Operations Management Forecasting Chapter 4

Operations Management Forecasting Chapter 4
PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

BİR İŞLETLETMENİN BAŞARISI İLERİYİ NE KADAR İYİ GÖREBİLMESİNE VE UYGUN STRATEJİLER GELİŞTİRMESİNE BAĞLIDIR PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

YÖNETİCİLERİN EN TEMEL GÖREVİ: PLAN YAPMAKTIR

PLANLAR GELECEĞE YÖNELİKTİR

ÖYLEYSE GELEÇEĞİ TAHMİNLEMEK ZORUNDAYIZ

YÖNETİÇİLERİN ALDIĞI KARARLARIN BİR ÇOĞUNDA AZ YADA ÇOK BİR TÜR TAHMİN YER ALIR

ÖRNEK BİR BÜRO ŞEFİNİN CUMA GÜNÜ BAZI MEMURLARINA İZİN VEREBİLMEK İÇİN CUMA GÜNÜN İŞ YÜKÜNÜ TAHMİN ETMESİ PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render)
© 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

ASLINDA GÜNLÜK HAYATIMIZIN BİR ÇOK KESİTİNDE DE TAHMİN YAPIYORUZ ÖRNEK;

ANCAK BU TAHMİNLERİN BİR KISMI OLDUKÇA KOLAYKEN TAHMİNLENMESİ ÇOK ZOR OLAN KONULARDA VARDIR

ÖRNEĞİN BİR OTOMOTİV ENDÜSTRİSİNİN FİNANS MÜDÜRÜNÜN GELEÇEK YILKI MEVSİMLİK FİNANS İHTİYACINI TAHMİNLEMESİ PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Forecasting and optimization are complex
Come on! It can‘t go wrong every time... PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Select significant attributes for your forecaster
Which one Is mine? PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

What is Forecasting? Process of predicting a future event
Underlying basis of all business decisions Production Inventory Personnel Facilities Sales will be $200 Million! PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

TAHMİNLEME NEDİR? EDMUND BURK’YE GÖRE: geçmişe bakarak geleceği hiçbir zaman planlayamassınız. PATRICK HENRY İSE; geçmiş olmadan geleceği hiçbir şekilde yargılayacak bir yol bilmiyorum der. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

tanımlar “ Tahmin;geleçekteki muhtemel olayların belirli bir zamanda saptanması,hesaplanması ya da kestirimidir. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

