Clickstream Data and Inventory Management: Model and Empirical Analysis

We consider firms that feature their products on the Internet but take orders offline. Click and order data are disjoint on such non‐transactional websites, and their matching is error‐prone. Yet, their time separation may allow the firm to react and improve its tactical planning. We introduce a dynamic decision support model that augments the classic inventory planning model with additional clickstream state variables. Using a novel data set of matched online clickstream and offline purchasing data, we identify statistically significant clickstream variables and empirically investigate the value of clickstream tracking on non‐transactional websites to improve inventory management. We show that the noisy clickstream data is statistically significant to predict the propensity, amount, and timing of offline orders. A counterfactual analysis shows that using the demand information extracted from the clickstream data can reduce the inventory holding and backordering cost by 3% to 5% in our data set.


Introduction and Related Literature
Recent Internet clickstream tracking technology has generated the fast growing practice of web analytics and extensive ongoing research in academia. Indeed, the Internet has changed the way business works by providing new information and distribution channels for both firms and customers. Customers can readily obtain product information online without physically visiting a firm.
Firms can use clickstream tracking technology to see in real time who is visiting their websites and analyze detailed clickstreams to learn more information in advance.
Clickstream tracking allows firms to "learn about customers without asking" (Montgomery and Srinivasan 2003), but the associated academic research has been largely focused on online shopping and e-commerce: Montgomery (2001) shows that quantitative models that are commonly used in brick-and-mortar distribution channels prove to be useful in optimizing the use of clickstream data. The associated literature is extensive, see e.g., Johnson et al. (2003), Moe and Fader (2004), Montgomery et al. (2004), Sismeiro and Bucklin (2004), Van den Poel andBuckinx (2005), Hui et al. (2009) and references therein. This literature is essentially about the marketing benefits of clickstream tracking because e-commerce websites serve primarily as sales channels. Clickstream tracking allows e-commerce firms to get accurate readings of the efficiency of their websites, quickly usher a visitor (referred to as "she" throughout the paper) who is about to purchase an item to a high-speed server, identify target visitors to show pop-up coupons, and so on.
In contrast to e-commerce settings, we investigate "non-transactional websites" that serve predominantly as a product catalog while orders are taken offline. Many B2B settings as well as some B2C settings fall in this category. Specifically, this study stems from our interaction with a U.S. manufacturer of industrial products, hereafter referred to as "the company." The company makes high-end roll-up doors that are customized for industrial and commercial buildings with regards to size, type of material, type of environment, etc. The doors can go into new buildings or can replace older doors. Prices for a door range from the thousands to tens of thousands of dollars.
Like many others, the company provides current and potential customers with company, product, and contact information on its website. However, the website is non-transactional and the company sells its products offline, either direct or through dealers. The company hires the services of a web analytics firm that specializes in clickstream tracking to help demand forecasting, procurement and inventory planning.
Our study focuses on the operational benefit of clickstream tracking by investigating its use as advance demand information for procurement, production and inventory planning. We are interested in how, and to what extent, clickstream data from non-transactional websites can improve demand forecasting for inventory management. In particular, in this setting of a B2B business with non-transactional informational websites, we address the following research questions: (1) How can we use clickstream data in inventory management? This requires a tactical model that explicitly incorporates clickstream data in operations management. (2) How can we identify the statistically significant clickstream data and prediction functions (needed in the model) and improve the demand forecast? (3) How large is the operational value of using the advance demand information from clickstreams to reduce inventory holding and backordering costs in our setting?
We believe these questions are timely and important for several reasons. The recent fast-growing research using clickstream data has already demonstrated the great interest and importance for ecommerce firms. The same applies to offline-selling firms. Understanding consumer online browsing behavior and its value helps firms make investment decisions regarding the adoption of clickstream tracking technology. Manyika et al. (2011) report that "big data-large pools of data that can be captured, communicated, aggregated, stored, and analyzed-is now part of every sector and function of the global economy." Clickstream tracking has allowed individuals around the world to contribute to the amount of big data available to companies. Our study examines the potential operational value that clickstream data, an important type of big data, can create for companies and seeks to illustrate and quantify that value. In a concrete setting of the company, we show that using the information extracted from the clickstream data can reduce the inventory holding and backordering cost by 3% to 5% in many representative parameter scenarios. The model and empirical methods we use in our study may be useful for other companies that aim to exploit big data to gain competitive advantage.
