TEACHING THE BASICS OF SALES FORECASTING TO BUSINESS STUDENTSA. Bruce Clark, Ph.D., Texas Southern University, P. O. Box 218655, Houston, TX 77218, 281-579-9103 Abstract: The American Marketing Association found that 74% of companies use a judgmental, correlation/regression or time series forecasting technique. Time series approaches, in general, and double exponential smoothing models, in particular, have broad industry appeal. Thus, we use a two-part spreadsheet project to teach double exponential smoothing. In Part 1, students prepare a baseline forecast on monotonically/uniformly increasing data. Then, in Part 2, they determine multipliers, before preparing daily baseline forecasts for two representatives, and then applying the multipliers to get realistic projections. Because sales forecasting software costs $20,000 to $34,000, this project potentially offers tremendous value to administrators and managers. INTRODUCTION To better plan their use of resources, 74% of 587 major business firms surveyed by the American Marketing Association used "formal forecasting systems," according to Kress and Snyder (1994). The forecasts generated by these systems, in turn, accounted for the success of 92% of the companies that Makridakis (1990) examined. The reason these systems accounted for the success of so many companies is because they allowed them to better predict the needs of different groups so they could decide how to best serve those groups (Zick and Widdows, 1995). Since those who understand forecasting will more likely have successful careers, it makes sense for business professors to dedicate at least some class time teaching forecasting (Winer 2000), which is the rationale for this article. In fact, this author can think of several situations where former students at two different universities obtained outstanding jobs with FORTUNE 500 companies, as well as career advancements, due to their understandings of double exponential smoothed forecasting. However, before introducing a classroom project, that involves this particular forecasting technique, a brief overview of forecasting will be provided. Although companies use many types of forecasting systems, there are three basic categories according to Kress and Snyder (1994) and Winer (2000). First are judgmental approaches, which include sales force composite, buyer surveys, juries of experts, Delphi methods, scenario building, technological forecasting, cross impact studies, analog/similar-store approaches, and simulation. Their strength is ease of implementation, while their weakness is that their outcomes are based on politics rather than what is best from a business standpoint (Zick and Widdows, 1995). Second are correlation/regression approaches, which include methods as diverse as linear, nonlinear, LOGIT, and PROBIT approaches. Their strength is that they forecast based on other variables that have in essence "already been forecast." For instance, direct marketers often build a LOGIT predictive model based on a sample mailing. They then give every household in the population a probability score between zero and one of buying the product(s), so they can mail to those predicted to be profitable or at least break even. Yet, their weaknesses are their dependence upon other variables and their not showing sales trends. Third are time series approaches, which include single and double moving averages, single and double exponential smoothing, Holt’s two-parameters exponential smoothing and the Winter’s triple exponential smoothing method. The weakness is that they do not show the influence of other variables. However, their strengths are that they require limited data input and can rapidly show trends. Thus, they are arguably the most widely used approach in corporate America (Winer 2000), which is why are focus will be here. The simplest time series model is the single moving average, which involves simply summing a series of values and then divides by the number of values. However, this approach provides a flat forecast that does not show any trend. Therefore, "moving average forecasters" often use a double moving average, where they calculate a trend by subtracting a number from an immediately succeeding number. Then for the forecast one can use the base value plus an "average trend component." Yet, while easy to understand, double moving average forecasters