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Vol. 40, No. 5, September–October 2010, pp. 385–396 issn 0092-2102 �eissn 1526-551X �10 �4005 �0385

informs ®

Improving New-Product Forecasting at Intel Corporation

S. David Wu P. C. Rossin College of Engineering and Applied Science, Lehigh University,

Bethlehem, Pennsylvania 18015, [email protected]

Karl G. Kempf Decision Technologies Group, Intel Corporation, Chandler, Arizona 85226, [email protected]

Mehmet O. Atan, Berrin Aytac Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, Pennsylvania 18015

{[email protected], [email protected]}

Shamin A. Shirodkar, Asima Mishra Customer Planning and Logistics Group, Intel Corporation, Chandler, Arizona 85226

{[email protected], [email protected]}

Forecasting demand for new products is becoming increasingly difficult as the technology treadmill continually drives product life cycles shorter. The task is even more challenging for electronic goods; these products have life cycles measured in quarters, manufacturing processes measured in months, and market volatility that takes place on a day-to-day basis. We present a model that perpetually reduces forecast variance as new market information is acquired over time. Our model extends Bass’ original idea of product diffusion [Bass, F. M. 1969. A new product growth for model consumer durables. Management Sci. 15(5) 215–227] to a more comprehensive theoretical setting. We first describe how forecast variances can be reduced when combining predictive informa- tion from multiple diffusion models. We then introduce the notion of demand-leading indicators in a Bayesian framework that reduces forecast variance by incorporating a wide variety of information emerging during the product life cycle. We describe a successful implementation of this model at Intel, where we tested one-third of the microprocessor products. When compared with the current forecasting method, our model reduced forecast- ing time from three days to two hours and decreased forecasting errors by 33 percent, leading to $11.8 million in cost savings over four months of demand realization.

Key words : technology forecasting; diffusion models; leading indicators; Bayesian statistics; industries: computer, electronic, communications, pharmaceutical.

History : Published online in Articles in Advance July 21, 2010.

In today’s fast-moving, ultracompetitive markets, companies are introducing new products at a

higher frequency and with shorter product life cycles. Electronic products, such as personal computers, mobile phones, and video games, are familiar exam- ples. In these dynamic market environments, a company’s competitive advantage and capability to achieve and sustain profitability come from its ability to manage frequent product entries and market exits. To hone this competency, the company must develop capabilities to use diverse and fast-changing market information so that its demand views sharpen perpet- ually and its demand forecasts improve over time. Upstream, in the supply chain, the challenges only

intensify. A component manufacturer may need to

introduce a growing variety of new products for multiple main market segments, all at a fast pace. For example, Intel’s microprocessor units (MPUs) have a prominent presence in three major vertical markets (server, desktop, and mobile devices). This leads to the introduction of more distinct products with shorter life spans, generating multiple product releases and transitions per year. To stay competi- tive, it is critical to release each new product to the right market(s), at the right time, with the right vol- ume, paced over its entire life cycle. There is a diffu- sion process for any new product introduced into the market; thus, appropriate timing and volume are crit- ical to its acceptance, adoption, and ultimate financial success. As such, an in-depth understanding of the

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demand process over a product’s life cycle and the ability to forecast life-cycle demand diffusion are vital to a company’s ability to manage product transitions and to maintain its competitive edge. Life-cycle forecasting is critical not only for demand

management, but also for operations management. After the introduction of a new product into the market, a production shortage of the product can seriously retard its adoption and negatively impact revenue. Excess inventory erodes profits and uses capacity that could have been better employed for other products. Production capacity can be extremely expensive; reallocating the right amount of capacity at the right time (e.g., from old to new products) is critical to avoid both stockout and inventory buildup. Because many products share a common capacity across multiple market segments, the ability to quickly generate a more accurate forecast that can be mapped onto appropriate capacity will lead to sig- nificant operational savings. Fortunately, during the new product’s life cycle, a

wealth of information that can be used for demand forecasting is available. The product life cycle typi- cally involves stages, including prelaunch (introduc- tion), ramp-up, maturity (saturation), ramp-down, and end-of-life—the stage in which the product is being replaced by a new generation of product(s). During each stage, different sources of information, which can be used to provide projections, advanced indications, or status updates for future demands, become available. With this massive amount of infor- mation, the challenge is how to systematically extract relevant information that will help the planners to comprehend future demands in the context of operations. In this paper, we address two prevailing business

