- Email: [email protected]
Forecasting for firms selling projects or jobs “to order”
Forecasting for Firms S e l l i n g Projects or Jobs "T o Orde r" William Rudelius Raymond W, Willis Steven W, Hartley Firms selling projects or jobs to specific customers on a "to order" basis face far different sales forecasting tasks than firms producing for inventory. The model described here utilizes a bottom-up approach in forecasting new business for a to-order firm using three key factors that can be estimated by a firm's marketing or sales manager. These three factors are analyzed empirically using a sample of one year's new business proposals from a large multiproject manufacturing firm.
The increasing importance of sales forecasting is reflected in the status and attention given to forecasting tasks and issues. Many authors have surveyed
Address correspondence to: William Rudelius, Professor of Marketing, University of Minnesota, 271 19th Avenue South, Minneapolis, MN 55455.
Industrial Marketing Management 15, 147 155 (1986) © Elsevier Science Publishing Co., Inc., 1986 52 Vanderbilt Ave., New York, New York 10017
executives and managers to evaluate the use of and effectiveness of various forecasting techniques [4, 8, 21, 27, 34]. Recent reviews and surveys of sales forecasting techniques [5, 20, 25], however, show that very few are available for the bottom-up forecasting applications needed by firms selling projects or jobs to specific customers on a "to-order" basis. These firms face a far different sales forecasting problem than more traditional ones like consumer products firms which produce cake mixes or personal computers for inventory and subsequent sale. On the surface, marketing research and advertising agencies, management consultants, architects, and firms manufacturing rapid-transit cars or aerospace systems appear to have little in common. Some, like aerospace system contractors, obtain much of their work through formal competitive bids. Others, like marketing research and advertising agencies, rely 147 0019-8501/86/$3.50
heavily on sole-source contracts, some of it being unsolicited business. What thcy scll ranges from idcas and services to designs and hardwarc. Yet all basically scll projects, jobs, or products to-order that involve a collcction of activities with sf~ccific starting and cnding points whose result is sold to individual customers. Because of the size and indivisibility of thcsc project activitics, a kcy problem which all of these firms face is forecasting thcir sales prccisely enough to plan production output, employmcnt levels, and capital cxpcnditurcs. For simplicity, wc shall call businesses with this kind of sales forccasting task "to-order firms." To-order firms oftcn divide future business into three catcgorics based on the likelihood of its being convcrtcd from prospects into billable salcs:( 1) work undcr contract, (2) follow-on work, and (3) ncw business. Work under contract is planned work for which a formal contract exists bctwecn buyer and seller and which will bc converted into billablc sales unless the contract is cancelled. Follow-on work is derived directly from present work under contract; an example is a new contract with a client satisfied with work on a past or prescnt project. Follow-on work is less predictablc than work under contract in terms of both size and timing. New busincss, the least predictable catcgory of sales for to-order firms, rcsults from submitting proposals for work not directly relatcd to existing pro.iccts or jobs. Many past research cfforts havc (1) focused on the mcthods of allocating or procuring goods and services through this "bidding" process [ III, 31)1 and (2) the implications of such methods for resource phmning [11, 28, 31]. Howevcr, the useful contributions of this literature havc not bccn utilized in the devclopmcnt of forecasting methods for the made-to-order situation. Because of the great uncertainty about future business [36], improving the accu-
WILLIAM RUDELtUS is Professor of Marketing, at the University of Minnesota RAYMOND W WILLIS is Professor of Management at the University of Minnesota. STEVEN W. HARTLEY is Assistant Professor of Marketing, at the University of Denver, College of Business Administration
148
racy of new business forecasts is a major goal in to-order businesses. The increasing use of formal competitive bidding by firms serving both industrial and governmental markets [12] emphasizes the importance of improved sales forecasts. The similarities between marketing research firms [24], advertising agencies, and management consultants to firms seeking to-order business through competitive bids mean that their sales forecasting tasks are also very similar.
OBJECTIVES This paper has three main objectives: 1. To describe a probability model, composed of elements from several forecasting techniques, which can be used by to-order firms in forecasting sales from new business for which bids or proposals are submitted. 2. To describe key factors that affect this model and to analyze them using actual data from a large manufacturing firm. 3. To show how the new business forecast can be related to forecasts of work under contract and follow-on work to give an overall sales forecast for the firm.
MODEL FOR FORECASTING NEW BUSINESS Components of the Model Hillsley and Harbury [13] and Wadel and Bush [32] have proposed probabilistic approaches to forecasting manpower requirements. Other researchers have elaborated on these basic approaches [3, 7, 14, 16, 18]. These approaches apply directly to developing sales forecasts for firms that charge on a "time-andmaterials" or a "cost-plus" basis for the direct manhours worked on a customer's project. This is the general situation for all to-order businesses that bill customers on a project or job basis. This approach can also be applied to sales forecasting for multicontract, project-oriented firms in which profit margins and sales dollars vary by project. Future sales dollars from new-business proposals clearly depend on the number of successful proposals a firm submits. So future sales from a specific proposal depend on (1) the probability of winning it [9, 23, 35], (2) the sales generated by the proposal each
month of its project life if it is won [6, 17], and (3) the date work on the project commences [35]. For example, suppose a firm is bidding on a contract that is expected to last 4 months and generate monthly sales of $10,000, $20,000, $30,000, and $10,000, respectively. The distribution of estimated monthly sales is shown in Figure 1. Further, suppose the firm does not know exactly when the contract will begin but estimates the probability of starting in January, February, and March as 0.3, 0.5, and 0.2, respectively (see Figure 2). Finally, assume that the firm thinks it has a 0.6 probability of winning the contract. The expected monthly sales from this contract are calculated in Table 1 and are plotted in Figure 3. Note that the firm can expect January sales only if the contract go-ahead is received in January--in which case the firm can expect sales related to the firstmonth data plotted in Figure 1. In contrast, February sales can result from two possibilities: (1) a January go-ahead and second-month sales or (2) a February .
~..
40-
go-ahead and first-month sales. The expected sales by month, if the probability of winning the contract is 1.0, are shown in the fourth row of Table 1. However, if the probability of winning the contract is 0.6, the expected monthly sales are shown in the fifth row of Table 1; values are plotted in Figure 3. The Generalized Model
By adapting the Wadel-Bush [32] approach to forecasting new-business sales, this example can be generalized. Expected sales resulting from a specific proposal k is given by: E [yk(t)] = P* 2 y,(t - s) [pk(s)] s--1
where E [yk(t)] = expected sales from proposal k in month t, given that the proposal is won so that the contract is obtained Pk = probability of winning the contract for proposal k (the "success probability"), 0~
20w
,.':I
0
0
1
2
3
Time After Contract Go-Ahead is Received. t-s (in Months)
FIGURE 1.
