AN ENGINEERING APPROACH TO LOGISTICS AND FORECASTING OF PRODUCT MARKET FLOW USING MODIFIED PROGRESSIVE
EVENT EXPONENTIAL SMOOTHING
Ahmed Samy AbdEIRehim
A Dissertation Submitted to the Graduate Faculty of
Auburn University in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
Auburn, Alabama
May 14, 2004
Trang 2UMI Number: 3124250
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Trang 3AN ENGINEERING APPROACH TO LOGISTICS AND FORECASTING OF PRODUCT MARKET FLOW USING MODIFIED PROGRESSIVE
EVENT EXPONENTIAL SMOOTHING
Except where reference is made to the work of others, the work in this dissertation is my own or was done in collaboration with my advisory committee This dissertation does not
include proprietary or classified information
, grr sew,
Z4 Ahmed Samy AbdElRehim
Certificate of Approval:
Michael R Solomon iaNEl-Mogahzy, Chair
Professor Professor
Consumer Affairs Textile Engineering
St€phen L McFarland
Assistant Professor Acting Dean
Trang 4VITA
Ahmed AbdEIRehim, son of Samy AbdEIRehim and Mona ElSherbiny, was born
February 16", 1977, in Mansoura, Egypt He graduated from Youssef ElSebaie High School in 1994 He attended Ain Shams University College of Engineering in Cairo, Egypt, for five years, and graduated as a computer systems engineer with a Bachelor of Science degree in Computer Engineering in November, 1999 After working as an e- business staff consultant at Newteck Solutions software department for one year, he entered Graduate School, Auburn University, in August, 2000 His graduate class work in support of his research was divided between software engineering and business administration In an attempt to improve his academic record, he decided to pursue a non- thesis Masters degree in Software Engineering, which was successfully completed in December, 2002 After building a solid software background both academically and professionally through various consultant software projects, his focus shifted to business systems analysis He decided to pursue a Master degree in Business Administration expected in May 2004
Trang 5DISSERTATION ABSTRACT
AN ENGINEERING APPROACH TO LOGISTICS AND FORECASTING OF PRODUCT MARKET FLOW USING MODIFIED PROGRESSIVE
EVENT EXPONENTIAL SMOOTHING
Ahmed Samy AbdEIRehim Doctor of Philosophy, May 14, 2004 M.B.A Auburn University, May 14, 2004
(M.S., Auburn University, 2002) (B.S., Ain Shams University, 1999)
Directed by Yehia El-Mogahzy
In today’s global competitive market and as the world continues to break economical and trade barriers, customers are the primary target of any business organization A key aspect of successful business lies in the ability to forecast the dynamic changes in market wants, needs, and demands Traditionally, forecasting has been primarily based on the use of historical data to predict future events When product demand is likely to change in unpredictable fashion due to complex interactive market factors, the traditional forecasting time-series analysis offers limited forecasting capabilities This is particularly true when special events represented by step or ramp trends are likely to occur Exponential smoothing techniques require a great deal of
subjective involvement in order to capture and accurately predict these types of events
Such subjective information is typically based on understanding the nature of product/service marketing, product/service lifecycle, and consumer reactions These factors have resulted in the need for integrating “judgmental forecasting” with
Trang 6exponential smoothing The challenge associated with this approach lies in structuring judgmental data in such a way that optimizes its usefulness in providing reliable
forecasting and logistical planning
This study aims at developing a forecasting model, which is based on both stochastic and judgmental forecasting techniques, of corporate sales performance The basis for this study stems from the need for the following criteria for an integrated judgmental and statistical model:
e The use of real rather than artificial data when developing and evaluating models The need for reliable adjustment for unusual future anticipated events
= The need for formulating and filtering experts inputs through justification and critical review of their judgmental estimates
« The need to use structured judgment as inputs to models
" The need to use evidence on each method’s accuracy to allow accurate adjustments of the weights on the component forecasts
In view of the above criteria, this study primarily aims at developing a realistic judgmental and statistical model that can reveal the true obstacles associated with structuring judgmental inputs and assist in overcoming their impacts The true challenge facing this goal lies in four aspects:
(1) The process of transforming judgmental information into data
(2) Filtering the data down to the relevant and critical forecasting-associated data (3) Structuring useful judgmental data into a model-ready format
(4) Integrating judgmental and past actual data to formulate a reliable forecasting
Trang 7In this study, new concepts are introduced in the process of structuring a reliable database for judgmental forecasting These include: Budget Analysis (BA) and Product Style Cluster Analysis (PSCA) BA is a comprehensive structured judgmental forecasting system that is capable of transforming contextual information into future sales estimates in quantitative form The purpose of the PSCA component is to track changes in product market flow, perform correspondence analysis between product substitutes, focus on enhancing current markets, and seek new markets that have high sales potential Another important aspect of product style analysis is improving the judgmental forecasting capability of sales agents when presented with sales time series that are in both tabular and graphical displays
Finally, we propose an integrated model, called Modified Progressive Event Exponential Smoothing (MPEES), which modifies the exponential smoothing technique (ES) by adjusting the level component of its forecasts using the outcome of Budget Analysis (BU) after being adjusted for bias (AdBU) using the Budget Efficiency Coefficients (BE) The judgmental adjustments are included within the damped-trend seasonal exponential smoothing model and not subject to any ad-hoc manipulation by the forecaster The model was tested with 15 real sales data series for an Italian textile manufacturing firm
