UNDERSTANDING PROCESSES 2 W ITH A BANKED SCHEDULE , MINIMUM CONNECT - - PowerPoint PPT Presentation

PROCESS ANALYSIS

PROFESSOR DAVID GILLEN (UNIVERSITY OF BRITISH COLUMBIA) & PROFESSOR BENNY MANTIN (UNIVERSITY OF WATERLOO)

Logistic Management in Air Transport Module 2-3 15-16 December 2014 Istanbul Technical University Air Transportation Management M.Sc. Program

UNDERSTANDING PROCESSES

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WITH A BANKED SCHEDULE, MINIMUM CONNECT TIMES DRIVE

TURNAROUND TIMES – NOT GROUND OPERATIONS

Ground Operations – Required Time for a Turnaround ( Carriers – 737-300)

41-46 min Extend jetway and

• pen door

(1 min) Deplane (10 min) (10-15 min) (13 min) Prearrival (2 min) Equipment Set Up (2 Min) Weight and Balance (2 min) Ramp (Outside) Inside

Cater

(15 min)

Clean cabin Boarding

33-43 min Ground power A/C bin door (3 min) Unload/load bags and cargo (20-30 min) Departure Dispatch (4 min) Close door and jetway (1 min) Close cargo door (1 min) Arrival Fuel (10-15 min)

Opportunities To Compress Ground Operations’ Turnaround Times

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Fuel (6-11 min)

BUT, WITH A CONTINUOUS SCHEDULE, GROUND OPERATIONS DRIVES

TURNAROUND TIME, AND THUS AIRPLANE/CREW UTILIZATION

21-31 min Extend jetway and

• pen door

(<1 min) Deplane (6 min) (2-5 min) (9-13 min) Prearrival (2-7 min) Equipment Set Up (1-2 Min) Weight and Balance (1-2 min) Ramp (Outside) Inside

Cater

(13-16 min) Cleaning

Boarding

23-32 min Ground power A/C bin door (<2 min) Unload/load bags and cargo (18-21 min) Departure Close door and jetway (<1 min) Close cargo door (<1 min) Arrival

The LCCs Have Engineered Rapid Turnaround Processes emulated on short haul routes by network carriers

Ground Operations – Required Time for a Turnaround ( Southwest – 737-300)

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AIRCRAFT TURNAROUND AT AIRPORTS:

• Activities:

– Passengers disembark – Unload luggage and freight – Load data – Clean – Fuel…

• Southwest says that if its boarding time increased by 10

minutes per flight, it would need 40 more planes at a cost

• f $40 million each to run the same number of flights it

does currently!!!

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AIRCRAFT TURNAROUND AT AIRPORTS:

• Passengers boarding is the longest activity.

In the mid-60s it took 20/minute, today 9/minute

• Have you ever wondered whether there is a better way for

boarding?

• Air Canada: back to front
• United Airlines: window first
• America West: reverse pyramid
• WestJet: random

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MATHEMATICIAN DEVISES WAY TO

BOARD AIRPLANES FASTER

A Chinese mathematician is touting a new way to get people onto commercial airline flights faster.

Dr Tie-Qiao Tang, along with a small team of researchers, has suggested that airlines should assign seating after evaluating each passenger on several variables. "Each passenger has their own individual properties. For example, each passenger's luggage has a different attribution and thus has different influences on boarding behavior; the time that the passenger's ticket is checked at the gate is different; the time that the passenger deals with his or her carried luggage is different; seat conflicts have different effects on the passenger. Each passenger has a different optimal speed, maximum speed and safe distance." Basically, passengers are evaluated by how fast they can board the plane, and

then are assigned a seat. The researchers compared their method to two others; the free-for-all, where passengers board in any order they like, and assigned seating.

According to Tang, "overtaking, queue-jumping, seat conflict congestions and jams may occur under the first two boarding strategies," but doesn't happen with Tang's proposed method. And to boot, the third method is the

fastest, according to the study.

The only problem with the method is that it would require airlines to keep detailed profile

information on their customers, like average boarding speed.

Last year, Jason Steffen, from the Fermilab Center for Particle Astrophysics, designed a system where passengers line up in a "very specific" order and then board. His method also proved faster than getting on a plane in groups or in a back-to-front order.

CBC November 13, 2012 You can find the paper at : http://www.sciencedirect.com/science/article/pii/S0968090X11001574

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http://leeds-faculty.colorado.edu/vandenbr/projects/boarding/boarding.htm 8

THE FLYING CARPET BY ROB WALLACE

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LEARNING OBJECTIVES

• Understand the following concepts:
• Tool: Process Analysis

– Process mapping – Capacity analysis (also called bottleneck analysis)

• Applications

– McDonald’s make-to-order system – Kristen’s Cookie Company

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Flow Time Bottleneck Capacity Rate Flow Time Capacity Rate

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PROCESSES

• What occurs during a transformation process?

