Production Management - Yazdtextile.yazd.ac.ir/ms.ahmadi/Downloads/Production... · 2015-09-19 · 9/19/2015 11 l. Choose the experts to participate. There should be a variety of

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مديريت توليد پوشاك

Production Management

In Apparel Industry

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محمدصالح احمدي: تهيه و تنظيم

دانشگاه يزدگروه مهندسي نساجي

منابع .1392آواي شيرين، تهران، هايده متقي، مديريت توليد و عمليات، •

.1372مهدي الواني، نصراهللا ميرشفيعي، مديريت توليد، آستان قدس رضوي، مشهد، •

.عبدالحسين صادقي، جزوه درس مديريت توليد، دانشگاه صنعتي اميركبير•

• ChaseAquilano, Jacobs, Operations Management For Competitive Advantage,

McGraw Hill Higher Education, 2006,.

• Heizer, Render, Operations Management, Prentice Hall, 2006.

• Joseph Sarkis, Hand-outs of the course “Introduction to Operations and Production

Management”, Clark University.

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تعاريف

،ريزيدر برنامه انساني وكارآمد منابع مادي و مؤثرفرايند به كارگيري :مديريت

و بر سازمان دستيابي به اهداف براي هدايت و كنترل ،امكانات وبسيج منابع ،سازماندهي

.قبولاساس نظام ارزشي مورد

تغيير در منابع خام و تبديل آن به محصوالت و ايجاد ارزش افزوده جهت : توليد

. نيازهاارضاي

كه به ارزش مواد خام براي تبديل به كاالي ساخته شده مبلغي : ارزش افزوده

.صرف شده و به آن اضافه مي شود

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: توليدعوامل

. (Man)نيروي كار -1

. (Machines)ماشين آالت ، تجهيزات ، ابزار و وسايل -2

. (Material)مواد -3

. (Methods)روش ها و شيوه هاي كار -4

. (Management)مديريت -5

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: وظايف مديريت

POSDCORB+

INNOVATION

PLANNING

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: ريزي برنامه يا ذهني تالش كار، انجام به اقدام يا فيزيكي تالش از قبل بايد ، نظر مورد هدف به يافتن دست براي

. دهد مي تشكيل را مديريت شالودة ريزي برنامه .بگيرد صورت كافي ريزي برنامه

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:ريزي وبرنامه اهداف تعيين

و اقدامات پيشاپيش و دقيق تدارك و سازمان اهداف تعريف و تعيين فرايند از است عبارت ريزي برنامه زمان، روشها، بيني پش از عبارتند نياز مورد وسايل و اقدامات .سازند مي ميسر را اهداف تحقق كه وسايلي كز متمر سازمان اهداف بر و نگري پيش را سازماني عمليات ريزي نامه بر كلي طور به د افرا و منابع مكان،. كند مي تسهيل را وكنترل نظارت عمل ساخته

:ريزي برنامه فرايند

goal گزاري هدف( آنها اولويت و اهداف تعييين• setting()forecasting نگري پيش(. كند مي كمك هدفها تحقق به كه امكاناتي و منابع وپيشبيني برسي•.دارند ضرورت هدفها تحقق براي كه واقداماتي فعاليتها تشخيص• عمل ومالك روشها و ها مشي خط تعيين•

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ORGANIZING

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: سازماندهي به آنان، ميان هماهنگي و كاري هاي وگروه افراد ميان كار تقسيم آن طي كه است فرايندي ، سازماندهي

.گيرد مي صورت اهداف كسب منظوراز طريق فرايند سازماندهي افراد به صورت گروهي در ساختار وروابط متشكلي قرار مي گيرند تا با تواناييهاي

.الزم و كافي كار موثري را براي رسيدن به هدفهاي معين انجام مي دهند

:فرايند سازماندهي فعاليتهاي الزم براي رسيدن به اهداف واجراي خط مشي وبرنامه ها تشخيص •گروه بندي فعاليتها با توجه به منابع انساني و مادي موجود و تشخيص بهترين طريقه استفاده كردن از آنها •

.