problems during new-product introduction. These problems are as follows: 1. The need to capture complex product diffu-

sion patterns across diverse and multifaceted vertical markets. 2. The need to use dynamically evolving mar-

ket information and business intelligence during the product diffusion process. The ultimate goal is to develop a new approach

to life-cycle demand forecasting that perpetually enhances forecast accuracy as more and different

information becomes available, thus leading to signif- icantly enhanced performance and consistency. The motivation of the work described here has been to generalize Bass’ original idea (Bass 1969) of product life-cycle diffusion to a more comprehensive theoreti- cal setting and then to apply the theory to realize the potential benefits. We have made significant progress toward this end. We have tested our model at a hand- ful of technology companies (Wu et al. 2006); we have also successfully implemented it at Intel, where it has provided significant improvement in forecasting accu- racy with corresponding savings in operational costs.

Previous Work in Technological Forecasting Technological forecasting literature uses diffusion models to characterize product demand life cycles. To predict patterns of future demand realization, researchers have proposed a variety of models that differ mainly in their cumulative diffusion pro- files throughout the product life cycle. Meade and Islam (1998) and Kumar and Kumar (1992) provide extended surveys of the various diffusion models used in technological forecasting. Bass (1969) intro- duced the most well-known and widely used diffu- sion model. When Bass’ model was initially tested on consumer durable goods, it was shown to pro- vide accurate predictions on both timing and mag- nitude of sales throughout the product life cycle. Since then, the Bass model has been extended to incorporate additional features of technology diffu- sion and widely used to forecast diffusion in mar- kets such as retail, education, pharmaceuticals, and agriculture (Mahajan et al. 1990). However, demand characteristics for technology products differ from most traditional markets because of the rapid inno- vation cycle that leads to significantly shorter life cycles and higher volatility. Studies that consider tech- nology product diffusion include Norton and Bass (1987), who built upon the Bass model to forecast successive generations of products in the semiconduc- tor industry. Kurawarwala and Matsuo (1996) incor- porated a seasonal influence parameter to the Bass model to predict demands for a personal computer manufacturer. Modis and Debecker (1988) also ana- lyzed the demand for computer manufacturers using

an S-shaped logistic diffusion curve. More recently, Wu et al. (2006) used diffusion models to generate forecasts while reducing forecast variation in a cus- tom semiconductor manufacturing setting. Aytac and Wu (2008) were the first to introduce a demand char- acterization framework based on multiple diffusion models and a Bayesian updating procedure that uses advanced demand signals (leading indicators) to sys- tematically reduce forecast variation. This last paper provides the theoretical underpinnings of the work we describe.

Demand Characterization and Forecast Analysis Technology products typically have a single-modal demand life cycle that goes through the phases of prelaunch, ramp-up, ramp-down, and end-of-life once. This life cycle demand can be expressed as a bell-shaped time-series curve (e.g., billings over time) or as a cumulative curve in which each point on the curve represents the percentage of life-cycle demand satisfied up to that time. Note that the cumulative curve is S-shaped; because it is in the second order, some of the short-term fluctuations in the time series are ignored. Researchers (Meade and Islam 1998) have proposed various S-shaped diffusion models (includ- ing the well-known Bass model) to forecast cumula- tive demand during a product’s life cycle. Each of these models differs in the rate of adoption achieved and the peak diffusion rate reached, and the steepness of growth or decline of the diffusion rate. In other words, each diffusion model projects, in a unique way, how a particular product’s life cycle unfolds over time. Given up-to-date information about realized de-

mand (e.g., early sales) and an estimation of total market volume, life-cycle forecasting (1) finds a dif- fusion model and determines its parameter values that provide a strong goodness of fit, and (2) gener- ates demand forecast by projecting the fitted diffusion model over the entire product life cycle.

