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History Concept Importance Manual Formula Software Package Experience Curve Societal Impact The Learning Curve The Learning Curve Phenomenon Phenomenon ment Science for Decision Making, 1e ment Science for Decision Making, 1e © 2012 Pearson Prentice-Hall, Inc. Philip A © 2012 Pearson Prentice-Hall, Inc. Philip A
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History Concept Importance Manual Formula Software Package Experience Curve Societal Impact

The Learning CurveThe Learning Curve Phenomenon Phenomenon

Applied Management Science for Decision Making, 1e Applied Management Science for Decision Making, 1e © 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD© 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD

The Learning CurveThe Learning CurveHISTORY

Introduced by Theodore Paul Wright in Factors Affecting The Cost of Airplanes, Journal of Aero Science ( 1936 )

The article covered the role of learning in the airplane production process, the methods of measuring learning, and the effect of learning on plane production volume and costs

Theodore Paul WrightTheodore Paul Wright1895 - 19701895 - 1970

M.I.T. ( 1918 ) - graduate, aeronautical engineering

Naval Reserve Officer ( WW I )

Curtiss Aeroplane Company - executive engineer (1921) - chief engineer (1925) - plant manager (1931) - vice-president, engineering (1935)

Office of Production Management - assistant director, aircraft (1942-1945)

Cornell University - acting president (1951) - vice-president, research (1948-1960)

The Learning Curve ConceptThe Learning Curve Concept

THIS APPLIES TO INDIVIDUALS,DEPARTMENTS, FIRMS, AND

ENTIRE INDUSTRIES

If a task is performedrepeatedly over time,its performance timewill drop dramaticallyand then continue todrop at a slower rateuntil a leveling off is

reached

80% Learning Curve80% Learning CurveINTERPRETATIONINTERPRETATION

If the base unit (1st unit) needed 200 hours of labor, then the doubled base unit (2nd unit) will only need 160 hours of labor.

If the base unit (2nd unit) needed 160 hours of labor, then the doubled base unit (4th unit) will only need 128 hours of labor.

[ 200 x .80 = 160 ]

[ 160 x .80 = 128 ]

80% Learning Curve80% Learning CurveINTERPRETATIONINTERPRETATION

If the base unit (4th unit) needed 128 hours of labor, then the doubled base unit (8th unit) will only need 102.4 hours of labor.

If the base unit (8th unit) needed 102.4 hours of labor, then the doubled base unit (16th unit) will only need 81.92 hours of labor.

128 x .80 = 102.4

102.4 x .80 = 81.92

80% Learning Curve80% Learning Curve

0 1 2 4 8 16 32

200 hours

150 hours

100 hours

50 hours

0 hours

UNITS

GRAPHGRAPH

LABOR HOURS

NegativeExponential

Curve

1st unit requires 200 hours 2nd unit requires 160 hours 4th unit requires 128 hours 8th unit requires 102 hours16th unit requires 82 hours

The Learning CurveThe Learning Curve

UNIT 70% 80% 90%

1st 200 200 200

2nd 140 160 180

4th 98 128 162

8th 68.6 102 145.8

16th 48.02 82 131.2

32nd 33.61 65.6 118.1

THE LOWER THE PERCENTAGE, THE MORE EFFICIENTTHE LOWER THE PERCENTAGE, THE MORE EFFICIENT

THE NORMAL RANGETHE NORMAL RANGE

Learning Curve ComparisonLearning Curve Comparison

0 1 2 4 8 16 32

200 hours

150 hours

100 hours

50 hours

0 hours

UNITS

GRAPHGRAPH

LABOR HOURS

80%80%70%70%

90%90%

The Learning CurveThe Learning CurveOTHER FACTORS REFLECTEDOTHER FACTORS REFLECTED

Improvements in layout design. Changes in product materials. Changes in work methods. Changes in labor policies. Engineering modifications. Equipment replacement. Equipment redesign. Worker training.

The Learning Curve PhenomenonThe Learning Curve PhenomenonOTHER APPLICATIONS

LABOR COST ESTABLISHMENT

SUBCONTRACTING DECISIONS

STRATEGIC EVALUATION OF THE FIRM IN ITS INDUSTRY

PURCHASING DECISIONS

LABOR SCHEDULING

LABOR BUDGETING

Learning Curve ImportanceLearning Curve Importance

Premature depletions of materials and components on the production line are avoided entirely.

Customer orders need not be rejected based on the mistaken notion that the factory is “booked solid” in the immediate future.

Human resources need not hire additional workers to meet future product demand.

It may eliminate or defer the need for factory expansion or new construction.

