UNDERSTANDİNG PROCESSES - Anasayfa

OPERATİONS & LOGİSTİCS MANAGEMENT İN AİR TRANSPORTATİON

PROFESSOR DAVİD GİLLEN (UNİVERSİTY OF BRİTİSH COLUMBİA )&PROFESSOR BENNY MANTİN (UNİVERSİTY OF WATERLOO)

Air Transportation Systems and Infrastructure

Strategic Planning

Module 2-3 : 9-10 June 2014

Istanbul Technical University

Air Transportation Management

M.Sc. Program

UNDERSTANDİNG PROCESSES

2

LEARNİNG OBJECTİVES• 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

3

Flow Time BottleneckCapacity RateFlow Time Capacity Rate

4

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

metalguitars

Universitystudents alumni

Distribution

centerbulk items small parcels

DellElectronic

ComponentsComputers

• Processes can involve both goods and services.

• Processes can have multiple inputs and/or multiple outputs.5

PROCESS ENTİTİES

• 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

6

Packed

Bread

Finished

Bread

Raw

Material

PROCESS FLOW DİAGRAM ELEMENTS

Activities, tasks or operations

Buffers: Queues or inventories

Decision points

Flow of materials

7

• Example: Bread making

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

Bread

MakingPacking

8

AN EXAMPLE OF PROCESSES AT DELL

Dell’s

Information

system

Dell online

or

Telephone

Uninformed

customers

Informed customersBuy?

Uninformed

suppliers

Informed

suppliers

No

Yes

Leave

Order information

TransportationComponents

at suppliers

Components

at Dell

Assembly

TransportationPC

delivered

PC

at Dell

LEVEL OF DETAİL İN PROCESS ANALYSİS

9

Transportation Assembly Transportation

Components Components PC PC

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:

10

PROCESS MEASURES

• Cost

• Quality measures

• Time (Flow measures)

• Flexibility measures

• Capacity

• This course focuses on capacity and flow measures.

11

PROCESS MEASURES İN PRODUCTİON AND SERVİCE

Production process Service process

Flow unit Materials Customers

Input rate Raw material releasing rate Customers arrival rate

Output rate Finished goods output rateCustomers departure rate (service

completion rate)

Flow timeTime required to turn materials into

a productTime 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 İN PROCESS ANALYSİS

Step 1: Determine the Purpose of the analysis

12

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 KİTCHEN

• 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)

13

Link to video

http://www.youtube.com/watch?v=FpwwcpubUIw

14

LİNEAR 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

pattiesPackage Deliver

Place an

order

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

SWİM-LANE (DEPLOYMENT) FLOWCHART

15

RESOURC

ESACTIVITIES

Cashier

Worker1

Toaster

Worker 2

Worker 3

Worker 4

Worker 5

Toast

buns

Add

dressings

Add meat

patties

Package

Deliver

Place an

order

SWİM-LANE FLOWCHART: MODİFİED

16

RESOURC

ESACTIVITIES

Cashier

Worker1

Toaster

Worker 2

Worker 3

Worker 4

Worker 5

Toast

buns

Add

dressings

Add meat

pattiesPackage

Deliver

Place an

order

GANTT CHART

17

RESOURCES ACTIVITIES Time Span

Cashier Place an order

Worker1

ToasterToast buns

Worker 2 Add dressings

Worker 3Add meat

patties

Worker 4 Package

Worker 5 Deliver

Time

10s

8 s

6s

2s

8 s

2s

18

CHOİCE 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 MAPPİNG: 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

20

21

BASİC PROCESS ANALYSİS

SİNGLE STAGE PROCESS

Toast buns

Toaster

Worker 1

Capacity Rate

???

Flow Time

(Time that buns spend in the toaster)

10 sec

22

Basic Process Analysis Multiple Stage Process

Toast

buns

Add

dressings

Add meat


Place an

order

CashierWorker 1Toaster

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: ???

23

GANTT CHART: MULTİPLE STAGE PROCESS

RESOURC

ES

ACTIVITIE

STime Span


Worker1

ToasterToast buns


Worker 3Add 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

24

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

25

INCREASİNG THE CAPACİTY RATE OF A PROCESS - WHAT İF WE ADD A CASHİER?

