalize Groups (Due Sunday, Jan 30, 11:59 pm – Quercus )
! Assignment 2 (Due Sunday, Feb 6, 11:59 pm UTORMAT)
! Assignment 3 (Due Sunday Feb 13, 11:59pm – UTORMAT)
! Case 1 (Due Sunday Feb 27, 11:59pm – Quercus) !
! Assignment 4 (Due Sunday March 20, 11:59pm – UTORMAT)
! Assignment 5 (Due Sunday March 27, 11:59pm – UTORMAT)
! Assignment 6 (Due Sunday, April 3, 11:59 pm – UTORMAT)
! Case 2 (Due April 8th, 11:59 pm – Quercus)
Midterm Exam: Feb 18th , 7pm-9pm, (2 hrs)
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The lectures will be virtual until after reading week.
Key Steps in Process Analysis
Process Analysis
Review of Lecture 2: Process Analysis
Determine the purpose of the analysis. Process Mapping: Define the process.
Determine the flow units
Determine the tasks (sub-processes), and the sequence of the tasks 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) flowchart Gantt chart
Capacity Analysis (also called Bottleneck Analysis): Determine the capacity of each resource and of the process.
Process Mapping Toolboxes
Process Analysis
Review of Lecture 2: Process Mapping Toolboxes
Linear Flow Chart: is a graphical way to describe the process. It is a collection of boxes, triangles, and arrows. Boxes stand for process steps (which can themselves be processes).Triangles represent waiting areas or bu↵ers holding inventory. Arrows represent the route of flow of the flow units. If there are di↵erent flow units that take di↵erent routes through the process flow diagram, it can be helpful to use di↵erent colors for the di↵erent routes.
Swimlane Chart: The swim lane flowchart di↵ers from other flowcharts in that processes and decisions are grouped visually by placing them in lanes. Parallel lines divide the chart into lanes, with one lane for each person, group or subprocess. Lanes are labelled to show how the chart is organized.
: is a type of bar chart, that illustrates a process schedule. Gantt chart shows the process steps and their durations (represented by the length of the bar). It also represents the dependency between various process activities.
Review of Lecture 2
Process Analysis
Process Analysis with one type of flow unit
Draw the process flow diagram. Find the capacity of every resource. If there are multiple resources performing the same activity, add their capacity together.
The resource with the lowest capacity is called the bottleneck. Its capacity determines the capacity of the entire process (process capacity).
The throughput rate is found based on
throughput rate or Output rate = min (input rate, process capacity). We find the utilization as
Utilization = Throughput rate , Capacity
When calculating utilization for resources aligned in series. NOTE: For parallel resources( their capacities are added), the utilization of each resource
Review: Basic Process Flow Analysis
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
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: __________ s
Add dressings
Add meat patties
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?
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
What if we buy a faster toaster?
Package Deliver
Cashier Worker 1 Worker 2 Worker 3 Worker 4 Worker 5
8s 6s 8s 6s 2s 2s 450/hr 600/hr 450/hr 600/hr 1800/hr 1800/hr
Place an order
Toast buns
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
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
Add meat patties
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.
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
! The bottleneck is fully utilized (ρ=1) while other
resources are not fully utilized (ρ≤1). ! 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?
Unbalanced multi-stage processes
Place an order
Flow time: 8s 10s Capacity rate: 450/hr 360/hr
Process is “blocked”
When the next stage is busy, the order cannot be sent to the next stage after finishing the current stage.
Toast buns
The role of inventory buffers
Place an order
Toast buns
Flow time: 8s Capacity rate: 450/hr
10s 360/hr
What role does the buffer play?
Place an order
Toast buns
Another “unbalanced” process
Add dressings
Add meat patties
Flow time: 8s 6s Capacity rate: 450/hr 600/hr
Process is “starved”
Buffer Examples
! 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 would you add buffers to the system (minimum number of buffer)?
Buffer Examples
Buffer and Bottleneck
! 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
Today’s Lecture:
Little’s Law, Inventory Build-up &
Capacity Analysis
! We return to process analysis
! with the flavor of variability – We learn about
– Implied utilization
– Inventory Build-up diagram – Little’s Law
! It now gets a little more realistic. 21
What is Variability?
! Definition:
– The randomness associated with a process.
– The extent at which measurements of the performance of a process differ from each other.
! In reality, all processes exhibit variability as nothing is completely predictable!
Types of Variability: Thanksgiving Example
! Predictable variability refers to “knowable” changes in input and/or capacity rates
– Mean demand for turkey will go up close to Thanksgiving
! Unpredictable variability refers to “unknowable” changes in input and/or capacity rates
– Supply of turkey changes each year due to crop yield
– Exact demand for turkeys each day
! Both types of variability exist simultaneously
– Turkey sales will go up during Thanksgiving, but we do not know the exact demand for turkey
Where does it come from?