Characterizing Demand Diffusion Across Multiple Markets A company may need to introduce a variety of new products for multiple vertical markets. Each verti- cal market has its own drivers and dynamics, which

overlap and interact. Demands in different verticals are likely to demonstrate a distinctly different good- ness of fit for particular diffusion models. Moreover, many products share the same capacity during the manufacturing process; thus, a cohesive understand- ing of their diffusion in the markets is critical. The goal of our model is to capture demand character- istics across diverse and multifaceted market envi- ronments by systematically combining the projections from multiple diffusion models. Although it has been suggested that combining

multiple forecasts outperforms forecasts that have been generated from any single model (Bates and Granger 1969), and many techniques have been sug- gested to combine the forecasts of individual mod- els and to estimate model parameters (Mahajan and Muller 1979, Sultan et al. 1990, Timmermann 2006), it is less clear that combining diffusion models derived from different vertical markets would necessarily help to characterize the overall multifaceted market demand. More importantly, when combining multiple diffusion models, does one risk introducing addi- tional variances and biases into the forecast? Is it bet- ter to find a particular diffusion model that performs the best across all markets? Below we will summarize some key theoretical insights that form the basis for our forecasting model. In forecasting life-cycle product demand, it is

important to find the cumulative percentage of total market demand that has been observed by time T + � , denoted by X�T +��, given that actual demand obser- vations up to time T , ��T �=X�1��X�2�� X�T �, are available. Let �Xk�T + � � ��T �� denote an estimate of cumulative demand percentage observed by time T + � , projected by diffusion model k. Then,

X�T + ��= �Xk�T + � ��T ��+ �T + � ��T ��

where the estimate �Xk�T + � � ��T �� is provided by Fk�T + ��, which is the cumulative percentage of total demand observed by time T + � , according to diffu- sion model k, and �T + � � ��T �� is the estimation error. Suppose the forecast generated from a diffusion

model represents an unbiased estimation for the actual demand and the estimation error is normally

distributed with mean zero and a known, fixed vari- ance �2 ; then, the actual cumulative demand at T + �

can be represented by a normal random variable:

�Xk�T + ��∼N� �Xk�T + � ��T ��2k ��

Note that the mean of the random variable is defined by diffusion model k �Fk�T + �� whereas the variance �2k is the sum of variances of the fore- cast and the estimation error (�2 ), assuming that they are independent. Although point estimates are used widely in practice, an uncertainty is inherent in fore- casts obtained by diffusion models. This uncertainty originates from the nonlinearity of model fitting and the errors in parameter estimation. The uncertainty in the estimate of a future realization of the random variable is described by a prediction interval. Fig- ure 1 illustrates the prediction intervals for the fore- cast obtained by a diffusion model. We are interested in determining if combining dif-

fusion models derived from different vertical markets would help to improve the overall market forecast. Specifically, does one introduce additional variances and biases into the forecast, and how does this compare to finding a diffusion model (e.g., Bass) that performs well across all markets? Some of these ques- tions can be answered using the setting above. Given a particular diffusion model, the actual cumulative demand at T + � , �Xk�T + ��, can be represented as a normally distributed random variable (assuming nor- mally distributed fitting errors). With the combina- tion of multiple diffusion models to forecast demands

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Figure 1: In this graph, we show prediction intervals for life-cycle forecast by a diffusion model.

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Figure 2: In this graph, we show prediction intervals after combining multiple diffusion models.

�-period ahead, �X�T + ��, the combined forecast is also normally distributed. Thus, as long as the combination of the diffusion models using weights inversely proportional to each model’s forecast vari- ances occurs, the variance of the combined forecast is always smaller than the variance of any individual diffusion model (Proposition 1 in Appendix A). Note that the prediction intervals for the life-cycle forecast will shrink with the decrease in the forecast variance (Figure 2).

Incorporating Dynamically Evolving Information The intent of our model is to effectively use diverse and fast-changing market information to improve forecast accuracy. The goal is to perpetually reduce forecast variance as new market information is acquired over time. Given the inherent diversity and complexity of market information, we propose a uni- fying view that considers market information as a leading indicator for product demands. We adopt the Bayesian statistical framework, as Aytac and Wu (2008) describe, and extend it to process informa- tion provided by a wide variety of demand-leading indicators. We define a leading indicator as a demand series,

typically in the form of a time series, that predicts the pattern of one or more new demand series before they materialize. Meixell and Wu (2001) first proposed the concept of demand-leading indicators; Wu et al. (2006) later verified and tested them in an indus- try setting. Multiple leading indicators can be used at the same time or over time. We generalize the

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Figure 3: In these graphs, we illustrate the incorporation of leading indicators in the Bayesian update.