Toast

buns

Add

dressings

Add meat


Place an

order

CashiersWorker 1

ToasterWorker 2 Worker 3 Worker 4 Worker 5


900/hr

(2 * 450/hr)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: ???

Capacity rate of the whole process: ???

Place an

order

26

INCREASİNG THE CAPACİTY RATE OF A PROCESS - WHAT İF WE ADD A TOASTER?

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

Toast bunsAdd

dressings

Add meat


Place an

order

CashierWorker 1

ToastersWorker 2 Worker 3 Worker 4 Worker 5


450/hr720/hr

(2 * 360/hr)450/hr 600/hr 1800/hr 1800/hr

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

Toast buns

Which task is the bottleneck?

27

ADDİNG A TOASTER: GANTT CHART

RESOURC

ES

ACTIVITIE

STime Span


Worker1

Toaster 1Toast buns

Worker1

Toaster 2Toast buns


Worker 3Add 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

28

THİNKİNG İN TERMS OF “UNİT 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

29

INCREASİNG CAPACİTY (1)

INCREASE THE SİZE OF THE “RESOURCE POOL”

• One Toaster

Capacity rate: 360/hr

• Two Toasters

Working in Parallel


Toast buns

10 sec

Toast buns

10 sec

Toast buns

10 sec

30

INCREASİNG CAPACİTY (2)

DECREASİNG THE UNİT LOAD

• This Toaster


• Faster Toaster

Works twice as fast


Toast buns

10 sec

Toast buns

5 sec

31

INCREASİNG THE CAPACİTY 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

32

INCREASİNG THE CAPACİTY RATE OF A PROCESS

EXPAND THE RESOURCE POOL AT THE BOTTLENECK


Toast bunsAdd

dressings

Add meat


Place an

order

CashierWorker 1

ToastersWorker 2 Worker 3 Worker 4 Worker 5


450/hr720/hr

(2 * 360/hr)450/hr 600/hr 1800/hr 1800/hr

Theoretical Flow Time of the whole process: 36 sec

Toast buns

33

Increasing the capacity rate of a process - Reduce Unit Load

at the BottleneckToast

buns

Add

dressings

Add meat


Place an

order

CashierWorker 1

ToasterWorker 2 Worker 3 Worker 4

Worker

5

Old Flow

Time8 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


New

Capacity

Rate

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

34

ANY OPERATİONAL BENEFİT OF REDUCİNG UNİT LOAD AT

NON-BOTTLENECKS?

Toast

buns

Add

dressings

Add meat


Place an

order

CashierWorker 1

ToasterWorker 2 Worker 3 Worker 4

Worker

5

Old Flow


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


New

Capacity

Rate

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

35

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”

36

ANOTHER EXAMPLE

Add dressings Add meat patties

Flow Time 8 sec 6 sec

Capacity Rate 450/hour 600/hour

Process is “starved”

37

• 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 CHARACTERİSTİCS

38

PROCESS ANALYSİS: MULTİPLE FLOW UNİTS

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 0 0

4 0 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 of C, what is your capacity rate? Bottleneck?

39


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 0 0 12 12

4 0 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

40

• 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


41

• 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

THEORETİCAL VERSUS EFFECTİVE CAPACİTY

42

WHAT İNFORMATİON DO UNİT LOADS GİVE 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

43


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

44


• 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

45

• 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 EXPERİMENT

UTİLİZATİON

• Utilization gives us information about “excess capacity”

• The utilization of each resource in a process can be presented

with a utilization profile

%100rateoutput maximum

rateoutput Actual

RateCapacity

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%

46

OPERATİONAL CHALLENGE

MİSMATCH BETWEEN DEMAND AND SUPPLY

• In any process, the input and output rates will vary over 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?

47

AN EXAMPLE: SECURİTY SCREENİNG AT YVR

48

Time

Input rate

(passengers/15 min slot)

Capacity rate


Excess

Demand

Excess

Capacity

6:15 7 15 0 8

6:30 10 15 0 5

6:45 8 15 0 7

7:00 12 15 0 3

7:15 9 15 0 6

7:30 16 15 1 0

7:45 14 15 0 1

8:00 19 15 4 0

8:15 22 15 7 0

8:30 17 15 2 0

8:45 13 15 0 2

9:00 11 15 0 4

9:15 12 15 0 3

9:30 8 15 0 7

9:45 10 15 0 5

10:00 7 15 0 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.