Estimated Monthly Sales for Proposal k
2 p,(s) = 1 s=l
---3 - • _
_ .4 .3
ii!iiii!i!iii!!iiiiii ii!iiiiii!i! .................................
.i0 i!ii!iiiii!;ii!! ii!i iiiiiiiiiiii!! i!iiiiiJi ii!ii.iiiiiiiii Jan. Feb. Mar. Calendar Month in Which Contract Go-Ahead is Received, s
FIGURE 2. Estimated Conditional Probability of Receiving Contract Go-Ahead on Proposal k in Calendar Months
For simplicity, t and s are treated as discrete variables so that yk(t) and y k ( t - s) are constant during each month and change stepwise between months. Also, for convenience, the monthly sales function, yk(t - s), does not depend on the month in which the go-ahead occurs. Wadel and Bush [32] allude to the more general case in which the monthly sales function for a specified proposal depends on the month in which the contract go-ahead is received. This occurs when a project must be finished by a fixed date although the go-ahead is delayed, making it necessary to accomplish the same work in less time and thus raising sales during the months remaining in the compressed time schedule. 149
TABLE 1 Calculation of Expected Sales by Calendar Month for Proposal k, Based on Data in Figures 1 and 2 Month Contract Go-Ahead is Expected (s)
Expected Sales by Month Following the Receipt of Contract Go-Ahead y.(t
January
s)p.(s)
January
February
March
April
(I.3 × $10,000 = $3,000
0.3 x $20,0(/0 = $6,000
0.3 x $30,000 = $9,000
0.3 x $10,000 = $3,000
0.5 x $10,000 = $5,000
0.5 × $20,000 = $10,000
0.5 x $30,000 = $15,000
0.5 x $10,000 = $5,000
0.2 x $10,000 = $2,000
0.2 x $20,000 = $4,000
0.2 x $30,000 = $6,000
0.2 x $L0,000 = $2,00O
February
March
May
June
Yk (t)"
$3,000
$11,000
$21,000
$22,000
$11,000
$2,000
E[yk(t)f'
$1,800
$ 6,600
$12,600
$13,200
$ 6,600
$1,20l)
" E x p e c t e d sales by c a l e n d a r m o n t h for p r o p o s a l k w h e n p r o b a b i l i t y of w i n n i n g the c o n t r a c t is 1.0. ~'Expected sales by c a l e n d a r m o n t h for p r o p o s a l k w h e n p r o b a b i l i t y of w i n n i n g the c o n t r a c t is 0.6.
FACTORS AFFECTING THE USE OF THE MODEL
14A
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v
~Z
Several key factors affect the practical value of this sales forecasting approach.
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12c
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..................... ili........... i i i i ! i { i il i!i!i!i!i!i!ili!iiiii i::iii~i::i::iiiii::i~i::~ !ii~iii!iii~{ii!{iii~ 4 ...................... i:i!i~:i:~:~:~):~iiii!i!i!iiii:~:~:<:~:<:~:~a :::::::::::::::::::::iil}i!~iS}i!}i! 2...................... is:si!:::~:#:i:#:!iiii!iiiiiiiiiii!iii~iii!iiiiiiiii~i~i~i~]
i!i i i {i i i i i i i i i i i i i i i i i
The model uses the expected value of future sales. So an ideal application is for a firm having a large number of active proposals in any one year with a reasonable number of them being accepted. As will be seen later, these conditions hold for the example studied here. Homogeneous Groupings of Proposals
lan.
Feb.
Mar.
Apr.
May
lun.
Calendar Month, t
FIGURE 3. Expected Sales from Project k by Month, Given That Contract Go-Ahead Is Received
The Sample
To test components of the forecasting model, all proposals submitted in a single year by a large, multiproject manufacturing firm were analyzed. This sample of 137 proposals was followed from the time of submission until the proposal was determined to be either won or lost. Because of the time lags in the sequence of submitting, modifying, and resubmitting proposals, the sample required following some specific proposals for up to 10 months, 150
The overall probability of winning a proposal, Pk, can vary by the proposal's characteristics, such as its size [1, 15]. So these characteristics can be used to develop relatively homogeneous groups of proposals. Each group can then be evaluated by its "success ratio' ' - - t h e average probability of winning proposals in that category. These average success ratios by proposal categories are important to management because they can be used to improve the accuracy of sales forecasts (analyzed here later) and also to help in reaching "bid-no bid" decisions about which proposals are worth submitting. For our purposes all the sample proposals are categorized on two bases. One is solicited (requested by the customer) and unsolicited (initiated by the seller) proposals. Solicited proposals are more likely
to be funded because the business or government agency requesting the bid has established a need for the project while for unsolicited proposals it has not. The other basis is bid value above and below $1,000,000--an arbitrary dividing line used by the firm to single out large (over $1,000,000) contracts for special management attention because of their important impact on sales. So the success rate may vary substantially between these two groups, and management's ability to make accurate probability assessments may vary as well. This model implicitly assumes that the success probability for one contract is independent of whether another proposal is won or lost. This is generally the case for small proposals but is problematic for large ones. The reason: a customer may choose not to award a large contract to a bidder it knows recently won another large contract for fear the new one may not get the attention it deserves-what is sometimes called the "hungry-contractor criterion" in government contracting. But we shall assume that success probability for a given proposal is independent of all others outstanding at the time it is submitted.
