Dr. Mohammad Abdul Mukhyi, SE.,...

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Capacity Planning Capacity Planning Capacity Planning Capacity Planning Capacity Planning Capacity Planning Capacity Planning Capacity Planning Dr. Mohammad Abdul Mukhyi, SE., MM

Transcript of Dr. Mohammad Abdul Mukhyi, SE.,...

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Capacity PlanningCapacity PlanningCapacity PlanningCapacity PlanningCapacity PlanningCapacity PlanningCapacity PlanningCapacity Planning

Dr. Mohammad Abdul Mukhyi, SE., MM

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Capacity

Capacity: Definition

Capacity Types

Capacity of the Supply Chain

Calculating Capacity

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Introduction to Facility

Planning

HOW MUCH long range capacity will be

needed?needed?

WHEN will the additional capacity be

required?

WHERE should the facility be located?

WHAT should the layout and

characteristics of the facility be?

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Strategic Capacity Planning

CapacityThe amount of resource inputs available

relative to output requirements at a

particular time

How does productivity relate to capacity?

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Defining Capacity

the rate of output from an OM system per unit of timethe rate at which the firm withdraws work from the systemJumlah masukan sumberdaya-sumberdaya yang Jumlah masukan sumberdaya-sumberdaya yang tersedia relatif untuk kebutuhan keluaran pada waktutertentu.

unit keluaranwaktu

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Defining Capacity

In general, production capacity is the maximum production rate of an organization (or maximum conversion rate of a production system) in any given period.system) in any given period.

Sustainable practical capacity is the greatest level of output that a plant can maintain:

within the framework of a realistic work schedule

taking account of normal downtime

assuming sufficient availability of inputs to operate the machinery and equipment in place

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Berbagai Definisi:

1. Design Capacity : tingkat keluaran per satuan untuk mana pabrikdirancang.

2. Rated Capacity ; tingkat keluaran per satuan waktu yang menunjukkan bahwa fasilitas secara teoritik mempunyai kemampuanmemproduksi.

3. Standard capacity : tingkat keluaran per satuan waktu yang ditetapkan3. Standard capacity : tingkat keluaran per satuan waktu yang ditetapkansebagai sasaran pengoperasian bagi manajemen, supervisi dan paraoperator mesin, dapat digunakan sebagai dasar bagi penyusunananggaran.

4. Actual dan atau operating capacity : tingkat keluaran rata-rata per satuan waktu selama periode waktu yang telah lewat = kapasitasstandar ± cadangan-cadangan, penundaan, tingkat sisa nyata.

5. Peak capacity : jumlah keluaran per satuan waktu yang dapat dicapaimelalui maksimisasi keluaran dengan kerja lembur, menambah tenagakerja, mengurangi jam istirahat dan sebagainya

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Steps in the Capacity Planning

Process

Estimate the capacity of the present

facilities.

Forecast the long-range future capacity Forecast the long-range future capacity

needs.

Identify and analyze sources of capacity

to meet these needs.

Select from among the alternative sources

of capacity.

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Measures of Capacity

Output rate capacity – Suitable for a single product or a few homogeneous products

Design capacity - The maximum capacity that Design capacity - The maximum capacity that can be achieved under ideal conditions

Effective capacity utilization - The percent of design capacity actually achieved

Aggregate capacity – Suitable when a common unit of output is used

. . . more

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Measures of Capacity

Rated capacity – Maximum usable

capacity of a particular facility

Input rate capacity – Suitable for service Input rate capacity – Suitable for service

operations

Percentage utilization of capacity -

Relates output measures to inputs

available

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Capacity Utilization

Capacity used

level operatingBest

usedCapacity nUtilizatio =

Capacity used

Rate of output actually achieved

Best operating level

Capacity for which the process was designed

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Capacity Utilization--Example

Best operating level = 120 units/week

Actual output = 83 units/weekActual output = 83 units/week

Utilization = ?Utilization = ?Utilization = ?Utilization = ?