notion of leading indicators to include any informa- tion indicative of future demand patterns so long as verifiable connections can be drawn in a consistent manner. For example, a leading indicator can be the historic demand series from an older-generation prod- uct, with a sales pattern demonstrating high correla- tion with that of the new product; it can be derived from prehorizon market research results or particu- lar market or business-cycle indexes that show strong connections to future demands of interest. As the first part of Figure 3 shows, at time T one

can fit a diffusion model to the observed demand data, ��T �, and then project the adopted model over the product life cycle, which provides a prior distri- bution, i.e., �Xk�T + ��. Now, suppose that time-series data are available from a group of m leading indi- cators that provide unbiased estimates for the actual demand from T + 1 through T + L. The data corre- sponding to each leading indicator are then projected over the entire product life cycle (using a diffusion model). The collection of m leading-indicator projec- tions form the sampling distribution, as the second part of Figure 3 illustrates. The sampling distribution can be summarized as

�Xk�T + ��∼N

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where the mean is provided by the diffusion curve k’s projection, using the data extended by m leading indicators for L periods. Using a Bayesian update procedure, we combine

the prior and sampling distributions to generate a

posterior distribution, which provides a distribution of life-cycle forecasts considering the new information provided by the leading indicator. Aytac and Wu (2008) provide an important theoretical insight—as long as each leading indicator represents an unbiased estimate of the actual demands, and this information is incorporated using the Bayesian procedure outlined above, then the variance of the life-cycle forecast will always decrease. This is because the variance of the posterior distribution is smaller than or equal to the variance of the prior distribution (Figure 3). Further- more, the variance asymptotically approaches zero as the number of leading indicators (m) increases, pro- vided that each leading indicator is an unbiased esti- mate of actual data (Proposition 2 in Appendix A). Note that the Bayesian updates may take place mul-

tiple times throughout the product life cycle; as new information becomes available, model parameters and combination weights for each leading-indicator- generated sample path are reestimated. Moreover, this procedure can be used at any stage during the prod- uct diffusion (prelaunch, ramp-up, ramp-down, etc.). The only difference in a stage would be the choice of leading indicators because the prediction quality of an indicator may vary at different points throughout the planning horizon; we discuss this in detail in the Improving Forecasting at Intel section.

The Integrated Forecasting Model We now describe an integrated model for new-product forecasting using the theoretical results we devel- oped above. The model’s objective is to (1) capture demand diffusion across multiple vertical markets and

(2) incorporate dynamically evolving market informa- tion using leading indicators. Implemented using a Bayesian statistical framework, the model provides continuous improvement of forecast accuracy because verifiable new data (leading indicators) are intro- duced as the life cycle unfolds. When multiple dif- fusion models are used, this procedure is repeated for each diffusion model, and a forecast is gener- ated by combining them as we described earlier. In Appendix B, we outline the specific algorithm in detail. Our model generalizes the concept of Bass diffu-

sion to broader dimensions, recognizing the richness of diffusion patterns across multiple markets and the importance of utilizing dynamically evolving mar- ket information using various indicators. The model’s intent is to perpetually reduce forecast variance—not to generate the best possible point forecast. Note that the forecast variance is guaranteed to be reduced if the leading-indicator-generated sampling distribution represents an unbiased estimate of the means of the actual data. In practice, it is possible to verify ad hoc through standard hypothesis testing if the indica- tors are indeed unbiased estimates. When systematic biases are identified, efforts should be made to adjust the bias for future uses. In Appendix C, we outline a simple procedure that uses learning to remove bias from the leading indicators.

Improving Forecasting at Intel We now describe our experience in implementing the new-product forecasting model at Intel. Intel Cor- poration, which was founded in 1968, is a sup- plier of MPUs, boards, systems, and software for the computing and communications industries. Over the past 40 years, it has emerged as the world’s largest semiconductor company; its 2008 revenues were $37.6 billion. The majority of Intel’s revenue is generated from three key market segments—the server, desktop, and mobile markets. To improve new-product forecasting, a team from three key groups was assembled and has been collaborating over the past few years. Researchers in supply chain management and operations research at Lehigh Uni- versity constitute the first group. The Lehigh group has been developing and integrating the notion of