TAHMİNLEME SİSTEMİ ÇİZİM

TAHMİNLEME SİSTEMİ SATIŞ TAHMİNİ GİRDİLER ÇIKTILAR
*PAZAR DURUMLAR *GEÇMİŞ SATIŞLAR *İŞLETME STRATEJİLERİ *ENDÜSTRİNİN DURUMU *EKONOMİNİN DURUMU *TİÇARİ REKABET DURUMU *ÜRETİM KAPASİTESİ *IHUKUKİ VE POLİTİK FAKTÖRLER *DİĞER FAKTÖRLER HER MAL İÇİN HER ZAMAN DÖNEMİNDE BEKLENEN TALEP *DİGER FAKTÖRLER TAHMİNLEME TEKNİKLERİ VEYA MODELLERİ SATIŞ TAHMİNİ BAŞKALARININ ÖNERİLERİ RİSK DURUMU TECRÜBE İNSİYATİF VE HİS KİŞİSEL DEĞERLER VE GÜDÜLER SOSYAL VE KÜLTÜREL DEGERLER ÖTEKİ FAKTÖRLER HER MAL İÇİN HER ZAMAN DÖNEMİNDE TALEP TAHMİNİ KARAR VERİCİ PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Types of Forecasts by Time Horizon
Short-range forecast Up to 1 year; usually less than 3 months Job scheduling, worker assignments Medium-range forecast 3 months to 3 years Sales & production planning, budgeting Long-range forecast 3+ years New product planning, facility location At this point, it may be useful to point out the “time horizons” considered by different industries. For example, some colleges and universities look 30 to fifty years ahead, industries engaged in long distance transportation (steam ship, railroad) or provision of basic power (electrical and gas utilities, etc.) also look far ahead (20 to 100 years). Ask them to give examples of industries having much shorter long-range horizons. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Short-term vs. Longer-term Forecasting
Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes. Short-term forecasting usually employs different methodologies than longer-term forecasting Short-term forecasts tend to be more accurate than longer-term forecasts. At this point it may be helpful to discuss the actual variables one might wish to forecast in the various time periods. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Influence of Product Life Cycle
Stages of introduction and growth require longer forecasts than maturity and decline Forecasts useful in projecting staffing levels, inventory levels, and factory capacity as product passes through life cycle stages This slide introduces the impact of product life cycle on forecasting The following slide, reproduced from chapter 2, summarizes the changing issues over the product’s lifetime for those faculty who wish to treat the issue in greater depth. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Strategy and Issues During a Product’s Life
Introduction Growth Maturity Decline Standardization Less rapid product changes - more minor changes Optimum capacity Increasing stability of process Long production runs Product improvement and cost cutting Little product differentiation Cost minimization Over capacity in the industry Prune line to eliminate items not returning good margin Reduce capacity Forecasting critical Product and process reliability Competitive product improvements and options Increase capacity Shift toward product focused Enhance distribution Product design and development critical Frequent product and process design changes Short production runs High production costs Limited models Attention to quality Best period to increase market share R&D product engineering critical Practical to change price or quality image Strengthen niche Cost control critical Poor time to change image, price, or quality Competitive costs become critical Defend market position OM Strategy/Issues Company Strategy/Issues HDTV CD-ROM Color copiers Drive-thru restaurants Fax machines Station wagons Sales 3 1/2” Floppy disks Internet PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Types of Forecasts Economic forecasts Technological forecasts
Address business cycle, e.g., inflation rate, money supply etc. Technological forecasts Predict technological change Predict new product sales Demand forecasts Predict existing product sales One can use an example based upon one’s college or university. Students can be asked why each of these forecast types is important to the college. Once they begin to appreciate the importance, one can then begin to discuss the problems. For example, is predicting “demand” merely as simple as predicting the number of students who will graduate from high school next year (i.e., a simple counting exercise)? PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Seven Steps in Forecasting
Determine the use of the forecast Select the items to be forecast Determine the time horizon of the forecast Select the forecasting model(s) Gather the data Make the forecast Validate and implement results A point to be made here is that one requires a forecasting “plan,” not merely the selection of a particular forecasting methodology. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Product Demand Charted over 4 Years with Trend and Seasonality
1 2 3 4 Seasonal peaks Trend component Actual demand line Average demand over four years Demand for product or service Random variation This slide illustrates a typical demand curve. You might ask students why it is important to know more than simply the actual demand over time. Why, for example, would one wish to be able to break out a “seasonality” factor? PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Jury of Executive Opinion
Involves small group of high-level managers Group estimates demand by working together Combines managerial experience with statistical models Relatively quick ‘Group-think’ disadvantage Ask your students to consider other potential disadvantages. (Politics?) PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J © 1995 Corel Corp.

Sales Force Composite Each salesperson projects their sales
Combined at district & national levels Sales rep’s know customers’ wants Tends to be overly optimistic Sales © 1995 Corel Corp. You might ask your students to consider what problems might occur when trying to use this method to predict sales of a potential new product. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Delphi Method Iterative group process 3 types of people
Decision makers Staff Respondents Reduces ‘group-think’ Decision Makers (Sales?) Staff (Sales will be 50!) (What will sales be? survey) You might ask your students to consider whether there are special examples where this technique is required. ( Questions of technology transfer or assessment, for example; or other questions where information from many different disciplines is required.) Respondents (Sales will be 45, 50, 55) PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Consumer Market Survey
How many hours will you use the Internet next week? © 1995 Corel Corp. Ask customers about purchasing plans What consumers say, and what they actually do are often different Sometimes difficult to answer You might discuss some of the difficulties with this technique. Certainly there is the issue that what consumers say is often not what they do. There are other problems such as that consumers sometime wish to please the surveyor; and for unusual, future, products, consumers may have a very imperfect frame of reference within which to consider the question. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Overview of Quantitative Approaches
Naïve approach Moving averages Exponential smoothing Trend projection Linear regression Time-series Models Associative models PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Quantitative Forecasting Methods (Non-Naive)
Time Series Associative Models Models A point you may wish to make here is that only in the case of linear regression are we assuming that we know “why” something happened. General time-series models are based exclusively on “what” happened in the past; not at all on “why.” Does operating in a time of drastic change imply limitations on our ability to use time series models? Moving Exponential Trend Linear Average Smoothing Projection Regression PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