The clickstream data and sales data we study has significant differences from the data from ecommerce stores studied in the literature because the company website is non-transactional. While it has been confirmed in the literature that online click behavior is correlated with purchasing behavior in e-commerce settings, it is much less clear whether such correlation persists in nontransactional settings because customers do not have to visit the website to make a purchase. This procedural separation reduces the predictive power of web visits to forecast purchase orders if there is any statistical relationship between them at all. It is reported that e-commerce sales only account for 1.2% of all retail sales. 1 Hence, the vast majority of commerce still is executed offline and thus our research setting addresses a larger part of the economy beyond e-commerce.
Due to the procedural separation, non-transactional websites provide the opportunity for firms to react. Clearly, in an e-commerce setting like Amazon, the time lag between clicks and orders could be on the order of minutes, too short to adjust operational plans. The longer time separation between clicks and orders has an important benefit: If it exceeds the production or procurement lead time, the firm can respond to changes in advance demand information. Matching supply with demand is one of the main issues for operations management. There is a vast body of literature modeling advance demand information; see, for example, Hariharan and Zipkin (1995), Raman and Fisher (1996), Chen (2001), Gallego andÖzer (2001Gallego andÖzer ( , 2003, Özer and Wei (2004), Tan et al. (2007), Wang and Toktay (2008), and Gayon et al. (2009).Özer (2011) provides a comprehensive literature review. All these papers assume that advance demand information is available and study how to use it in inventory management. On one hand, our study is in the same spirit of, and complementary to, this literature by introducing a practical decision support model that endows classic inventory management with clickstreams as a flow of advance demand information. On the other hand, our study is the logical precedent: To what extent can advance demand information be obtained from clickstreams? Although the value of advance demand information is well established and understood 1 http://www.ecommercetimes.com/story/19145.html?wlc=1292379670, Retrieved on December 08, 2012. theoretically, research on how advance demand information is obtained in practice and its empirical evidence seems largely absent in the operations management literature.Özer (2011) offers several examples of obtaining advance demand information in practice such as flexible delivery at the time of ordering, ordering customized products, and advance selling. All these practices share the same feature that advance demand information is obtained at the time of customer ordering. Clickstream data, in contrast, provides advance demand information in a completely different way: First, it can be unrelated to customer ordering. Second, such information can be obtained well before customer ordering. (For example, the earliest lead time in our data set is 438 days before a customer actually placed an order and the mean time is around 90 days.) Hence, this kind of demand information can be truly "advance." More importantly, such information is obtained "without asking" customers, which is also called "inferring" (Fay et al. 2009). Our empirical study of this novel information technology shows that clickstream data is useful for operation managers to predict demand and helps firms "do the right thing at right time in right quantities." Our work is also related to recent empirical study in the information systems literature of using keyword search and social mentions to predict future events, based on the idea that what people are searching for today is predictive of what they will do in the future (cf. Asur and Huberman 2010, Goel et al. 2010, Joo et al. 2011. Our research shares the same theme in spirit in that we all demonstrate the promise of using online data to forecast future consumer demand.
While their studies are typically at the aggregate level using public data, our study shows that an individual firm can actually exploit its private data from click tracking and directly translate it to profit.
The main contributions and findings of the paper are as follows: 1. We introduce a practical dynamic decision support model that augments the traditional inventory management with clickstreams as additional state variables in the dynamic programming formulation for demand forecasting.
2. We conduct an empirical study to identify i ) which clickstream variables are statistically significant for demand forecasting, ii ) how to include them into the state variables of the dynamic model, and iii ) to estimate the extent to which utilizing the clickstreams creates operational value.
We find that customer clicking behavior is a statistically significant predictor of the corresponding offline purchasing behavior, in terms of not only ordering probabilities and ordering amount (in monetary value), but also ordering timing (lead time).
3. Through a counterfactual study, we show that using the information extracted from the clickstream data can reduce the inventory holding and backordering cost by 3% to 5% in many representative parameter scenarios. 4. To the best of our knowledge, this study is the first in the operations management literature that provides both a model and empirical evidence to demonstrate how the recent clickstream tracking technology can be used to improve operational decisions. Our study aims to stimulate future empirical and theoretical work in this practice-and data-driven field.
The outline of this paper is as follows. The next section presents a theoretical model to demonstrate how clickstream data can be used to improve demand forecasting and inventory management.
In §3, we empirically identify the clickstream variables that are significant for demand forecasting.