must determine how many periods to go back and must recognize that it treats the first period used as equal to the last period in importance. However, this does not seem reasonable in that the most recent period’s decisions likely have a greater impact on the next period, when compared to several periods ago, and while one can apply weighting coefficients, it takes considerable effort to determine their magnitudes. Although the "moving average approaches" are the least complicated of the time series approaches, hybrid Box-Jenkins, which incorporate regression and time series methods, fall on the other end of the "difficulty continuum." The reason is they rely on autocorrelations, meaning the association between a variable at one time period and that same variable at some other time period, which means Box-Jenkins techniques handle almost any type of time series data and provide accurate short-range forecasts. Even so, Box-Jenkins models are not widely used due to their: (1) complexity, (2) inability to yield accurate long-term projections, and (3) requiring 6+ years of data if seasonal influences are present. Furthermore, new Box-Jenkins models are needed whenever sales data is updated, which means constant maintenance, due to the "instability" of the parameter estimates. In between Box-Jenkins and moving averages are exponential forecasting time series techniques, which are "better than" judgment, econometric regression, and Box-Jenkins methods (Guerts and Kelly 1986). On one hand, single exponential smoothing, like single moving average, does not reflect trends. On other hand, Winter's triple exponential smoothing procedure, provides a 478 when one goes back two periods.. Thus.. Next. S. they will also comprehend triple (e. C. for t+m periods in the future is that of a straight line and it is: St+m=a+bm In this latter formula. the "b" value in E27 is set equal to [$G$10/(1-$G$10)]*[E24-F24]. the sales forecast. uniformly) increasing pattern. This is done to "jump start" the process.e. Nevertheless. Nielsen. he/she sees smooth. when this author built forecasting systems relying on five years of daily data. To aid understanding. students are given fifteen days of monotonically/uniformly increasing historical data. since many students desire to work for such companies. on September 15. Thus. the weighting coefficient ∝ needs to be set (Lilien and Kotler 1983). Likewise. The goal is to find the ∝ value that yields a difference (i.30. this paper will focus on double exponential smoothing systems. and leading consumer goods corporations like Anheuser Busch. comes determination of the "a" value to place in cell E26. the a and b are: a=2S’t+1–S’’t+1 b=[∝/(1-∝)][S’t+1–S’’t+1] (4) (5) (3) Yet. before beginning process." Xt is the actual sales figure during period "t. and the F11 value is equal to ∝*E10+(1-∝)*F10.forecast that increases or decreases at accelerating or decelerating rates. This means that 5% to 30% of the determination of a period's sales come from the immediately preceding period. Similarly. Likewise.. personal experience has revealed that double exponential smoothing techniques are preferred by leading marketing research companies like A. since most house buyers focus more upon their current earnings than their high school income. one must understand that the formula for the first smooth and second smooth.05 to 0. Another useful fact is that an ∝ value is closer to 0. In industry. In this case. most consumer goods companies annually check this weighting coefficient. after entering formulas. S’t+1 represents the first smooth for period "t+1. Then. 95% of 5%) to 21% (i. only the ∝ value results of 0. the ∝ value is usually determined to the onehundredths place and occasionally to the one-thousandths place. students can be told that setting an ∝ value is similar to setting an engine’s timing. Specifically. Next. S’’t represents the second smooth for the preceding period and ∝ is a weighting coefficient (Kotler 1997). Yet. they can envision how to use two different sets of weights.. the acceptable range of ∝ is from 0.g. by comparing the predicted last day's sales to its actual sales. the influence ranges from 4. using an analogy. 