What is a Time Series? 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 Example Year: Sales: This and subsequent slide frame a discussion on time series - and introduce the various components. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Time Series Components
Trend Seasonal Cyclical Random PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Trend Component Persistent, overall upward or downward pattern
Due to population, technology etc. Several years duration Mo., Qtr., Yr. Response © T/Maker Co. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Seasonal Component Regular pattern of up & down fluctuations
Due to weather, customs etc. Occurs within 1 year Mo., Qtr. Response Summer © T/Maker Co. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

 Cyclical Component Repeating up & down movements
Due to interactions of factors influencing economy Usually 2-10 years duration Mo., Qtr., Yr. Response Cycle  PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Random Component Erratic, unsystematic, ‘residual’ fluctuations
Due to random variation or unforeseen events Union strike Tornado Short duration & nonrepeating © T/Maker Co. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

General Time Series Models
Any observed value in a time series is the product (or sum) of time series components Multiplicative model Yi = Ti · Si · Ci · Ri (if quarterly or mo. data) Additive model Yi = Ti + Si + Ci + Ri (if quarterly or mo. data) This slide introduces two general forms of time series model. You might provide examples of when one or the other is most appropriate. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Naive Approach Assumes demand in next period is the same as demand in most recent period e.g., If May sales were 48, then June sales will be 48 Sometimes cost effective & efficient © 1995 Corel Corp. This slide introduces the naïve approach. Subsequent slides introduce other methodologies. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

 Moving Average Method MA is a series of arithmetic means
Used if little or no trend Used often for smoothing Provides overall impression of data over time Equation MA n   Demand in Previous Periods At this point, you might discuss the impact of the number of periods included in the calculation. The more periods you include, the closer you come to the overall average; the fewer, the closer you come to the value in the previous period. What is the tradeoff? PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Moving Average Example
You’re manager of a museum store that sells historical replicas. You want to forecast sales (000) for 1998 using a 3-period moving average © 1995 Corel Corp. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Moving Average Solution