The study concludes with the finding that both the MPEES and AdBU models were superior to either the ES model or the BU model when applied solely Gains in accuracy were as low as 2% and as high as 59% Higher gains in accuracy are usually associated with discontinuities in the series in the shape of future progressive events anticipated by the sales force
Trang 8ACKNOWLEDGMENTS
The author would like to thank Dr Yehia El-Mogahzy for his unlimited support and assistance with this research both academically and professionally I’m thankful and grateful for his thoughtful direction and understanding leadership throughout the whole process One of the most important contributions of this study comes from its significant outreach to the industry The model developed in this study was tested and evaluated using real data provided by an Italian yarn manufacturing company, Manifattura di Legnano The company provided unlimited support in sponsoring the development of this study I would like to express my great appreciation and gratitude to all my colleagues at Manifattura di Legnano; and more specifically to Mr Paolo Morelli, the director of logistics and Mr Mario Formanti, the general manager
I would also like to thank the committee members Dr Michael Solomon and Dr Aliecia McClain for their help and guidance in the preparation of this manuscript In addition, thanks are also due to Dr Faissal Abdel-Hady for assistance with LabVIEW programming during the early preparation phase of this undertaking In closing, no words would describe my sincere appreciation and deep respect to my parents, whom I owe each and every single accomplishment achieved, and to my brothers for their help and
support
Trang 9TABLE OF CONTENTS
I0 ý040/96 40/9) 1 „N›4:) 4Ì 5À 09)500695)2.v0160).142111 11 2.1 BASIC CONCEPTS OF FORECASTING óc n9 1111213 281 1g 11H re 12 2.2 EXPONENTIAL SMOOTHING .- 5 <1 x19 HH TH TH n0 ng 0 1013 11121Te 21 2.2.1 Applications oƒ damped-trend seasonal exponenfIal smoothing - 28 2.3 FORECASTING ACCURACY Ác S990 H0 H0 0110111101121 1011111011001 116 32 2.3.1 Mean Square Error (M'SE:) canh HH HH Hi ng g1 12L 4 32
2.3.2 Percentage Error (PE) and Mean Absolute Percentage Error (MAPE) 33
2.4 ADAPTTVE EXPONENTIAL SMOOTHING .- 5-5 n9 E191 xe, 34 2.5 JUDGMENTAL TIME-SERIES FORECASTING - c5 5n HH in 37 2.5.1 Judgmental versus Quantitative ƒorecasting methodlS .««cc««ccsece« 37 2.5.1.1 Series/task charaCf©TISẨICS - G G + 1S nọ HH 11 914 39 2.5.1.2 Judge/environmental charaCt€TiSfICS - 5c sS+c+cesisertesresrer 46 2.5.2 Integrating judgmental and quantitafiVe ƒOr€CSEÍH -àcằcccseneiiesiesre 49 °, 9Š Ni 200i) 7 50 2.5.2.2 Combination of objective and subJectIve ÍOreCasfS series 53 2.5.2.3 Judgmental adjustment of objective ÍOr€CasfS .- - sec 56 2.5.2.4 Judgmental decompOSItIOI .-.- ch HH 9 1011 1k ru 60 2.6 CLOSING REMARKS 5 ng TT HH TH 1001011410111 64 3 DEVELOPING AN APPLIED INTEGRATED STATISTICAL AND JUDGMENTAL I9):45 0.60006890920015 69 SN hy 66x09 101117175 69 3,2 JUDGMENTAL UNANTICIPATED PROGRESSIVE EVENTS cà oSSssehnneieire 71 3.3 BUDGET ANALLYSIẨ 5 1k1 HH KH 911 1000111111001 171114 75 3.4 INTEGRATING STATISTICAL AND ÏUDGMENTAL FORECAST 5< «<< s<+2 84 3.5 HYPOTHETICAL APPLICATIONS OF THE ÏNTEGRATED MODEL .- - + - 87
Trang 103.5.1 First Scenario: (Significanf PL) «chì HH ng hy 88 3.5.2 Second Scenario: (Mintmal BL43) cách # 92 3.5.3 6n nan 95
4 APPLICATION DEVELOPMENT - QG Q0 t4 99
“vì 3100601 200070077 100 “VU ?)09€20 0/1004) 71 e 105 4.3 PRODUCT STYLE CLUSTER ANALYSIS c<* 231221 9x 11118 ry 111
no (202000 0c70/ 10.7 115
N0 nnố ốc ee 115 4.4.2 Data PFOCHFY€HGHÍÍ Ặ S ST TT ni 117 4.4.3, Data Preparation ccccceccccssccerecesssessseeseeessececsccnesesaesesaesensesensesenseessanessnaeeses 118 4.5 APPLICATION RESULTS USING REAL DA TA - (5 5S 2E + VVESEsterrsesreree 120 4.6 DISCUSSION AND ANALLYSIS G << HH0 0001 101114 137 5 CONCLUSION AND FUTURE WORK . Gà LH 141
3355503590 S1 — 147
Trang 11LIST OF TABLES
TABLE] FORECASTING SALES USING SINGLE EXPONENTIAL SMOOTHING [WHEELWRIGHT AND MAKRIDAKIS 1985] ccccccssssecsesecesseecesseecssceeesseecessnceeeseneecessaeesesneeenseeesonanens 23
TABLE 2 EXPONENTIAL SMOOTHING STATE SPACE FRAMEWORK [HYNDMAN, KOEHLER, AND SNYDER 2002] cc:ccccssssseccesssccecsssseeccsssnececesseacececesnenaeeeeesessnaceseeeseaeseseseseseeeees 27 TABLE 3 APPLICATION OF DAMPED-TREND SEASONAL EXPONENTIAL SMOOTHING WITH
PROGRESSIVE EVENTS ccccsscccessssccecsssccecesssaeeeeessnaceeseessnaneesereessaaaeeesesssaeeecsenesgaeece 72
TABLE4 SALES AND CORRESPONDING BUDGET FOR FOUR QUARTERLY BUDGET REVIEW
CYCLES ccsessesssccecessccsssssssssucececcesseeesaeeeeseesessceneusaeeeeeeeeeceeseeseesesnsnsinenseateeeeesseteteeaes 77
TABLE 5 MONTHLY SALES AND CORRESPONDING BUDGET FOR TWO YEARS PERIOD 81
TABLE 6.1 ACTUAL MONTHLY SALES AND ADJUSTED BUDGET WITH NO EVENT 81
TABLE 6.2 ACTUAL MONTHLY SALES AND ADJUSTED BUDGET WITH STEP EVENT 82
TABLE 6.3 ACTUAL MONTHLY SALES AND ADJUSTED BUDGET WITH RAMP EVENT 82
TABLE 7.1 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND BUDGET ESTIMATES WITH AN OBVIOUS BIAS AND NO EVENT G0933 1301 9910 31 1 ng re 89 TABLE 7.2 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND BUDGET ESTIMATES
WITH AN OBVIOUS BIAS AND STEP EVENT :sssccsesseceesseesesneecessaeecessaueecsuaeecnsneeesenarees 90
TABLE 7.3 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND BUDGET ESTIMATES WITH AN OBVIOUS BIAS AND RAMP EVENT G4 91 TABLE 8.1 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND BUDGET ESTIMATES
WITH A MINIMAL BIAS AND NO EVENT .cccccccccseessesssnsneneceececceeeecsesseessesseuseanegeeeeeeesenss 92
TABLE 8.2 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND BUDGET ESTIMATES
WITH A MINIMAL BIAS AND STEP EVENT Ăn ng re 93
TABLE 8.3 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND BUDGET ESTIMATES
Trang 12LIST OF FIGURES
FIGURE 1 COMPETITOR CLASSIFICATION USING THE QS TRIANGLE [KAMEL 2001, EL
i67 ):v2@200220 5= — 3 FIGURE 2 THE PLANNING- FORECASTING CYCLE [ARMSTRONG 1982B, EL MOGAHZy 2002]4
FIGURE 3 FORECAST SUBJECTS AND THEIR INTERACTION WITH THE COMPETITIVE LOOP
[ARMSTRONG 1999, EL MoGAHZY 202] -. - - 5 223218111 eˆ 5 FIGURE 4 FORECASTING METHODOLOGIES INTERRELATIONSHIP FRAMEWORK [ARMSTRONG
Jb8›):49)9)128 1007757 16 FIGURE 5 QUANTITATIVE FORECASTING METHODOLOGIES [MAKRIDAKIS AND
);122819:3/6560065723 000277 17 EIGURE 6 EXTRAPOLATION MODELS - TIME SERIES PATTERNS - Sài 18 FIGURE 7 WEIGHT EXPONENTIAL DECAY AS APPLIED TO HISTORICAL DATA 22 FIGURE 7.2 FORECASTING SALES USING SINGLE EXPONENTIAL SMOOTHING [WHEELWRIGHT
0Ä 74:30) 06 510 24