.دادن اختيار عمل وحق دستور دهي و تصميم گيري براي انجام دادن كار به مسئول هر گروه•

ارتباط دادن واحد هاي گروه بندي شده به يكديگر به صورت عمودي وافقي •

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مدير عامل

مدير كارخانه مدير عملياتي مدير طراحيمدير مالي مدير بازاريابي

مدير توليد مدير پرسنليمدير تعميرات

و نگهداريمدير مهندسي

صنعتيمدير فروش

مدير كيفيت مدير خريدمدير

برنامه ريزي مدير توزيع

مدير دوخت مدير برشمدير تكميل

سرپرست بخش سرپرست بخشسرپرست بخش

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هيئت مديره مديرعامل

تداركات

داخلي

خارجي

فروش

فروش داخلي

صادرات

تحقيقات بازار

بازاريابي

توليد

برش و آماده سازي

دوزندگي

تكميل و بسته بندي

تعمير و نگهداري

آموزش

مهندسي

كنترل توليد

كنترل كيفيت

برنامه ريزي

برنامه ريزي و

هماهنگي توليد

كنترل موجودي و

سفارشات

توسعه محصول

طراحي محصول

الگوسازي

توليد پروتوتايپ

اجرايي

حسابداري

كارگزيني

انبار

دبيرخانه

امور عمومي

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STAFFING نيرو جذب

عمدتاً از طريق مدارس، مراكز كاريابي، دانشگاه ها و يا چاپ آگهي

انجام آزمايش هاي روانكاوي، هوش سنجي و فيزيكي متناسب با موقعيت شغلي

آموزش نيروي انساني براي كليه رئه هاي پرسنلي الزامي است

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DIRECTING

COORDINATING

: هدايت.افراد استخدام شده به منظور دست يابي به وظايف در نظر گرفته شدههدايت

.زدن استبه تنهايي سازمان شبيه استارت ” جذب نيرو“و ” سازماندهي“، ”برنامه ريزي“انجام

.آن استبه منزله حركت دادن ” هدايت“عمليات

هماهنگ سازي

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REPORTING

BUDJETING

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گزارش دهي و گزارش گيري

بودجه بندي

پيش بيني تقاضاDemand Forcasting

Which markets to pursue?

What products to produce?

How many people to hire?

How many units to purchase?

How many units to produce?

And so on……

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Forecasts are rarely perfect

Forecasts are more accurate for aggregated data than for individual items

Forecast are more accurate for shorter than longer time periods

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روشهاي پيش بيني تقاضا

Qualitative (Judgmental) Methodsروشهاي كيفي •

Quantitative Methodsروشهاي كمي •

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روشهاي كيفي

ايده هاي مديران•

نظرخواهي از فروشندگان•

)نظرات مشتريان(تحقيق بازار •

روش دلفي•

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�� Involves small group of highInvolves small group of high--level managerslevel managers

�� Group estimates demand by working Group estimates demand by working togethertogether

�� Combines managerial experience with Combines managerial experience with statistical modelsstatistical models

�� Relatively quickRelatively quick

�� ‘Group‘Group--think’think’disadvantagedisadvantage

Executive Executive OpinionOpinion ايده هاي مديران ايده هاي مديران

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�� Each salesperson projects his or her salesEach salesperson projects his or her sales

�� Combined at district and national levelsCombined at district and national levels

�� Sales reps know customers’ wantsSales reps know customers’ wants

�� Tends to be overly optimisticTends to be overly optimistic

Sales Force Sales Force CompositeComposite فروشندگان فروشندگان نظرخواهي از نظرخواهي از

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�� Ask customers about purchasing Ask customers about purchasing plansplans

�� What consumers say, and what they What consumers say, and what they actually do are often differentactually do are often different

�� Sometimes difficult to answerSometimes difficult to answer

Consumer Market SurveyConsumer Market Survey ) ) نظرات مشترياننظرات مشتريان((بازار بازار تحقيق تحقيق

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l. Choose the experts to participate. There should be a variety of

knowledgeable people in different areas.

2. Through a questionnaire (or E-mail), obtain forecasts (and any

premises or qualifications for the forecasts) from all participants.

3. Summarize the results and redistribute them to the participants

along with appropriate new questions.

4. Summarize again, refining forecasts and conditions, and again

develop new questions.