In §4, we quantify the operational value of advance demand information from the clickstream data using our model. §5 contains the discussions and limitations.

A Model of Using Clickstream Data in Inventory Management
We start by introducing a tactical model of using clickstream data in demand forecasting and inventory management that can serve as a decision support system in practice. This practical model endows classic inventory management with clickstreams as a dynamic flow of advance demand information. In §3, we will empirically identify relevant model variables. This model will also be our tool for estimating the operational value of clickstream data in §4.
We explain how to use clickstreams in inventory management first in a single-period newsvendor model, and then in a multi-period dynamic model. In a single-period model, before the company's production or procurement decisions, clickstreams are observed to predict demand. For each visitor i who clicked, the company can use clickstreams to estimate her purchasing probability P i ≡ f (X i ) for i = 1, 2, ..., where X i is a vector of independent variables including clickstream variables and f denotes a general prediction function. We shall empirically specify both X i and f in the next section.
Assuming all the visitors are independent decision makers, a simple combinatorial calculation then yields the predicted distribution of the total demand that can be used to derive the optimal inventory for this single-period newsvendor model.
To explain how to use clickstream data in a dynamic setting, consider a discrete-time inventory control model endowed with clickstream data. Suppose there are T replenishment periods. In each period t, the company can observe the clickstreams for each visitor i who clicked in this period. To formulate the company's inventory control problem as a dynamic programming problem, we need a description of the company's operations.
Timing. At the beginning of each replenishment period t, the company first satisfies or backorders any realized demand D t and observes clickstreams of new visitors K t = (K 1,t , K 2,t , ..., K J,t ) that arrived between the beginning of period t − 1 and the beginning of period t, where J denotes the number of customer classes to be defined below. All the clickstreams observed up to the beginning of period t serve as imperfect advance information of the future demand. Then the company updates its demand forecast, and determines its ordering quantity q t for input (e.g., a key "patented part") which would arrive at the beginning of the next period. This cycle repeats, as depicted in Figure 1.
Extending the previous single-period model to a multi-period model introduces significant analytical complications for at least three reasons: First, the demand distribution in period t depends on what happened in previous periods. Second, visitors are heterogenous. Third, in addition to "purchasing" or "never purchasing," a customer now has an additional decision: wait and perhaps purchase later. The model has to keep track of the richness of the system dynamics. We adopt the following approach: (i) To account for visitor heterogeneity while still retaining analytical tractability, we classify all visitors into J classes or categories. Within each class j, each visitor is homogenous, i.e., each visitor in class j who clicked in period t but had not clicked before has prior purchasing probability p j,t in period t for j = 1, 2, ..., J and t = t + 1, t + 2, ... Choosing J is at the company's disposal. Intuitively, it is natural to assume that visitors who share the same value of the predictors X i constitute a class. Similar to the single-period model, the purchasing probability p j,t can be estimated using P i ≡ f (X i ). The only difference is that we will use the empirical distribution of the click lead time to predict when (i.e., in which period) a purchase will occur. (ii) We assume that each visitor in class j has the prior probability γ j,t in period t for t = t + 1, t + 2, ... of never purchasing the product. Clearly, 1 − p j,t − γ j,t ≥ 0, where the equality always holds in the single-period model but not necessarily in this model for the third reason we pointed out. Non-buyers in period t are defined as visitors who will never purchase the product in any future period t ≥ t. In a single-period setting, non-buyers are the customers who do not purchase. Hence, non-buyers include what Moe and Fader (2004) define as "hard-core never-buyers." However, in a dynamic setting non-buyers include more than those hard-core never-buyers. It is possible that a customer is interested in purchasing the product initially, say at period t 1 , but becomes a non-buyer at period t 2 > t 1 . Using Moe and Fader (2004)'s term, non-buyers in period t include the "hard-core never-buyers" in all the future periods t ≥ t. Estimating these probabilities for non-buyers is trivial for the single-period model given the equality relationship, but can be difficult in the multi-period model. We will demonstrate how to indirectly estimate them in §4.