FIGURE 8 COMPARISON OF STANDARD WINTERS AND DAMPED WINTERS FORECASTS
[ WHEELWRIGHT AND MAKRIDAKIS [O8Š] - 5c 255B S112 9 11112112 mxer 26
FIGURE 9 EXPONENTIAL SMOOTHING MODELS [HYNDMAN, KOEHLER, AND SNYDER 2002] ¬ 28 FIGURE 10.1 RANDOM WALK WINTERS FORECASTT .- Ăn 99 9 1g ng 28 FIGURE 10.2 RANDOM WALK FOLLOWED BY ÏNCREASING TREND -. -2<<<S<<<<+2 29 FIGURE 10.3 RANDOM WALK FOLLOWED BY DECREASING TREND <5- 29 EIGURE 10.4 INCREASING TREND FOLLOWED BY RANDOM WALK . <<<< + 29
FIGURE 10.5 DECEEASING TREND FOLLOWED BY RANDOM WALK -. - <5 30
FIGURE 10.6 DECREASING TREND - Gì HH ng H0 110011001 1101 t8 30 FIGURE 10.7 INCREASING 'TREND - . - G11 n HH KH ng KH 001111115088 1 tk 30 FIGURE 10.8 DECREASING TREND FOLLOWED BY ÏNCREASING TREND - - 31 FIGURE 10.9 [NCREASING TREND FOLLOWED BY DECREASING TREND . ‹ 31
Trang 13FIGURE 10.10 SEASONAL AND [NCREASING TREND Ă SH ng HH1 x14 31 FIGURE 11 JUDGMENTAL TIME-SERIES FORECASTING: MODEL BUILDING FLOW CHART
DIAGRAM [MODIFIED AFTER WEBB & O’ CONNER 1996] cccsecssessesesseeeeesesesenaeenees 50 FIGURE 12 JUDGMENTAL TIME-SERIES FORECASTING: COMBINATION MODEL FLOW CHART
DIAGRAM [MODIFIED AFTER WEBB & O’ CONNER 1996] ccceescesscessesssesseesesesneeseeens 53 FIGURE 13 JUDGMENTAL TIME-SERIES FORECASTING: JUDGMENTAL ADJUSTMENT MODEL
FLOW CHART DIAGRAM [MODIFIED AFTER WEBB & O”CONNER 1996] . 56
FIGURE 14 JUDGMENTAL TIME-SERIES FORECASTING: JUDGMENTAL DECOMPOSITION
MODEL FLOW CHART DIAGRAM [WEBB & OCONNER 1996] - c5 5S 60
FIGURE 15 TYPES OF PROGRESSIVE EVENTS - G11 vn ng ng 1100212 1 mg 71 FIGURE 16.1 SALES FORECAST WITH NO EVENT - SH H1 vip 73 FIGURE 16.2 SALES FORECAST WITH STEP EVENT - 55+ +kretreererreerrrrke 73 FIGURE 16.3 SALES FORECAST WITH RAMP EVENT + HH th g0 1117111 cv 74 FIGURE 17.1 BUDGET PREPARATION CONCEPTUAL FRAMEWORK . ccSsàeeehreee 76 FIGURE 17.2 BUDGET REVIEW CONCEPTUAL FRAMEWORK ccsccsssseseeseesesenseeeseaeeesseaeeese 76 FIGURE 18 APPLICATION OF BUDGET REVIEW csssssssssssssesccseessnaeeeesensnaasenesessanaeeeerensaes 78 FIGURE 19 COMPARISON OF FORECASTING ACCURACY MEASURED BY MAPE FOR
DIFEERENT BUDGET ADIUSTMENT SCENARIOS - SH ng cư 83
FIGURE 20 COMPARISON OF STATISTICAL AND RAMP EVENT JUDGMENTAL FORECAST 85 FIGURE 21 SCHEMATIC DIAGRAM FOR INTEGRATING JUDGMENTAL AND STATISTICAL
9:79 12617 ỊỊƠ 86
FIGURE 22.1 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND BUDGET
ESTIMATES WITH AN OBVIOUS BIAS AND STEP EVENT «nen re 89
FIGURE 22.2 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND BUDGET
ESTIMATES WITH AN OBVIOUS BIAS AND STEP EVENT - nhe 90
FIGURE 22.3 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND BUDGET
ESTIMATES WITH AN OBVIOUS BIAS AND RAMP EVENT cccccssssscescerensesereseueeeaoeeeeees 91 FIGURE 23.1 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND NEAR PERFECT
BUDGET ESTIMATES WITH NO EVENT .- S9 Ki th n7 18g 93 FIGURE 23.2 APPLICATION OE INTEGRATING STATISTICAL FORECAST AND NEAR PERFECT
BUDGET ESTIMATES WITH A STEP EVENT < CS S910 nh ke và 94
Trang 14FIGURE 23.3 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND NEAR PERFECT BUDGET ESTIMATES WITH A RAMP EVENT G0 ng tt 95
FIGURE 24.1 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND BUDGET
ESTIMATES FOR SCENARIO 1 cecesseceessssseceeesnececessenenecceesssneeseteessdaeessessseeessessnneenees 96
FIGURE 24.2 APPLICATION OF INTEGRATING STATISTICAL FORECAST AND BUDGET
ESTIMATES FOR SCENARIO 2 ccccsessseesscecescecesseessssssessssecesseessesseeseesaeeessaneeensnesesaees 97 FIGURE 25.1 OVERALL SYSTEM DATABASE STRUCTURE 5 5 cty 101 FIGURE 25.2 SALES ORGANIZATION HIERARCHY 5 1 ng 1 11x xee 102 FIGURE 25.3 DESIGN VIEW FOR AGENT 'TABLE 756 11v HH vn, 102 EIGURE 25.4 DESIGN VIEW FOR CUSTOMER TT ABLE - ĂĂ nhi ng re, 102 FIGURE 26.1 PRODUCT STYLE ATTRIBUTES c ng g0 1v 0102x516 103 FIGURE 26.2 DESIGN VIEW FOR PRODUCT ÏABLE c5 23199 9 11111 ree 104 FIGURE 27 DESIGN VIEW FOR BUDGET TABLE - 6 5 <3 3 v9 kg nh ng ưhg 107 FIGURE 28 SCHEMATIC DIAGRAM OF THE BUDGET PREPARATION PROCESS FLOW CHART
¬ 107
FIGURE 29.1 FRONT PANEL FOR ANNUAL BUDGET PREPARATION -c << c2 108 FIGURE 29.2 FRONT PANEL FOR BUDGET REVIEW PREPARATION (FIRST CYCLE) 109
FIGURE 30 BUDGET CONTROL SELECTION CRITERIA - 5S ni 110 FIGURE 31.1 PRODUCT STYLE ANALYSIS PERIOD/PROFILE SPECIFICATION 112
FIGURE 31.2 PRODUCT STYLE ANALYSIS SALES HIERARCHY STRUCTURE 113
FIGURE 31.3 PRODUCT STYLE ANALYSIS PRODUCT STYLE/TYPE/CATEGORY 113
FIGURE 31.4 PRODUCT STYLE ANALYSIS PRODUCT SALES MONTHLY PROFILE 113
FIGURE 31.5 PRODUCT STYLE ANALYSIS PRODUCT SALES COMPARISON MONTHLY PROPFILE .cccccccessssecccesssececesssseeecnsnsneeceessaaeseesseeeesessssscessesssueeesusseesseesusesnsaesserenenaees 114 Bế 114 FIGURE 32.2 PRODUCT STYLE ANALYSIS PRODUCT SALES CUMULATIVE CHART 114
FIGURE 33 FORECASTING ANALYSIS PERIOD/VARIABLE SPECTFICATION 116
FIGURE 33.2 FORECASTING ANALYSIS SALES HIERARCHY/REGION SPECIFICATION 116
FIGURE 33.3 FORECASTING ANALYSIS PRODUCT STYLE SPECIFICATION - 117 FIGURE 34 ADIUSTMENTS FOR [NTERMITTENT DEMAND 5c SS S3 xs<ssssss 119
Trang 15FIGURE 35 FORECASTING SYSTEM SETTINGS .-. .- nọ cán về 120
FIGURE 36.1 SALES FORECASTS FOR COMPANY SALES IN FRANCE .sscccsssecersssceneeeseneues 122 FIGURE 36.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR COMPANY SALES IN
FIGURE 37.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR COMPANY SALES IN
€;::2 7.00 aa 123
FIGURE 38.1 SALES FORECASTS FOR COMPANY SALES IN ÏTALY «Ă << 52+ 124
FIGURE 38.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR COMPANY SALES IN
FIGURE 40.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR COMPANY SALES OF
21, Ả &&ỲĂ'ỲẴẰỲẰ'ỶAÝỶ 126
FIGURE 41.1 SALES FORECASTS FOR COMPANY SALES OF OL,BRAND «< +2 127
FIGURE 41.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR COMPANY SALES OF OL
FIGURE 42.1 SALES FORECASTS FOR COMPANY SALES OF OE BRAND cc.cccscreesseseseneeesens 128
FIGURE 42.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR COMPANY SALES OF OE
FIGURE 43.1 SALES FORECASTS FOR SALES BY AGENT (A084) ĂẶẶ «se 129
FIGURE 43.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR SALES BY AGENT (A04) FIGURE 44.1 SALES FORECASTS FOR SALES BY AGENT (AOC) ch 130
FIGURE 44.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR SALES BY AGENT (A0C)
FIGURE 45.1 SALES FORECASTS FOR SALES BY AGENT (A70) cà Ằ Si e 131 FIGURE 45.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR SALES BY AGENT (A70)
Trang 16FIGURE 46 SALES FORECASTS FOR SALES BY AGENT (AQŠ) .cẶĂseeneeere 132 FIGURE 46.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR SALES BY AGENT (AQ5)
:10)8990/œ 03807 133