2002. The reason is that the Southwest Demand Solutions' web site. if an alpha value is placed in cell G10. These equations are as follows: S’t+1=∝Xt +(1-∝)S’t S’’t+1=∝S’t+(1-∝)S’’t (1) (2) In these equations." the logic can be reinforced with a home purchase analogy. it is rarely used (Kress and Snyder 1994).75% (i. students can be told that they are receiving an incredible value. Lastly. different ∝ values are entered into cell G10.. Then. monotonically (i. the values for S’t+1 and S’’t+1 must be obtained. cell E29) closest to zero. before one can get the "a" and "b" values. The reason is that this is the ∝ value used in Appendix 3. Whenever. one can then enter the formula =$G$10*D10+(1-$G$10)*E10 in cell E11. Winter’s) exponential smoothing. As indicated in directions. listed the "normal installation" price for sales forecasting software at $20. and the forecast value that goes into cell E28 is E26+E27*1.05 when one has large amounts of data. E29 is set equal to E28-D24. while weighting coefficients vary for different companies. that older individuals less likely weight any recent event very heavily. the proper ∝ value is determined.e. the ∝ values were 0. coefficient weights) for both the first and second smooth. in Appendix 2.13 are shown. it is often helpful to have students submit the results for multiple ∝ values. which makes sense when one explains. Since this is the case. the most recent day is predicted.e. it will be mentioned that when readers understand double exponential smoothing. Using the data for the first fourteen days. where one drops the t-14 sales 479 . and copy and paste this into cells E11 through F24. and when one does this for contrived data in Appendix 1. Nevertheless. because it often "greatly overshoots" or "greatly undershoots" reality. when students understand how to use one set of parameters (i.000 for a single user system and $34. as done with Holt's technique.e. the value in cell E10 is set equal to that in D10. and while an alpha value normally does not change much (if at all) over time. before teaching them how to add multiplier effects. personal experience has shown that it is best to teach students how to prepare a baseline forecast. Yet. As an added benefit to learning these sales forecasting techniques. However.. Similarly.000 for a multiple user system. the value of 3046 is the most recent actual value. one builds a forecasting system the data should be graphed to examine what it looks like." S’t represents the first smooth for the preceding period. Instead. As shown in Appendix 1. Moreover. TEACHING STUDENTS TO BUILD SALES FORECASTING SYSTEM To teach double exponential smoothing. While students generally understand merits of not putting much weight on "ancient history. 70% of 30%).05. the "a" is set equal to (2*E24)-F24. value in F10 is set equal to that in E10. In fact. Similarly.e. the value in E11 is equal to ∝*D10+(1-∝)*E10. 13255 + 13402 + 13226 + 12615 + 5081 + 2817 + 15096).” as equal to 2*E19-F19 and [$G$5/(1-$G$5)]*[E19-F19] are straightforward.54. Similarly the reciprocal of this last value is 1.. one must remember what day is being predicted in the determination of the ∝ value section. from second. equals the 6399 value times 0. and the first week's sales are 75492 (i. it represents 15096+15266. one normally needs only one ∝ value. as before. and F7 all have the same value. 1+2*0. before removing the day of week effects from the actual sales using the seven (i. one determines how large sales would have been in previous days. where inclement weather or a holiday can drastically impact a given day's sales." Thus. for instance. the appropriate ∝ value is found using both sales representatives. As shown. "no more than say 5% off" from the actual value. While instructors can put several twists on the project at this juncture. E6. since it "takes time to get the process rolling. the 27097. they forget that first fourteen days are used to build a model to predict "most recent day. students can be asked to see whether they can legitimately use one ∝ value and one set of multipliers for both representatives. if the firm. E5. This being the case. Then.004315 (i. As indicated by Appendix 3.002157).e.73 value. before working back from that day. which represents t+1). 2 and 3. "simple interest rate approach” is instead used in this example. When this is done. personal experience has shown that this additional "mathematical kink" often causes students to lose sight of process. going back to the Tuesday) it is 1. This is shown by the growth multiplier for Sunday being 1. Following this.e. This latter formula of =F26+$D$22 can then be copied and pasted into cells F28 through F32. 