Moving Average Graph 95 96 97 98 99 00 Year Sales 2 4 6 8 Actual
Forecast This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Weighted Moving Average Method
Used when trend is present Older data usually less important Weights based on intuition Often lay between 0 & 1, & sum to 1.0 Equation Σ(Weight for period n) (Demand in period n) This slide introduces the “weighted moving average” method. It is probably most important to discuss choice of the weights. WMA = ΣWeights PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Actual Demand, Moving Average, Weighted Moving Average
Actual sales Moving average This slide illustrates one of the simplest forecasting techniques - the moving average. It may be useful to point out the lag introduced by exponential smoothing - and ask how one can actually make use of the forecast. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Disadvantages of Moving Average Methods
Increasing n makes forecast less sensitive to changes Do not forecast trend well Require much historical data © T/Maker Co. These points should have been brought out in the example, but can be summarized here. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Exponential Smoothing Method
Form of weighted moving average Weights decline exponentially Most recent data weighted most Requires smoothing constant () Ranges from 0 to 1 Subjectively chosen Involves little record keeping of past data This slide introduces the exponential smoothing method of time series forecasting. The following slide contains the equations, and an example follows. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Exponential Smoothing Equations
Ft = At (1-)At (1- )2·At (1- )3At (1- )t-1·A0 Ft = Forecast value At = Actual value  = Smoothing constant Ft = Ft-1 + (At-1 - Ft-1) Use for computing forecast You may wish to discuss several points: - this is just a moving average wherein every point in included in the forecast, but the weights of the points continuously decrease as they extend further back in time. - the equation actually used to calculate the forecast is convenient for programming on the computer since it requires as data only the actual and forecast values from the previous time point. - we need a formal process and criteria for choosing the “best” smoothing constant. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Exponential Smoothing Example
You’re organizing a Kwanza meeting. You want to forecast attendance for 2000 using exponential smoothing ( = .10). The1995 forecast was This slide begins an exponential smoothing example. © 1995 Corel Corp. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Exponential Smoothing Solution
Ft = Ft-1 + ·(At-1 - Ft-1) Forecast, F t Time Actual ( α = .10) 1995 180 (Given) 1996 168 1997 159 1998 175 1999 190 2000 NA PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft = Ft-1 + ·(At-1 - Ft-1) Forecast, F t Time Actual ( α = .10) 1995 180 (Given) 1996 168 ( 1997 159 1998 175 1999 190 2000 NA PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft = Ft-1 + ·(At-1 - Ft-1) Forecast, F t Time Actual ( α = .10) 1995 180 (Given) 1996 168 (180 - 1997 159 1998 175 1999 190 2000 NA PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft = Ft-1 + ·(At-1 - Ft-1) Forecast, F t Time Actual ( α = .10) 1995 180 (Given) 1996 168 ( ) 1997 159 1998 175 1999 190 2000 NA PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft = Ft-1 + ·(At-1 - Ft-1) Forecast, F t Time Actual ( α = .10) 1995 180 (Given) 1996 168 ( ) = 1997 159 1998 175 1999 190 2000 NA PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft = Ft-1 + ·(At-1 - Ft-1) Forecast, F t Time Actual ( α = .10) 1995 180 (Given) 1994 168 ( ) = 1995 159 ( ) = 1996 175 1997 190 1998 NA PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft = Ft-1 + ·(At-1 - Ft-1) Forecast, F Time Actual t ( α = .10) 1995 180 (Given) 1996 168 ( ) = 1997 159 ( ) = 1998 175 ( )= 1999 190 2000 NA PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft = Ft-1 + ·(At-1 - Ft-1) Forecast, F t Time Actual ( α = .10) 1995 180 (Given) 1996 168 ( ) = 1997 159 ( ) = 1998 175 ( ) = 1999 190 ( ) = 2000 NA PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft = Ft-1 + ·(At-1 - Ft-1) Forecast, F t Time Actual ( α = .10) 1995 180 (Given) 1996 168 ( ) = 1997 159 ( ) = 1998 175 ( ) = This slide illustrates the result of the steps used to make the forecast desired in the example. In the PowerPoint presentation, there are additional slides to illustrate the individual steps. 1999 190 ( ) = 2000 NA ( ) = PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Exponential Smoothing Graph
Year Sales 140 150 160 170 180 190 93 94 95 96 97 98 Actual Forecast This slide illustrates graphically the results of the example forecast. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Forecast Effects of Smoothing Constant 
Ft =  At (1- )At (1- )2At Weights Prior Period  2 periods ago (1 - ) 3 periods ago (1 - )2 = = 0.10 = 0.90 10% PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft =  At (1- ) At (1- )2At Weights Prior Period  2 periods ago (1 - ) 3 periods ago (1 - )2 = = 0.10 = 0.90 10% 9% PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft =  At (1- )At (1- )2At Weights Prior Period  2 periods ago (1 - ) 3 periods ago (1 - )2 = = 0.10 = 0.90 10% 9% 8.1% PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft =  At (1- )At (1- )2At Weights Prior Period  2 periods ago (1 - ) 3 periods ago (1 - )2 = = 0.10 = 0.90 10% 9% 8.1% 90% PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft =  At (1- ) At (1- )2At Weights Prior Period  2 periods ago (1 - ) 3 periods ago (1 - )2 = = 0.10 = 0.90 10% 9% 8.1% 90% 9% PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Ft =  At (1- ) At (1- )2At Weights Prior Period  2 periods ago (1 - ) 3 periods ago (1 - )2 = = 0.10 = 0.90 This slide illustrates the decrease in magnitude of the smoothing constant. In the Power Point presentation, the several previous slides show the steps leading to this slide. 10% 9% 8.1% 90% 9% 0.9% PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Choosing  Seek to minimize the Mean Absolute Deviation (MAD)
If: Forecast error = demand - forecast Then: This slide indicates one method of selecting . PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J

Operations Management Forecasting Chapter 4

Similar presentations

Presentation on theme: "Operations Management Forecasting Chapter 4"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

Operations Management Forecasting Chapter 4

Similar presentations

Presentation on theme: "Operations Management Forecasting Chapter 4"— Presentation transcript:

Similar presentations

About project

Feedback