FIGURE 48.1 SALES FORECASTS FOR TOWELS FINAL PRODUCTT - «55c < + +zs=c+ 134 FIGURE 48.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR TOWELS FINAL
:1999 20012255 134
FIGURE 49.1 SALES FORECASTS FOR OUTWEAR WEAVING FINAL PRODUCT 135 FIGURE 49.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR OUTWEAR WEAVING
100/.903:49)90/ 0001210105577 135
EIGURE 50.1 SALES FORECASTS FOR UPHOLSTERY WEAVING FINAL PRODUCT 136
FIGURE 50.2 MAPE COMPARISONS OF DEVELOPED FORECASTS FOR UPHOLSTERY WEAVING
IJi/-1083:19)9190/ 02225 136 FIGURE 51 ACCUARCY GAIN AS A % CHANGE IN MAPE Ghi, 138 FIGURE 52 API EFFECT ON FORECASTING MODEL CHOICE sssecessseesesscseeseeeeesseeseeeenes 138 FIGURE 53 MAPE COMPARISONS FOR THE FOUR MODELS FOR EACH CASE 139
Trang 171.INTRODUCTION
In today’s global competitive market and as the world continues to break economical and trade barriers, a number of key challenges are facing the Manufacturing and Service industry These challenges primarily stem from two main aspects:
e The ability of the manufacturing industry to survive against a multiplicity of interactive factors including manufacturing cost, labor cost, R&D cost, marketing and advertising cost, market transients or spoilers, unfair trade regulations, quality cost, and image cost
e The ability of the service industry to provide a competitive-proof service to different areas in the world against a multiplicity of interactive cultural and dynamic consumer behavior factors
The competitive status of any manufacturing company depends largely on its ability to read the market both domestically and globally and on timely-fashion That is, to be able to forecast dynamic market shifts using effective and efficient techniques In a previous study by (Kamel 2001 and El Mogahzy 2002), the authors proposed three basic components of competitive superiority:
(1) Company or product/service image expressed by the so-called “Image Index,
Trang 18(2) Company or product/service consumer price acceptance expressed by the so-
called “Consumer Price Acceptance Index, CPAT)
Trang 19Zs Top Contenders 4 Halancers RX "/ đ » Transients (Spoilers) : GP AI cal
FIGURE 1 COMPETITOR CLASSIFICATION USING THE QS TRIANGLE [KAMEL 2001, EL MoGaHzy 2002]
Trang 20Planning and forecasting are two complementary tasks that must be performed by management to achieve certain goals Planning calls for an explicit written process for determining the firm's long-range objectives, the generation of alternative strategies for achieving these objectives, the evaluation of these strategies, and systematic procedures for monitoring results Forecasting methods, on the other hand, are explicit procedures for translating information about the environment and the firm's proposed planning strategy into statements about future results Both planning and forecasting interact together as (Armstrong 1982b) put it “Planning concerns what the world should look like, while Forecasting is about what it will look like.” Figure 2 shows the interaction between planning and forecasting
Database Bank Result Measuring 4 a x
The Plan Specific Actions =
3 wm
External Factors Personnel
G = Consultants
Quality — _, Planning Image
a 4 \
Coxt Resources
FIGURE 2 THE PLANNING- FORECASTING CYCLE [ARMSTRONG 19828, EL MoGAHzy 2002]
Forecasting has long been important to marketing practitioners For example, (Dalrymple 1987), in his survey of 134 U.S companies, found that 99 percent prepared formal forecasts when they used formal marketing plans In (Dalrymple 1975), 93 percent
Trang 21of the companies sampled indicated that sales forecasting was one of the most critical aspects, or a ‘very important’ aspect of their company's success Managers’ forecasting needs vary considerably They may need to forecast the size and growth of a market or product category When strategic issues are being considered, they need to forecast the actions and reactions of key decision makers such as competitors, suppliers, distributors, governments, their own actions, and complementors (organizations with whom they cooperate) actions These actions can help to forecast market share The resulting forecasts allow one to calculate a sales forecast If strategic issues are not important, one can extrapolate sales directly Finally, by forecasting costs and using the sales forecast, one can forecast profits and other financial outcomes Figure 3 shows a graphical representation of the various subjects of forecasting and the interaction between them internally within the firm and externally within the environment:
Consumer Market «Competitors
«Suppliers and distributors *Government
*Firm own actions
| Market Share | Costs Ỉ Sales Ỷ Profits I 1 1 I
Actions by key decision makers:
1 I ! I i ¥ Competitive Loop
FIGURE 3 FORECAST SUBJECTS AND THEIR INTERACTION WITH THE COMPETITIVE LOOP [ARMSTRONG 1999, EL MoGauzy 2002]
The lack of planning and forecasting has been one of the primary reasons for the fall of many manufacturing industries in highly industrial countries such as the U.S and
Trang 22Europe This is particularly true for industries that have traditionally dealt with commodity products such as textile, apparel and food industries Ironically in these countries, the service and information technology industries have grown immensely and this has been a direct result of planning and forecasting
Obviously, planning and forecasting aspects involve a great deal of complex analysis that goes beyond a single study Indeed, there have been many studies dealing
with these two aspects as will be seen in the extensive review of literature However, a
number of critical points were not addressed in these studies to the extent of depth they deserve These include:
= Formalization of market feedbacks from the most market-intimate sources (e.g sales people and distributors, etc)
« Product style sales profiling, particularly at intermediate or supporting product levels
« Planning and forecasting of special events both random and periodic
In light of the above unresolved issues, this study deals specifically with ways to deal with each issue This was carried out using three primary approaches:
(1) Developing suitable planning and estimation algorithms that provide reliable evaluations of feedbacks of market-intimate sources This approach will be called “Budget Analysis”
Trang 23(3) Developing realistic forecasting techniques through modification of the familiar exponential smoothing algorithms to account for progressive dynamic changes and special events