The Learning Curve FormulaThe Learning Curve Formula

• A firm historically has had an 85% learning curve.

• The 1st unit of a new product is estimated to require 3,000 labor hours.

• The firm wants to know how many labor hours will be needed for the 50th unit.

APPLICATIONAPPLICATION

The LearningThe Learning Curve FormulaCurve Formula

Y = Y x Nn 1

x

where:

Y = time required for a specific unit

Y = time required for the 1st unit

N = the unit for which a time is sought

the learning rate

n

1

x / r =

The Learning Curve FormulaThe Learning Curve FormulaEXECUTIONStep 1

Compute the learning rate: the sensitivity of unit labor time to cumulative productive output

X = natural logarithm of the learning curve

natural logarithm of 2.0

X =natural logarithm of “ .85 “

natural logarithm of “ 2.0 “

X =- .162518

.693147= - .23446

Logarithm CalculationLogarithm Calculation CALCULATOR KEYS AND STROKE SEQUENCES

For Natural LogarithmsFor Natural Logarithms

lnln

..

lnln

22

88

22

..

88

55

..

00

55

00

==

==

==

==

..OROR - .1625- .1625

OROR + .6931+ .6931

lnln

lnln

Logarithm CalculationLogarithm Calculation CALCULATOR KEYS AND STROKE SEQUENCES

For ‘Base 10’ LogarithmsFor ‘Base 10’ Logarithms

log

.

log

2

8

2

.

8

5

.

0

5

0

=

=

=

=

.OROR - .070581- .070581

OROR + .30103+ .30103

log 10x

log 10x

The Learning Curve FormulaThe Learning Curve FormulaEXECUTION

Step 2Insert the values of all variables in the general formula:

Y = Y Nn 1.

x

becomes:

Y = 3,000 x 50- .23446

50

= 3,000 x 1

2.5023065

= 3,000 x .39963

= 1,198.9hours required toproduce the 50th

unit in the series

50- .23446

becomes…..

1

50+ .23446

Exponential OperationExponential OperationCALCULATOR KEYS AND STROKE SEQUENCECALCULATOR KEYS AND STROKE SEQUENCE

To computeTo compute 50 50 + .23446+ .23446

5 0 . y . 2 3

4 4 6 =

x

≈ ≈ 2.50 2.50

Exponential OperationExponential OperationCALCULATOR KEYS AND STROKE SEQUENCECALCULATOR KEYS AND STROKE SEQUENCE

To computeTo compute 50 50 + .23446+ .23446

5 0 . . 2 3

4 4 6 = ≈ ≈ 2.50 2.50

Λ

FOUND ON NEW CALCULATORS

Learning Curve with QM for WINDOWSLearning Curve with QM for WINDOWS

MANAGEMENTMANAGEMENTFOR THEFOR THE

2121stst

CENTURYCENTURY

We Select This Module

We Want ToSolve A New

Problem, GivenThe Learning

Curve Coefficient

TheDialogue Box

Appears

The Data TableLooks Like This,

With The Base UnitAutomatically

The 1st Unit

THE NUMBER OFHOURS TO MAKE

THE 1st UNIT

THE UNIT FORWHICH WE WANT

TO FIND THENUMBER OF HOURS

THE LEARNINGCURVE OF 85%

( GIVEN )

THE 50th UNIT WILLTAKE 1,198.87

HOURS TO COMPLETE

THE 15th UNIT WILL TAKE1,589.896 HOURS TO

COMPLETE.CUMULATIVE PRODUCTION

HOURS AT THAT POINTARE 29,583.17 HOURS

THE 50th UNIT, OFCOURSE, WILL TAKE

1,198.87 HOURSTO COMPLETE

THE 85%

LEARNINGCURVE

THE 50th UNIT

WE CAN CHANGETHE LEARNING CURVE

TO 75% BYADJUSTING THE

COUNTERTHE 50th UNIT

WOULD THEN TAKEONLY 591.54HOURS TO

COMPLETE !

THE 95%LEARNING CURVE

CAN ALSO BEFOUND

Crude Estimation of the Learning CurveCrude Estimation of the Learning Curve

Suppose that the labor content, in hours, for the firsteight units of production were as follows:

UNIT NUMBER LABOR CONTENT

1 41

2 34

3 29

4 26

5 24

6 24

7 23

8 21

What is the approximate learning curve for this firm?