.692units/wk 120

units/wk 83=

level operatingBest

usedCapacity nUtilizatio ==

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Capacity Cushion

A capacity cushion is an additional amount of

capacity added onto the expected demand to

allow for:allow for:

greater than expected demand

demand during peak demand seasons

lower production costs

product and volume flexibility

improved quality of products and services

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Supply Chain Capacity

Tactical perspective

output driven

units of output, hours workedunits of output, hours worked

strategic perspective

capability

what you can and cannot do

match capabilities with marketing needs

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Ratedcapacity

=JumahMesin

Jam KerjaMesin

Persentasepenggunaan

EfisiensiSistem

X X X

Contoh:Contoh:Suatu pusat kerja beroperasi 6 hari per minggudengan basis dua sift (8 jam per sift), ada empatmesin dengan kemampuan sama. Bila mesindigunakan 75% dari waktu pada tingkat efisiensisistem sebesar 90%

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Jawab :

Rated Capacity = (4) (8x6x2) (0,75) (0,90)

= 259 jam kerja standar/minggu= 259 jam kerja standar/minggu

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Types of Capacity

Maximum

Effective

DemonstratedDemonstrated

Planning Effects of Capacity Types

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Types of Capacity:

Maximum Capacity (aka Design)

Defined: The highest rate of output that a process can achieve

Calculation involves the following assumptions:Calculation involves the following assumptions:

equally skilled workers

no time loss due to changeovers or product differences

no loss of capacity due to PM or planned downtime

no OT work or heroic employee efforts

Are these assumptions realistic?

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Types of Capacity:

Effective Capacity

Defined: the output rate that managers

expect for a given process

Why would you operate below maximum?Why would you operate below maximum?

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Types of Capacity:

Demonstrated Capacity

Defined: the actual level of output for a

process over a period of time, i.e., the process over a period of time, i.e., the

average of output over time

Why might this number be different than

maximum or effective capacity?

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Types of Capacity:

Demonstrated Capacity

Demonstrated capacity

what we actually observewhat we actually observe

can be affected by numerous factors

problems with input

problems internally

nature of the product

new vs standard

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Capacity within the Supply

Chain

Must deal with the issue of bottlenecks and

system constraints.

Capacity defined by:Capacity defined by:

information systems

infrastructure

physical capacity

logistics capacity

supplier capacity

relationship management

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Bottlenecks

Must look for bottleneck

constraining resource

how identifiedhow identified

too much or too little inventory

overtime

why important

limits output

determines lead time

determines ability of system to make money

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Bottlenecks - Con’t

Types of bottlenecks

output based

time-basedtime-based

These bottlenecks may the same or they may be

different

Keys to success

keep the bottlenecks busy

inventories/signals

invest in bottlenecks

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Capacity - calculating

Level of output of a plant or system is

dependent on how it is organized

capacity in sequencecapacity in sequence

linear operations

capacity in parallel

multiple alternative operations

any machine can be used

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Capacity - Sequential

Capacity of a system or process is based

on the operation with the lowest amount

of capacityof capacity

Keys

convert into the same units of measurement

ensure that we are talking about the same

dimensions

effective vs design vs demonstrated

capacity taken over the same time

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Capacity - Sequential

We have a process that makes cans

Operation 1 - punches out tops and bottoms

2 lids for every can2 lids for every can

produces 250 lids per minute

Operation 2 - body

1 body for every can

produces 175 bodies per minute

Operation 3 - mating

makes the can

produces 7500 cans per hour

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Capacity - Parallel

Capacity of the system or operation is based on

the sum of the capacities of the various

machines that make up the operation.

Operation 3 has 4 machines

machine 1 - 90 pieces per minute

machine 2 - 110 pieces per minute

machine 3 -120 pieces per minute

machine 4 - 80 pieces per minute

Total capacity for operation 3 = 400 pieces/min

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Capacity Management Tools:

Calculating Capacity

1. Describe the general flow of activities within the process

2. Establish the time period

3. Establish a common unit3. Establish a common unit

4. Identify the Maximum capacity for the overall process

5. Identify the Effective capacity for the overall process

6. Determine the Demonstrated capacity

7. Compare the Demonstrated, Effective and Maximum Capacities and take appropriate actions

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Capacity - Example

Mondavi Plant

Draw a diagram

What is its capacity

Why is it hard to calculate

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Other Factors to Consider

Setups

reduce the capacity of the facility

capacity is finite wrt timecapacity is finite wrt time

Relevant vs irrelevant

relevant also depends on the options

considered

also depends on the level of capacity

utilization

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Relevant Analysis

Consider the following

for a machine, what is the impact of one for a machine, what is the impact of one

additional hour of setup if the machine is

50% utilized?