In order to demonstrate the capability of the above approaches in planning and forecasting applications, two further steps were taken:
(1) Utilization of actual data generated from a dynamic database of a large textile company (one of the largest spinners of fine yarns in Europe)
(2) Developing a Planning/Forecasting Software Program capable of dynamic data manipulation, product style profiling, and timely forecasting
The study is based on two main assumptions:
(1) Historical and current sales and product data are reliable and measurement errors
are minimal
(2) Company’s sales forces have access to reliable and accurate current market information such as: change in customer demand or taste, competitors launching new products, or change in competitors pricing strategy
Trang 24some degree of accuracy On the other hand, based on historical sales data alone,
(Winters 1960) model lacks the ability to detect and forecast these events
In order to develop a model that is capable of forecasting progressive events that has no historical precedence and make use of the valuable information embedded in the
historical sales records, two main issues were to be tackled First, the accessibility of current market information, regarding future sales events, that are assumed to be within
the reach of field sales agents; and the ability to communicate such information in a quantitative manner to logistics and production planning management The second issue is related to applying such information effectively to adjust the exponential smoothing forecasting model for the sole purpose of improving forecasting accuracy
Trang 25model is first applied to the historical sales time-series to develop the level, trend, and
seasonal components of the forecast model The budget estimates are then adjusted for inherent bias and applied to the exponential smoothing forecasting model to adjust the level component The adjustment uses differential weights that are determined before the forecast is developed
The developed model was first tested hypothetically using artificial time-series data for both sales and budget in order to assess its viability Results were promising as the forecasting accuracy improved significantly compared to the accuracy of either the Statistical forecasts developed by the conventional exponential smoothing model or the budget forecasts developed by the sales agents alone Based upon such hypothetical results, the developed model was then applied for testing on real sales and budget data provided by an Italian company in the spinning industry The results concluded supported those produced by the hypothetical testing and proved the viability of the developed system
In chapter 2, a review of prior research introduces the principles behind building a forecasting system, the different forecasting methodologies, a study of different time- series patterns, and the concept of exponential smoothing and the modifications done so far to enhance the model capabilities The chapter then proceeds by investigating judgmental time-series forecasting and the different theoretical approaches for integrating judgmental and statistical forecasts
Trang 26forecasting system (Budget Analysis) and the associated system framework design The last section discusses the schematic diagram for integrating output of the Budget Analysis system and that of the Exponential smoothing system This section also explains different methods for adjusting the output of the Budget Analysis system and the procedure adopted for integration with the statistical exponential smoothing model Finally, the chapter ends with a demonstration of the developed model application on two different scenarios with artificial data for a hypothetical assessment of the developed model effect on overall forecasting accuracy
Chapter 4 discusses the implementation of the model within the context of software development as a dynamic enterprise forecasting system The first section describes the enterprise database structure that the system uses to access historical sales and order data The next section discusses the software development flowchart for the Budget Analysis and Product Cluster Analysis system components The chapter then proceeds with an explanation of the design and requirements specification for the third system component (Forecasting Analysis) It starts with a discussion of the different stages the input data (historical and budget) goes through from specification to procurement to preparation Finally, the developed model is applied to real sales and budget time-series data that exhibits different patterns and progressive events illustrating the improvement gained in forecasting accuracy The chapter concludes with a detailed discussion and analysis of the resulting gain accuracy when applied to real data Chapter 5 presents the final conclusion of this study illustrating the benefits achieved and the assumptions that should be considered when applying our developed model to any forecasting application
Trang 272 REVIEW OF LITERATURE
Before proceeding with the literature review, it should be pointed out that in addition to some of the papers presented in journals and conference proceedings, a great deal of this review relied on other critical reviews in the field including:
« Armstrong J.S (2001) Principles of Forecasting: Handbook for Researchers and
Practitioners (Norwell, MA: Kluwer Academic Publishers)
= Montgomery, et al (1990) Forecasting & Time Series Analysis (McGraw Hill, _ New York)
« Wheelwright S.C and’ Makridakis S (1985) Forecasting Methods for Management (Wiley, New York)
Some of the views represented in these references were discussed strictly based on the concepts presented by former reviewers and others were modified to reflect the viewpoints of this study This review will cover the following topics:
e Basic concepts of forecasting e Exponential smoothing
e Judgmental time-series forecasting e Closing remarks
Trang 282.1 Basic Concepts of Forecasting
Before 1960, little empirical research was done on sales forecasting methods Since then, the literature has grown rapidly, especially in the area of judgmental forecasting Forecasts serve many needs in organizations and are employed for both short-range and long-range planning They help in making decisions on production, personnel, finance, and marketing For example, forecasts of competitive actions can help to assess a proposed strategy The same needs for forecasts existed in 1960 There are eight guidelines: six for making forecasts, one for estimating uncertainty in the forecasts, and one for gaining acceptance of the forecasts; that were in use in such period These guidelines as a result of prior research studies by (Armstrong 2001), (McLaughlin 1983),