Estimating a Proposal's Success Probability One m e t h o d for estimating a proposal's probability of success (Pk) is to assume that all bidders have an equal chance of winning. So Pk would then simply be the reciprocal of the numbers of bidders in the competition. Other alternatives might involve using historical success ratios or managerial judgment. For example, if data have been kept on past proposal competitions, the ratio of proposals won to all those submitted might be used as an estimate of Pk. In the sample year considered here, Table 2 shows the firm won 36 of the 137 proposals it submitted. Using this success ratio gives an estimate of 0.26 for Pk, based on the percentage value shown in the lower right-hand corner of Table 2. But the success ratios in Table 2 show that the firm's success varied by g r o u p - - f r o m a high of 29% success rate for large, solicited proposals to a low of 0% for large, unsolicited proposals. Historical success rates for specific groups of proposals like those in the right-hand column of Table 2 are used by many firms to develop expected-value sales forecasts but they are limited by being backward looking. In practice what is often used to estimate the
TABLE 2 Win-Loss Records of Four Categories of Proposals Proposal Values at Submission Less than $1,000,000
$1,000,000 or more
Total
Type of Proposal
Number of Proposals Won Lest Total
Percent Won
Solicited Unsolicited
24 8
61 27
85 35
28 23
Total
32
88
120
27
Solicited Unsolicited
4 0
10 3
14 3
29 0
Total
4
13
17
24
Solicited Unsolicited
28 8
71 30
99 38
28 21
Total
36
101
137
26
success probability of a proposal is a subjective estimate of one or a group of managers familiar with the proposal and bidding environment. Brooks [2] has observed that the probability estimates of such managers (specifically in the case of follow-on contracts) "are usually more realistic and reliable than probabilities derived any other w a y . . . " In the manufacturing firm analyzed here the marketing manager responsible for the proposal development effort was asked for an estimate of the likelihood of winning the competition at the time the proposal was submitted. The estimate was made either by only the manager or in consultation with other knowledgeable company personnel. These managerial estimates are special cases of two prevalent methods of sales forecasting-jury of executive opinion and sales force estimates [33, 37]. Although a danger in subjective estimates is the possibility of systematic forecast errors by individuals making the estimates [19, 26, 29], recent research has found management judgment forecasts to be very accurate [22]. The manager involved was asked to place each proposal in one of three categories indicating his assessment of the likelihood of success in winning the contract. The categories were A, B, and C, were intended to represent approximately 90, 50, and 10% chances of winning the associated contract. So these subjective estimates are used here as inputs to the forecasting process, not in making "bid-no bid" decisions. Table 3 shows how accurate the marketing managers' subjective initial estimates of success were. Lost proposals were either (1) won by another contractor
151
TABLE 3 Win-Loss Records of Four Categories of Proposals With Subjective Estimates of Success Made at Submission
TABLE 4 Results of Chi-Square Tests on Win-Loss Records of Proposals <$1,000,000 in Value
Number of Proposal Value at Submission
Type of Proposal
Subjective Proposals Percent Rating ~ Won Lost Total Won A B C
10 8 6
A B C
1 2 5
$1,000,000
A B C
2 1 1
or more
A B C
Solicited Less than
$1,000,(100 Unsolicited
Solicited
Unsolicited
5 25 31
15 33 37
67 24 16
l
2
9 17
11 22
50 18 23
0 6 4
2 7 5
100 14 20
0
0
0
0 0
2 1
2 1
0 0 0
"At the time of submission the responsible marketing manager estimated the probability of winning the proposal as A, 90%; B, 50%; or C, 10%. ~'The "'percent won" when expressed as a decimal is the "success ratio.'"
or (2) d r o p p e d because of a decision by the buying firm not to award a contract, Table 3 shows that while the 90, 50, and 10% success values for A, B, and C ratings, respectively, are not accurate, there is a tendency for A-rated proposals to have a better success record than B- or C-rated proposals. Also, although the totals are not shown in Table 3, the success ratios decrease from A to B to C ratings for (1) all proposals combined and (2) all proposals <$1,000,000. For example, in the case of all proposals <$1,000,000, the success ratios of A-, B-, and C-rated proposals are 0.65, 0.23, and 0.19, respectively. So at least the ordering of the success ratios based on the marketing managers' subjective judgments is correct. The sample size of 120 for the proposals whose bid value was <$1,000,000 permits a more detailed analysis of this group. The results of four chi-square tests on the smaller proposals summarized in Table 4 lead to the following conclusions: 1. There is no statistically significant difference b e t w e e n the win-loss records of small solicited and small unsolicited proposals. Data from
152
Hypothesis Tested-Difference Between:
Degrees of Freedom
Chi-Square Value
p Value
Win-loss records of solicited and unsolicited proposals
1
0.367
ns
Win-loss records of A-, B-, and C-rated solicited and unsolicited proposals
2
14.870
< 0.001
Win-loss records of A- and B-rated solicited and unsolicited proposals
1
9.572
<0.005
Win-loss records of B- and C-rated solicited and unsolicited proposals
1
0.259
ns
these two groups can therefore be combined in subsequent statistical tests. 2. There is a statistically significant difference between the win-loss records for small proposals on the basis of A, B, and C ratings. As shown in Table 4, this result is highly significant. 3. There is a statistically significant difference between win-loss records of small proposals rated A and B but not b e t w e e n those rated B and C. The managerial importance of these results is that small, A-rated proposals have a statistically better chance of being won than either I3- or C-rated ones. At least in this instance, the ability of the firm's marketing managers to discriminate high-probabilityof-success proposals (A-rated ones) from the other proposals submitted (B- and C-rated ones) warrants the use of the managers' subjective estimates of Pk in the forecasting model rather than using overall winloss percentage as an estimate of Pk. Relation of Time Probability
L a g in A w a r d
to Success
The time lag between proposal submission and the contract award d e c i s i o n - - t h e contract go-ahead date for proposals the firm wins--in the sample of proposals ranges from 1 to Ill months with a mean of about 3.3 months. It is a critical ingredient in the sales forecast because of the impact of the lag on the timing of sales on contracts that tire won. This time lag can be
affected by a number of factors, such as the organizational buyer involved, the point in the fiscal year, the urgency of the award, whether the proposal is solicited or unsolicited, and whether the award is won or lost. The past relationship of the time lag to any of these factors can be studied if there is a large enough sample to warrant analysis. As an example of the value of this kind of analysis, let us study the relationship between proposal type (solicited or unsolicited) and disposition (won or lost) and the time lag between the proposal's being submitted and when the contract decision is made and the bidder informed of the result. A 2 x 2 table giving the time lags in months shows: Proposal Dispositions Proposal Type
Won
Lost
Solicited Unsolicited
3.32 4.05
2.62 3.49
Analysis-of-variance results for two factors, proposal type and proposal disposition, are presented in Table 5, and show significant F-ratios at the 0.05 level for the proposal-type effect (solicited or unsolicited) and the proposal-disposition effect (won or lost) but not the interaction. The results suggest that the time lag between proposal submission and decision is (1) greater for unsolicited proposals than solicited proposals and (2) greater for proposals which are won than those which are lost. This state of the analysis has great practical significance to the forecaster: it not only develops the probability distribution of go-ahead dates for various categories of contract--the Pk(s) function--but also shows how the success probability (Pk) varies with the time lag in the award decision. Long time-lags are of special consolation to the firm studied here, because they show that the firm's probability of winning the award is increasing. If desired, this variation in the probability of success for a proposal can be used in fine-tuning the firm's sales forecast. The kind of analysis shown in Table 5 also illustrates another key advantage to using this sales forecasting model: errors in the final sales forecast can be traced to one of the factors that comprise the model. This, in turn, can suggest where special effort can be placed to try to improve the overall sales forecast. For
TABLE 5 Anova Table to Study the Effect of Proposal Type and Disposition on the Time Lag Between Proposal Submission and Contract Award Decision Source Variable Proposal type (solicited or unsolicited) Proposal disposition (won or lost) Interaction Error Total
Sum of Degrees of Squares Freedom
Mean F Square Value
p Value
17.647
1
17.647
5.508
<0.025
14.458
1
14.458
4.510
<0.05
0.453 371.808
1 116
0.453 3.205
0.141
ns
404.366
119
example, if a contract that is won is not generating the sales expected during a specific month, the cause might be an error in either (1) the estimated monthly sales from the contract after go-ahead is received, or (2) the probability distribution of likely starting months. Analysis might reveal that the firm systematically estimates an earlier go-ahead month than it is experiencing. It can then improve such estimates in the future. A n o t h e r possibility is to adjust probability-of-success judgments by the estimator, the customer involved, or the kind of contract if enough bidding history exists for these to do so.