1+6*0. meaning one might want to compare total sales for an entire month to the aggregated daily predictions.. the problem. territories and brokers will very often have different multipliers. an individual might want to aggregate it. This is especially the case for retailers. and if one graphs the t-14 through t+7 values." Additionally. because these are not concerns of this project. with the ∝ value determined to the one-thousandths place. The difference is then divided by the first week's sales. one obtains each day's sales for two weeks. for instance.26 value equals 26751 times 1. Yet. after determining each day's adjusted sales values. 13496 + 13630 + 13437 + 12802 + 5149 + 2852 + 15266). This baseline forecast is then "adjusted" using the “adjusted/average multipliers” that account for the day of week effects. The sales with the day of week effects removed for the Representative 1 and Representative 2 sales are shown. sales force efficiency as at "present. In so doing. This pattern continues until six days back (i. as revealed. In essence.value in order to run the model using the same number of periods as were used to build the model.807740.. Once this is done. one assigns a growth multiplier value of "1" to Monday. In this particular example. This might involve summing individual sales representative's data to "the office level" or comparing actual sales for an extended period to a forecast for an extended period.e. it should be noted that.e..002157). enters appropriate formula in cell E6 and copies this formula into cells E6 to F19 and. Taking this latter number and dividing by 27097. which is why the percentage increase in sales is calculated. brand loyalty. the projections for the two representatives are each compared to their actual values. while for two periods forward (i. students often erroneously add the 13632 value. 2 and 3...238022.012944 (i.2157% higher than the "1" value.807740. Yet. the second week's sales are 76632 (i.012944. going back two days from Monday) the multiplier is 1.002157 which is 0. (Readers might find it interesting to note that the daily multipliers and growth rates were based upon a "real consulting project" that this author performed that was simplified for teaching purposes. for the next period forecast (i. Thus. it should be noted that for unstable daily data. these seven values are totaled and divided by seven to get the average value of 21887. At this juncture.. and while this is a slightly better approach. F6." Thus. Once one determines the sales with day of week effects removed.) Based upon personal experience at this nation’s largest research firms. except that one has to first control for the day of week influences. then there is probably little to be gained from using two sets of multipliers or two different ∝ values. In the case of the 30362 value for Monday. the value equals F26+$D$22. cells D5.26 yields 0. cell F27). Therefore. for the Tuesday value. one is predicting a "Tuesday value.." To reduce this tendency. the logic is that of "dividing and conquering. The 5168. the methodology used by leading syndicated marketing firms and consumer goods companies to handle daily variations provides an informative variation. These differences are then summed and the alpha that yields a sum of differences closest to zero is chosen. the value equals D21+D22. let's say. one can. rather than "simple interest rate type" calculation. The other values in the "average/adjusted" and "adjusted/average" columns are likewise determined. one again “jump starts” process. after one has the proper entries. is seen to be very similar to the problem shown in Appendices 1. Similarly. average/adjusted) multipliers.e. week sales. OTHER MORE ADVANCED ASSIGNMENTS 480 . one should plot the data to see how well the system is working.e. After the growth rate for the one week period is obtained. Using the growth multiplier. Then for Saturday (i.e. than their "fringe" items. in this case. the plot reveals that the baseline forecasting system works quite well. One reason is that it teaches students about how to calculate "multipliers. immediately forecast a baseline forecast using the data with the day of week influences removed. If the projection for each representative