and (Sanders and Ritzman 1989) are as follows:
1 Decomposition should be used whenever feasible Complex problems should
be broken into a series of sub-problems, each of which is to be solved, and the
results then synthesized Of particular importance are decompositions to separate the forecasting of company sales into industry sales and market share, estimate current status separately from forecasting change, and provide forecasts separately for each consumer market Decomposition can be used with judgment, econometric or extrapolation methods Its use in extrapolation (whereby average, trend, and seasonal components are examined) is especially
popular
2 Extrapolation should be used as one of the forecasting methods whenever the data allow Exponential smoothing of de-seasonalized data using a trend estimate will produce adequate results
Trang 293 Obtain opinions from experts in the topic area, and do this in highly structured ways Use these opinions to estimate current status, make forecasts of change, forecast in situations where data on the variable of interest (for example, the sales variable) are absent or of poor quality, and forecast the effects of actions by the firm when considering the reactions of major competitors, but do not use expert opinion to adjust the forecasts produced by objective methods 4 Consumer/client surveys should be used to forecast short-term behavior for
important events
5 Causal-objective methods, such as econometric models, are preferred whenever sufficient data exist They should be developed from a priori theory, and estimates should be obtained from a variety of sources Highly reliable data are desirable
6 Combine forecasts from at least two different approaches Each forecast should be weighted according to the confidence one has in it
7 Uncertainty estimates should accompany the forecasts The accuracy of a given method in similar situations (that is, the method's track record) should be used as the primary means for assessing uncertainty Independent judgmental assessments of accuracy should also be used
8 Before the forecasts are obtained, key decision makers should commit themselves to how they will use the information
The above guidelines had been discussed in academic literature, but were not based on much empirical evidence Few of these guidelines were used by practitioners in 1960 Currently, these guidelines do not meet with strong approval due to the extensive
Trang 30study performed since the 1960 on the validity of the previously mentioned guidelines The outcome of these studies with respect to the previous guidelines is presented below
in the same order:
1 Decomposition has been widely recommended as a strategy for management science However, little study has been done on its value in forecasting At present, research is lacking on how best to decompose problems and on the situations in which decomposition is most useful (Armstrong 2001)
Much research activity has concentrated on sophisticated extrapolation methods However, the empirical research in the area suggests there has been negligible gain in accuracy from the use of sophisticated methods
(McLaughlin 1983)
The growth of research on judgmental forecasting has been rapid The number of publications in this area has been growing at about 14 percent per year over the past 30 years (Kahneman and Tversky 1974) Expert opinion is useful in estimating current status, although the direct evidence for this point is sparse
More experts should be used where the cost of errors is high, uncertainty is
high, the experts have some ability to forecast, and the cost of the experts is low Surprising evidence has been obtained on forecasting change For many years, it was suggested that expert opinion was especially relevant for long- range forecasts However, research shows it to be less accurate than objective methods in situations where large changes are expected (Armstrong 1985) Therefore, forecasters should rely more on objective methods than on expert opinion, especially for long-range forecasts Forecasts obtained from objective
Trang 31methods should not be revised by expert opinion Expert revisions lessened forecasting accuracy (Kelly and Fiske 1950)
Research on intentions has been extensive, and the results useful The net
effect has been substantial (Perry 1979) Intentions are useful for short-range predictions of important events given that respondents are willing and able to report their intentions accurately, and that new information is unlikely to change the plan (Sewall 1981)
Causal objective methods have not proved useful for short-term forecasting They have not been less accurate than alternative methods Causal objective methods might be used as one of several approaches to be combined They are effective for long-range forecasting Extensive data from different sources should yield better estimates of a given causal relationship (Armstrong 1985) Combine forecasts from extrapolation, judgment, and econometric methods
Use data from independent sources such as consumers, producers, retailers,
and experts The combination of forecasts from two different methods yielded a 6.6 percent reduction in error compared to the average component (Armstrong 1984)
Organizations do not like to discuss uncertainty Unfortunately, uncertainty 1s typically estimated by judgments and thus is subject to many biases A useful technique is to ask experts to summarize arguments against their prediction as
well as those in favor; this leads to more realistic assessments of uncertainty
Objective (quantitative) approaches should be used to estimate uncertainty whenever possible (March and Simon 1963)
Trang 328 Without prior commitment, decision makers are unlikely to be influenced by forecasts that conflict with their expectations (Griffith and Wellman 1979) The ranges of situations in which forecasts are required vary widely in time horizons, factors determining actual outcomes, types of data patterns, and many other respects Several forecasting techniques have been developed These techniques fall into two major categories: judgmental and quantitative These techniques and the relationships between them are shown in the flowchart in Figure 4 Going down the flowchart, there is an increasing amount of integration between judgmental and quantitative data and procedures This integration, which has been studied by researchers in the last decade, can improve forecast accuracy (Armstrong and Brodie 1999)