49

• 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?

RateCapacity

Rate Throughput n Utilizatio

IMPLİED UTİLİZATİON

• Implied utilization also allows us to capture the idea of

overtime

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

overtime to meet excess demand

50

• To capture the idea that there may be excess demand in the short-run, another measure of utilization is often useful

RateCapacity

RateInput on UtilizatiImplied

SECURİTY SCREENİNG EXAMPLE REVİSİTED

• 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)?

51

INVENTORY BUİLD-UP DİAGRAM

52

Time

Input rate


Capacity rate


Excess

Demand

Excess

Capacity

INVENTO

RYBUILD-

UP

6:15 7 15 0 8 0

6:30 10 15 0 5 0

6:45 8 15 0 7 0

7:00 12 15 0 3 0

7:15 9 15 0 6 0

7:30 16 15 1 0 1

7:45 14 15 0 1 0

8:00 19 15 4 0 4

8:15 22 15 7 0 11

8:30 17 15 2 0 13

8:45 13 15 0 2 11

9:00 11 15 0 4 7

9:15 12 15 0 3 4

9:30 8 15 0 7 0

9:45 10 15 0 5 0

10:00 7 15 0 8 0

TOTAL 195 240


53

0

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?

CALCULATİNG “AVERAGE INVENTORY”

54

Time

Input rate

(passengers/15

min slot)

Capacity rate

(passengers

/ 15 min slot)

Excess

Demand

Excess

Capacity

INVENTO

RY BUILD-

UP

6:15 7 15 0 8 0

6:30 10 15 0 5 0

6:45 8 15 0 7 0

7:00 12 15 0 3 0

7:15 9 15 0 6 0

7:30 16 15 1 0 1

7:45 14 15 0 1 0

8:00 19 15 4 0 4

8:15 22 15 7 0 11

8:30 17 15 2 0 13

8:45 13 15 0 2 11

9:00 11 15 0 4 7

9:15 12 15 0 3 4

9:30 8 15 0 7 0

9:45 10 15 0 5 0

10:00 7 15 0 8 0

195 240 3.1875

Empty

Buffer

(No

Queue)

Buffer

NOT

empty

Average

Inventory

= 3.1875

CONSİDER ANOTHER EXAMPLE …

55

Time

Input rate

(passengers/15

min slot)

Capacity rate

(passengers

/ 15 min slot)

Excess

Demand

Excess

Capacity

INVENTO

RY BUILD-

UP

6:30 17 30 0 13 0

7:00 20 30 0 10 0

7:30 25 30 0 5 0

8:00 33 30 3 0 3

8:30 39 30 9 0 12

9:00 24 30 0 6 6

9:30 20 30 0 10 0

10:00 17 30 0 13 0

195 240 2.625

0

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 …

56

Time

Input rate

(passengers/15

min slot)

Capacity rate

(passengers

/ 15 min slot)

Excess

Demand

Excess

Capacity

INVENTO

RY BUILD-

UP

7:00 37 60 0 23 0

8:00 58 60 0 2 0

9:00 63 60 3 0 3

10:00 37 60 0 23 0

195 240 0.75

Average

Inventory

0

0,5

1

1,5

2

2,5

3

3,5

07:00 08:00 09:00 10:00

Inventory Build-Up

… AND ANOTHER

57

Time

Input rate

(passengers/15

min slot)

Capacity rate

(passengers

/ 15 min slot)

Excess

Demand

Excess

Capacity

INVENTO

RY BUILD-

UP

8:00 95 120 0 25 0

10:00 100 120 0 0 0

195 240 0

Average

Inventory 0

0,2

0,4

0,6

0,8

1

07:00 08:00

Inventory Build-Up

ESTİMATİNG 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

output processes

58

DEFİNİTİONS

• Instantaneous Flow Rates

59

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 DYNAMİCS

• Let (t1,t2) denote an interval of time starting at t1 and ending at t2

• Suppose ∆R(t) is constantover (t1,t2) and equals ∆R. Then,

60

t1 t2

I(t1)

I(t2)

I(t)

t

∆R *(t2-t1)

)()()( 1212 ttRtItI

2

Inventory EndingInventory StartingInventory Average

Ending

Inventory

Starting

Inventory

Change in

Inventory


Capacity rate = 100/hr

61

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 BUİLD-UP EXAMPLE

620

200

400

I(t)

Inventory in week t

1 2 3

Week Input Rate Throughput Rate Inventory

0 400

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

630

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?