is. shelf-space or.. this value is divided by seven to yield the average percentage sales increase per day. the first step for the problem in Appendix 4 is to plot the data to see what it looks like. the calculations of “a” and “b. we have a week column with the values 1. it should be mentioned that when companies are developing such systems they are normally much more concerned about predicting "bread and butter" products.e. F5." meaning one has to control for the growth rate before addressing the day of week issue. Next." However. In a like vein.e. as alluded to in its directions. it may be helpful to note that while different products. In this case. cell F26 in Appendix 3. Lastly. having two sales representatives provides another dilemma. had same advertising. While one can use a compound growth rate function. before one plots the results that readily show the developed system working quite well. This is done by subtracting first. the adjusted sales column is obtained. holiday. Similarly. as well as opportunities. and its sales increased by 28% during next year. the sales of what became a successful turkey noodle product were predicted long before it was ever made. but instead derive them from the data of other products. while correlation/regression approaches may be best when studies are done to discover the attributes of likely buyers so that they can be better targeted. which has led to better job offers and decisions that helped advance careers. promotions and holidays can simultaneously occur. or to buy a sales forecasting package." Further analysis. whenever such systems are designed for companies. The result of this business decision was that the morale of the eight representatives increased. of these bands. students can develop a "zone" where predicted sales are likely to occur with say 80%. can be taught to build regression equations that determine the relative influences of components and package sizes. To further compound a problem. For instance." and most households seemingly relocate during the summer when children are not in school." Yet another interesting assignment is to have students build systems that "fit multiplicative regression equations. with the height of the peak being roughly 10% higher than what the sales would otherwise be. as one goes "further out. Moreover. the insights gained in this project should prove helpful in those decisions. Another very interesting twist is to examine price promotion and post-promotion effects. with the "band" becoming wider. In such cases. Along with multipliers for seasonal. the industry did indeed have a seasonal element. additional "twists" are possible. salesperson. The reason is to empower them to know the best approach for a particular situation and the sources where they can. since a longer duration leads to individuals assuming that a price reduction is permanent. sales normally peak at the midpoint of a price promotion. decreasing sales. Nevertheless. As an example. and packaging differences. showed that eight had increasing sales. In other words. according to feedback received. in more advanced courses. Based on personal experience. corporate forecasting situations. In essence these two factors "canceled each other. which allow managers to rapidly spot problem areas like declining sales or market share. if not most. there are times when other approaches are more appropriate. these safeguards are almost always incorporated. as well as noodle and rice multipliers. this did not make sense. rather than temporary. it did not have a turkey noodle soup. where sales per client declined from June to December. along with other soups. students might be asked to examine which days of the week are statistically different from other days. chicken rice. students can be given situations with multicollinearity. another interesting project is to see how many different multipliers are really needed. brand. exchange rate. this author built a system for a "soup manufacturer" that made chicken noodle. In so doing. since its business was strongly tied to the "moving industry. Thus. Thus. there is a post-promotion decrement that lasts for about two weeks. 481 . the company reduced the base salaries that it was paying by 20%. one can incorporate business cycle. everyone was a "winner. they will realize the strengths of double exponential smoothing which are that it (1) uses historical data to predict the exact same variable and (2) shows trends. However. 