MAKING AND USING THE OVERALL SALES FORECAST The flexibility, simplicity, and value of the model are illustrated by describing (1) how the overall sales forecast is made and (2) how it can be used by marketing managers.
Making the Overall Sales Forecast The overall sales forecast for a to-order firm using this probability model is obtained by simply summing the sales expected during each time interval in the forecast period for the three kinds of business expected: work under contract, follow-on work, and new business. An example is shown in the top band in Figure 4. Ytotal, company sales for k proposals in month t, can therefore be expressed as: Ytotal =
~ yk(t) k=l
•
153
i
6 5
~ l
4
l 7
[
--]
3 -~ 2 | •~ ~_, 1
0
Estimated Sales From //New BusinessProposals
CONCLUSIONS
Estimated Sales From Follow-0nWork
Estimated Sales From Work UnderContract
10 I 2Q I 3Q I 4Q ] 1Q I 2Q YEAR 1 FIGURE 4.
3Q I 4Q
YEAR2
Two-Year Sales Forecast
In this bottom-up forecasting approach, each of the three kinds of business shown in Figure 4 is composed of a number of individual projects that for simplicity are not shown in Figure 4. Figure 4 shows also that sales in the 2-year forecast are estimated monthly for the first 6 months, quarterly for the second 6 months, and semiannually for the last 12 months. The forecast may be made monthly after the first 6 m o n t h s if desired, but carrying detailed monthly sales estimates throughout the analysis more than 6 months or 1 year into the future may cost more than it is worth. Using the Sales Forecast
State-of-the-art developments in personal computers during the past 5 years mean that tabular or graphic sales forecast information comparable to that in Figure 4 is available to even small businesses having access to microcomputers. Further, the vertical axis in Figure 4 can be used to forecast sales revenue, units, product lines, and kinds of people needed. When one or several large contracts can have especially great impacts on future sales, "what-if" computer simulations may be run as part of the sales forecasting activity. This is a level of detail possible with bottomup methods that is not feasible with most top-down techniques. The forecasting also facilitates both short-run and long-run marketing decisions. Short-run sales turndowns 2 or 3 months in the future may suggest marketing efforts geared to obtaining immediate contracts, even with low margins, to keep the operating personnel employed. Over the longer run, perhaps a year into the future, both encouraging and threaten-
154
ing trends in product lines may be identified and necessary strategies developed. AND IMPLICATIONS
To-order firms--those selling a limited number of projects, products, or services "to-order" to a restricted number of buyers--face a far different sales forecasting situation than firms manufacturing products for inventory that are eventually sold to thousands or millions of buyers. In contrast to these produce-for-inventory firms, to-order firms typically use bottom-up sales forecasting approaches in which sales expected from individual projects or jobs are s u m m e d to give the forecast of total sales. The method analyzed here can be used by virtually all project-oriented or job-shop firms, regardless of size. This m e t h o d requires estimates of only three key factors related to each project or job--probability of winning the contract, a frequency distribution of monthly sales if the contract is won, and a frequency distribution of probable starting times. Further, by using this method, important errors in sales forecasts can be traced to one of these three basic factors in the model and steps taken to try to improve the accuracy of the factor which is the most important source of error. Besides offering the opportunity for improving future bottom-up sales forecasts for firms selling projects or jobs on a to-order basis, the m e t h o d offers the forecaster the opportunity for systematic diagnosis of the sources of past forecast error. The flexibility and simplicity of the model, along with the ease of computerizing it, offers potential for a variety of firms selling projects or jobs on a to-order basis.
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8. Dalrymple, Douglas J., Sales Forecasting Methods and Accuracy, Business Horizons 18, 69-73 (1975). 9. Edelman, Franz, Art and Science of Competitive Bidding, Harvard Business Review 43, 53-66 (1965). 10. Engelbrecht-Wiggans, Richard, Auctions and Bidding Models: A Survey, Management Science 26, 119-142 (1980).