– Processing – Waiting – Storage

Inputs Outputs

Goods Services Raw material, people, information, capital etc.

Transformation Process

EXAMPLES OF PROCESSES

Factory wood metal guitars University students alumni Distribution center bulk items small parcels Dell Electronic Components Computers

• Processes can involve both goods and services.
• Processes can have multiple inputs and/or multiple outputs.

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PROCESS ENTITIES

• Flow units: The items that flow through the process

– May be homogenous or heterogeneous

• Activities: The transformation steps in the process

– Each activity takes some time to complete

• Resources: They perform the activities

– Have capacities

• Buffers: Storage units for flow units

– May have finite size

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Packed Bread Finished Bread Raw Material

PROCESS FLOW DIAGRAM ELEMENTS

Activities, tasks or operations Buffers: Queues or inventories Decision points Flow of materials

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• Example: Bread making

Note: If different types of breads, the bread-making and packing activities may differ for each Bread Making Packing

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AN EXAMPLE OF A RESERVATION PROCESSES

Opodo’s Information system Online agency (Opodo) Uninformed customers Informed customers Buy? Uninformed Airline Informed Airline No Yes Leave Order information

LEVEL OF DETAIL IN PROCESS ANALYSIS

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Transportation to catering facility Tray assembly A/c catering Food ingredients Food ingredients Trays Catered galley

• Transportation and assembly can contain many sub-processes:
• The purpose of the process analysis determines the level of detail in

modeling the processes.

• A process can be defined at an aggregate level:

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PROCESS MEASURES

• Cost
• Quality measures
• Time (Flow measures)
• Flexibility measures
• Capacity
• This course focuses on capacity and flow measures.

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PROCESS MEASURES IN PRODUCTION AND SERVICE

Production process Service process Flow unit

Materials Customers

Input rate

Raw material releasing rate Customers arrival rate

Output rate

Finished goods output rate Customers departure rate (service completion rate)

Flow time

Time required to turn materials into a product Time that a customer is being served

Inventory

Amount of work-in-process Number of customers being served

Capacity

Maximum output rate Maximum service completion rate

KEY STEPS IN PROCESS ANALYSIS

Step 1: Determine the Purpose of the analysis

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Step 2: 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) flow chart, Gantt chart)

Step 3: Capacity Analysis (also called Bottleneck Analysis)

• Determine the capacity of each resource, and of the process

Further analysis will be covered later during the course

EXAMPLE: MCDONALD’S KITCHEN

• Purpose of the analysis: To determine the capacity rate of a

McDonald’s restaurant

• Given this purpose, we draw the process boundary around the

kitchen

– We do not consider customers’ queue – We do not consider meat cooking processes (we assume cooked meat is always available when needed during the make-to-order process)

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Link to video

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LINEAR FLOW CHART

• Flow unit: An order (each order = one burger)
• Tasks and sequences
• Flow time of each task
• Determine which resources are used in each task
• Could indicate resources along each task
• Swim-lane diagram or Gantt chart may be better

Toast buns Add dressings Add meat patties Package Deliver Place an

• rder

8s 10s 8s 6s 2s 2s

SWIM-LANE (DEPLOYMENT) FLOWCHART

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RESOURC ES ACTIVITIES Cashier Worker1 Toaster Worker 2 Worker 3 Worker 4 Worker 5

Toast buns Add dressings Add meat patties Package Deliver Place an

• rder

SWIM-LANE FLOWCHART: MODIFIED

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RESOURC ES ACTIVITIES Cashier Worker1 Toaster Worker 2 Worker 3 Worker 4 Worker 5

Toast buns Add dressings Add meat patties Package Deliver Place an

• rder

GANTT CHART

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RESOURCES ACTIVITIES Time Span Cashier Place an order Worker1 Toaster Toast buns Worker 2 Add dressings Worker 3 Add meat patties Worker 4 Package Worker 5 Deliver Time 10s 8 s 6s 2s 8 s 2s

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CHOICE OF CHARTS

• Flow chart (linear):

– how things flow

• Swim-lane flowchart:

– how things flow – how resources are shared

• Gantt chart:

– when and where things flow – when and which resources are used

• Typically, we start with flow-charting a process. If shared resources can be

clearly indicated on flow charts, we can further analyze bottlenecks, etc. Otherwise, we need to rearrange the flow chart in swim-lanes to understand how resources are shared. Gantt chart is most useful in analyzing bottlenecks of complicated systems.