We Select ThisSub Menu

To Estimate TheLearning Curve

THE DIALOGUEBOX

THE DATA INPUT TABLEREQUIRES THE NUMBER OFHOURS IT TOOK TO MAKE

THE 1st UNIT AND THENUMBER OF HOURS IT

TOOK TO MAKE A LATER UNIT( YOUR CHOICE )

WE CHOSE TO USE THE8th UNIT IN THE SERIES

WITH 21 HOURS OFACTUAL PRODUCTION

TIME

THE ESTIMATEDLEARNING CURVE,

BASED ON THE 1st AND 8th UNITSPRODUCED, IS

80%

THE ESTIMATED

80%LEARNING

CURVE

THE PROGRAM’SESTIMATED

PRODUCTIONHOURS

FOR UNITS 1 THROUGH 8

ACTUAL HOURS

1st UNIT - 412nd UNIT - 343rd UNIT - 294th UNIT - 265th UNIT - 246th UNIT - 247th UNIT - 238th UNIT - 21

The Learning Curve The Learning Curve PhenomenonPhenomenon

Applied Management Science for Decision Making, 1e Applied Management Science for Decision Making, 1e © 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro, PhD© 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro, PhD

Just-in-Time SystemsJust-in-Time SystemsJIT

• History• Concept• System Elements• System Operation• Prerequisites• Selected Applications MANUFACTURING AND SERVICE

Applied Management Science for Decision Making, 1e Applied Management Science for Decision Making, 1e © 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD© 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD

Just-in-Time SystemsJust-in-Time SystemsHISTORYHISTORY

THE LITTLE KNOWN ORIGIN OF JIT

In 1912 Ford Motor Company begins using ferries to ship automobile hoods, doors, and

trunk lids from its factories on the east side of Lake Erie to its assembly plants in Detroit on

a twice-daily basis, and in the quantities needed to support daily production

Just-in-Time SystemsJust-in-Time SystemsHISTORYHISTORY

Developed by Toyota Industries, Japan’s largest defense contractor in 1936.

Its purpose was to transform farm workers into skilled manufacturers in the quickest and in the simplest manner possible, in preparation for World War II .

This new method of manufacturing made full use of the Japanese individual’s quest for simplicity and excellence in all aspects of life.

Just-in-Time SystemsJust-in-Time SystemsTHE CONCEPTTHE CONCEPT

A part, subassembly, or material is pulled through the system to wherever it is needed, exactly when it is needed. This “pull” system is employed both by the factory and its external suppliers.

This “pull” system utilizes signaling devices to request production and delivery from upstream centers to downstream centers.

CENTERS ARE EITHER PRODUCTION OR MATERIAL SUPPLY

Just-in-Time SystemsJust-in-Time SystemsTHE CONCEPTTHE CONCEPT

The pulling of parts and materials through the system in small lots to wherever they are needed, when they are needed, removes the need for inventory cushions.

Elimination of inventory cushions exposes operational problems to the full light of day, which in turn, are then eliminated on a prioritized basis.

Continuous improvement is emphasized by the firm thereafter.

MANUFACTURING CYCLE TIMES ARE ALSO REDUCED

Excessive InventoriesExcessive InventoriesCONCEAL SERIOUS PROBLEMSCONCEAL SERIOUS PROBLEMS

Unreliable deliveries of materials & components. Lost production due to defective materials.

Improper human and equipment processing. Delays caused by long setup times and machine breakdowns.

Managerial incompetency in planning, ordering, and scheduling.

FIRMS USE INVENTORIES TO MASK THEIR MISTAKES

Draining The Inventory LakeDraining The Inventory Lake

POORSCHEDULING

IMPROPEREQUIPMENTOPERATION

EQUIPMENTBREAKDOWNS

LATEDELIVERIES

DEFECTIVEMATERIALS

AS INVENTORY LEVELSARE SYSTEMATICALLY

REDUCED, OPERATIONALPROBLEMS MAKE THEIR

APPEARANCE

ROCKSROCKS

The Two-Card Scheduling System THE PRODUCTION CARD

Issued by a downstream work center to one or more upstream manufacturing

work centers

Authorizes delivery of a previouslyproduced tray of parts/subassemblies,

or new production of a tray of same,in order to replenish a tray sent earlier

PRODUCTIONCARD

LOOKS LIKE ANOLD COMPUTERPUNCH CARD

BASICALLY,

A MATERIALS

REQUISITION

ORDER

The Two-Card Scheduling SystemTHE MOVE CARDTHE MOVE CARD

Issued by a downstream work centerto one or more upstream supply centers

located across the street or up to 100 miles away !