24. Myers, James H., Competitive Bidding for Marketing Research Services, Journal of Marketing 33, 40-45 (1969).
11. Graves, Stephen C., A Review of Production Scheduling, Operations Research 29, 646-675 (1981). 12. Hill, Richard M., Alexander, Ralph S., and Cross, James S., Industrial Marketing. Richard D. Irwin, Inc., Homewood, IL, 1975, pp. 81. 13. Hillsley, Richard W. and Harbury, Albert L., Simple Estimates for Complex Work Loads, Harvard Busines Review 38, 87-96 (1960). 14. Kidd, John B., The Utilization of Subjective Probabilities in Production Planning, Acta Psychologica 34, 338-347 (1970). 15. Klein, Dieter, Obel, Borge, and Holm, Soren J., Soliciting and Evaluating Bids for a Complex Big Ticket Item, Industrial Marketing Management 8, 154-160 (1979). 16. Kwak, N. K., Garrett, Walter A., Jr., and Barone, Sam, A Stochastic Model of Demand Forecasting for Technical Manpower Planning, Management Science 23, 1089-1099 (1977). 17. Lee, Sang M., Park, O. E., and Economides, S. C., Resource Planning for Multiple Projects, Decision Sciences 9, 46-67 (1978). 18. Lejk, Richard A. and Wortham, A. W., The Complete Data Model-A New Approach to the Probabilistic Forecasting of Manpower Requirements, IEEE Transactions on Engineering Management 15, 27-29 (1968). 19. Lorie, James H., Two Important Problems in Sales Forecasting, Journal of Business 30, 172-179 (1957). 20. Makridakis, Spyros and Wheelright, Steven C., Forecasting: Issues and Challenges for Marketing Management, Journal of Marketing 41, 24-38 (1977). 21. Mentzer, John T. and Cox, James E., Jr., Executive Familiarity and Usage of State-of-the-Art Sales Forecasting Techniques, in Educators' Conference Proceedings, Kenneth Bernhardt et al., eds. American Marketing Association, Chicago, (1981), pp. 9-12. 22. Moriarty, Mark M. and Adams, Arthur J., Management Judgment
25. Rao, Vithala R. and Cox, James E., Jr., Sales Forecasting Methods: A Survey of Recent Developments. Marketing Science Institute, Cambridge, MA, 1978. 26. Roshwalb, Irving, A Consideration of Probability Estimates Provided by Respondents, Journal of Marketing Research 12, 100-103 (1975). 27. Rothe, James T., Effectiveness of Sales Forecasting Methods, Industrial Marketing Management 7, 114-118 (1978). 28. Silver, Edward A., Operations Research in Inventory Management: A Review and Critique, Operations Research 29, 628-645 (1981). 29. Staelin, Richard and Turner, Ronald E., Error in Judgmental Sales Forecasts: Theory and Results, Journal of Marketing Research 10, 10-16 (1973). 30. Stark, Robert M. and Rothkopf, Michael H., Competitive bidding: A Comprehensive Bibliography, Operations Research 27, 364-390 (1979). 31. Taylor, Bernard W., Moore, Lawrence J., and Clayton, Edward R. R&D Project Selection and Manpower Allocation with Integer Nonlinear Goal Programming, Management Science 28, 1149-1158 (1982). 32. Wadel, L. B. and Bush, C. M., An Approach to Probabilistic Forecasting of Engineering Manpower Requirements, IEEE Transactions on Engineering Management 8, 158-159 (1961). 33. Walton, John R., A Comparison of Opinion and Regression Forecasting for an Industrial Product, Industrial Marketing Management 8, 7-11 (1979). 34. Wheelright, Steven C. and Clarke, Darral G., Corporate Forecasting: Promise and Reality, Harvard Business Review 54, 40-64 (1976). 35. Wood, D., A Decision System for Competitive Bidding, European Journal of Marketing 5, 168-177 (1971). 36. Woods, Donald H., Improving Estimates that Involve Uncertainty, Harvard Business Review 44, 91-98 (1966). 37. Wotruba, Thomas R. and Thurlow, Michael L., Sales Force Participation in Quota Selling and Sales Forecasting, Journal of Marketing 40, 11-16 (1976).
155
The increasing importance of sales forecasting is reflected in the status and attention given to forecasting tasks and issues. Many authors have surveyed
Address correspondence to: William Rudelius, Professor of Marketing, University of Minnesota, 271 19th Avenue South, Minneapolis, MN 55455.
Industrial Marketing Management 15, 147 155 (1986) © Elsevier Science Publishing Co., Inc., 1986 52 Vanderbilt Ave., New York, New York 10017
executives and managers to evaluate the use of and effectiveness of various forecasting techniques [4, 8, 21, 27, 34]. Recent reviews and surveys of sales forecasting techniques [5, 20, 25], however, show that very few are available for the bottom-up forecasting applications needed by firms selling projects or jobs to specific customers on a "to-order" basis. These firms face a far different sales forecasting problem than more traditional ones like consumer products firms which produce cake mixes or personal computers for inventory and subsequent sale. On the surface, marketing research and advertising agencies, management consultants, architects, and firms manufacturing rapid-transit cars or aerospace systems appear to have little in common. Some, like aerospace system contractors, obtain much of their work through formal competitive bids. Others, like marketing research and advertising agencies, rely 147 0019-8501/86/$3.50
heavily on sole-source contracts, some of it being unsolicited business. What thcy scll ranges from idcas and services to designs and hardwarc. Yet all basically scll projects, jobs, or products to-order that involve a collcction of activities with sf~ccific starting and cnding points whose result is sold to individual customers. Because of the size and indivisibility of thcsc project activitics, a kcy problem which all of these firms face is forecasting thcir sales prccisely enough to plan production output, employmcnt levels, and capital cxpcnditurcs. For simplicity, wc shall call businesses with this kind of sales forccasting task "to-order firms." To-order firms oftcn divide future business into three catcgorics based on the likelihood of its being convcrtcd from prospects into billable salcs:( 1) work undcr contract, (2) follow-on work, and (3) ncw business. Work under contract is planned work for which a formal contract exists bctwecn buyer and seller and which will bc converted into billablc sales unless the contract is cancelled. Follow-on work is derived directly from present work under contract; an example is a new contract with a client satisfied with work on a past or prescnt project. Follow-on work is less predictablc than work under contract in terms of both size and timing. New busincss, the least predictable catcgory of sales for to-order firms, rcsults from submitting proposals for work not directly relatcd to existing pro.iccts or jobs. Many past research cfforts havc (1) focused on the mcthods of allocating or procuring goods and services through this "bidding" process [ III, 31)1 and (2) the implications of such methods for resource phmning [11, 28, 31]. Howevcr, the useful contributions of this literature havc not bccn utilized in the devclopmcnt of forecasting methods for the made-to-order situation. Because of the great uncertainty about future business [36], improving the accu-
WILLIAM RUDELtUS is Professor of Marketing, at the University of Minnesota RAYMOND W WILLIS is Professor of Management at the University of Minnesota. STEVEN W. HARTLEY is Assistant Professor of Marketing, at the University of Denver, College of Business Administration
148
racy of new business forecasts is a major goal in to-order businesses. The increasing use of formal competitive bidding by firms serving both industrial and governmental markets [12] emphasizes the importance of improved sales forecasts. The similarities between marketing research firms [24], advertising agencies, and management consultants to firms seeking to-order business through competitive bids mean that their sales forecasting tasks are also very similar.
OBJECTIVES This paper has three main objectives: 1. To describe a probability model, composed of elements from several forecasting techniques, which can be used by to-order firms in forecasting sales from new business for which bids or proposals are submitted. 2. To describe key factors that affect this model and to analyze them using actual data from a large manufacturing firm. 3. To show how the new business forecast can be related to forecasts of work under contract and follow-on work to give an overall sales forecast for the firm.