• Choice of charts is an art.

PROCESS MAPPING: SOME NOTES

• There is no one way to draw a process map
• Get feedback from all the people involved in the

process to validate the process map  Do not map the process as you think it works  Map it as it actually works

• Process maps are surprisingly informative

 Common response: “I never knew we did it that way!”

• Starting point for process analysis, and a great tool

for brainstorming process improvements

27

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BASIC PROCESS ANALYSIS SINGLE STAGE PROCESS

Toast buns Toaster Worker 1

Capacity Rate ??? Flow Time (Time that buns spend in the toaster) 10 sec

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Basic Process Analysis Multiple Stage Process

Toast buns Add dressings Add meat patties Package Deliver Place an

• rder

Cashier Worker 1 Toaster Worker 2 Worker 3 Worker 4 Worker 5 8 sec 10 sec 8 sec 6 sec 2 sec 2 sec 450/hr 360/hr 450/hr 600/hr 1800/hr 1800/hr

Theoretical Flow Time of the whole process: 36 sec

Note: The theoretical flow time ignores the possibility of waiting; so it is the lowest possible flow time

Capacity rate of the whole process: 360 orders/hr Flow Time of the whole process: ??? Capacity rate of the whole process: ???

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GANTT CHART: MULTIPLE STAGE PROCESS

RESOURC ES ACTIVITIE S Time Span Cashier Place an order Worker1 Toaster Toast buns Worker 2 Add dressings Worker 3 Add meat patties Worker 4 Package Worker 5 Deliver Time 10s 8 s 6s 2s 8 s 2s 10s 8 s 6s 2s 8 s 2s

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THE BOTTLENECK

• The resource with the lowest capacity rate

– The “slowest” resource (or the resource with the highest “unit load”) – Unit load: Total amount of time the resource works to process each flow unit

• Determines the capacity rate of the entire process
• Increasing the capacity of non-bottleneck resources

does not increase the capacity rate of the process

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INCREASING THE CAPACITY RATE OF A PROCESS - WHAT IF WE ADD A CASHIER?

Toast buns Add dressings Add meat patties Package Deliver Place an

• rder

Cashiers Worker 1 Toaster Worker 2 Worker 3 Worker 4 Worker 5 8 sec 10 sec 8 sec 6 sec 2 sec 2 sec 900/hr (2 * 450/hr) 360/hr 450/hr 600/hr 1800/hr 1800/hr

Theoretical Flow Time of the whole process: 36 sec Capacity rate of the whole process: 360 orders/hr Theoretical Flow Time of the whole process: ??? Capacity rate of the whole process: ???

Place an

• rder

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INCREASING THE CAPACITY RATE OF A PROCESS - WHAT IF WE ADD A TOASTER?

Capacity rate of the whole process: 450 orders/hr Capacity rate of the whole process: ???

Toast buns Add dressings Add meat patties Package Deliver Place an

• rder

Cashier Worker 1 Toasters Worker 2 Worker 3 Worker 4 Worker 5 8 sec 10 sec 8 sec 6 sec 2 sec 2 sec 450/hr 720/hr (2 * 360/hr) 450/hr 600/hr 1800/hr 1800/hr

Theoretical Flow Time of the whole process: 36 sec Theoretical Flow Time of the whole process: ???

Toast buns

Which task is the bottleneck?

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ADDING A TOASTER: GANTT CHART

RESOURCES ACTIVITIES Time Span Cashier Place an order Worker1 Toaster 1 Toast buns Worker1 Toaster 2 Toast buns Worker 2 Add dressings Worker 3 Add meat patties Worker 4 Package Worker 5 Deliver Time 10s 8 s 6s 2s 8 s 2s 10s 8 s 6s 2s 8 s 2s Worker 1 is not busy all the time, and can take care of 2 toasters

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THINKING IN TERMS OF “UNIT LOADS”

Unit Load: Total amount of time the resource works to process each flow unit

Resource Unit Load (sec/unit) Capacity Rate (units/min) Capacity rate (units/hr) Cashier 8 7.5 450 Toaster 10 6 360 Worker 1 10 6 360 Worker 2 8 7.5 450 Worker 3 10 6 360

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INCREASING CAPACITY (1) INCREASE THE SIZE OF THE “RESOURCE POOL”

• One Toaster

Capacity rate: 360/hr

• Two Toasters

Working in Parallel Capacity rate: 720/hr

Toast buns 10 sec Toast buns 10 sec Toast buns 10 sec

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INCREASING CAPACITY (2) DECREASING THE UNIT LOAD

• This Toaster

Capacity rate: 360/hr

• Faster Toaster

Works twice as fast Capacity rate: 720/hr

Toast buns

10 sec

Toast buns

5 sec

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INCREASING THE CAPACITY RATE OF A PROCESS