demand-leading indicators and life-cycle diffusion models as a means to reduce forecast variations (Wu et al. 2006, Wu 2008, Aytac and Wu 2008). The second group, the microprocessor marketing and business planning (MMBP) team at Intel, has historically been responsible for the MPU forecast. The third group, decision technologies (DT) at Intel, has acted as the conduit between the Lehigh and MMBP groups. DT is chartered to identify critical business problems and to supply effective decision support tools to the appropriate decision makers. Collaboration between the three groups led to the development of a new set of decision support tools that supports demand life-cycle analysis using extensive Intel business data sets. The data tested include 60 Intel products with life cycles that were completed by the end of 2008; the data set spanned products in three vertical mar- kets, including 17 mobile, 17 desktop, and 26 server products. The tools and the extensive data set allow the team rigorous validation of theoretical insights using real-world data. In implementing the decision support software, the team gave special attention to the ease-of-use features for demand planners, includ- ing a graphical interface. The system has been in use for 10 monthly forecasting cycles on a large seg- ment (about one-third) of Intel’s MPU products, which makes possible an in-depth quantitative and qualita- tive assessment of its performance. This section docu- ments the implementation details and summarizes the performance assessment. Although the improvements in forecast quality (over existing methods) and the overall impact on streamlining Intel’s business pro- cesses are both overwhelming and positive, evaluation of sustained performance using Intel’s data-driven, continuous-improvement process is still ongoing.

Combining Demand Diffusion Models Based on the analysis we describe above, the team implemented a procedure to combine a selected num- ber of diffusion models that collectively characterize the multifaceted aspects of Intel’s three vertical markets. The team initially selected 10 distinct diffusion models (i.e., Bass, Cumulative Lognor- mal, Extended Riccati, Simple Logistics, Extended Logistics, Gompertz, Skiadas, Mansfield, Floyd, and Weibull). The intent was to start with a wide variety of models that encompass a good mix of differing sym- metry and points of inflection characteristics in the

S-shaped diffusion curves. The 10 diffusion models were further tested to see which would best fit Intel’s historical MPU demand data. These models were fit to the demand data that we described in the previ- ous section. The top five models that minimized the sum of squares error (SSE) over the life cycle of the products were selected. The five models that consis- tently performed well across the three verticals were the Skiadas, Extended Logistics, Bass, Weibull, and Simple Logistics. The bar chart in Figure 4 presents the average fore-

cast error across all mobile families (six months into the product life cycle). The first five bars starting from the left represent the average forecast errors for the five individual models. The sixth bar shows the error for the combined forecast; the last bar depicts the error for the diffusion model that demonstrates the best goodness of fit six months into the life cycle. As Figure 4 shows, the combined forecast outperforms all individual model forecasts. However, note that the performance of an individual diffusion model is not known a priori. If one would select a diffusion model that demonstrates the best goodness of fit six months into the life cycle to project the rest of the life-cycle demand, the model presented by the last bar would be chosen. Hence, model combination not only per- forms better than each individual model on average, but it also avoids the risk of choosing the “wrong” model given limited information.

Incorporating New Information at Different Stages of the Life Cycle Before the introduction of a new Intel product through to its end of life, many sources can provide

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Figure 4: In this graph, we show average forecasting error across all mobile families.

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Figure 5: In this graph, we show Intel’s timing of leading-indicator data collection and different phases of a product life cycle.

a wealth of information that can serve as demand- leading indicators. To use different sources of infor- mation during the product life cycle, we divide the life cycle into its stages (Figure 5); these stages are defined formally based on time (percentage of the esti- mated life realized) and volume (total percentage of estimated market size realized). A product is defined to be in the ramp-up phase from the beginning of pro- duction until 40 percent of the estimated life cycle or 40 percent of the estimated market size for the prod- uct has been realized. Similarly, a product is defined to be in the end-of-life phase when at least 90 percent of its estimated life cycle or 90 percent of its estimated market size has been realized. The rest of the prod- ucts are classified to be in the ramp-down phase. For each product, the percentage of total life realized is defined as the ratio (number of months into life cycle/T) and the percentage of total market size realized is given by (volume realized until now/M), where T is the estimated total length of the product life cycle and M is the estimated total volume of sales (market size) over the product life cycle. For each product, T is a forecast that is published by the long-range planning group at Intel, and M is calculated as the sum of past demand realized and the estimated future sales that is obtained from forecasts by the MMBP and long- range planning groups at Intel. Because at least three data points are necessary to fit the life-cycle diffusion models, these models are used once a product is three months into its life cycle.