??????

LİTTLE’S LAW

64

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

LİTTLE’S LAW

• Throughput rate: 1 car/min

• 900 cars in the system

• Flow time?

65

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

LİTTLE’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?

66

Patients matched to

donated organs

INPUT

Patients in need

of a transplant

OUTPUTS

Patients leaving the

list hopefully with a

successful transplant


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?

67

300 patients ?? / year

3 years in system

I = R * TInventory I = 300 patients

Flow Time T = 3 years

Throughput Rate

R = I/T = 100 patients / year


68

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 * TInventory I = 300 patients

Throughput R= 100 patients/year

Flow Time

T = I/R = 3 years


• 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.

69

INPUT

Containers to be

shipped

OUTPUT

Containers shipped


Question (a)

• On average, your container storage yard can hold 500

containers.

• Is your yard big enough?

70

LİTTLE’S LAW: EXAMPLE 2Question (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?

71

INSİGHTS FROM LİTTLE’S LAW

• Throughput rate, flow time, and inventory are related

• Depending on the situation, a manager can influence any

one 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

72

INSİGHTS FROM LİTTLE’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”

73

LİTTLE’S LAW: EXAMPLE 3• Wal-mart imports Product X from an overseas factory. Each

order 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

74

Port

1 day

Ship WarehouseFactory

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

75

LİNE BALANCİNG: BATCHİNG DECİSİONS

76

Milling

Machine

Assembly

Process

LİNE BALANCİNG: BATCHİNG DECİSİONS

77

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 İMPACT OF SET-UP TİMES ON CAPACİTY

78

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)


= 720min

Capacity = 300/720=0.4166

1/p

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

10

50

90

13

0

17

0

21

0

25

0

29

0

33

0

37

0

41

0

45

0

49

0

53

0

57

0

61

0

65

0

Batch Size

Capacity as a function of the batch size

BATCHİNG AND INVENTORY

79

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


Cycle

Inventory

End of

Month

Beginning of

Month

Cycle

Inventory

End of

Month

Beginning of

Month

Produce Sedan



Cycle

Inventory

End of

Month

Beginning of

Month

Cycle

Inventory

End of

Month

Beginning of

Month

Produce Sedan



Cycle

Inventory

End of

Month

Beginning of

Month

Cycle

Inventory

End of

Month

Beginning of

Month

Produce Sedan


THE İMPACT OF SET-UP TİMES ON CAPACİTY

80

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 12001060 1120 1400 1460

Idle time

133

Rib

inventory

Steer support

inventory

Consider B=20060 min (set up) + 200 min (steering)


= 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

ELİMİNATE IDLE TİMES

• If B=12:

• To balance the line, solve:

• B=12081

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

𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝐵 =𝐵𝑎𝑡𝑐ℎ 𝑠𝑖𝑧𝑒

𝑆𝑒𝑡𝑢𝑝 𝑡𝑖𝑚𝑒 + 𝐵𝑎𝑡𝑐ℎ 𝑆𝑖𝑧𝑒 ∗ 𝑃𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔 𝑡𝑖𝑚𝑒

= 𝐵

𝑆+𝐵∗𝑝=

12

120+12∗2= 0.0833 𝑢𝑛𝑖𝑡/𝑚𝑖𝑛

𝐵

120 + 𝐵 ∗ 2=1

3𝑢𝑛𝑖𝑡/𝑚𝑖𝑛

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

10

50

90

13

0

17

0

21

0

25

0

29

0

33

0

37

0

41

0

45

0

49

0

53

0

57

0

61

0

65

0

Capacity of slowest step other than the

one requiring set-up

Batch size is too large

Batch

size is

too

small,

82

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?

Documents

UNDERSTANDİNG PROCESSES - Anasayfa