• Increase the capacity rate of the bottleneck
• Some other resources may become a

bottleneck when capacity is added

– Important when we justify additional capacity

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INCREASING THE CAPACITY RATE OF A PROCESS EXPAND THE RESOURCE POOL AT THE BOTTLENECK

Capacity rate of the whole process: 450 orders/hr

Toast buns Add dressings Add meat patties Package Deliver Place an

• rder

Cashier Worker 1 Toasters Worker 2 Worker 3 Worker 4 Worker 5 8 sec 10 sec 8 sec 6 sec 2 sec 2 sec 450/hr 720/hr (2 * 360/hr) 450/hr 600/hr 1800/hr 1800/hr

Theoretical Flow Time of the whole process: 36 sec

Toast buns

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Increasing the capacity rate of a process - Reduce Unit Load at the Bottleneck

Toast buns Add dressings Add meat patties Package Deliver Place an

• rder

Cashier Worker 1 Toaster Worker 2 Worker 3 Worker 4 Worker 5

Old Flow Time

8 sec 10 sec 8 sec 6 sec 2 sec 2 sec

Old Capacity Rate

450/hr 360/hr 450/hr 600/hr 1800/hr 1800/hr

Theoretical Flow Time : ??? Capacity rate of the process: ???

New Flow Time

8 sec 5 sec 8 sec 6 sec 2 sec 2 sec

New Capacity Rate

450/hr 720/hr 450/hr 600/hr 1800/hr 1800/hr

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ANY OPERATIONAL BENEFIT OF REDUCING UNIT LOAD AT

NON-BOTTLENECKS?

Toast buns Add dressings Add meat patties Package Deliver Place an

• rder

Cashier Worker 1 Toaster Worker 2 Worker 3 Worker 4 Worker 5

Old Flow Time

8 sec 10 sec 8 sec 6 sec 2 sec 2 sec

Old Capacity Rate

450/hr 360/hr 450/hr 600/hr 1800/hr 1800/hr

Theoretical Flow Time : ??? Capacity rate of the process: ???

New Flow Time

4 sec 10 sec 6 sec 4 sec 1 sec 1 sec

New Capacity Rate

900/hr 360/hr 600/hr 900/hr 3600/hr 3600/hr

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PROCESSES MAY BE UNBALANCED

• When the next stage is busy, the order cannot be

sent to the next stage after finishing the current stage, unless an inventory buffer is introduced

Place an Order Toast buns

Flow Time 8 sec 10 sec Capacity Rate 450/hour 360/hour

Process is “Blocked”

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ANOTHER EXAMPLE

Add dressings Add meat patties

Flow Time 8 sec 6 sec Capacity Rate 450/hour 600/hour

Process is “starved”

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• The bottleneck is fully utilized while other resources are not

utilized

• If a buffer is provided at some upstream stage to the

bottleneck, inventory may build up at the buffer

• Inventory will not build up at the (immediately) downstream

stages to the bottleneck even if buffers are provided

• Shortening non-bottleneck tasks decreases flow time but does

not affect capacity rate

– Reducing flow time improves response time

BOTTLENECK CHARACTERISTICS

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PROCESS ANALYSIS: MULTIPLE FLOW UNITS

Resource Unit Load (minutes/unit) Product A Product B Product C 1 2.5 2.5 2.5 2 1.5 2 2.5 3 12 4 3 3 5 3 3 3

• If you produce only Product A, what is capacity rate of the

process (per hour)? Which resource is the bottleneck?

• If your product mix is 1 unit of A, 2 units of B and 2 units
• f C, what is your capacity rate? Bottleneck?

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PROCESS ANALYSIS: MULTIPLE FLOW UNITS

Resource Unit Load (minutes/unit)1 Product A Product B Product C 1A + 1B + 1C 1A+2B+2C 1 2.5 2.5 2.5 7.5 12.5 2 1.5 2 2.5 6 10.5 3 12 12 12 4 3 3 6 12 5 3 3 3 9 15

• When multiple flow units go through a process,

the “product mix” needs to be considered while determining the unit load and the capacity

• The bottleneck depends on the product mix

c

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• Flow diagrams are not easy to draw
• How to identify bottleneck?

– Count the total amount of work per resource (also known as the “unit load”)

• When multiple flow units go through a process, a “product

mix” needs to be considered while determining capacity

• The bottleneck depends on the product mix
• The bottlenecks can move as the product mix changes

PROCESS ANALYSIS: MULTIPLE FLOW UNITS

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• Some capacity is lost due to machine maintenance,

machine set-ups, etc.