Authorizes delivery of a previouslyproduced tray of materials/supplies, or

another delivery of same, in order toreplenish a tray sent earlier

The Two-Card Scheduling SystemKANBAN CONCEPT & PRACTICE

USERUSERCENTERCENTER

SUPPLYSUPPLYCENTERCENTER

MFG.CENTER

MOVECARD

PRODUCTIONCARD

TRAYTRAYOFOF

MATERIALSMATERIALS

TRAYTRAYOFOF

PARTSPARTS

THEDOWNSTREAM

CENTER

THE UPSTREAM

CENTER

THE UPSTREAM

CENTER

sends

sends

receives

receives

The Two-Card Scheduling SystemKANBAN CONCEPT & PRACTICE

USERUSERCENTERCENTER

SUPPLYSUPPLYCENTERCENTER

MFG.CENTER

MOVECARD

PRODUCTIONCARD

TRAYTRAYOFOF

MATERIALSMATERIALS

TRAYTRAYOFOF

PARTSPARTS

THEDOWNSTREAM

CENTER

THE UPSTREAM CENTERS

MFG.CENTER TRAY TRAY

OFOFPARTSPARTS

PRODUCTIONCARD

The user center canissue several move

and production cards at thesame time

STREETSTREET

The Two-Card Scheduling SystemCYCLISTS CARRIED EMPTY TRAYS AND FILLED TRAYS BETWEEN FACTORY AND VENDORS

STREETSTREET

MAINASSEMBLY

PLANT GLASSPRODUCER

METALPART

PRODUCER

SSTTRREEEETT

SSTTRREEEETT

EMPTYEMPTY

TRAY TRAY

EMPTY

EMPTY

TRAYTRAY

CARDCARD

CCEENNTTEERR

CCEENNTTEERR

INDUSTRIAL PARKINDUSTRIAL PARK

FILLEDFILLED

TRAYTRAY CARD

FILLEDFILLED

TRAYTRAY

The Two-Card Scheduling System

100 mile100 mile

radiusradius

GLASSMFG

CHIPMFG

METALMFG

ASSEMBLYPLANT

HARDWAREMFGCOATINGS

MFG

WHEN THEDISTANCES

ARESUBSTANTIAL

STANDINGSTANDINGPURCHASEPURCHASE

AGREEMENTSAGREEMENTSREPLACE

MOVECARDS

TRUCKS, PLANES,

AND TRAINSREPLACEREPLACEBICYCLES

The Two-Card Scheduling System

Standing purchase agreements with external vendors for a specific number of trays of parts or materials to be delivered daily by truck, rail, boat, or plane, at dawn or mid-day, or both.

Flashing lights, bells, whistles, rags, and flags between the work centers.

E-commerce isincreasingly

popular

PRODUCTION AND MOVE CARD ALTERNATIVESPRODUCTION AND MOVE CARD ALTERNATIVES

OVER LONG DISTANCES

WITHIN THE PLANT ITSELF

The Two-Card Scheduling SystemKANBAN CONCEPT & PRACTICE

USERUSERCENTERCENTER

SUPPLY SUPPLY oror

MFGMFGCENTERCENTER

USERUSERCENTERCENTER

SUPPLYSUPPLYoror

MFGMFGCENTERCENTER

EMPTYEMPTYTRAYTRAY

EMPTYEMPTYTRAYTRAY

( NO CARD )( NO CARD )

TO REFILL

CARD

TO STOP REFILL

SENDS

The Two-Card Scheduling SystemKANBAN CONCEPT & PRACTICE

EMPTY TRAYEMPTY TRAY( NO CARD )( NO CARD )

SUPPLYSUPPLYoror

MFGMFGCenterCenter

REFILLEDREFILLEDTRAYTRAY

WHEN AN EMPTY TRAY IS RETURNED

WITH NO CARD, IT IS IMMEDIATELY

REFILLED AND KEPT UNTIL IT IS ONCE

AGAIN NEEDED BY THE USER CENTER.

THIS COULD BE THE NEXT

DAY OR THE SAME

AFTERNOON

The Kanban TrayThe Kanban Tray

holds a particular part or subassembly.

holds a prescribed number of parts or subassemblies.

lined with foam or silk in order to avoid damaging the contents when moved from center to center.

compartments are shaped so as to accom- modate only properly-crafted parts or sub- assemblies.

usually carried by hand from center to center.