What is the impact of one additional hour

of setup if the machine is 85% utilized?

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Importance of Setup Reduction

Setup reduction (SMED) can reduce setup times

by 30 to 50% without significant investments.

When teams work to reduce process variation or

to improve safety, handling, preventive

maintenance or housekeeping, they also tend to

reduce setup times.

When setup times decrease, setup labor and

startup problems decrease.

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Setup Reductions

When setup times decrease, it is economical to

run smaller lots, which tend to reduce

inventories, scrap, and rework.inventories, scrap, and rework.

The habit of continuous improvement must not

be discouraged (even if your equipment is not

the bottleneck).

As conditions change, a non-bottleneck can

easily become a bottleneck.

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Capacity Management Tools:

Input/Output Control

A tool that manages work flows to

match the demonstrated capacity of

processprocess

Prevent problems by using “plan your

work, work your plan” rule

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Economies of Scale

Best operating level - least average unit cost

Economies of scale - average cost per unit

decreases as the volume increasesdecreases as the volume increases

Diseconomies of scale - average cost per unit

increases as the volume increases

Other considerations

Subcontractor and supplier networks

Focused production

Economies of scope

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Economies and Diseconomies

of ScaleAverage Unit

Cost of Output ($)

Economies DiseconomiesDiseconomies

Annual Volume (units)Annual Volume (units)

Best Operating Level

Economiesof Scale

DiseconomiesDiseconomiesof Scaleof Scale

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Economies and Diseconomies

of Scale

Average UnitCost of Output ($)

100100100100----unitunitunitunitplantplantplantplant

Optimum Plant Size

Annual Volume (units)

200200200200----unitunitunitunitplantplantplantplant

300300300300----unitunitunitunitplantplantplantplant

400400400400----unitunitunitunitplantplantplantplant

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The Learning Curve Effect

60

70

80

90

100

Co

st/

Tim

e p

er

rep

eti

tio

n

Cost

10

20

30

40

50

60

0 20 40 60 80 100

Number of repetitions (Volume)

Co

st/

Tim

e p

er

rep

eti

tio

n

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The Learning Curve Effect

Observe, that the per unit cost (or price) of

the product (or service) declines the product (or service) declines

exponentially as the number of

repetitions increases

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Capacity Focus

Should manufacturers attempt to excel on all production objectives?on all production objectives?

Plants within plants (Skinner)Extend focus concept to operating level

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Capacity Flexibility

Flexible plantsFlexible processesFlexible processesFlexible workers

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Capacity Planning

Units

per

Stage 1 Stage 2 Stage 3

6,000 7,000 4,500

What will happen to WIP inventory?

Issue: How to maintain system balance?

per

month

6,000 7,000 4,500

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Analyzing Capacity-Planning

Decisions

Break-even Analysis

Present-Value AnalysisPresent-Value Analysis

Decision Tree Analysis

Computer Simulation

Waiting Line Analysis

Linear Programming

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Determining Capacity

Requirements

Forecast sales within each individual product lineproduct lineCalculate equipment and labor requirements to meet the forecastsProject equipment and labor availability over the planning horizon

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Example: Capacity

Requirements

A manufacturer produces two lines of ketchup, FancyFineand a generic line. Each is sold in small and family-size plastic bottles. plastic bottles. The following table shows forecast demand for the next four years.

Y ear: 1 2 3 4

F a ncyF ine

S mall (0 0 0 s) 5 0 6 0 8 0 1 0 0

F amily (0 0 0 s) 3 5 5 0 7 0 9 0

G eneric

S mall (0 0 0 s) 1 0 0 1 1 0 1 2 0 1 4 0

F amily (0 0 0 s) 8 0 9 0 1 0 0 1 1 0

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Example: Capacity

Requirements

The Product from a Capacity Viewpoint

Are we really producing two different types of ketchup from the standpoint of capacity ketchup from the standpoint of capacity requirements?

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Example: Capacity RequirementsEquipment and Labor Requirements

Year: 1 2 3 4

Small (000s) 150 170 200 240

Family (000s) 115 140 170 200

Three 100,000-units-per-year machines are available for small-bottle production. Two operators required per machine.