Knowledge Source judgicntal watistleal
self others tualvarlate touldvariate
role fa role theory-Hused | data-haved
co | | |
Role : Expert Extrapolation -
Plavi laying Intentions Opinions cae Models Multivariate Models
3 _ | =— 4 % fl " Ệ Analogies £5 , sk 4 me I
Ee: Conjoint Judgmental [fi Rule-Based
a3 Analysis Bootstrapping |]! Forecasting
ez : Ị en
& = i » 1
5 w | r $ Ý
i ỉ
tac me meeeye ke se _— i s xpert Systens em = Econometric Models
FIGURE 4 FORECASTING METHODOLOGIES INTERRELATIONSHIP FRAMEWORK [ARMSTRONG AND BRODIE 1999]
Trang 33Quantitative forecasting can be applied when three conditions exist: There is information about the past; this information can be quantified in the form of data; and the assumption that past behavior can be used to predict the future This last condition is known as the assumption of constancy and it is the underlying premise of all quantitative methods Quantitative forecasting techniques vary considerably, having been developed by diverse disciplines for different purposes Each has its own properties, accuracies and costs that must be considered in choosing a specific method One way of classifying quantitative forecasting methods is the underlying model involved There are two major types of forecasting models: time-series and causal models Figure 5 illustrates the differences between the two forecasting models
Quantitative Forecasting Models J 3 |5
inputs; Cause &Effect | Oưtpuis inputs Generating Outputs
Relationship Process
Random Noise ode Noise
GOP = f (manetary policy , inflation, capital spending, wu) GDP.,, = f(GDP,+ GDP,, + + uJ
FIGURE 5 QUANTITATIVE FORECASTING METHODOLOGIES [MAKRIDAKIS AND WHEELWRIGHT 1998]
Causal models assume that the factor to be forecasted exhibits a cause-effect relationship with one or more independent variables For example: sales as function of income, prices, advertising, and competition The purpose of the causal methods is to discover the form of that relationship and use it to forecast future values of the dependent
variable
Trang 34Time series methods, on the other hand, forecasts the future based on past values
of the variable to be forecasted and past errors The objective is to discover the pattern in the historical data series and extrapolate that pattern into the future An important step in selecting an appropriate time-series method is to consider the types of data patterns, so that the methods most appropriate to those patterns can be tested Four types of data patterns can be distinguished: horizontal (random walk), trend, seasonal, and cyclical These patterns are shown in Figure 6 and are briefly discussed below
Yt va Yt) Yt
Noise (Horizontal) Trend | Damp Tend
ha ALL prem 5 t 5 t —E—— oc
Irregular Fluctuation The Tendency to increase or | | Regular intra Year Pattern Changes Associated
Decrease over the long run With the business Cycle
«Products with stable sales * Products with seasonal (i.e macro-economy)
* Number of defects ina « Sales af many companies sales TỐ
stable process » Steadily growing company " Sales of products such as * Business cycle data
« Campany sales over short « Steadily growing or soft drinks, ice creams, and » Company Mergers
time periods i.e days or deteriorating product heating oil
weeks « Weather
" Holidays
« Schoo! Calendar
«Tax Season
* Trading Day Variation
* Madel-year transition
** The major distinction between a seasonal and a cydical pattern is thatthe former is of a constant ength and reours on a regular periodic basis, while the fatter varies in length and magnitude
FIGURE 6 EXTRAPOLATION MODELS - TimME SERIES PATTERNS
1 A horizontal (also called random, or noise) pattern exists when data values fluctuate around a constant mean A product whose sales do not increase or decrease over time would be of this type Similarly, a quality control situation involving sampling from a continuous production process that theoretically does not change would also be of this type
Trang 352 A trend pattern exists when there is a long-term secular increase or decrease in the data The sales of many companies, the gross national product, and many other business or economic indicators follow a trend pattern in their movement over time
3 A seasonal pattern exists when a series is influenced by seasonal factors leading to a significant change in the series level at the seasonal period (e.g high Christmas sales) Sales of products such as soft drinks, ice creams, and heating oil all exhibit this type of pattern
4 A cyclical pattern exists when the data are influenced by longer-term economic fluctuations such as those associated with the business cycle The sales of products such as automobiles, steel, and major appliances exhibit this type of pattern The major distinction between a seasonal and a cyclical pattern is that the former is of a constant length and recurs on a regular periodic basis, while the latter varies in length and magnitude
Many data series include combinations of the above patterns Forecasting methods that are capable of distinguishing each of the patterns must be employed if a separation of the component pattern is needed Similarly, alternative methods of forecasting can be used to identify the pattern and to best fit the data so that future values can be forecasted
As the title of this study implies, we focus on product market flow as the subject to be forecasted Product market flow is the outcome of logistics planning and production control that ultimately lead to sales Both judgmental and extrapolation forecasting methods can be deployed to achieve reliable product market flow forecasts Exponential
Trang 36smoothing is one of the most widely used techniques in sales forecasting analysis today However, very few companies are implementing this approach in other critical applications such as logistic strategies and product-flow forecasting Many of the attractive features of this technique include its simplicity, its outstanding capability of forecasting trends and seasonality performance of sales data, its reasonable accuracy, and its low strict requirement of historical data (Montgomery 1990) Perhaps, the most important advantage of exponential smoothing is the authority level by the analyst to determine weights reflecting the relative emphasis given to the recent vs the distant past However, the technique suffers fundamental deficiencies including: the lack of exploratory or explanatory power, the negligence of business cycle, and the failure to recognize and incorporate consecutive events occurring over a short period of time in the competitive loop (El Mogahzy 2002) which we call progressive events