90% or 95% accuracy. the company was growing its market share. time zone. and the presence or absence of a Leap Year. An example of the latter is performed by natural gas pipeline companies. Thus. in keeping with the New Testament parable of the talents. and turkey rice products. The reason that the peak is "relatively larger than the valley" is that a company captures sales that would otherwise go to its competitors during a promotional period. they will at least have a better appreciation of double exponential smoothing approaches. the eight representatives made more money than they had ever made before. one should try not to hard-code information. the optimum promotional period is six weeks. another interesting "twist" is to have students build "reasonability defaults" into their systems to prevent "negative sales" or absurd growth rates for new product introductions. Simultaneously. student feedback has shown that it is important to address these issues in order that they develop better understandings of the strengths and weaknesses of each forecasting technique.Although the first two portions of this project give students the skills needed to handle many. Yet. if need be. CONCLUSIONS The project just presented provides students with a good understanding of forecasting systems." except the "deadbeat employees. obtain more information. A client claimed that its business was not seasonal based on a comparison of the June and December results during a single year. during the two-week post-promotion period. and hence sales. as did their commissions. even if students decide to hire expert(s) to build their forecasting systems. economic. with a 95%+ probability." and then solve for component multipliers. of this company's ten sales representatives. However. can be seen by a real situation that this author encountered. In the process. terminated the two poor performing sales representatives. for most consumer products. Nevertheless. On the other hand. which have "degree day" multipliers that adjust for temperature effects upon natural gas consumption. For instance. when it comes to these overrides. Even if former students later decide that it is best to hire an expert.5% below the norm. by determining turkey and chicken multipliers. for large pipeline databases. or at a minimum have an "input screen. the company. territory. Thus." The implications." On the one hand. In fact. and reassigned their accounts to the eight solid performers. Box-Jenkins methods may be better when highly accurate short-term forecasts are desired and calibration efforts are not a primary concern. they can then determine where to best focus a company's new product activities. However. Subsequently. Explained differently. on the other hand. judgmental techniques may be better when employee involvement positively affects motivation. the results for February of one year might differ from the February of another year due to a difference in the number of work days versus weekend days. A subsequent analysis showed why the June to December sales appeared "flat. Therefore." Likewise one might want to have students build confidence interval logic into their systems that is derived from a comparison of actual and projected values. the loss in sales is associated with the "on deal stockpiling" of brand-loyal patrons. However. In a like vein. type of customer. From the first to second post promotional week the sales go from approximately 1. two had. However.0% below "average" to about 0. students. and even weather effects. Moreover. 7 2965.01 BELOW BEST LASTLY Day t-14 t-13 t-12 t-11 t-10 t-9 D VALUES BUILD DAY. TO BY RESULTS FOR OTHER AND 0. TO ITS ABOVE THE ALPHA SHOW Sales 2958 2968 2978 2987 2995 3003 3010 3017 3023 3028 3033 3037 3041 3044 3046 "a"? "b"? Forecast (last day) E FOR 15 DAYS FORECASTING GET BEST FORECAST. IF RESULTS.6 2959.9 F ARE MODEL ALPHA SHOW AND IN 0.2 2958.APPENDIX 1 Assignment Sheet Given to Students A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 B SMOOTHED USING FIRST PREDICT COMPARING FOR ALPHA ALPHA 0.3 2961. IS 0. BEST ALPHA BEST ALPHA.10 SHOW RESULTS FOR 1st Smooth F ARE MODEL ALPHA SHOW AND IN 0. TO BY RESULTS FOR OTHER AND 0. IS 0. Alpha-used 0. C OUTPUT 14 DAYS 15TH DAY 15 0.0 2968. BEST ALPHA BEST ALPHA. TO ITS ABOVE THE ALPHA SHOW Sales 2958 2968 2978 2987 2995 3003 E FOR 15 DAYS FORECASTING GET BEST FORECAST.01 BELOW BEST LASTLY Day t-14 t-13 t-12 t-11 t-10 t-9 t-8 t-7 t-6 t-5 t-4 t-3 t-2 t-1 Last Day What is What is Forecast Minus Actual D VALUES BUILD DAY. Alpha-used APPENDIX 2 Choice of Best Alpha Value A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 B SMOOTHED USING FIRST PREDICT COMPARING FOR ALPHA ALPHA 0.11 BEST 2nd Smth G SHOWN.01 WORDS.09 ALPHA.13 482 . C OUTPUT 14 DAYS 15TH DAY 15 0.5 G SHOWN. IF RESULTS.11 BEST 2nd Smth 2958 2958 2958 2958.01 WORDS.09 ALPHA.10 SHOW RESULTS FOR 1st Smooth 2958 2958 2959. 