Depending on the stage within the product’s life cycle, different forms of leading indicators are used to generate the forecast. Leading indicators serve a dual role. They add business intelligence to the diffusion models by capturing changing dynamics in the mar- ket as early as possible. They also help by extending the demand data set needed to fit the models, which is very valuable early in the product life cycle. In the following sections, we describe specific leading indi- cators implemented at Intel.

Design Wins. Design wins are early leading indi- cators that are available from the prelaunch stage. Designs are declared as wins when a customer takes preproduction MPU samples and conducts prelimi- nary evaluations. The customer then produces prelim- inary designs for the printed circuit board for a new end product. The customer supplies an initial forecast of the expected order quantity in addition to the tim- ing of the entry into the market. Figure 6 (left chart) shows the design wins for the same product col- lected prior to its launch. In this case, the correlation between actual demand and the design wins leading indicator is 0.81; this is typical for MPU products.

Field Sales Intelligence. Field sales personnel who are in daily contact with major customers often develop dynamic forecasts at a customer- and product-granularity level. This type of field sales intelligence, which is available from the prelaunch phase and continues throughout ramp-up and ramp- down phases, has proven to be a good leading indicator. Figure 6 (right chart) shows examples of

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Figure 6: In these graphs, we show design wins (left) and forecasts from field sales (right) as leading indicators for an Intel product.

“x-months-ahead” forecasts from field sales for an Intel product in comparison to the actual demand realized for the product. Each point in the “x-months- ahead” curve was collected x months ahead of the realization of the actual demand. For example, the forecast on the “one-month-ahead curve” correspond- ing to period 10 was forecasted in period 9. Notice that, as expected, the quality of the leading indicator improves as one moves closer to the actual realiza- tion of demand, which is also reflected in the cor- relation between the actual demand and the leading indicators.

Chipset Sales. Chipsets are microprocessor chips that cover functionalities ranging from input-output to memory to graphics and are typically paired with the MPUs in the customers’ end products. Chipsets are historically much less expensive than MPUs and are shipped to the customer weeks ahead of the corre- sponding MPUs to facilitate circuit board testing; the chipset “ship-aheads” serve as strong leading indica- tors for the MPUs. As we cautioned above, each type of leading indica-

tor could have some degree of bias for a variety of rea- sons. The bias in design wins is primarily because the information is collected prior to product launch and the customers may not have visibility very far into the future. In addition, the customer’s product-design group, which typically provides the design-win esti- mates, may be psychologically inclined to believe its next product will be a winner; this translates into positive biases. The field sales intelligence could also be biased in that some customers may intentionally

exaggerate field-forecasted quantity as a means to reserving future capacity. Hence, the quality of these leading indicators can be improved by correcting for bias. The theoretical results established earlier asserted that if the projection made by the combined diffusion model and (or) the leading indicator repre- sents an unbiased estimate for the mean of the actual demand, then the forecast variance will be reduced. We implemented the “unbiasing” or “learning” mech- anism described in Appendix C, which allows the forecasting performance to improve over time.

Business Results and Conclusions Intel’s MMBP team is a strategic group responsible for supply-demand matching and pricing for all MPU products. One of its main tasks is to forecast customer demand for MPU products in the desktop, mobile, and server markets. Each month, MMBP generates a new 12-month demand forecast for each active prod- uct by relying on historical data systems, collective mental models, and current market news. The MMBP forecast is communicated first to the senior manage- ment team for final approval and then to supply chain operations for execution. The monthly forecast has at least three operational

uses. Given Intel’s three-month production cycle, the first few months of the forecast serve to reprioritize work in progress, reposition existing inventory, and finalize logistics arrangements. The fourth month of the forecast is the most critical because it is used to release raw materials into the fabrication facilities at the beginning of the production process and to trigger the placement of orders for materials used in assem- bly factories. The remaining months of the forecast are used by the operational team as an input for pro- duction, materials, inventory, and logistics planning activities. The integrated forecast model was incorporated

into the forecasting process over 10 forecasting cycles, beginning with a trial run in December 2008. It has been used to generate forecasts for 10 desktop MPU products that form 32 percent of Intel’s active MPU products. The team has been tracking the per- formance of the new forecast model as the actual demand volumes are realized every month. Because there is a three-month production cycle for forecasts

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Figure 7: In this graph, we show a comparison of the mean absolute percentage error of the forecasting methods for nine products over four demand cycles.