5. Repeat Step 4 if necessary. Distribute the final results to all

participants.

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Delphi methodDelphi method روش دلفي روش دلفي

Type Characteristics Strengths Weaknesses

Executive

opinion

A group of managers

meet & come up with

a forecast

Good for strategic or

new-product

forecasting

One person's opinion

can dominate the

forecast

Market

research

Uses surveys &

interviews to identify

customer preferences

Good determinant of

customer preferences

It can be difficult to

develop a good

questionnaire

Delphi

method

Seeks to develop a

consensus among a

group of experts

Excellent for

forecasting long-term

product demand,

technological

changes, and

Time consuming to

develop

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كمي روشهاي

Time Series methodsروشهاي سري هاي زماني •

Casual methodsروشهاي سببي •

Assumes the future will follow same

patterns as the past

Explores cause-and-effect relationships

Uses leading indicators to predict the future

E.g. housing starts and appliance sales

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روشهاي سري هاي زماني

� Set of evenly spaced numerical data

� Obtained by observing response variable at

regular time periods

� Forecast based only on past values

� Assumes that factors influencing past and

present will continue influence in future

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دوره ايجزء Cyclical

تصادفيجزء Random

جزء روندTrend

فصليجزء Seasonal

سري هاي زمانياجزاء

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Dem

an

d fo

r p

rod

uct

or

serv

ice

| | | |1 2 3 4

Year

Average demand over four years

Seasonal peaks

Trend component

Actual demand

Random variation

Figure Figure 44..11

اجزاء سري هاي زماني

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� Persistent, overall upward or downward pattern

� Changes due to population, technology, age,

culture, etc.

� Typically several years duration

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جزء روند

� Regular pattern of up and down fluctuations

� Due to weather, customs, etc.

� Occurs within a single year

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Number ofPeriod Length Seasons

Week Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52

جزء فصلي

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� Repeating up and down movements

� Affected by business cycle, political, and economic

factors

� Multiple years duration

� Often causal or

associative

relationships

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جزء دوره اي

� Erratic, unsystematic, ‘residual’

fluctuations

� Due to random variation or

unforeseen events

� Short duration and

nonrepeating

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جزء تصادفي

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سري هاي زماني انواع روشهاي

روش نايو•

ميانگين ساده•

ميانگين متحرك•

ميانگين متحرك وزني•

نمو هموار ساده•

تعديل شدهنمو هموار •

حداقل مجذورات•

نوسانات فصلي•

Naïve Forecasting

Simple Mean

Moving Average

Weighted Moving Average

Single Exponential Smoothing

Adjusted Exponential Smoothing

Least square method

Seasonal variation

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روش نايو

Next period forecast = Last Period’s actual:

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ttAF =+1

JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323

JulyJuly

Actual Actual NaiiveNaiiveMonthMonth Sales Sales ForcastForcast

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ميانگين سادهروش

Next period’s forecast = average of all historical data

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n

AAAF

ttt

t

.............211

+++= −−

+

JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323

JulyJuly

Actual SimpleActual SimpleMonthMonth Sales AverageSales Average

ميانگين متحركروش

Next period’s forecast = simple average of the last N periods

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N

AAAF

Nttt

t

111

......... +−−+

+++=

The Effect of the Parameter N

A smaller N makes the forecast more responsive

A larger N makes the forecast more stable

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JanuaryJanuary 1010

FebruaryFebruary 1212

MarchMarch 1313

AprilApril 1616

MayMay 1919

JuneJune 2323

JulyJuly 2626

ActualActual 33--MonthMonthMonthMonth Shed SalesShed Sales Moving AverageMoving Average

((12 12 + + 13 13 + + 1616)/)/3 3 = = 13 13 22//33((13 13 + + 16 16 + + 1919)/)/3 3 = = 1616

((16 16 + + 19 19 + + 2323)/)/3 3 = = 19 19 11//33

1010

1212

1313

((1010 + + 1212 + + 1313)/)/3 3 = = 11 11 22//33

1مثال –متحرك روش ميانگين

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Week Demand 3-Week 6-Week

1 650

2 678

3 720

4 785 682.67

5 859 727.67

6 920 788.00

7 850 854.67 768.67

8 758 876.33 802.00

9 892 842.67 815.33

10 920 833.33 844.00

11 789 856.67 866.50

12 844 867.00 854.83

F4=(650+678+720)/3

=682.67

F7=(650+678+720

+785+859+920)/6

=768.67

1مثال –متحرك روش ميانگين

محاسبه ميانگين متحرك سه و شش هفته اي

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500

550

600

650

700

750

800

850

900

950

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Week

De

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ميانگين متحرك وزنيروش

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1.........