0 3054.5 2998. ∝-used 0.9 2991.1 2974.7 2962.1 3062.13 7 days.05 for next E results for forecasts 1st Smth 2968 2968 2969.4 2986.16 17 18 19 20 21 22 23 24 25 26 27 28 29 t-8 t-7 t-6 t-5 t-4 t-3 t-2 t-1 Last Day What is What is Forecast Minus Actual 3010 3017 3023 3028 3033 3037 3041 3044 3046 "a"? "b"? Forecast (last day) 2973.4 3001.2 3074.3 alpha are: 483 . Future Day 1 2 3 4 5 6 7 for “best” Expected Sales 3050.4 2970.7 2976.3 2982. 7 days.6 2972.3 2978. D smooth and the Sales 2968 2978 2987 2995 3003 3010 3017 3023 3028 3033 3037 3041 3044. 3046 N.1 3005.6 2978.21 2960.43 3047.92 4.2 2988.3 2964.1 3042.8 F the “best” for next 2nd Smth 2968 2968 2968 2968.9 2988.6 2974.4 3014.6 2996.4 APPENDIX 3 Forecast of Sales for Next Week A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 B Below are the first Next are the “a” & C & second “b” values Day t-13 t-12 t-11 t-10 t-9 t-8 t-7 t-6 t-5 t-4 t-3 t-2 t-1 Last Day t+1 What is a? What is b? Forecasts.3 2993.6 3003.4 2966.5 3013.3 2978.3 2971.2 2991.8 2984.7 G Alpha.21 1.6 2969.8 2969.9 2981.7 3018.1 2983.1 3066.7 2983. 3045.6 3008.6 2972.0 3058.1 2979.8 3010.78 4.A.0 2976.2 3070.2 2968. 855600 2. what projections for next seven days will you give to your boss? Obs.136. 1 w/o DOW Effect 5168. Thurs.238022 1.852606 Rep. Sat. and that he forecast the total sales (for both representatives) seven days out to be 13.57 5613.801050 0.51009% % sales increase/day = 0.79 5196. The rationale is that you can use a multiplier to remove the day of week effect from sales.008629 1.49 10274. Thus. 2 – sales wk. Fri.228694 1.163 or 0.002157 1.87 5552. it is highly important that your firm know how much the two sales representatives will sell during the next seven days.54 Average/Adjusted 0.2157% Now. Using the below sales data.54 Rep.130353 3.130353 3.25 484 .004315 1. which is sold by your two sales representatives.26 27323.758. so you can use a double exponential smoothing technique to forecast baseline sales. 2 Sales 6856 6932 6841 6525 2628 1457 7808 6981 7050 6950 6622 2663 1475 7896 7051 Total Sales 13255 13402 13226 12615 5081 2817 15096 13496 13630 13437 12802 5149 2852 15266 13632 %increase in sales = ((sales wk. Wed.807740 0.006472 1. you believe one set of multipliers and also one alpha will work.000000 Average Adjusted Sales 27097. Moreover. Sun. 1)/sales wk.79 5598. The multiplier calculations that you show your boss are as follows: Day of Week Tues.813873 0.248362 1. Because it is very expensive for you to inventory components.88 5567. the daily patterns.14 5681. your boss has asked you to give her your best forecast of the sales for the two representatives for the next week. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Week 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 Day of Week Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Rep.387182 The historical sales with the Day of Week effects removed that you show your boss are as follows: Obs. and growth rates appear similar.168770 0.259565 1.58 5210.801050 0. When you graph the output for each representative's sales.720886 Adjusted/Average 1.73 5182.61 5225.813873 0.010786 1. 1)*100 = 1. 1 2 3 4 5 6 Week 1 1 1 1 1 1 Day of Week (DOW) Tuesday Wednesday Thursday Friday Saturday Sunday Average/ Adjusted 0.70 5582. 2 w/o DOW Effect 5537.76 5239.855600 2. Since you have a college degree.852606 0. that you have the % sales increase/day you can develop a multiplier to handle day of week effects.APPENDIX 4 Second Portion of Project Assume you work for a Houston-based manufacturer of refinery equipment.08 25581.807740 0. Total Week 1 & 2 Sales 26751 27032 26663 25417 10230 5669 30362 Growth Multiplier 1.00 21887.012944 1. a trustworthy colleague (who quickly solved the problem) told you that the correct alpha is either 0. Mon.23 30362.469406 0.58 26893. 