We are now ready to describe the system dynamics analytically. Our approach allows for a classby-class analysis. Recall that K j,t denotes the number of new visitors of class j in period t, meaning Description of the Dynamic Programming Model the visitors of class j who visited the website in period t but never visited the website before period t. This definition precludes the "double counting" as will become clear in the flow equation. Notice that we count "visitors" rather than "clicks" given that a visitor typically clicks multiple times. We will call these K j,t visitors potential buyers. For brevity, we shall drop the class subscript by writing K t ≡ K j,t wherever no confusion arises. They represent potential future demand, as they may convert to real buyers in future periods. For analytical convenience, we assume that each visitor buys at most one unit of the product. This assumption is reasonable in our setting of a durable industrial product. Let the random variable Z t+1 ≡ Z j,t+1 denote the total number of potential buyers of class j at the beginning of period t + 1, i.e., the cumulative number of customers of class j who clicked up to period t + 1 and are still part of the potential buyers for future periods, i.e., they have not purchased or have not been identified as non-buyers yet. Then we have the dynamic flow equation as follows: which is the previous realized number z t , plus the number of new potential buyers K t+1 from the clickstreams observed in period t + 1, minus the demand D t+1 and non-buyers L t+1 . The non-buyers may not be identifiable from clickstreams, in which case L t+1 = 0. Typically companies can indirectly estimate the probability that a customer never purchases from clickstreams.
Non-buyers can be identified in cases where the company can obtain some offline information by communicating with the visitors, in which cases the firm should exclude non-buyers from the clickstreams according to equation (1). Notice that the terms in lower case denote the realizations of general non-Markovian model is analytically challenging. From now on, we will work with a Markovian model by assuming that all z j,t potential buyers have the same purchasing probability p j,1 and never-purchasing probability γ j,1 for any period t ≥ 1 given that they did not purchase in previous periods. This assumption implies that p j,t = p j,1 (1 − p j,1 − γ j,1 ) t−1 and γ j,t = γ j,1 (1 − p j,1 − γ j,1 ) t−1 for t ≥ 2. Hence, we can drop the dependence on H t , and the vector Z t suffices to fully describe the system in period t.
The Markovian assumption allows us to formulate the company's inventory management problem as a finite-horizon discounted dynamic programming problem using x, the inventory position, and z, the vector of the cumulative number of potential buyers in each visitor-class over the future. Let V t (x, z t ) denote the minimum expected discounted cost at state (x, z t ) starting from the beginning of period t to the end of the planning horizon. We assume that any remaining inventory is salvaged with per-unit revenue equal to the per-unit procurement cost c and any outstanding backorders are satisfied with per unit cost of c at the end of the planning horizon. Then we have 2 For t = 1, 2, ..., T , we have the Bellman equation: where β 0 is the usual time discount factor and y is the order-up-to level as the company's decision variable. This formulation is motivated by Gallego andÖzer (2001),Özer (2011) and references therein where they include an observed part of lead time demand in classic inventory models (cf. Porteus 1990). 3 While our inventory model endowed with clickstreams is novel, the dynamic flow of advance demand information z extracted from these clickstreams K essentially provides observable lead time demand in spirit. Using a similar technique as Gallego andÖzer (2001), one 2 This assumption is also made for technical convenience so that we have the unified expression regardless of the sign of the inventory level x. In all other non-terminal period t < T + 1, the backorder cost b per unit of time is different from the production cost c. Our assumption is conservative (given c < b), hence provides a lower bound for the operational value of clickstreams.
3 Notice that our model can be adapted to capture demand from customers who never visited the website. Suppose there is a separate demand Dt that does not come from the clickstreams in each period t, then our dynamic programming formulation becomes can prove that the optimal inventory policy is a "clickstreams-dependent" base stock policy, where the optimal order-up-to levels are y * t (z t ). All the parameters required to evaluate the cost saving due to using clickstream data in §4 will be estimated from the data in our subsequent empirical study.

Empirical Analysis
In this section, we will empirically demonstrate that clickstreams are indeed useful to estimate the purchasing probability P i = f (X i ) for i = 1, 2, ... in our model in §2. To this end, we first discuss our data sets and variable definitions, then specify the general prediction function f as a simple logit or a random-coefficient logit regression equation, and finally show which click variables among X i are statistically significant.

Background, Data Source and Characteristics
The company is in the Midwest of the USA and has some smaller rivals in neighboring states.
Consumers can freely shop around and visit websites of multiple similar providers. The website provides comprehensive information to customers; however, due to the customized nature of the product, committing to purchasing is done typically over the phone either through the company directly or through dealers.