The Kanban TrayThe Kanban Tray

ONE ONE TYPETYPEPARTPART

ORORMATERIALMATERIAL

UNITUNIT

FOAM-LINEDFOAM-LINED COMPARTMENTSCOMPARTMENTS

CUTOUTS ONLY CUTOUTS ONLY ACCOMMODATE ACCOMMODATE

PROPERLY MADE PROPERLY MADE UNITSUNITS

The Kanban Tray / BinThe Kanban Tray / BinCALCULATING THE NUMBER REQUIREDCALCULATING THE NUMBER REQUIRED

MANAGEMENT MUST FIRST ESTABLISH THE NUMBER OF

COMPARTMENTS WITHIN EACH TRAY / BIN AND ITS SIZE

The number of trays / bins sets the amount of

authorized inventory for a particular part

or material

It is based on the item’s daily demand, production lead time, and safety stock

needed to compensatefor system uncertainty

““Authorized Inventory”Authorized Inventory”

JIT system manufacturing is also known as “stockless production”, that is, daily manufacturing without stand- ing beginning or work-in-process inventories.

In reality however, there will always be some permanent inventories in the JIT system, usually 1% to 2% of the ori- ginal amounts.

These inventories are the pre-made parts, subassemblies, and materials that are contained in the kanban trays.

Their purpose is to quickly start production on that same afternoon or next day, rather than wait for items to be pro- duced from scratch.

The Kanban TrayThe Kanban TrayTHE NUMBER FORMULATHE NUMBER FORMULA

Numberof

Trays=

Lead Time Demand + Safety Stock

Number of Tray Compartments

DAILY DEMAND - CAMERA “X” = 12 UNITS ( world-wide ) THEREFORE……. DAILY DEMAND - CAMERA “X” LENS ASSEMBLY = 12 UNITS ( derived ) DAILY DEMAND - CAMERA “X” HOUSING = 12 UNITS ( derived ) PRODUCTION LEAD TIME = 30 MINUTES ( 1/2 HOUR ) FOR EACH WORK CENTER SAFETY STOCK = 3 UNITS FOR EACH WORK CENTER

FROM THECAMERAEXAMPLE( TEXT )

The Kanban SystemThe Kanban System

FINALFINALASSEMBLYASSEMBLY

AREAAREA

CAMERACAMERAHOUSINGHOUSING

WORKWORKCENTERCENTER

CAMERACAMERALENSLENS

WORK WORK CENTERCENTER

PRODUCTIONCARD

PRODUCTIONCARD

TRAYTRAYCAMERACAMERA

““X”X”HOUSINGSHOUSINGS

TRAYTRAYCAMERACAMERA

““X”X”LENSESLENSES

WHERE THEHOUSING

ANDLENS

ASSEMBLIESCOME

TOGETHER

SENT

SENT

TRAYSDELIVERED

HOW MANY TRAYSAUTHORIZED ?

Calculating the Number of Trays

Lead Time Demand

Lead Time is the time required to prepare for a component or assembly

production run.

The firm needs to produce additionalunits in order to compensate

for this loss of time

The Kanban TrayThe Kanban TrayTHE NUMBER FORMULA

=Lead Time Demand + Safety Stock

Number of Tray Compartments

=[ 12 units x 1/16th day ] + 3 units

6 compartments

=[ 12 x .0625 ] + 3

6

DAILY DEMAND LEAD TIME

ONE TRAYEACH FORHOUSINGSAND LENS

ASSEMBLIES( CAMERA “X” )

= .625 ≈ 1 tray

Ifdaily

demandequals

12units

The Kanban TrayThe Kanban TrayTHE NUMBER FORMULA

=Lead Time Demand + Safety Stock

Number of Tray Compartments

=[ 120 units x 1/16th day ] + 3 units

6 compartments

=[ 120 x .0625 ] + 3

6

DAILY DEMAND LEAD TIME

TWO TRAYSEACH FORHOUSINGSAND LENS

ASSEMBLIES( CAMERA “X” )

= 1.75 ≈ 2 trays

Ifdaily

demandequals

120units

The Kanban TrayThe Kanban TrayTHE NUMBER FORMULA

=Lead Time Demand + Safety Stock

Number of Tray Compartments

=[ 500 units x 1/16th day ] + 3 units

6 compartments

=[ 500 x .0625 ] + 3

6

DAILY DEMAND LEAD TIME

SIX TRAYSEACH FORHOUSINGSAND LENS

ASSEMBLIES( CAMERA “X” )

= 5.71 ≈ 6 trays

THERE COULDBE THREE

OTHERCAMERAMODELS

THAT USECAMERA ‘X’s

HOUSINGSANDLENS

ASSEMBLIESWITH A

COMBINEDDEMANDOF 500

The Kanban BinThe Kanban BinTHE NUMBER FORMULATHE NUMBER FORMULA

=Lead Time Demand + Safety Stock

Size of Container

=[ 500 bolts x 2 days ] + 250 bolts

250 bolts ( bin size )

=[ 1,000 ] + 250

250

DAILY DEMAND LEAD TIME

5bins

neededfor this

item

2nd

EXAMPLEpartor

assembly

= 5 bins

Small Batch SizesSmall Batch Sizes

JIT systems use the smallest batch sizes possible.