Two 120,000-units-per-year machines are available for family-sized-bottle production. Three operators required per machine.

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Example: Capacity RequirementsEquipment and Labor Requirements

• Total machine capacity available for small-bottle production: 3*100,000=300,000 units/year

• Total machine capacity available for family-sized-bottle • Total machine capacity available for family-sized-bottle production: 2*120,000=240,000 units/year

• Total labor capacity required for small-bottle production: 3*2=6 operators

• Total labor capacity required for family-sized-bottle production: 2*3=6 operators

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Example: Capacity

Requirements

Y ear: 1 2 3 4

S mall (000s) 150 170 200 240

F amily (000s) 115 140 170 200

S m all M ach. C ap . 300 ,000 Labor 6S m all M ach. C ap . 300 ,000 Labor 6

F am ily-size M ach. C ap . 240 ,000 Labor 6

S m all

P ercen t capacity used 50 .00% 56.67% 66.67% 80.00%

M achine requ irement 1 .50 1 .70 2 .00 2 .40

Labor requ irement 3 .00 3 .40 4 .00 4 .80

F am ily-size

P ercen t capacity used 47 .92% 58.33% 70.83% 83.33%

M achine requ irement 0 .96 1 .17 1 .42 1 .67

Labor requ irement 2 .88 3 .50 4 .25 5 .00

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The Decision-Making Process

Problem Decision

Quantitative AnalysisLogicHistorical DataMarketing ResearchScientific AnalysisProblem

?Decision

!Scientific AnalysisModeling

Qualitative AnalysisEmotionsIntuitionPersonal Experience& MotivationRumors

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Six Steps of the Decision

Process

1 Defining the problem and the factors that influence it

2 Establishing decision criteria and goals

3 Formulating a model or relationship between goals and variables3 Formulating a model or relationship between goals and variables

4 Identifying and evaluating alternatives

5 Selecting the best alternative

6 Implementing the decision

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Fundamentals of Decision

Theory

The three types of decision models:

1 Decision making under certainty

2 Decision making under risk

3 Decision making under uncertainty

Terms:

Alternative: course of action or choice

State of nature: an occurrence over which the decision maker has no control

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Decision Making Under

Uncertainty

Maximax

find the alternative that maximizes the maximum outcome for every alternative.outcome for every alternative.

Maximin

find the alternative that maximizes the minimum outcome for every alternative.

Equally likely

find the alternative with the highest average outcome

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Decision Tree Analysis

Structures complex, multiphase decisions

Allows objective evaluation of Allows objective evaluation of

alternatives

Incorporates uncertainty

Develops expected values

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Decision Tree Analysis

Symbols used in decision tree:Symbols used in decision tree:Symbols used in decision tree:Symbols used in decision tree:

A decision node from which one of several A decision node from which one of several

alternatives may be selected.

A state of nature node out of which one

state of nature will occur.

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Decision Tree Analysis

1 Define the problem

2 Structure or draw the decision tree

3 Assign probabilities to the states-of-nature

4 Estimate the payoffs for each possible combination of alternative and state-of-nature

5 Solve the problem by computing expected monetary values (EMV) for each state-of-nature node

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Example 1: Decision Tree

Analysis

Good Eats Café is about to build a new restaurant. An architect has developed three building designs, each with a different seating capacity. Good Eats estimates that with a different seating capacity. Good Eats estimates that the average number of customers per hour will be 80, 100, or 120 with respective probabilities of 0.4, 0.2, and 0.4. The payoff table showing the profits for the three designs is on the next slide.

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Example 1: Decision Tree

Analysis

Payoff TablePayoff TablePayoff TablePayoff Table

Average Number of Customers Per Hour

c1 = 80 c2 = 100 c3 = 120

Design A $10,000 $15,000 $14,000

Design B $ 8,000 $18,000 $12,000

Design C $ 6,000 $16,000 $21,000

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� Expected Value ApproachExpected Value ApproachExpected Value ApproachExpected Value Approach

Calculate the expected value for each decision. The

Example 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree Analysis

Calculate the expected value for each decision. The decision tree on the next slide can assist in this calculation. Here d1, d2, d3 represent the decision alternatives of designs A, B, C, and c1, c2, c3 represent the different average customer volumes (80, 100, and 120) that might occur.