.........

21

11211

=+++

+++= +−−+

N

NtNttt

CCC

where

ACACACF

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Weights:

t-1 .5

t-2 .3

t-3 .2

Week Demand

1 650

2 678

3 720

4

Note that the weights place more emphasis on the

most recent data, that is time period “t-1”.

1مثال –متحرك وزني روش ميانگين

.چهارم محاسبه كنيد) هفته(با توجه به جدول تقاضا و اوزان داده شده، تقاضا را در دوره

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Week Demand Forecast

1 650

2 678

3 720

4 693.4

F4 = 0.5(720)+0.3(678)+0.2(650)=693.4

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نمو هموار سادهروش

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( )10

1

≤≤

−+=+

α

α

where

FAFFtttt

The Effect of the Parameter αααα

A smaller α makes the forecast more stable

A larger α makes the forecast more responsive

نمو هموار سادهروش

� Form of weighted moving average

� Weights decline exponentially

� Most recent data weighted most

� Requires smoothing constant (α)

� Ranges from 0 to 1

� Subjectively chosen

� Involves little record keeping of past data

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Predicted demand = Predicted demand = 142142

Actual demand = Actual demand = 153153

Smoothing constant Smoothing constant αα = .= .2020

New forecastNew forecast = = 142 142 + .+ .22((153 153 –– 142142))

= = 142 142 + + 22..22

= = 144144..2 2 ≈ ≈ 144 144

1مثال –ساده روش نمو هموار

Week Demand

1 820

2 775

3 680

4 655

5 750

6 802

7 798

8 689

9 775

10

• Question: Given the weekly

demand data, what are the

exponential smoothing

forecasts for periods 2-10

using α=0.10 and α=0.60?

• Assume F1=D1

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2مثال –ساده روش نمو هموار

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Week Demand 0.1 0.6

1 820 820.00 820.00

2 775 820.00 820.00

3 680 815.50 820.00

4 655 801.95 817.30

5 750 787.26 808.09

6 802 783.53 795.59

7 798 785.38 788.35

8 689 786.64 786.57

9 775 776.88 786.61

10 776.69 780.77

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Note how that the smaller alpha the smoother the line in this example.

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Mean Absolute Deviation (MAD)Mean Absolute Deviation (MAD)

MAD =MAD =∑∑ |actual |actual -- forecast|forecast|

nn

Mean Squared Error (MSE)Mean Squared Error (MSE)

MSE =MSE =∑∑ (forecast errors)(forecast errors)22

nn

اندازه گيري خطاي پيش بيني

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Mean Absolute Percent Error (MAPE)Mean Absolute Percent Error (MAPE)

MAPE =MAPE =100 100 ∑∑ |actual|actualii -- forecastforecastii|/actual|/actualii

nn

nn

i = i = 11

اندازه گيري خطاي پيش بيني

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RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded αα = .= .1010 αα = .= .1010 αα = .= .5050 αα = .= .5050

11 180180 175175 55 175175 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100

مقايسه خطاي پيش بيني با دو ضريب نمو هموار

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RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviationTonageTonage withwith forfor withwith forfor

QuarterQuarter UnloadedUnloaded αα = .= .1010 αα = .= .1010 αα = .= .5050 αα = .= .5050

11 180180 175175 55 175175 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100

MAD =∑ |deviations|

n

= 84/8 = 10.50

For αααα = .10

= 100/8 = 12.50

For αααα = .50

مقايسه خطاي پيش بيني با دو ضريب

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11 180180 175175 55 175175 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100MADMAD 1010..5050 1212..5050

= 1,558/8 = 194.75

For αααα = .10

= 1,612/8 = 201.50

For αααα = .50

MSE =∑ (forecast errors)2

n


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11 180180 175175 55 175175 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100MADMAD 1010..5050 1212..5050MSEMSE 194194..7575 201201..5050