Security Checking
! Variability comes from – Variable input rate
– Variable capacity rate
Predictable Variability
! Predictable variability can be controlled by making changes to the system
– We could increase or decrease the demand for turkeys by increasing or decreasing the price
! Other examples of predictable variability
– Demand for swimsuits in the winter
– Students in office hours right before the midterm – Demand for uber during rush hours
Review from Class 2:
long run, Single Stage, Single Machine/Server (no variability)
Input rate
[units/hr] … … …
Output rate
[units/hr] … …
Inventory [units]
Flow Time [hr]
Capacity Rate = 1 / FlowTime [units/hr]
§ For large input rate, only for single stage.
§ The maximum possible output rate that can be achieved.
Output rate = min{Input Rate, Capacity Rate} [units/hr]
Utilization = Throughput Rate / Capacity Rate (dimensionless) 26
So far we focused on the long run
Input rate
[units/hr]
… … …
Output rate
[units/hr]
Coffee Shop
Capacity rate is defined as the maximum possible output rate.
! But, we also discussed that in the short run: – Input Rate > Capacity Rate
» Throughput rate = Capacity rate
– Input rate < Capacity rate
» Throughput rate = Capacity rate if Inventory>0 » Throughput rate = Input rate if Inventory=0
Short Run Analysis: Funnel Analogy
• In the short run, the input rate can be larger than the capacity rate for a period of
§ A properly sized buffer is
needed to store units waiting Buffer to be processed (build-up
inventory)
Implied Utilization vs. Utilization
! Utilization = Throughput Rate / Capacity Rate
= Actual output rate / maximum output rate
! Implied Utilization= Input Rate / Capacity Rate
! Note that in the short-run, the implied utilization can be greater than 100% (i.e., utilization > 1.0).
! In the long run, Implied Utilization = Utilization. 29
Utilization Profile
! Assume “short run” input rate = 7 units/hr à throughput rate = 5 units/hr
Capacity rate
Utilization
“Short run” Implied utilization
Inventory In Process Analysis
! Flow units (ex. Customers, raw materials, vehicles) awaiting their turn to enter the process as well as units that are currently being served.
! They are waiting in a queue or a buffer.
! Flow units can be extracted from the buffer or
served in a variety of ways.
– The way in which flow units are served is called the service policy (FCFS, LCFS, Priority Service).
! How do we track the queued inventory? 31
Class Exercise (Five minutes breack)
! A Clinic is providing service from 8:00 until 9:45 AM to patients. To keep track of demand and how much time people spent waiting in the clinic, you as an observer arrived there at 7:45, made yourself comfortable at the entrance of the unit. You observed that 7 customers arrived to clinic from 8 AM-9:45 AM and you recorded the following chart of the number of people waiting in the waiting room (no patient is waiting from 9:30 to 9:45).
1. What does the area under the curve represents (the blue area)?
2. Using the chart, what is the average number of patients waiting in the waiting area during your stay(average inventory) from 8-9:45AM? (hint: use (1)).
3. Using only the chart, can you calculate the average amount of time in minutes that a patient spent waiting to be called in the clinic? (hint: use (1) ).
4. What does average inventory over average time patients spend waiting represents? (hint: use (2) and (3)).
Class Exercise
1. What does the area under the curve represents (the blue area)?
(2+3+4+3+2+1) (15) = (15)(15) = 225
Total minutes patients waiting!
Class Exercise
2. Using the chart, what is the average number of patients waiting in the waiting area during your stay(average inventory) from 8-9:45AM? (hint: use (1)).
I = !”#$ = !”#$ =++) =2.14 %&'() *&) *&)
Class Exercise
3. Using only the chart, can you calculate the average amount of time in minutes that a patient spent waiting to be called in the clinic? (hint: use (1) ).
T= 𝑨𝒓𝒆𝒂 = 𝟐𝟐𝟓 = 32.14 min 𝟕𝟕
Average Waiting Time
Class Exercise
4. What does average inventory over average time patients spend waiting represents? (hint: use (2) and (3)).
!!”#$ # = %&'() =
” !”#$ $%&'( *
Number of patient served per unit of time = Average Throughput Rate
Little’s Law
Average Inventory = (Average Throughput Rate) . (Average Waiting Time)
Build-up Diagrams
Think of work as being liquid
• Predictable Variability
• Short Run Analysis
• Input Rate > Capacity Rate ok • Variable rates ok
• Build-up Rate = Input Rate – Capacity Rate
Inventory build-up: example 1 , Coffeeshop
co↵ee shop opens at 11AM and the sta↵ reported that the demand rate between 11AM till noon is 75 customers per hour and from noon to 1PM it is at the rate of 100 customers per hour. Also they reported that their serving capacity is at the constant rate of 50 customers per hour. Draw the inventory build up diagram from 11AM until 1PM.
Inventory Buildup:
Coffee Example #1
– Input Rate = 75 units/hour, 11:00am – 12:00noon = 100 units/hour, 12:00noon – 1:00pm
– Capacity Rate = 50 units/hour – Build-up Rate = ?