generated (and used to release materials into fabrica- tion) in January, February, March, and April, we col- lect actual shipment data in April, May, June, and July, respectively. This provides matching pairs of time- series data that allow us to compare the forecast and actual demands in detail. Because Intel uses a one- month accounting cycle, we are able to report four months of demand realization at the conclusion of this analysis in September 2009. Figure 7 summarizes the overall performance of the

integrated forecast model (new method) compared with the original MMBP methodology (old method) for 9 of the 10 desktop MPUs. On average, the new method shows a 9.7 percent reduction in the 12-month forecast error measured in mean absolute percent error (MAPE) per product; however, if we focus our comparison on the critical fourth-month forecast, the new method shows a 33 percent improvement in fore- cast accuracy. We have excluded one of the 10 desk- top products because of the multimodal nature of its life cycle: it rises to maximum volume in the first six months, falls to 60 percent in the next six months, rises back to 95 percent in the following half year, and then sits at 35 percent during the following year. The single-modal diffusion models are not appropriate for such cyclic demand patterns. We are studying mod- els that will allow us to extend the integrated forecast model to handle products with multimodal life cycles; we are also studying products 3 and 9 to determine what information in the MMBP forecast we can use to improve the integrated forecast model.

Impact on Operational Costs To estimate the financial impact of the integrated fore- cast model, we compared the fourth-month forecasts for the old method and the new method to actual shipments realized for April, May, June, and July of 2009. The analysis proceeded using the following steps. • We assumed that no inventory was on hand at

the beginning of April. • For each forecast, if production in a given period

resulted in more product than was actually shipped in that period, then (1) the excess product was held for use in future periods when production would be insufficient to meet actual demand, and (2) an inven- tory holding cost was charged for each unit for each period held. • For each forecast, if production in a given period

supplied less product than was actually shipped in that period, and sufficient inventory was not available to cover the shortfall, an underage cost was charged for each unit for each period in which the shortage would persist. The inventory holding costs and the underage cost

were both supplied by the MMBP based on finan- cial data. Figure 8 summarizes the financial perfor- mance of the integrated forecast model (new method) compared with the original MMBP methodology (old method). On average, the new method shows over $1.3 million of revenue enhancement per product; this translates to a gain of $11.8 million for the nine prod- ucts over the four-month analysis period. In a broader

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500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

4,000,000

B en

ef it

re la

tiv e

to o

ld m

od el

( $)

1 2 3 4 5 6 7 8 9 Avg Product

Figure 8: In this graph, we show a financial comparison of the forecasting methods for nine products over four demand cycles.

sense, the underage costs should reflect both potential loss in revenue and cost increases because of supply- demand mismatch. Historical data show that when Intel misses an on-time shipment, the customer turns to a competitor or the open market approximately 7.5 percent of the time. Therefore, Intel may have to shift (more expensive) capacity from other prod- ucts to increase production to avoid long-term con- sequences, such as loss of market share. This could cause significant and compounded increases in oper- ating costs. Our current financial analysis does not consider the compounded effect of underforecasting; thus, the above cost saving is likely to be understated. Comparing Figures 7 and 8 shows that the forecast

errors and financial metrics capture related but dif- ferent assessments of the performance of these meth- ods. Using the new method, products 1, 5, and 7 show the largest improvement in forecast accuracy (Figure 7); however, products 2, 6, and 8 show the largest financial improvement (Figure 8). Although by the MAPE metric the new method performs the worst for product 9, the impact on the financial metric is minimal, partially because each product has differ- ent inventory holding and underage costs (e.g., prod- uct 9 has among the lowest inventory holding and underage costs). Moreover, the financial metric cap- tures dynamics of the system that the MAPE metric does not. For example, overforecasting in an earlier period can cause inventory to build (with a relatively low cost penalty), thus covering underforecasting in a later period (with a relatively high cost penalty if the inventory had not been covered). Conversely, underforecasting followed by overforecasting results in more severe financial consequences. In addition to improvements in forecast accuracy

and revenue, the new forecast tools can decrease the time and effort required to generate the forecast. The old process takes approximately three days; the new tools can produce an initial base forecast in two hours. They also facilitate evaluating additional business sce- narios with small additional investments of time and energy. The integrated approach also helps to stan- dardize the forecasting methodology and to make the forecasting process both systematic and repeatable compared with the old methodology. Considering the high attrition rate in this profession, this is especially useful during knowledge transfer from forecaster to forecaster.