= 45.62/8 = 5.70%

For αααα = .10

= 54.8/8 = 6.85%

For αααα = .50

MAPE =100 ∑ |deviationi|/actuali

n

n

i = 1


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RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded αα = .= .1010 αα = .= .1010 αα = .= .5050 αα = .= .5050

11 180180 175175 55 175175 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100MADMAD 1010..5050 1212..5050MSEMSE 194194..7575 201201..5050

MAPEMAPE 55..7070%% 66..8585%%


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When a trend is present, exponential smoothing When a trend is present, exponential smoothing must be modifiedmust be modified

Forecast Forecast including (including (FITFITtt) ) = = trendtrend

exponentiallyexponentially exponentiallyexponentiallysmoothed (smoothed (FFtt) ) ++ (T(Ttt)) smoothedsmoothedforecastforecast trendtrend

نمو هموار تعديل شدهروش

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FFtt = = αα(A(At t -- 11) + () + (1 1 -- αα)(F)(Ft t -- 11 + T+ Tt t -- 11))

TTtt = = ββ(F(Ft t -- FFt t -- 11) + () + (1 1 -- ββ)T)Tt t -- 11

Step Step 11: Compute F: Compute Ftt

Step Step 22: Compute T: Compute Ttt

Step Step 33: Calculate the forecast FIT: Calculate the forecast FITtt = F= Ftt + T+ Ttt

روش نمو هموار تعديل شده

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ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding

Month(t)Month(t) Demand (ADemand (Att)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt

11 1212 1111 22 1313..000022 171733 202044 191955 242466 212177 313188 282899 3636

1010

Table Table 44..11

مثال -شده روش نمو هموار تعديل

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11 1212 1111 22 1313..000022 171733 202044 191955 242466 212177 313188 282899 3636

1010

Table Table 44..11

F2 = ααααA1 + (1 - αααα)(F1 + T1)

F2 = (.2)(12) + (1 - .2)(11 + 2)

= 2.4 + 10.4 = 12.8 units

Step 1: Forecast for Month 2


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11 1212 1111 22 1313..000022 1717 1212..808033 202044 191955 242466 212177 313188 282899 3636

1010

Table Table 44..11

T2 = ββββ(F2 - F1) + (1 - ββββ)T1

T2 = (.4)(12.8 - 11) + (1 - .4)(2)

= .72 + 1.2 = 1.92 units

Step 2: Trend for Month 2


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11 1212 1111 22 1313..000022 1717 1212..8080 11..929233 202044 191955 242466 212177 313188 282899 3636

1010

Table Table 44..11

FIT2 = F2 + T1

FIT2 = 12.8 + 1.92

= 14.72 units

Step 3: Calculate FIT for Month 2


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11 1212 1111 22 1313..000022 1717 1212..8080 11..9292 1414..727233 202044 191955 242466 212177 313188 282899 3636

1010

Table Table 44..11

1515..1818 22..1010 1717..28281717..8282 22..3232 2020..14141919..9191 22..2323 2222..14142222..5151 22..3838 2424..89892424..1111 22..0707 2626..18182727..1414 22..4545 2929..59592929..2828 22..3232 3131..60603232..4848 22..6868 3535..1616


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| | | | | | | | |

11 22 33 44 55 66 77 88 99

Time (month)Time (month)

Pro

du

ct d

em

an

dP

rod

uct

de

ma

nd

35 35 –

30 30 –

25 25 –

20 20 –

15 15 –

10 10 –

5 5 –

0 0 –

Actual demand (AActual demand (Att))

Forecast including trend (FITForecast including trend (FITtt))


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Time periodTime period

Valu

es o

f D

ep

en

den

t V

ari

ab

le


DeviationDeviation11







Actual observation Actual observation (y value)(y value)

Trend line, y = a + bxTrend line, y = a + bx^̂

حداقل مجذوراتروش

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Time periodTime period

Valu

es o

f D

ep

en

den

t V

ari

ab

le









Actual observation Actual observation (y value)(y value)

Trend line, y = a + bxTrend line, y = a + bx^̂

Least squares method minimizes the sum of the

squared errors (deviations)