• Example. Changing over from one product type to

another may require adjustments to the machine, tools, etc (“set-ups”)

• Railways/London Underground shut down lines to

inspect and maintain track

THEORETICAL VERSUS EFFECTIVE CAPACITY

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WHAT INFORMATION DO UNIT LOADS GIVE US?

Process with four tasks (A, B, C, D) each taking 5 minutes to complete One worker does all four tasks 4 workers working in parallel (The resource pool has four resources)

• Unit Load (for each worker) = 20 min
• Capacity rate for each worker = 3 units/hour
• Capacity rate for the resource pool = 12 units/hour

A +B+C+D (20 min) A +B+C+D (20 min) A +B+C+D (20 min) A +B+C+D (20 min) Worker 1 Worker 2 Worker 3 Worker 4

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WHAT INFORMATION DO UNIT LOADS GIVE US?

Now, suppose the work is redistributed among the four workers as follows:

• Unit Load (for each worker) = 5 min
• Capacity rate for each worker = 12 units/hour
• Capacity rate for the resource pool = 48 units/hour

Task A (5 min) Task B (5 min) Task C (5 min) Task D (5 min) Worker 1 Worker 2 Worker 3 Worker 4

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WHAT INFORMATION DO UNIT LOADS GIVE US?

• Unit Load tells you something about how work is organized

Small Unit Load for Each Resource High Unit Load for Each Resource Labor Skills Low High Equipment Specialization High Low Process Type Flow Shop Job Shop

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• An Experiment in “humanistic” production at its Kalmar and

Uddevalla plants (late 1980s)

• Teams jointly assemble cars at a fixed location, no moving

assembly line

• Plants shut down in 1993-1994
• Recommended reading

– “Edges Fray on Volvo’s Brave New Humanistic World” New York Times, July 7, 1991.

THE VOLVO EXPERIMENT

UTILIZATION

• Utilization gives us information about “excess capacity”
• The utilization of each resource in a process can be presented

with a utilization profile % 100 rate

• utput

maximum rate

• utput

Actual Rate Capacity Rate Throughput n Utilizatio   

• What is the optimal utilization of a resource?

Resource Capacity Rate (units/hour) Input Rate (units/hour) Utilization 1 6 4 66.67% 2 7 4 57.14% 3 8 4 50.00% 4 6 4 66.67% 5 5 4 80.00%

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OPERATIONAL CHALLENGE MISMATCH BETWEEN DEMAND AND SUPPLY

• In any process, the input and output rates will vary
• ver time
• A key operational challenge is matching supply

and demand

– i.e., matching the input and output rates

• For a variety of reasons, a perfect match is not

possible

– What are some of these reasons?

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AN EXAMPLE: SECURITY SCREENING AT YVR

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Time Input rate (passengers/15 min slot) Capacity rate (passengers/15 min slot) Excess Demand Excess Capacity 6:15 7 15 8 6:30 10 15 5 6:45 8 15 7 7:00 12 15 3 7:15 9 15 6 7:30 16 15 1 7:45 14 15 1 8:00 19 15 4 8:15 22 15 7 8:30 17 15 2 8:45 13 15 2 9:00 11 15 4 9:15 12 15 3 9:30 8 15 7 9:45 10 15 5 10:00 7 15 8

TOTAL 195 240

Enough capacity for the shift …

Data for a 4-hour shift in 15-min time slows: 7 arrive between 6:00 and 6:30 etc.

…but not at all times Do we have enough capacity?

SHORT-RUN VS. LONG-RUN AVERAGES

• Since the input and output rates may vary over time, both the

short-run average and the long-run average rates provide useful information.

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• Long-run average input rate must be less

than the long-run average capacity rate

• Long-run average throughput rate

= Long-run average input rate

• Short-run average input rate can be

greater than the short-run average capacity rate

But what would this lead to? Why? Why?

Rate Capacity Rate Throughput n Utilizatio 

IMPLIED UTILIZATION

• Implied utilization also allows us to capture the idea of
• vertime

– Organizations often budget for a fixed amount of capacity, and work

• vertime to meet excess demand

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• To capture the idea that there may be excess

demand in the short-run, another measure of utilization is often useful

Rate Capacity Rate Input

• n

Utilizati Implied 

SECURITY SCREENING EXAMPLE REVISITED

• What is the capacity rate?

Note: In this example, the capacity rate is given. In practice, it may not be obvious. Finding the capacity rate will involve drawing a process flow map, identifying activities, times, resources, etc, and finding the bottleneck

• What is the (average) size of the line?
• How long do passengers wait (flow time)?