MODEL FOR FORECASTING NEW BUSINESS Components of the Model Hillsley and Harbury [13] and Wadel and Bush [32] have proposed probabilistic approaches to forecasting manpower requirements. Other researchers have elaborated on these basic approaches [3, 7, 14, 16, 18]. These approaches apply directly to developing sales forecasts for firms that charge on a "time-andmaterials" or a "cost-plus" basis for the direct manhours worked on a customer's project. This is the general situation for all to-order businesses that bill customers on a project or job basis. This approach can also be applied to sales forecasting for multicontract, project-oriented firms in which profit margins and sales dollars vary by project. Future sales dollars from new-business proposals clearly depend on the number of successful proposals a firm submits. So future sales from a specific proposal depend on (1) the probability of winning it [9, 23, 35], (2) the sales generated by the proposal each
month of its project life if it is won [6, 17], and (3) the date work on the project commences [35]. For example, suppose a firm is bidding on a contract that is expected to last 4 months and generate monthly sales of $10,000, $20,000, $30,000, and $10,000, respectively. The distribution of estimated monthly sales is shown in Figure 1. Further, suppose the firm does not know exactly when the contract will begin but estimates the probability of starting in January, February, and March as 0.3, 0.5, and 0.2, respectively (see Figure 2). Finally, assume that the firm thinks it has a 0.6 probability of winning the contract. The expected monthly sales from this contract are calculated in Table 1 and are plotted in Figure 3. Note that the firm can expect January sales only if the contract go-ahead is received in January--in which case the firm can expect sales related to the firstmonth data plotted in Figure 1. In contrast, February sales can result from two possibilities: (1) a January go-ahead and second-month sales or (2) a February .
~..
40-
go-ahead and first-month sales. The expected sales by month, if the probability of winning the contract is 1.0, are shown in the fourth row of Table 1. However, if the probability of winning the contract is 0.6, the expected monthly sales are shown in the fifth row of Table 1; values are plotted in Figure 3. The Generalized Model
By adapting the Wadel-Bush [32] approach to forecasting new-business sales, this example can be generalized. Expected sales resulting from a specific proposal k is given by: E [yk(t)] = P* 2 y,(t - s) [pk(s)] s--1
where E [yk(t)] = expected sales from proposal k in month t, given that the proposal is won so that the contract is obtained Pk = probability of winning the contract for proposal k (the "success probability"), 0~
20w
,.':I
0
0
1
2
3
Time After Contract Go-Ahead is Received. t-s (in Months)
FIGURE 1.
Estimated Monthly Sales for Proposal k
2 p,(s) = 1 s=l
---3 - • _
_ .4 .3
ii!iiii!i!iii!!iiiiii ii!iiiiii!i! .................................
.i0 i!ii!iiiii!;ii!! ii!i iiiiiiiiiiii!! i!iiiiiJi ii!ii.iiiiiiiii Jan. Feb. Mar. Calendar Month in Which Contract Go-Ahead is Received, s
FIGURE 2. Estimated Conditional Probability of Receiving Contract Go-Ahead on Proposal k in Calendar Months
For simplicity, t and s are treated as discrete variables so that yk(t) and y k ( t - s) are constant during each month and change stepwise between months. Also, for convenience, the monthly sales function, yk(t - s), does not depend on the month in which the go-ahead occurs. Wadel and Bush [32] allude to the more general case in which the monthly sales function for a specified proposal depends on the month in which the contract go-ahead is received. This occurs when a project must be finished by a fixed date although the go-ahead is delayed, making it necessary to accomplish the same work in less time and thus raising sales during the months remaining in the compressed time schedule. 149
TABLE 1 Calculation of Expected Sales by Calendar Month for Proposal k, Based on Data in Figures 1 and 2 Month Contract Go-Ahead is Expected (s)
Expected Sales by Month Following the Receipt of Contract Go-Ahead y.(t
January
s)p.(s)
January
February
March
April
(I.3 × $10,000 = $3,000
0.3 x $20,0(/0 = $6,000
0.3 x $30,000 = $9,000
0.3 x $10,000 = $3,000
0.5 x $10,000 = $5,000
0.5 × $20,000 = $10,000
0.5 x $30,000 = $15,000
0.5 x $10,000 = $5,000
0.2 x $10,000 = $2,000
0.2 x $20,000 = $4,000
0.2 x $30,000 = $6,000
0.2 x $L0,000 = $2,00O
February
March
May
June
Yk (t)"
$3,000
$11,000
$21,000
$22,000
$11,000
$2,000
E[yk(t)f'
$1,800
$ 6,600
$12,600
$13,200
$ 6,600
$1,20l)
" E x p e c t e d sales by c a l e n d a r m o n t h for p r o p o s a l k w h e n p r o b a b i l i t y of w i n n i n g the c o n t r a c t is 1.0. ~'Expected sales by c a l e n d a r m o n t h for p r o p o s a l k w h e n p r o b a b i l i t y of w i n n i n g the c o n t r a c t is 0.6.
FACTORS AFFECTING THE USE OF THE MODEL
14A
:::::::::::::i:!:i:!:!:i:i:i:i:i:! ::::: ..............-....
::::::::::::::::::::: :::::::::::::::::::::::::::: ,:.:+:.:.:+:+:.
v
~Z
Several key factors affect the practical value of this sales forecasting approach.
~,. -..,.............
12c
:::::::::::::::::::::: !ii~ili!i~!i!ii~ilil
iiiiliiiii!iiiii!ii i!i!iiiiiiiiii~#!i
10 --
Number of Proposals
::::::::::::::::::::: .................... .:.:.:.:,:.:.:.:.:.: ..¢=
g
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8--
..................... .....v,-.....,,-. :::::::::::::::::::::
.,,j:
:::::::::::::::::::::
6 --
,7,
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..................... ili........... i i i i ! i { i il i!i!i!i!i!i!ili!iiiii i::iii~i::i::iiiii::i~i::~ !ii~iii!iii~{ii!{iii~ 4 ...................... i:i!i~:i:~:~:~):~iiii!i!i!iiii:~:~:<:~:<:~:~a :::::::::::::::::::::iil}i!~iS}i!}i! 2...................... is:si!:::~:#:i:#:!iiii!iiiiiiiiiii!iii~iii!iiiiiiiii~i~i~i~]
i!i i i {i i i i i i i i i i i i i i i i i
The model uses the expected value of future sales. So an ideal application is for a firm having a large number of active proposals in any one year with a reasonable number of them being accepted. As will be seen later, these conditions hold for the example studied here. Homogeneous Groupings of Proposals
lan.
Feb.
Mar.
Apr.
May
lun.