Equations to calculate the regression variablesEquations to calculate the regression variables

b =b =ΣΣxy xy -- nxynxy

ΣΣxx22 -- nxnx22

y = a + bxy = a + bx^̂

a = y a = y -- bxbx


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b = = = b = = = 1010..5454∑∑xy xy -- nxynxy

∑∑xx22 -- nxnx22

33,,063 063 -- ((77)()(44)()(9898..8686))

140 140 -- ((77)()(4422))

a = y a = y -- bx = bx = 9898..86 86 -- 1010..5454((44) = ) = 5656..7070

TimeTime Electrical Power Electrical Power YearYear Period (x)Period (x) DemandDemand xx22 xyxy

19991999 11 7474 11 747420002000 22 7979 44 15815820012001 33 8080 99 24024020022002 44 9090 1616 36036020032003 55 105105 2525 52552520042004 66 142142 3636 85285220052005 77 122122 4949 854854

∑∑x = x = 2828 ∑∑y = y = 692692 ∑∑xx22 = = 140140 ∑∑xy = xy = 33,,063063x = x = 44 y = y = 9898..8686


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b = = = b = = = 1010..5454ΣΣxy xy -- nxynxy

ΣΣxx22 -- nxnx22

33,,063 063 -- ((77)()(44)()(9898..8686))

140 140 -- ((77)()(4422))

a = y a = y -- bx = bx = 9898..86 86 -- 1010..5454((44) = ) = 5656..7070

TimeTime Electrical Power Electrical Power YearYear Period (x)Period (x) DemandDemand xx22 xyxy

19991999 11 7474 11 747420002000 22 7979 44 15815820012001 33 8080 99 24024020022002 44 9090 1616 36036020032003 55 105105 2525 52552520042004 66 142142 3636 85285220052005 77 122122 4949 854854

ΣΣx = x = 2828 ΣΣy = y = 692692 ΣΣxx22 = = 140140 ΣΣxy = xy = 33,,063063x = x = 44 y = y = 9898..8686

The trend line is

y = 56.70 + 10.54x^


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| | | | | | | | |19991999 20002000 20012001 20022002 20032003 20042004 20052005 20062006 20072007

160 160 –

150 150 –

140 140 –

130 130 –

120 120 –

110 110 –

100 100 –

90 90 –

80 80 –

70 70 –

60 60 –

50 50 –

YearYear

Po

we

r d

em

an

dP

ow

er

de

ma

nd

Trend line,Trend line,

y = y = 5656..70 70 + + 1010..5454xx^̂


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1.1. We always plot the data to insure a We always plot the data to insure a linear relationshiplinear relationship

2.2. We do not predict time periods far We do not predict time periods far beyond the databasebeyond the database

3.3. Deviations around the least squares Deviations around the least squares line are assumed to be randomline are assumed to be random


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The multiplicative seasonal model can modify The multiplicative seasonal model can modify trend data to accommodate seasonal variations in trend data to accommodate seasonal variations in demanddemand

1.1. Find average historical demand for each season Find average historical demand for each season

2.2. Compute the average demand over all seasons Compute the average demand over all seasons

3.3. Compute a seasonal index for each season Compute a seasonal index for each season

4.4. Estimate next year’s total demandEstimate next year’s total demand

5.5. Divide this estimate of total demand by the number Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for of seasons, then multiply it by the seasonal index for that seasonthat season

نوسانات فصلي

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JanJan 8080 8585 105105 9090 9494

FebFeb 7070 8585 8585 8080 9494

MarMar 8080 9393 8282 8585 9494

AprApr 9090 9595 115115 100100 9494

MayMay 113113 125125 131131 123123 9494

JunJun 110110 115115 120120 115115 9494

JulJul 100100 102102 113113 105105 9494

AugAug 8888 102102 110110 100100 9494

SeptSept 8585 9090 9595 9090 9494

OctOct 7777 7878 8585 8080 9494

NovNov 7575 7272 8383 8080 9494

DecDec 8282 7878 8080 8080 9494

DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20032003 20042004 20052005 20032003--20052005 MonthlyMonthly IndexIndex

مثال -نوسانات فصلي

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JanJan 8080 8585 105105 9090 9494