Diverse plans have been set for continuously improving forecasting of product transitions. Real- izing and measuring the theoretical predictions for manufacturing cost saving is also useful. Expansion and refinement of the theory as well as the use of the new-product forecast model across broader sets of Intel products will continue to generate improved forecasts and to streamline the overall busi- ness processes.

Appendix A Proposition 1. Combining forecasts of different diffu-

sion models by using weights that are inversely propor- tional to their forecast variances yields a combined forecast variance that is smaller than forecast variance of each indi- vidual diffusion model.

Proof. Let K be the set of different diffusion mod- els that are used in forecasting (k ∈ K). Because the combined forecast is a linear combination of indepen- dent normal random variables �Xk�T +��, it is also nor- mally distributed with mean

∑ k∈K wk · �Xk�T +� ��T ��

and variance ∑

k∈K w2 k · �2k , where wk is the weight

assigned to model k’s forecast by the combination method. Note that the combined forecast’s variance is

�2c = ∑ k∈K

( 1/�2k∑ i∈K 1/�2i

)2 ·�2k =

∑ k∈K

1 �2k · �

∑ i∈K 1/�2i �2

= 1∑ i∈K 1/�2i

< �2k ∀k ∈K� �

Proposition 2. The variance of the (estimates for) pos- terior distribution is smaller than or equal to the variance of the (estimates for) prior distribution. Furthermore, the variance (of the estimates) asymptotically approaches zero as the number of leading indicators (m) increases, provided that each leading indicator is an unbiased estimate of actual data.

Proof. The prior distribution for Xk�T + �� is N� �Xk�T + � � ��T ��2k �; the sampling distribution is obtained from leading-indicator-based projec- tions, which can be viewed as observations that are independently and identically distributed with respect to N� �Xk�T + � ��j�T +L�� 2k �. If we simplify�Xkj�T + � ��j�T +L�� by �Xkj , and Xk�T + �� by Xk,

according to the Bayes theorem, the posterior proba- bility density function for Xk�T + �� can be obtained from the following formula:

p�Xk � �Xk1� � � � � �Xkm�= p� �Xk1� � � � � �Xkm �Xk�p�Xk�∫ p� �Xk1� � � � � �Xkm �Xk�p�Xk�dXk

�

After substituting the probability density functions of prior and sampling distributions in the above formula, the variance of the posterior distribution is found as

��2k = �2k ��2k

m�2k + ��2k � �

Aytac and Wu (2008) give more detailed proofs.

Appendix B

Algorithm (Integrated new-product forecasting) Input at time T : • Actual demand observations ��T � = �X�1�� X�T ��.

• Leading indicators l1� � � � � lm. • Diffusion models k ∈K.

begin For each diffusion model k ∈K, do: begin {�K� passes} Estimate parameters for diffusion model k by fitting demand observations ��T �.

Project a demand series from �T + 1� to �T + �� using parameters fitted for model k;

Add the demand series to the prior distribution. For each leading indicator li� i ∈ �1� � � � �m�, do: begin {�m� passes} Use leading indicator li to extend

��T � by Li periods; Estimate parameters for diffusion model k by fitting data ��T +Li�.

Project a demand series from �T +Li� to �T + �� using parameters fitted for model k; add the demand series to the sampling distribution.

end; {�m� passes} Perform Bayesian updates using the prior distribution and the sampling distribution from above to obtain the posterior distribution for model k.

end; {�K� passes} Combine the �K� posterior distributions to obtain final forecast. end;

Appendix C Procedure. Unbias a leading indicator. Step 1. Regress the time series of past actual

demand onto the time series of past leading indi- cators to obtain the extent of bias in the leading- indicator data. At the beginning of time t + 1, let X1�X2� � � � �Xt be the time series of the demand data realized, and let I1� I2� � � � � It� � � � � It+k� � � � � It+L be the time series of leading indicators observed at t + L, where L is the time lag between the realization of product demand and the collection of leading indi- cators for each point t. Linearly regress the t actual demand onto the t leading indicators to get the fol- lowing relationship: Xt = +! · It . Step 2. The relationship established in Step 1 is then

used to unbias the leading-indicator data for future periods. Let I ′t+k be the unbiased leading indicator for future period t+ k; then I ′t+k = +! · It+k.

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