1 Sales 6399 6470 6385 6090 2453 1360 7288 6515 6580 6487 6180 2486 1377 7370 6581 Rep. 15 5198.42 5581.91 5279.54 Rep.75 5563.45 5583.14 5572.21 5234.17 5695.59 5692.79 5598.45 5217.12 Rep.57 5572.98 8.97 5214.06 5305.88 5552.79 5598.94 Obs.69 5549.11 5570.40 5656.19 5193.79 5196.807740 0.25 5628.69 5170.38 First Smooth Rep.03 5576.99 5570.91 5279.64 5174.18 5229.29 5563.69 5564.83 5647.15 5553.47 5192. 1 5182.37 What is b? 7. 2 5537.87 5537.38 5545.43 5270. 1 w/o DOW Effect 5168. 2 3 4 5 6 7 8 9 10 11 12 485 .855600 2.25 5628. 2 w/o DOW Effect 5552.04 5312. 2 5552. 1 5168.90 5540.41 5665.79 5182.82 Second Smooth Rep.06 5305.20 Obs.79 5673.88 5552.98 5172. Rep.91 Second Smooth Rep.37 5558.05 5183. you show your boss the first and second smoothed values for the two sales representatives.70 5582.720886 0.88 5554.79 5196.13 First Smooth Rep.74 5193.40 5656.12 5635.13 5682.56 5242.23 0.61 5225.91 5279.51 5222.88 5553.130353 3.83 5647.720886 0.29 Sum of Differences is: As a final step.17 5179.88 5552.82 5262.136 Rep. 2 w/o DOW Effect 5537. You do this by forecasting the sales with the day of week effects removed. 1 5168.10 5197.61 5296.82 5201.61 5225.54 5253.11 5183.93 5315.78 5211. 2 5552.95 5175.38 Next.40 5560.87 5537.813873 0.42 5611.95 5553.06 5201.75 Second Smooth Rep.93 5251.05 5187.7 8 9 10 11 12 13 14 15 1 2 2 2 2 2 2 2 3 Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday 0.43 5617. you predict the sales for each representative for the next seven days.79 5182.73 5182.87 5539.74 First Smooth Rep.15 -0.58 5210.73 5168.67 5188.12 5695.82 5262.94 5193.41 5665.40 5656.59 5206.30 5199.06 Rep.73 5168.79 5673.90 5568.29 5557.09 Second Smooth Rep.801050 0.65 5179.57 5613.41 5665. as well as the best alpha: Alpha used is: 0.79 5184.807740 5253.12 5185.61 5296.06 First Smooth Rep.02 5189.59 5287.57 5613.24 5187.12 5695.87 5552.42 5599.59 5287.68 5638.04 5312.70 5582.45 5590.40 5608.83 5647. 1 w/o DOW Effect 5182.82 5262.73 5170.90 5555.59 5287.79 5578.73 5168.88 5567.76 5239. 1 What is a? 5308.41 5563. 2 5686.01 5555.93 5315.03 Frcsts minus Actual: 0.08 5603.76 5239.88 5567.13 5682.59 5692.81 5226.61 5296. 2 5537.852606 0.67 5586.43 5270.58 5210.54 5253. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Rep.12 5209.99 5237.14 5538.87 5537.23 5626. and then applying the appropriate day of week multiplier to each of these values.68 5638.85 5595.65 What are forecasts? 5316.89 5558.74 5628.37 5259.99 5169.75 5185.43 5270.79 5182.78 5204.26 5548.87 5538.68 5638.73 5168.79 5183.79 5673. 1 5182.27 5542.91 5543. 23 5578.. Sat. Zick.469406 0. Multiplier 1. 2 5701. Tues. Forecasting and Market Analysis Techniques: A Practical Approach. Free Press: New York.12 5695.93 5315.34 5645. Philip.53 5350.04 5312.81 5217. and Control. 1 6644 6548 6237 2508 1389 7432 6642 Predicted Sales Rep.13 14 15 16 5305. Lilien. "Forecasting the Future of Consumer Programs in Higher Education. Harper and Row: New York. REFERENCES Guerts.17 5336. 1997. 29: 460-469. Thurs. 2000. Gary L. 2(3): 261-272. 1990. Mon. Cathleen D. Baseline Rep. Kress." Journal of Consumer Affairs.71 Adj. You then give these projections to your boss.01 5724. Prentice-Hall: Upper Saddle River.e.238022 Predicted Sales Rep.36 5740.69 5732. 1995. Forecasting: Planning and Strategy for the 21st Century. Winer.99 7. Kotler.07 Baseline Rep.66 5709.89 5365. and J.52 5223. Marketing Management: Analysis. Marketing Decision Making: A Model-Building Approach. "Forecasting Retail Sales Using Alternative Models. 1986.18 5206. Prentice-Hall: Upper Saddle River. and Philip Kotler. 2 5693." International Journal of Forecasting. Russell S. 486 .85 5269..248362 1. for the next seven days./Avg. 1 5321.758 (i.98 5329.259565 1.38 NA Rep.23 5628. S.04 5596.47 The predicted sales. NY. Patrick Kelly.95 5590. Quorum Books: Westport.24 5583.34 5717.168770 0.55 5682.80 What is b? 7. G. George. 1994..74 5253. Implementation.. Michael D. 1 What is a? 5314. 2 7118 7015 6682 2687 1488 7962 7116 Checking the sales seven days out (against what your colleague found) reveals sales of 13.04 5747. NY.228694 1.71 5637. Marketing Management. CT. and Richard Widdows. Fri. 6642+7116). who gives you a raise. and John Snyder. NJ.71 5357.81 5261. 1983.74 NA Rep.387182 1. Planning. Sun. are: Period 16 17 18 19 20 21 22 DOW Wed.67 5620. Makridakis.47 5211.18 5245. NJ.59 5692.35 5343.