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� Decision Tree

.2.2

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dd11

cc11

cc

cc22

cc33

PayoffsPayoffs

10,00010,000

15,00015,000

14,00014,000

22

Example 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree Analysis

11

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.4.4

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8,0008,000

18,00018,000

12,00012,000

6,0006,000

16,00016,000

21,00021,000

33

44

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�� Expected Value For Each DecisionExpected Value For Each DecisionExpected Value For Each DecisionExpected Value For Each DecisionExpected Value For Each DecisionExpected Value For Each DecisionExpected Value For Each DecisionExpected Value For Each Decision

dd11

EV = .4(10,000) + .2(15,000) + .4(14,000)EV = .4(10,000) + .2(15,000) + .4(14,000)= $12,600= $12,600

Design ADesign A22

Example 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree AnalysisExample 1: Decision Tree Analysis

hoosehoose the design with largest EV the design with largest EV ---- Design C.Design C.

33

44

dd22

dd33

EV = .4(8,000) + .2(18,000) + .4(12,000)EV = .4(8,000) + .2(18,000) + .4(12,000)= $11,600= $11,600

EV = .4(6,000) + .2(16,000) + .4(21,000)EV = .4(6,000) + .2(16,000) + .4(21,000)

= = $14,000$14,000

Design BDesign B

Design CDesign C

1 1

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A Sequence of Decisions

National DecisionNational Decision

Political, social, economic stability;

Currency exchange rates; . . . . .

Climate; Customer concentrations;

Regional DecisionRegional Decision

Community DecisionCommunity Decision

Site DecisionSite Decision

Climate; Customer concentrations;

Degree of unionization; . . . . .

Transportation system availability;

Preference of management; . . . . .

Site size/cost; Environmental impact;

Zoning restrictions; . . . . .

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Region Location Decision

Corporate desires

Attractiveness of region (culture, taxes, climate, etc.)

Labor availability, costs, attitudes toward unionLabor availability, costs, attitudes toward union

Cost and availability of utilities

Environmental regulations of state and town

Government incentives

Proximity to raw materials & customers

Land/construction costs

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Site Location Decisions

Site size and cost

Air, rail, highway, waterway systemsAir, rail, highway, waterway systems

Zoning restrictions

Nearness of services/supplies needed

Environmental impact issues

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Factors Affecting the

Location Decision

Economic

Site acquisition, preparation and construction Site acquisition, preparation and construction

costs

Labor costs, skills and availability

Utilities costs and availability

Transportation costs

Taxes

. . . more

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Factors Affecting the

Location Decision

Non-economic

Labor attitudes and traditionsLabor attitudes and traditions

Training and employment services

Community’s attitude

Schools and churches

Recreation and cultural attractions

Amount and type of housing available

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Facility Types and Their

Dominant Locational Factors

Mining, Quarrying, and Heavy Manufacturing

Near their raw material sources

Abundant supply of utilities

Land and construction costs are inexpensiveLand and construction costs are inexpensive

Light Manufacturing

Availability and cost of labor

Warehousing

Proximity to transportation facilities

Incoming and outgoing transportation costs

. . . more

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Facility Types and Their

Dominant Locational Factors

R&D and High-Tech Manufacturing

Ability to recruit/retain scientists, engineers, etc.

Near companies with similar technology interests

Retailing and For-Profit Services

Near concentrations of target customers

Government and Health/Emergency Services

Near concentrations of constituents

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Some Reasons the

Facility Location Decision

Arises

Changes in the market

Expansion

ContractionContraction

Geographic shift

Changes in inputs

Labor skills and/or costs

Materials costs and/or availability

Utility costs

. . . more

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Some Reasons the

Facility Location Decision

Arises

Changes in the environment

Regulations and lawsRegulations and laws

Attitude of the community

Changes in technology

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Analyzing Location Decisions

Quantitative Approaches

Qualitative ApproachesQualitative Approaches

Integrating Qualitative and Quantitative

Data

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Analyzing Location Decisions

Quantitative Approaches

Decision trees

Center of Gravity Method

Finds best distribution center locationFinds best distribution center location

Location Breakeven Methods

Special case of breakeven analysis

Transportation Method

Special case of LP method

NPV analysis

Computer Simulation

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Analyzing Location Decisions