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INVENTORY BUILD-UP DIAGRAM

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Time Input rate (passengers/15 min slot) Capacity rate (passengers/15 min slot) Excess Demand Excess Capacity

INVENTOR YBUILD-UP

6:15 7 15 8 6:30 10 15 5 6:45 8 15 7 7:00 12 15 3 7:15 9 15 6 7:30 16 15 1 1 7:45 14 15 1 8:00 19 15 4 4 8:15 22 15 7 11 8:30 17 15 2 13 8:45 13 15 2 11 9:00 11 15 4 7 9:15 12 15 3 4 9:30 8 15 7 9:45 10 15 5 10:00 7 15 8

TOTAL 195 240

INVENTORY BUILD-UP DIAGRAM

60 2 4 6 8 10 12 14 06:1506:3006:4507:0007:1507:3007:4508:0008:1508:3008:4509:0009:1509:3009:4510:00

Inventory Build-Up

• What is the “average inventory” in the buffer?

CALCULATING “AVERAGE INVENTORY”

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Time Input rate (passengers/15 min slot) Capacity rate (passengers / 15 min slot) Excess Demand Excess Capacity

INVENTORY BUILD-UP

6:15 7 15 8 6:30 10 15 5 6:45 8 15 7 7:00 12 15 3 7:15 9 15 6 7:30 16 15 1 1 7:45 14 15 1 8:00 19 15 4 4 8:15 22 15 7 11 8:30 17 15 2 13 8:45 13 15 2 11 9:00 11 15 4 7 9:15 12 15 3 4 9:30 8 15 7 9:45 10 15 5 10:00 7 15 8

195 240

3.1875

Empty Buffer (No Queue) Buffer NOT empty Average Inventory = 3.1875

CONSIDER ANOTHER EXAMPLE …

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Time Input rate (passengers/15 min slot) Capacity rate (passengers / 15 min slot) Excess Demand Excess Capacity

INVENTORY BUILD-UP 6:30 17 30 13 7:00 20 30 10 7:30 25 30 5 8:00 33 30 3 3 8:30 39 30 9 12 9:00 24 30 6 6 9:30 20 30 10 10:00 17 30 13

195 240

2.625

2 4 6 8 10 12 14 07:00 08:00 09:00 10:00 08:30 09:00 09:30 10:00

Inventory Build-Up

Average Inventory

… AND ANOTHER …

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Time Input rate (passengers/15 min slot) Capacity rate (passengers / 15 min slot) Excess Demand Excess Capacity

INVENTORY BUILD-UP 7:00 37 60 23 8:00 58 60 2 9:00 63 60 3 3 10:00 37 60 23

195 240

0.75

Average Inventory

0.5 1 1.5 2 2.5 3 3.5 07:00 08:00 09:00 10:00

Inventory Build-Up

… AND ANOTHER

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Time Input rate (passengers/15 min slot) Capacity rate (passengers / 15 min slot) Excess Demand Excess Capacity

INVENTORY BUILD-UP 8:00 95 120 25 10:00 100 120

195 240

Average Inventory

0.2 0.4 0.6 0.8 1

07:00 08:00

Inventory Build-Up

ESTIMATING PROCESS MEASURES

• Process measures changes over time

– Depending on the mismatch between input rate and the capacity rate the inevitably occurs over time

• We are interested in averages of these quantities
• “Average” values of process measures can be misleading
• It is often convenient to assume continuous input and
• utput processes

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DEFINITIONS

• Instantaneous Flow Rates

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Ri(t) The input rate to the process at time t Ro(t) The output rate of the process at time t ∆R(t) = Ri(t) – Ro(t) Instantaneous inventory accumulation at time t

• Inventory Level
• Flow Time

I(t) The number of units within the process boundaries at time t T(t) The time that a unit which enters (leaves) the process at time t spends (has spent) within the process

This can be defined in many ways

INVENTORY AND FLOW DYNAMICS

• Let (t1,t2) denote an interval of

time starting at t1 and ending at t2

• Suppose ∆R(t) is constant
• ver (t1,t2) and equals ∆R.