Although conventional exponential smoothing allows for the inclusion of some events (promotion discount, expected high sales- week or month, etc), these events are introduced in discrete fashion and the effectiveness of their inclusion strictly depends on the specifics associated with each event As such, modifying exponential smoothing to account for such progressive events through an integrated approach that makes use of judgmental forecasts provided by field experts represent the heart of this study The remaining of this chapter is divided into two main sections: exponential smoothing theory, techniques, and applications; judgmental time-series forecasting in which we describe several approaches for integrating judgment with exponential smoothing to
forecast a time-series
Trang 372.2 Exponential Smoothing
Exponential Smoothing is one of the statistical extrapolation models that are based on the simple assumption that past behavior is a good predictor of future behavior Prior literature showed that past behavior can be extrapolated into the future and provide reasonable results when the data series is stable no abnormal future events are anticipated Exponential Smoothing weights past data unequally in an exponential decaying manner provided that measurement errors are small, forecast horizons are short to medium, and the series is stable Some of the features that favor exponential smoothing over other quantitative methods are its being simple, objective, stable, popular, cost effective, easily automated, and reasonably accurate (Montgomery 1990) Besides, exponential smoothing methods handle several different types of time-series patterns with low strict requirement of historical data compared to alternative quantitative methods On the other hand, there are shortcomings to exponential smoothing such as its inadequacy for long-term forecast horizons, lack of explanatory power, and finally, although the algorithm have been studied and modified for decades to account for different historical
patterns, still it fails to recognize consecutive events i.e level shifts or discontinuities
occurring over a short period of time in the competitive loop due to external policy changes such as competitors releasing new product into the market, change in technology, or change in consumer purchasing behavior
Exponential smoothing methods have been around since the 1950s Single
exponential smoothing (ES) by (Brown 1956) assumes only level and random noise in the
data The model is mathematically represented as follows:
F t+ = aX,-(1-a)F
Trang 38ES substantially reduces any storage problem, only the most recent observation X,, the most recent forecast F;, and a value for the weighting factor @ must be stored The implication of exponential smoothing can be better seen if equation (3.1) is expanded by replacing F, with its components as follows:
F,, =aX,-(l-a)laX,, +(1-a)F,]
Fis = ax, -a(l ~aX,,) + q ~a)’ F.,
If this substitution process is repeated by replacing F,., by its components, F,.2 by its components, etc., the resulting equation would be as follows:
Fi = AX, ~a(l-@)X,_, t+a(l-a)’X,, + 4a(l-a)" XxX t-(N-l)
Figure 7.1 shows the exponential decay of the weight applied, denoted by a, to past data observations to develop next period forecast according to the exponential smoothing algorithm It can be seen that the weights applied to each of the past values decrease exponentially, thus the name exponential smoothing It should be pointed out that even though the objective may still be to minimize the MSE, the estimation involved in exponential smoothing is nonlinear
——s=91 —u=96 —a=09 | Exponetial Weight (qj) B r a a m 11 12 11 14 Ww Past Obsarvations
Trang 39An alternative way of writing (3.1) is to rearrange the terms in the following manner:
Fi =F, +X, —F,)
From this equation, it can be seen that the forecast provided by exponential smoothing is simply the old forecast plus an adjustment for the error that occurred in the last forecast
In this for it is evident that when @ has a value close to 1, the new forecast will include a
substantial adjustment for the error in the previous forecast and the forecast for the next period will be close to the actual data observation in the current period Conversely, when
@ is close to 0, the new forecast will include very little adjustment and the forecast for the
next period will be close to the forecast for the current period The application of single exponential smoothing can be illustrated by using the following example Table 1 and Figure 7.2 shows an application for developing sales forecast using single exponential
smoothing with a@ values of 0.1, 0.5, and 0.9
TABLE1 FORECASTING SALES USING SINGLE EXPONENTIAL SMOOTHING [WHEELWRIGHT AND MAKRIDAKIS 1985
_ Month ý âu go Shipments Exponential Smoothed Values
Trang 40
Sales " = 'ơ=Q11 "mm cơ O5 = © ‹ơ<=OQQ
350 300 + 250 ¬ 200 + 150 + 100 + 50 +
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
Period (months)
FIGURE 7.2 FORECASTING SALES USING SINGLE EXPONENTIAL SMOOTHING [WHEELWRIGHT AND MAKRIDAKIS 1985]
Single exponential smoothing requires only a minimal amount of data and number of computations It is therefore attractive when a large number of items require forecasting The main drawback for single exponential smoothing is that it does not account for both the trend and seasonal components in a time-series Accordingly, the resulting forecast lacks adjustment for both components making the algorithm inadequate for time series that exhibits either trend or seasonal patterns For such purpose (Holt 1957) introduced the two-parameter linear exponential smoothing that adjusts the forecast for the trend component followed by (Winters 1960) introduction to linear and seasonal exponential smoothing that accounts for both the trend and seasonal components Winters’ adopted Holt’s linear exponential smoothing and modified it to account for the seasonal component of a time-series
Winters’ linear and seasonal exponential smoothing is based on three equations, each of which smoothes a parameter associated with one of three components of the pattern: level, trend, and seasonal In this respect it is very similar to Holt’s method, but