Mixed Approaches

Weighted Methods which:

Assigns weights and points to various factors

Determines tangible costsDetermines tangible costs

Investigates intangible costs

Examples:

Rating scale approach

Relative-aggregate-scores approach

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Example 1: Locational Breakeven

Analysis

200

250

Akron

Bowling Green

Chicago

0

50

100

150

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Akron

Lowest cost Bowling Green

Lowest cost

Chicago

Lowest cost

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Penentuan kebutuhan

kapasitas

∑=

++=

x

1iiiiiistd ]NB)ST(O[ H

Hstd = jumlah total jam sumber daya yang dibutuhkan untukstd

memenuhi permintaanOi = jumlah unit keluaran X yang diperlukanTi = waktu pengoperasian standar per unit XSi = waktu persiapan standar peru unit keluaran XBi = waktu standar untuk mempersiapkan sekumpulan XNi = jumlah kumpulan X yang diperlukanX = jumlah jenis produk

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mwo

stdact

E P E

H H =

Hact = jumlah sumberdaya nyata yang dibutuhkanHstd = jumlah total jam sumber daya yang dibutuhkan untuk

memenuhi permintaanEo = efisiensi organisasionalPw = produktivitas operatorEm = efisiensi mesin, faktor pemeliharaan, faktor mesin rusak

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avl

actr

H

HN =

Nr = jumlah unit sumberdaya yang dibutuhkanH = jumlah jam yang tersedia per unit sumberdaya selama

r

Havl = jumlah jam yang tersedia per unit sumberdaya selamaperiode waktu tertentu

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Permintaan produk sebesar 200 unit, ada 22 hari kerja per bulan. Waktu pengoperasian standar per unit sebesar 8 jam, waktupersiapan setengah jam setiap unit. 200 unit akan diproses dalam 10 kumpulan, pada setiap akhir kumpulan, mesin harus diuji dandisesuaikan kembali sebelum kumpulan berikutnya diproses, waktudisesuaikan kembali sebelum kumpulan berikutnya diproses, waktupenyiapan memerlukan 4 jam. Efisiensi organisasional diperkirakan95% dan mesin beroperasi dengan efisiensi 90%. Selama mesindioperasikan dengan kecepatan wajar diperlukan waktu penundaanuntuk pemeliharaan selama 48 menit per hari, mesin-mesindijalankan 8 jam per hari dan para operator mesin bekerja sesuaidengan standar (1,00).

Berapa jumlah mesin yang dibutuhkan untuk memenuhi permintaanbulanan?

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nyata jam 2.035,1 90,0)(0,1(95,0

740.1H

standar jam 1.7404(10)0,5)200(8H

act

std

==

=++=

mesin 56,11)8(22

1,035.2N r ==

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Learning Curve dan Kapasitas

Y = C XS

Log Y = S log X + Log C

X = jumlah unit produk yang dibuatX = jumlah unit produk yang dibuat

C = jam kerja langsung yang diperlukan oleh produksi

pertama

Y = jumlah jam kerja rata-rata per unit produk

S = slope = (log % -2)/log 2

Untuk kurva 80%S = log 80-2/log 2

= 1,90309 – 2 / 0,30103 = -0,322

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Perusahaan menerima kontrak pembuatan produk sejumlah 50 unit. Produk

pertama memerlukan 2.000 jam tenaga kerja langsung, dengan learning curve

yang berlaku sebesar 80% waktu yang diperlukan per unit produk :yang berlaku sebesar 80% waktu yang diperlukan per unit produk :

Log Y = -0,322. log 50 + log 2.000

= -0,322(1,69897) + 3,30103

= 2,75396

Y = 567,491 jam kerja langsung

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literatur

T. Hani Handoko, Dasar-dasar manajemen produksi dan

operasi, bPFE, UGM, Yogyakarta.

Sheri Nemeth and Mick Peters, Production and Operating Sheri Nemeth and Mick Peters, Production and Operating

Management.

N. Gaither and Frazier, Production and Operations

Management, 8th Edition, Duxbury Press, NY, NY, 1999.

(Road server) Handouts for most classes are available on

the ROAD server. The handouts can be accessed at: _

HYPERLINK http://road.uww.edu

__http://road.uww.edu_