Calendar Month, t
FIGURE 3. Expected Sales from Project k by Month, Given That Contract Go-Ahead Is Received
The Sample
To test components of the forecasting model, all proposals submitted in a single year by a large, multiproject manufacturing firm were analyzed. This sample of 137 proposals was followed from the time of submission until the proposal was determined to be either won or lost. Because of the time lags in the sequence of submitting, modifying, and resubmitting proposals, the sample required following some specific proposals for up to 10 months, 150
The overall probability of winning a proposal, Pk, can vary by the proposal's characteristics, such as its size [1, 15]. So these characteristics can be used to develop relatively homogeneous groups of proposals. Each group can then be evaluated by its "success ratio' ' - - t h e average probability of winning proposals in that category. These average success ratios by proposal categories are important to management because they can be used to improve the accuracy of sales forecasts (analyzed here later) and also to help in reaching "bid-no bid" decisions about which proposals are worth submitting. For our purposes all the sample proposals are categorized on two bases. One is solicited (requested by the customer) and unsolicited (initiated by the seller) proposals. Solicited proposals are more likely
to be funded because the business or government agency requesting the bid has established a need for the project while for unsolicited proposals it has not. The other basis is bid value above and below $1,000,000--an arbitrary dividing line used by the firm to single out large (over $1,000,000) contracts for special management attention because of their important impact on sales. So the success rate may vary substantially between these two groups, and management's ability to make accurate probability assessments may vary as well. This model implicitly assumes that the success probability for one contract is independent of whether another proposal is won or lost. This is generally the case for small proposals but is problematic for large ones. The reason: a customer may choose not to award a large contract to a bidder it knows recently won another large contract for fear the new one may not get the attention it deserves-what is sometimes called the "hungry-contractor criterion" in government contracting. But we shall assume that success probability for a given proposal is independent of all others outstanding at the time it is submitted.
Estimating a Proposal's Success Probability One m e t h o d for estimating a proposal's probability of success (Pk) is to assume that all bidders have an equal chance of winning. So Pk would then simply be the reciprocal of the numbers of bidders in the competition. Other alternatives might involve using historical success ratios or managerial judgment. For example, if data have been kept on past proposal competitions, the ratio of proposals won to all those submitted might be used as an estimate of Pk. In the sample year considered here, Table 2 shows the firm won 36 of the 137 proposals it submitted. Using this success ratio gives an estimate of 0.26 for Pk, based on the percentage value shown in the lower right-hand corner of Table 2. But the success ratios in Table 2 show that the firm's success varied by g r o u p - - f r o m a high of 29% success rate for large, solicited proposals to a low of 0% for large, unsolicited proposals. Historical success rates for specific groups of proposals like those in the right-hand column of Table 2 are used by many firms to develop expected-value sales forecasts but they are limited by being backward looking. In practice what is often used to estimate the
TABLE 2 Win-Loss Records of Four Categories of Proposals Proposal Values at Submission Less than $1,000,000
$1,000,000 or more
Total
Type of Proposal
Number of Proposals Won Lest Total
Percent Won
Solicited Unsolicited
24 8
61 27
85 35
28 23
Total
32
88
120
27
Solicited Unsolicited
4 0
10 3
14 3
29 0
Total
4
13
17
24
Solicited Unsolicited
28 8
71 30
99 38
28 21
Total
36
101
137
26
success probability of a proposal is a subjective estimate of one or a group of managers familiar with the proposal and bidding environment. Brooks [2] has observed that the probability estimates of such managers (specifically in the case of follow-on contracts) "are usually more realistic and reliable than probabilities derived any other w a y . . . " In the manufacturing firm analyzed here the marketing manager responsible for the proposal development effort was asked for an estimate of the likelihood of winning the competition at the time the proposal was submitted. The estimate was made either by only the manager or in consultation with other knowledgeable company personnel. These managerial estimates are special cases of two prevalent methods of sales forecasting-jury of executive opinion and sales force estimates [33, 37]. Although a danger in subjective estimates is the possibility of systematic forecast errors by individuals making the estimates [19, 26, 29], recent research has found management judgment forecasts to be very accurate [22]. The manager involved was asked to place each proposal in one of three categories indicating his assessment of the likelihood of success in winning the contract. The categories were A, B, and C, were intended to represent approximately 90, 50, and 10% chances of winning the associated contract. So these subjective estimates are used here as inputs to the forecasting process, not in making "bid-no bid" decisions. Table 3 shows how accurate the marketing managers' subjective initial estimates of success were. Lost proposals were either (1) won by another contractor
151
TABLE 3 Win-Loss Records of Four Categories of Proposals With Subjective Estimates of Success Made at Submission
TABLE 4 Results of Chi-Square Tests on Win-Loss Records of Proposals <$1,000,000 in Value
Number of Proposal Value at Submission
Type of Proposal
Subjective Proposals Percent Rating ~ Won Lost Total Won A B C
10 8 6
A B C
1 2 5
$1,000,000
A B C
2 1 1
or more
A B C
Solicited Less than
$1,000,(100 Unsolicited
Solicited
Unsolicited
5 25 31
15 33 37
67 24 16
l
2
9 17
11 22
50 18 23
0 6 4
2 7 5
100 14 20
0
0
0
0 0
2 1
2 1
0 0 0
"At the time of submission the responsible marketing manager estimated the probability of winning the proposal as A, 90%; B, 50%; or C, 10%. ~'The "'percent won" when expressed as a decimal is the "success ratio.'"