They reduce the average level of inventory.

They pass through the system faster.

They allow for relatively early detection of any quality problems.

They help achieve a uniform workload on the system.

They simplify scheduling.

They can be moved around more effectively, enabling schedulers to utilize capacities efficiently.

A batch is a quantity of products that are produced

together

Small Batch SizesSmall Batch Sizes

Unfortunately, small batch sizes increase the number of setups and total setup costs.

A setup is a set of activities needed to change or readjust a process between successive batches of different products.

Typically, a setup takes the same amount of time and money regardless of the batch size.

Traditionally, producers select the batch size that provides the most economical solution.

An equation similar to the EOQ inventory model is used to find the optimum batch size.

Optimal Batch Size FormulaOptimal Batch Size Formula

( 2 ) ( D ) ( s )

h√Where: D = daily demand for the product 2 = constant

s = setup time ( cost units or time units )

h = processing time ( cost units or time units )

A larger batch size is more economical than a smaller batch size if the setup times are long.

Batch Size Cost TradeoffBatch Size Cost Tradeoff

0 Optimal Batch Size ∞

Setuptime / cost

Processing time / cost

Co

st /

Tim

e

Total Cost

AS BATCH SIZE INCREASES, THE NUMBER OF SETUPS AND SETUP COSTS DECREASESAS BATCH SIZE INCREASES, THE NUMBER OF SETUPS AND SETUP COSTS DECREASES

UNFORTUNATELY LARGER BATCH SIZES INCREASE PRODUCTION TIME AND INVENTORY CARRY COSTSUNFORTUNATELY LARGER BATCH SIZES INCREASE PRODUCTION TIME AND INVENTORY CARRY COSTS

Batch Size FormulaBatch Size Formula

The camera plant uses the same assembly line to produce all its models.

The setup time for initiating production of camera ‘X’ is 30 minutes.

After setup, one camera can be assembled every 6 minutes.

The daily demand for camera ‘X’ is 12.EXAMPLE

Batch Size FormulaBatch Size Formula

( 2 ) ( D ) ( s )

h√√

( 2 ) ( 12 ) ( 30 )

6

Most Economical Batch Size ≈ 11 units

EXAMPLE

This means that we should produceapproximately eleven (11) units of

camera model ‘X’, everytime we pro-duce them. This will minimize the

total costs of processing and setup.

Batch Size FormulaBatch Size Formula

The bolt plant uses the same assembly line to produce all its output.

The setup time for initiating production of the concrete bolt is 2 days ( 960 minutes ) .

After setup, one bolt can be produced every 1 minute.

The daily demand for this bolt is 500 .EXAMPLE

Batch Size FormulaBatch Size Formula

( 2 ) ( D ) ( s )

h√√

( 2 ) ( 500 ) ( 960 )

1

Most Economical Batch Size ≈ 980 units

EXAMPLE

The Batch Size FormulaThe Batch Size Formula

The formula considered the impact of setup time on only oneone process or piece of equipment. ( It ignored the other centers.)

A larger batch will always result in higherhigher inventory storage and handling costs throughout the production process, lead- ing to several other types of waste and inefficiency.

Therefore, in JIT firms, the focus is shifted from identifying

the optimum batch size to reducing setup timesreducing setup times.

If setup times are decreased, then the most economical batch

size will automatically automatically be reduced.

The desired “ideal” batch size in JIT is considered to be “one” ( 1 unit ) .

Batch size could be reduced to one unit, if the setup time were able to be reduced to near zero over all batch sizes.

An effort would be made to reduce setup times to as close to zero as possible, at each work center in the JIT facility.

A near zero setup time would allow the firm to respond to real-time consumer product demand even faster !

The “Ideal” Batch Size The “Ideal” Batch Size

Assembly Line BalancingUNDER THE KANBAN SYSTEM

PROBLEMS ENCOUNTERED DURING PRODUCTION ARE PROBLEMS ENCOUNTERED DURING PRODUCTION ARE TEMPORARILY SOLVED BY SUPERVISORS, ENGINEERS, TEMPORARILY SOLVED BY SUPERVISORS, ENGINEERS, AND WORKERS IN ORDER TO KEEP THE LINE MOVING.AND WORKERS IN ORDER TO KEEP THE LINE MOVING.