FebFeb 7070 8585 8585 8080 9494

MarMar 8080 9393 8282 8585 9494

AprApr 9090 9595 115115 100100 9494

MayMay 113113 125125 131131 123123 9494

JunJun 110110 115115 120120 115115 9494

JulJul 100100 102102 113113 105105 9494

AugAug 8888 102102 110110 100100 9494

SeptSept 8585 9090 9595 9090 9494

OctOct 7777 7878 8585 8080 9494

NovNov 7575 7272 8383 8080 9494

DecDec 8282 7878 8080 8080 9494


00..957957

Seasonal index = average 2003-2005 monthly demand

average monthly demand

= 90/94 = .957


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JanJan 8080 8585 105105 9090 9494 00..957957

FebFeb 7070 8585 8585 8080 9494 00..851851

MarMar 8080 9393 8282 8585 9494 00..904904

AprApr 9090 9595 115115 100100 9494 11..064064

MayMay 113113 125125 131131 123123 9494 11..309309

JunJun 110110 115115 120120 115115 9494 11..223223

JulJul 100100 102102 113113 105105 9494 11..117117

AugAug 8888 102102 110110 100100 9494 11..064064

SeptSept 8585 9090 9595 9090 9494 00..957957

OctOct 7777 7878 8585 8080 9494 00..851851

NovNov 7575 7272 8383 8080 9494 00..851851

DecDec 8282 7878 8080 8080 9494 00..851851



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JanJan 8080 8585 105105 9090 9494 00..957957

FebFeb 7070 8585 8585 8080 9494 00..851851

MarMar 8080 9393 8282 8585 9494 00..904904

AprApr 9090 9595 115115 100100 9494 11..064064

MayMay 113113 125125 131131 123123 9494 11..309309

JunJun 110110 115115 120120 115115 9494 11..223223

JulJul 100100 102102 113113 105105 9494 11..117117

AugAug 8888 102102 110110 100100 9494 11..064064

SeptSept 8585 9090 9595 9090 9494 00..957957

OctOct 7777 7878 8585 8080 9494 00..851851

NovNov 7575 7272 8383 8080 9494 00..851851

DecDec 8282 7878 8080 8080 9494 00..851851


Expected annual demand = 1,200

Jan x .957 = 961,200

12

Feb x .851 = 851,200

12

Forecast for 2006


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140 140 –

130 130 –

120 120 –

110 110 –

100 100 –

90 90 –

80 80 –

70 70 –| | | | | | | | | | | |

JJ FF MM AA MM JJ JJ AA SS OO NN DD

TimeTime

De

ma

nd

De

ma

nd

2006 2006 ForecastForecast

2005 2005 Demand Demand

2004 2004 DemandDemand

2003 2003 DemandDemand


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سببيروشهاي

• Often, leading indicators hint can help predict changes in demand

• Causal models build on these cause-and-effect relationships

• A common tool of causal modeling is linear regression:

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bxaY +=

Linear Regression رگرسيون خطي

( )( )( )( )∑ ∑

∑ ∑−

−=

XXX

YXXYb

2

XbYa −=

• Identify dependent (y) and independent (x) variables

• Solve for the slope of the line

• Solve for the y intercept

• Develop your equation for the trend line

Y=a + bX

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∑

∑

−

−=

22

XnX

YXnXYb

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Linear Regression Problem: A maker of golf shirts has been tracking the

relationship between sales and advertising dollars. Use linear regression

to find out what sales might be if the company invested $53,000 in

advertising next year.

∑

∑

−

−=

22

XnX

YXnXYb

Sales $ (Y)

Adv.$ (X)

XY X^2 Y^2

1 130 48 4240 2304 16,900

2 151 52 7852 2704 22,801

3 150 50 7500 2500 22,500

4 158 55 8690 3025 24964

5 153.85 53

Tot 589 205 30282 10533 87165

Avg 147.25 51.25

( )( )( )

( )

( ) 153.54533.58-36.20Y

3.58x-36.20bXaY

-36.20a

51.253.58147.25XbYa

3.5851.25410533

147.2551.25430282b

5

2

=+=

+=+=

=

−=−=

=−

−=

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