or (2) d r o p p e d because of a decision by the buying firm not to award a contract, Table 3 shows that while the 90, 50, and 10% success values for A, B, and C ratings, respectively, are not accurate, there is a tendency for A-rated proposals to have a better success record than B- or C-rated proposals. Also, although the totals are not shown in Table 3, the success ratios decrease from A to B to C ratings for (1) all proposals combined and (2) all proposals <$1,000,000. For example, in the case of all proposals <$1,000,000, the success ratios of A-, B-, and C-rated proposals are 0.65, 0.23, and 0.19, respectively. So at least the ordering of the success ratios based on the marketing managers' subjective judgments is correct. The sample size of 120 for the proposals whose bid value was <$1,000,000 permits a more detailed analysis of this group. The results of four chi-square tests on the smaller proposals summarized in Table 4 lead to the following conclusions: 1. There is no statistically significant difference b e t w e e n the win-loss records of small solicited and small unsolicited proposals. Data from
152
Hypothesis Tested-Difference Between:
Degrees of Freedom
Chi-Square Value
p Value
Win-loss records of solicited and unsolicited proposals
1
0.367
ns
Win-loss records of A-, B-, and C-rated solicited and unsolicited proposals
2
14.870
< 0.001
Win-loss records of A- and B-rated solicited and unsolicited proposals
1
9.572
<0.005
Win-loss records of B- and C-rated solicited and unsolicited proposals
1
0.259
ns
these two groups can therefore be combined in subsequent statistical tests. 2. There is a statistically significant difference between the win-loss records for small proposals on the basis of A, B, and C ratings. As shown in Table 4, this result is highly significant. 3. There is a statistically significant difference between win-loss records of small proposals rated A and B but not b e t w e e n those rated B and C. The managerial importance of these results is that small, A-rated proposals have a statistically better chance of being won than either I3- or C-rated ones. At least in this instance, the ability of the firm's marketing managers to discriminate high-probabilityof-success proposals (A-rated ones) from the other proposals submitted (B- and C-rated ones) warrants the use of the managers' subjective estimates of Pk in the forecasting model rather than using overall winloss percentage as an estimate of Pk. Relation of Time Probability
L a g in A w a r d
to Success
The time lag between proposal submission and the contract award d e c i s i o n - - t h e contract go-ahead date for proposals the firm wins--in the sample of proposals ranges from 1 to Ill months with a mean of about 3.3 months. It is a critical ingredient in the sales forecast because of the impact of the lag on the timing of sales on contracts that tire won. This time lag can be
affected by a number of factors, such as the organizational buyer involved, the point in the fiscal year, the urgency of the award, whether the proposal is solicited or unsolicited, and whether the award is won or lost. The past relationship of the time lag to any of these factors can be studied if there is a large enough sample to warrant analysis. As an example of the value of this kind of analysis, let us study the relationship between proposal type (solicited or unsolicited) and disposition (won or lost) and the time lag between the proposal's being submitted and when the contract decision is made and the bidder informed of the result. A 2 x 2 table giving the time lags in months shows: Proposal Dispositions Proposal Type
Won
Lost
Solicited Unsolicited
3.32 4.05
2.62 3.49
Analysis-of-variance results for two factors, proposal type and proposal disposition, are presented in Table 5, and show significant F-ratios at the 0.05 level for the proposal-type effect (solicited or unsolicited) and the proposal-disposition effect (won or lost) but not the interaction. The results suggest that the time lag between proposal submission and decision is (1) greater for unsolicited proposals than solicited proposals and (2) greater for proposals which are won than those which are lost. This state of the analysis has great practical significance to the forecaster: it not only develops the probability distribution of go-ahead dates for various categories of contract--the Pk(s) function--but also shows how the success probability (Pk) varies with the time lag in the award decision. Long time-lags are of special consolation to the firm studied here, because they show that the firm's probability of winning the award is increasing. If desired, this variation in the probability of success for a proposal can be used in fine-tuning the firm's sales forecast. The kind of analysis shown in Table 5 also illustrates another key advantage to using this sales forecasting model: errors in the final sales forecast can be traced to one of the factors that comprise the model. This, in turn, can suggest where special effort can be placed to try to improve the overall sales forecast. For
TABLE 5 Anova Table to Study the Effect of Proposal Type and Disposition on the Time Lag Between Proposal Submission and Contract Award Decision Source Variable Proposal type (solicited or unsolicited) Proposal disposition (won or lost) Interaction Error Total
Sum of Degrees of Squares Freedom
Mean F Square Value
p Value
17.647
1
17.647
5.508
<0.025
14.458
1
14.458
4.510
<0.05
0.453 371.808
1 116
0.453 3.205
0.141
ns
404.366
119
example, if a contract that is won is not generating the sales expected during a specific month, the cause might be an error in either (1) the estimated monthly sales from the contract after go-ahead is received, or (2) the probability distribution of likely starting months. Analysis might reveal that the firm systematically estimates an earlier go-ahead month than it is experiencing. It can then improve such estimates in the future. A n o t h e r possibility is to adjust probability-of-success judgments by the estimator, the customer involved, or the kind of contract if enough bidding history exists for these to do so.
MAKING AND USING THE OVERALL SALES FORECAST The flexibility, simplicity, and value of the model are illustrated by describing (1) how the overall sales forecast is made and (2) how it can be used by marketing managers.
Making the Overall Sales Forecast The overall sales forecast for a to-order firm using this probability model is obtained by simply summing the sales expected during each time interval in the forecast period for the three kinds of business expected: work under contract, follow-on work, and new business. An example is shown in the top band in Figure 4. Ytotal, company sales for k proposals in month t, can therefore be expressed as: Ytotal =
~ yk(t) k=l
•
153
i
6 5
~ l
4
l 7
[
--]
3 -~ 2 | •~ ~_, 1
0
Estimated Sales From //New BusinessProposals
CONCLUSIONS
Estimated Sales From Follow-0nWork
Estimated Sales From Work UnderContract
10 I 2Q I 3Q I 4Q ] 1Q I 2Q YEAR 1 FIGURE 4.
3Q I 4Q
YEAR2
Two-Year Sales Forecast
In this bottom-up forecasting approach, each of the three kinds of business shown in Figure 4 is composed of a number of individual projects that for simplicity are not shown in Figure 4. Figure 4 shows also that sales in the 2-year forecast are estimated monthly for the first 6 months, quarterly for the second 6 months, and semiannually for the last 12 months. The forecast may be made monthly after the first 6 m o n t h s if desired, but carrying detailed monthly sales estimates throughout the analysis more than 6 months or 1 year into the future may cost more than it is worth. Using the Sales Forecast
State-of-the-art developments in personal computers during the past 5 years mean that tabular or graphic sales forecast information comparable to that in Figure 4 is available to even small businesses having access to microcomputers. Further, the vertical axis in Figure 4 can be used to forecast sales revenue, units, product lines, and kinds of people needed. When one or several large contracts can have especially great impacts on future sales, "what-if" computer simulations may be run as part of the sales forecasting activity. This is a level of detail possible with bottomup methods that is not feasible with most top-down techniques. The forecasting also facilitates both short-run and long-run marketing decisions. Short-run sales turndowns 2 or 3 months in the future may suggest marketing efforts geared to obtaining immediate contracts, even with low margins, to keep the operating personnel employed. Over the longer run, perhaps a year into the future, both encouraging and threaten-
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ing trends in product lines may be identified and necessary strategies developed. AND IMPLICATIONS
To-order firms--those selling a limited number of projects, products, or services "to-order" to a restricted number of buyers--face a far different sales forecasting situation than firms manufacturing products for inventory that are eventually sold to thousands or millions of buyers. In contrast to these produce-for-inventory firms, to-order firms typically use bottom-up sales forecasting approaches in which sales expected from individual projects or jobs are s u m m e d to give the forecast of total sales. The method analyzed here can be used by virtually all project-oriented or job-shop firms, regardless of size. This m e t h o d requires estimates of only three key factors related to each project or job--probability of winning the contract, a frequency distribution of monthly sales if the contract is won, and a frequency distribution of probable starting times. Further, by using this method, important errors in sales forecasts can be traced to one of these three basic factors in the model and steps taken to try to improve the accuracy of the factor which is the most important source of error. Besides offering the opportunity for improving future bottom-up sales forecasts for firms selling projects or jobs on a to-order basis, the m e t h o d offers the forecaster the opportunity for systematic diagnosis of the sources of past forecast error. The flexibility and simplicity of the model, along with the ease of computerizing it, offers potential for a variety of firms selling projects or jobs on a to-order basis.
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