The assembly line is rebalanced each timeanother product is started in production

Supervisors are positioned along the assembly line to ensure that each

work center is producing at the same pace as all the other work

centers

Assembly Line BalancingAssembly Line BalancingUNDER THE KANBAN SYSTEM

no maximum and minimum cycle times.

no minimum number of work stations.

no formal efficiency and effectiveness measures.

no standard task times.

BASICALLY THE WORK CENTERS ARE CONSIDERED TO BEPERFORMING ADEQUATELY AS LONG AS TRAYS ARE BEING

FILLED AND EMPTIED ON A TIMELY BASIS WITHIN THE PERIODSCHEDULED FOR A PARTICULAR PRODUCT’S PRODUCTION

The Kanban SystemThe Kanban SystemTEXT EXAMPLE – PARTIAL OVERVIEW

CORPORATEHQ

FINALFINALASSEMBLYASSEMBLY

AREAAREA

CAMERACAMERAHOUSINGHOUSING

WORKWORKCENTERCENTER

CAMERACAMERALENSLENS

WORK WORK CENTERCENTER

OVERNIGHTINCOMINGORDERS

PRODUCTIONCARD

PRODUCTIONCARD

TRAYTRAYCAMERACAMERA

““X”X”HOUSINGSHOUSINGS

TRAYTRAYCAMERACAMERA

““X”X”LENSESLENSES

PRODUCE12

MODEL “X”CAMERASAT 9:00 AM

SENT

SENT

TRAYSDELIVERED

The Kanban SystemThe Kanban SystemTEXT EXAMPLE – PARTIAL OVERVIEWTEXT EXAMPLE – PARTIAL OVERVIEW

COMPUTERCHIP

PRODUCERCAMERACAMERAHOUSINGHOUSING

WORKWORKCENTERCENTER

CAMERACAMERALENSLENS

WORK WORK CENTERCENTER

MOVE CARD

MOVE CARD

TRAYTRAYCAMERACAMERA

““X”X”CHIPSCHIPS

TRAYTRAYCAMERACAMERA

““X”X”RAWRAW

GLASSGLASS

Trays Delivered by Bike or Vehicle

RAWRAWGLASSGLASS

PRODUCERPRODUCER

Across the street or 100 MILES away

( TWO HOURS DRIVE TIME )

SENT

SENT

Successful JIT SystemsSuccessful JIT SystemsPREREQUISITES

Better equipment maintenance and repair Reliable materials deliveries Quick machine setups Worker empowerment Better process quality Better product quality

Dr. Shigeo ShingoDr. Shigeo ShingoTHE FATHER OF MACHINE SETUP REDUCTION

In 1950, this Mazda engineer discovered that setup operations consisted of two distinct activities: internal and external.

Internal activities are those performed when the equipment is stopped, i.e. changing an ink cartridge.

External activities are those performed while the equipment is still operating, i.e. unpacking an ink cartridge from its carton.

This discovery formed the basis of a procedure for reducing setup time called SMED ( single minute exchange of dies), named after a particular project but now applicable to any type of machine setup.

REDUCEDSETUP TIMES

ARE AMAJOR

JITCOMPONENT

The Goals of Setup Reduction

standardize sizes and shapes of molds standardize parts for easy insertion and removal use the same fasteners for each setup use pre-marked settings on dials and levers

I. Convert as many internal setup activities into external setup activities as possible, for quicker machine setups.

II. Reduce the external setup activities themselves.

Steps to Reduce Setup Times

Separate setup into preparation and actual setup,doing as much as possible while the

machine/process is operating( save 30 minutes )

Move material closer andimprove material handling

( save 20 minutes )

Standardize andimprove tooling

( save 15 minutes )

Use one-touch system toeliminate adjustments

( save 10 minutes )

Training operators andstandardizing work

procedures( save 2 minutes )

Repeat cycle untilsub-minute setup

is achieved

INITIAL SETUP TIME

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Desired Setup Time FormulaDesired Setup Time FormulaOnce a lot size has been determined, the EOQ production orderquantity model can be modified to determine the desired setuptime. The original model is shown below:

Q* = 2DS

H [1 - ( d/p )]√ where:

D = annual demand S = setup cost H = carry cost d = daily demand p = daily production

Desired Setup Time ExampleDesired Setup Time Example

Flair Furniture, Inc., a firm that produces rustic furniture, desires to move toward a reduced lot size. Their production analyst, determined that a two hour production cycle would be acceptable be- tween two work centers. Further, the analyst concluded that a setup time that would accommodate the two hour cycle time should be achieved.