Then,

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t1 t2 I(t1) I(t2) I(t) t ∆R *(t2-t1)

) ( ) ( ) (

1 2 1 2

t t R t I t I     

2 Inventory Ending Inventory Starting Inventory Average  

Ending Inventory Starting Inventory Change in Inventory

INVENTORY BUILD-UP DIAGRAM

Capacity rate = 100/hr

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10AM 50 200 Input Rate 12PM 2PM 6PM 10AM 100 200 Inventory (or Backlog) 12PM 2PM 6PM Assumes inventory level changes in “discrete amounts” Assumes inventory level changes in “continuous amounts”

ANOTHER INVENTORY BUILD-UP EXAMPLE

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200 400 I(t) Inventory in week t 1 2 3

Week Input Rate Throughput Rate Inventory 400 1 900 800 500 2 900 1200 200 3 900 1000 100

Week

Under the continuous assumption: The average inventory? “Area under the curve”

AVERAGE INVENTORY

Average inventory depends on whether inventory is assumed to change in discrete steps, or continuously

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200 400 I(t) 1 2 3 Week

Under the discrete assumption: The average inventory over weeks 0 to 3 is 300 Under the continuous assumption: The average inventory? ??????

LITTLE’S LAW

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Average Inventory I

[units]

Average throughput rate R

[units/hr]

... ...

Average Flow Time T [hrs]

... ... ...

• Establishes a relationship between average inventory, average

throughput rate, and average flow time

LITTLE’S LAW

• Throughput rate: 1 car/min
• 900 cars in the system
• Flow time?

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car/min 1 cars 900 ) min/car 1 )( cars 900 ( Time Flow  

inventory throughput rate

(Average) Inventory = (Average) Throughput Rate * (Average) Flow Time

I = R * T

LITTLE’S LAW: EXAMPLE 1

• Patients waiting for an organ transplant are placed on a list

until a suitable organ is available. We can think of this as a

• process. Why?

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Patients matched to donated organs

INPUT Patients in need

• f a transplant

OUTPUTS Patients leaving the list hopefully with a successful transplant

LITTLE’S LAW: EXAMPLE 1

Question (a)

• On average, there are 300

people waiting for an organ transplant

• On average, patients wait on

the list for 3 years

• Assume that no patients die

during the wait

• How many transplants are

performed per year?

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300 patients

?? / year

3 years in system

I = R * T

Inventory I = 300 patients Flow Time T = 3 years Throughput Rate R = I/T = 100 patients / year

LITTLE’S LAW: EXAMPLE 1

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Question (b)

• On average, there are

300 people waiting for an organ transplant

• On average, 100

transplants are performed per year

• Assume that no patients

die during the wait

• How long do patients

stay on the list?

300 patients

100/year

??? years in system

I = R * T

Inventory I = 300 patients Throughput R= 100 patients/year Flow Time T = I/R = 3 years

LITTLE’S LAW: EXAMPLE 2

• You are managing the construction of a new container terminal

at the Port of Vancouver. You expect to “process” 1000 contains/day, and you have promised customers that containers will spend no more than 1 day waiting to be shipped.

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INPUT Containers to be shipped OUTPUT Containers shipped

LITTLE’S LAW: EXAMPLE 2

Question (a)

• On average, your container storage yard can hold 500

containers.

• Is your yard big enough?

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LITTLE’S LAW: EXAMPLE 2

Question (b)

• Suppose the yard is expanded to hold 2000 containers
• Since container traffic is growing rapidly, you are soon

processing 2000 containers/day

• You are asked to make improvement to the terminal to

handle 4000 containers/day

• But there is no more room to expand the yard
• What changes can you make in order to process 4000

containers/day?

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INSIGHTS FROM LITTLE’S LAW

• Throughput rate, flow time, and inventory are related
• Depending on the situation, a manager can influence any
• ne of these measures by controlling the other two

– You cannot independently choose flow time, throughput and inventory levels! – Once two are chosen, the third is determined – For example, if the flow time is fixed, the only way to reduce inventory is to increase throughput

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INSIGHTS FROM LITTLE’S LAW

• How would you reduce wait time for patients on the

transplant waiting list?

– Increase throughput rate – Decrease number of people on the list (inventory)

• How would you increase throughput rate of containers at

the port

– Decrease flow time – Increase “inventory”

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LITTLE’S LAW: EXAMPLE 3

• Wal-mart imports Product X from an overseas factory. Each
• rder from Wal-mart goes through several stages before it gets

through several stages before it gets to the store, and it takes time to “flow” each stage

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Port 1 day Ship Warehouse Factory 2 days 5 days 3 days

• How much inventory is tied up at the warehouse?

[Hint: What information is missing?]

• How much inventory is tied up in the supply chain?