Inventory (or backlog)
11am 12pm 1pm
Metropolis co↵ee shop opens at 11AM, and the sta↵ reported that the demand rate between 11-12noon is 75 customers/hour, and from 12-1PM it is at the rate of 100
co↵ee shop opens at 10AM, and the sta↵ reported that the demand rate between 10-12noon is 50 customers/hour, from 12-2PM it is at the rate of 200 customers/hour, and from 2-6PM it is at the rate of 50 customers/hour. Also, they reported that their serving capacity is the constant rate of 100 customers/hour. Draw the inventory build-up diagram between 10-6PM. Can they serve all demand before closing at 6PM?
city is the constant rate
of 50 customers/hour. Draw the inventory build-up diagram between 11-1PM.
Inventory Build-up: Example 2
Input Rate
Inventory Build up = Input rate – Capacity
10:00-12:00
50-100 = -50 C/h (No Inventory)
12:00-2:00
200-100 = 100 C/h
50-100 = -50 C/h
Inventory Buildup: Example #2
Input Rate
10am 12pm 2pm
Inventory 200
10am 12pm 2pm
Customers/hour
Capacity rate = 100 units/hour
10am 12pm 2pm 6pm
Inventory Buildup: Example #2
Customers/hour 200
Capacity rate = 100 units/hour
Input Rate
10am 12pm 2pm 6pm
Inventory 200
Inventory Buildup: Cranberry Example
During harvesting season, a processing factory works around the clock.
! Farmers deliver their loads of cranberries from 12am to 12pm (last
truck arrives at 11 am) at a constant rate of 2 tons/hour.
! The fruits are dumped into a big storage bin and processed at a rate of 1 ton/hour.
• Draw an Inventory buildup diagram.
(Assume the flow unit is cranberries and that the they arrive
at the station at a constant pace all day).
• What is the average inventory of cranberries in the factory?
Inventory Buildup: Cranberry Example
Input: 2 Tons/h
Capacity: 1 Ton/h
Drop hours of Trucks: 12 hours Processors work for 24 hours
12 AM-12 PM:
Input rate = 2 Tons/hour:
Build up inventory = 2-1 Ton/hour 12 PM-12 AM:
Input rate = 0
Build up inventory = 0-1 = -1 Ton/h
Inventory Buildup: Cranberry Example
Average Inventory in the System (Area Under the Curve) / (Time)
Inventory Buildup: Cranberry Example
! What is the average inventory? Average Inventory = ()*+ ,- .)/0123+)
Area = (78) (78:78) = (6)(24) = 144 8
Average Inventory = ()*+ = 7;; = 6 8; 8;
.,4+3 ./5*
Inventory Buildup: Cranberry Example Continued
Suppose the storage bin has room to hold only 6 tons of cranberries. Once this space is filled, the farmers’ trucks must wait to dump their contents
! Notice there are now two buffers: » Cranberry buffer
» Truck buffer
Questions:
What would happen if there was no truck buffer? What is the average inventory of cranberries
• In the bin?
• In the trucks?
• In both?
Do we lose any cranberries?
Inventory Buildup: Cranberry Example
Average Inventory in the System (Area Under the Curve) / (Time)
Storage bin
Inventory Buildup: Cranberry Example Continued
Now let us change the flow unit to a “truck”
! Assumptions:
– Each truck carries 1 ton of cranberries, i.e., two trucks arrive
every hour between 12:00am to 12:00pm.
– The storage bin has a capacity of 6 tons.
– At the start of every hour, the processor takes 1 ton of cranberries from the storage bin.
• Draw an Inventory buildup diagram of trucks.
• At what time will the trucks likely start to wait to unload?
• What is the “average” inventory of trucks waiting? 51
Inventory Buildup: Cranberry Example Continued
7 6 5 4 3 2 1 0
Inventory of trucks
0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00
10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00
Number of trucks waiting
Little’s Law: Introduction & Capacity Analysis
! Establishes a relationship between:
! Average Inventory
! Average Throughput Rate
! Average Flow Time
… … …
Average Inventory
Average Throughput Rate [units/hr]
… … …
Average Flow Time
Little’s Law:
Coffee Example
… … … … …
Average Waiting Time (T) [hr]
! Time to make one coffee: 30 seconds
What is the throughput rate in minutes?
! 60 customers in the system (Inventory) Waiting time:
Waiting Time = 60 customers * 0.5 (min/customer) Waiting Time = 60 customers / 2 (customer/min) Waiting Time = Inventory / Throughput Rate Inventory = Throughput Rate x Waiting Time
Coffee Shop
Little’s Law:
Big Reveal & Key Equation
Inventory = Throughput Rate x Waiting Time I= RxT
! We are talking about an inventory of flow units: – Could be customers in a restaurant
– Claims in an insurance company
– Materials in a manufacturing industry
! This equation can be re-arranged to solve for other quantities depending on the question!
Little’s Law:
Remember the Units
Inventory = Throughput
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