Desired Setup Time ExampleDesired Setup Time Example

The analyst developed the following data and procedure todetermine optimum setup time analytically:

D = annual demand = 400,000 unitsd = daily demand = 400,000 per 250 days = 1,600 units per dayp = daily production rate = 4,000 units per dayQ = EOQ desired = 400 ( which is the 2-hour demand; that is, 1,600 units per day per four 2-hour periods )H = carry cost = $20.00 per unit per yearS = setup cost ( to be determined )

Desired Setup Time ExampleDesired Setup Time Example

The analyst determines that the cost, on an hourly basis, of setting up equipment is $30.00 . Further, the analyst computes that the setup cost per setup should be:

Q* = 2DS

H (1 - d / p) √Q =

2 2DS

H (1 - d / p)

Desired Setup Time ExampleDesired Setup Time Example

S = (Q) (H) (1 - d/p)

2D

2

S =(400) (20) (1 - 1,600 / 4,000)

2 (400,000)

2

S = (3,200,000) (0.6)

800,000= $2.40

Setup time = $2.40 / (hourly labor rate) = $2.40 / ($30.00 per hour) = 0.08 hour or 4.8 minutes

Desired Setup Time ExampleDesired Setup Time Example

Now, rather than produce components in large lots (batches), Flair Furniture can produce in a two-hour cycle with the advantage of an inventory turnover of ‘4’ per day.

If, for example, labor cost rises to $40.00 per hour, setup time should then be .06 hour or 3.6 minutes.

Closing CommentsClosing Comments

For any JIT work center, we can suggest the following:

The daily production or usage rate. The ideal lot or batch size to be produced. The number of lots or batches to be produced daily. The ideal setup cost for each lot or batch. The ideal setup time for each lot or batch. The number of authorized trays or bins for each part or assembly to be produced.

Of course, the actual nature of the process, transport time, type of transport, purchasing agreements, levelof automation, materials handling, scheduling system, and many other factors will affect the above.

INDUSTRIAL ENGINEERINDUSTRIAL ENGINEERADVISING WORKERSADVISING WORKERS

ON THE LINEON THE LINE

Successful JIT SystemsSuccessful JIT SystemsPATIENCEPATIENCE

5 to 15 years could pass before required changes to the production system, employees’ work, corporate philosophy, and work culture materialize. Inventories should be reduced slowly while making reductions in setup time, batch sizes, defects, and machine breakdowns.

That said, inventory reductions of 20% to 40% and productivity improvements of 5% to 10% annually for each of the first three years are common!

Successful JIT SystemsSuccessful JIT SystemsCUSTOMIZED IMPLEMENTATIONCUSTOMIZED IMPLEMENTATION

Every firm has a different level of experience and sophistication with regard to quality management, setup methods, job design, and maintenance.

Accordingly, the problems exposed by inventory reduction will vary.

The firm would be wise to wait for the most press- ing problems to appear and then respond to them quickly, rather than establishing its improvement programs in advance.

Successful JIT SystemsSuccessful JIT SystemsFLEXIBILITYFLEXIBILITY

There are occasions when product demand rises unexpectedly, and JIT will need to respond by in- creasing inventories temporarily. This can be done by simply increasing the num- ber of production and move cards for a product, or temporarily abandoning JIT before a seasonal surge in product demand so that inventory stock- piles can be built.

Successful JIT SystemsSuccessful JIT SystemsEXCESS CAPACITYEXCESS CAPACITY

JIT systems function best when they are designed to operate routinely at 80% to 90% of capacity, in turn, allowing production to accelerate when de- mand surges.

This also makes it possible to temporarily halt pro- duction immediately to correct quality problems. This also gives employees time to experiment with, and test improvements to the process, which will enhance productivity and capacity over time.

The “Just-for-You” SystemThe “Just-for-You” SystemJIT – “McDonald’s Style”

Trays for beef and fish patties are called universal holding cabinets and their number changes from hour to hour based on computer-forecasted de- mand.

Production cards have been superceded by closed- circuit television that relays orders received at the front counter to the backroom operation.

Setup times for patty cooking and bun warming have been slashed to seconds using equipment designed and produced by McDonald’s operations researchers and industrial engineers.

JIT at Federal Signal CorporationJIT at Federal Signal Corporation

Computer-controlled machinery mounted on rollers ( zero setup times & flexibility )

Workers responsible for their own setups, maintenance, quality control inspections, housekeeping, and assis- tance to others ( open job descriptions )

Morning classes to learn new product assembly steps.

Engineers on shop floor are workers’ technical resource.

Production problems receive a quick-fix on the line until a permanent solution is found at the workers’ regularly- scheduled quality circle meeting.

Just-in-Time SystemsJust-in-Time Systems

Applied Management Science for Decision Making, 1e Applied Management Science for Decision Making, 1e © 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD© 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD


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