Little’s Law can be applied to any process, or any part of a process

LESSONS

• Capacity rate versus throughput rate (Utilization)
• “Short-run” versus “long-run” averages
• Input and output rates vary over time resulting in

– Excess capacity – Inventory build-ups

• Inventory build-up diagrams are useful tools, but

– Average can be misleading; need to be carefully calculated

• Little’s Law helps make the connection between average

flow measures

• 3 key performance measures-inventory, flow rate, flow

time

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LINE BALANCING: BATCHING DECISIONS

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Milling Machine Assembly Process

LINE BALANCING: BATCHING DECISIONS

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Milling Machine Assembly Process Steer support parts: 1 min; 1 per unit Two ribs: 0.5 min; 2 per unit

• Set up times: 1 min to switch over.
• What is optimal batch size?

THE IMPACT OF SET-UP TIMES ON CAPACITY

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Batch of 12 Batch of 60 Batch of 120 Batch of 300 Time [minutes] 60 120 180 240 300 Set-up from Ribs to Steer support Set-up from steer support to ribs Produce ribs (1 box corresponds to 24 units = 12 scooters) Produce steer supports (1 box corresponds to 12 units = 12 scooters) Production cycle Production cycle

60 min (set up) + 12 min (steering) + 60 min (set up) +12 min (ribs) = 144 min  Capacity = 12/144=0.0833 60 min (set up) + 300min (steering) + 60 min (set up) +300 min (ribs) = 720min  Capacity = 300/720=0.4166

1/p 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 10 50 90 130 170 210 250 290 330 370 410 450 490 530 570 610 650 Batch Size

Capacity as a function of the batch size

BATCHING AND INVENTORY

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Production with large batches Production with small batches Cycle Inventory End of Month Beginning of Month Cycle Inventory End of Month Beginning of Month Produce Sedan Produce Station wagon Production with large batches Production with small batches Cycle Inventory End of Month Beginning of Month Cycle Inventory End of Month Beginning of Month Produce Sedan Produce Station wagon Production with large batches Production with small batches Cycle Inventory End of Month Beginning of Month Cycle Inventory End of Month Beginning of Month Produce Sedan Produce Station wagon Production with large batches Production with small batches Cycle Inventory End of Month Beginning of Month Cycle Inventory End of Month Beginning of Month Produce Sedan Produce Station wagon

THE IMPACT OF SET-UP TIMES ON CAPACITY

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Inventory [in units of xootrs] Time [minutes] 200 260 600 Set-up from Ribs to Steer support Set-up from steer support to ribs Produce ribs Produce steer supports Production cycle 460 520 800 860 1200 1060 1120 1400 1460 Idle time 133 Rib inventory Steer support inventory

Consider B=200

60 min (set up) + 200 min (steering) + 60 min (set up) +200 min (ribs) = 520 min

Milling Assembly: 3 min

Produce ribs at 1 per min Assembly requires 1 per 3 min So inventory accumulates at 2 per 3 min  200*2/3=133.3 This amount of 133.3 is sufficient for 133.3*3 = 400 min. That is, until 200 + 400 = 600 min Hence, 80 min idle time

ELIMINATE IDLE TIMES

• If B=12:
• To balance the line, solve:
•  B=120

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Milling Machine Assembly Process

Set-up time, S 120 minutes

• Per unit time, p

2 minutes/unit 3 minutes/unit Capacity (B=12) 0.0833 units/minute 0.33 units/minute Capacity (B=300) 0.4166 units/minute 0.33 units/minute

𝐷𝑏𝑞𝑏𝑑𝑗𝑢𝑧 𝐶 = 𝐶𝑏𝑢𝑑ℎ 𝑡𝑗𝑨𝑓 𝑇𝑓𝑢𝑣𝑞 𝑢𝑗𝑛𝑓 + 𝐶𝑏𝑢𝑑ℎ 𝑇𝑗𝑨𝑓 ∗ 𝑄𝑠𝑝𝑑𝑓𝑡𝑡𝑗𝑜𝑕 𝑢𝑗𝑛𝑓 =

𝐶 𝑇+𝐶∗𝑞 = 12 120+12∗2 = 0.0833 𝑣𝑜𝑗𝑢/𝑛𝑗𝑜

𝐶 120 + 𝐶 ∗ 2 = 1 3 𝑣𝑜𝑗𝑢/𝑛𝑗𝑜

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 10 50 90 130 170 210 250 290 330 370 410 450 490 530 570 610 650 Capacity of slowest step other than the

• ne requiring set-up

Batch size is too large Batch size is too small,

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PROCESS MEASURES: FLOW MEASURES

• Identify “flow units”

– What is my “product”?

• Flow Rates (Input Rate and Output Rate)

– What is the demand on my system, and what is my capacity?

• Flow Times (Time spent in process)

– How long does it take me to produce one “product”?

• Inventory

– How much inventory (of flow units) is building up? – Where do I need to hold inventory?