The company's website provides the company profile information, product specification information based on different industries, contact information for the company and its dealers, and a webpage where customers can send an email to the company. However, price is not shown on the website, and is communicated offline. Customers can acquire information from a few other channels such as phone calls, word of mouth, and brochures from industry conferences. Visiting the website is not a prerequisite for purchasing the product. We do not have an exact percentage of customers that visit the website, since some customers may visit through private computers or their internet service providers that prevent identity identification. 4 Hence, this study focuses on only those identifiable customers who ever visited the website.
Let us discuss the current inventory management at the company we studied. The company has to keep inventory for a "patented part" (required for assembling an end product) that is supplied from Europe with a transportation lead time of three months. The company procures this component every three months, which we model as one "period" using Figure 1 in §2. The supply lead time is one period. The "demand lead time" (Hariharan and Zipkin 1995, Gallego andÖzer demand is satisfied in less than two weeks. (The company can assemble-to-order within two weeks if all required components are available.) The challenge for inventory management is that the supply lead time is much longer than the demand lead time, and that backordering customer demand is costly. The intangible adverse effect of the future loss of customer goodwill due to backordering is estimated by managers at around five times of the per unit procurement cost.
We use two data sets of the company that sells high-end roll-up doors in North America. The In our setting, web visitors do not identify themselves because they do not purchase and reveal contact or payment information online. The firm can only learn each visitor's identity through her IP address. In addition, we study a business-to-business (B2B) setting where the customers themselves are firms. This has benefits and drawbacks: About 82% of the visits in our clickstream data come from a company-registered IP address so that the visitor is easily identified with a company.
Then we can manually match clickstream data with sales data to investigate the correlation between clicking behavior and ordering behavior. The other 18% of visits come from large service provider IP addresses (e.g.,@comcast.com, @cox.com, @att.com)-perhaps visits from home-computers or cellular devices, which prevents the identification of the visitor and the matching with order data.
These visits are deleted from the data set. While one expects corporate online browsing behavior to be less frivolous than that in a business-to-consumer (B2C) setting, another challenge is that we cannot identify the various individuals who are involved in the purchasing process. Only IP addresses are tracked, typically at the level of a firm's computer center/connection to the Internet but not at the level of individual computers inside the firm. Therefore, the unit of analysis in our data is a firm and all visits from a firm are aggregated and indistinguishable from one visitor. In addition, a potential customer may also browse the website from her home computer(s). Thus, our clickstream-order data is more noisy than in e-commerce.
In the clickstream data, the unit of data corresponds to a customer who clicked and has the following fields: the name of the customer identified from her IP address, the clickstream which is a summary of the recorded click behavior that includes the time of visits/clicks, cumulative visits (i.e., the cumulative number of visits), average time stayed online per visit, average number of Each unit in the sales data records the customer name, the ordering amount (in U.S. dollars), and the time of ordering.
Before statistical analysis could be commenced, several preprocessing tasks were executed. First, we cleaned the clickstream data by deleting unidentifiable clicks. The second preprocessing step deleted some organizations that we excluded in our study such as universities, public organizations, etc. In the ordering data set, indeed, no universities or public organizations ever purchased any product from the company. Their visits may have been research-inspired.
Third, as discussed in the introduction, we aggregated all the visitors within a company as a single visitor by their company names even if a company has multiple locations. 5 The reason of doing this is simply because of the limitation in our information availability, i.e., the clickstream data only shows the company names, not the persons who actually visit.
Finally, we matched the clickstream data set with the sales data set together by the firm/customer names. We have 9694 visits in our clickstream data set after preprocessing and matching with the sales data. 6

Variable Definitions
We use the (binary)  avoid any multicollinearity problem. We also include webpage-specific variables to capture more individual heterogeneity. In our setting, the contact information pages appear informative in terms of predicting purchase propensity.
We have four different kinds of variables that comprise our explanatory variables. First, we have "general clickstream measures" which concern data measured at a rather general level of the clickstreams. They represent the information at the level of the session which is defined as a single visit to the website. Cumulative visits, defined as the cumulative number of visits, is among the most often used metrics in the e-commerce literature (cf. Moe and Fader 2004). Unlike typical e-commerce clickstream data, one characteristic of our clickstream data is that customers typically returned (if they did return) to the website after some time in the order of "days." For the few cases of multiple sessions within a day, we aggregated these sessions within a day as one visit in our setting. Average time length per visit is defined as the total time a visitor stayed on the website divided by cumulative visits. Average number of pages per visit is defined similarly.
Second, we have "detailed clickstream measures" that indicate whether some specific pages were visited or not. There are essentially two categories of web pages on the firm's website: one category of pages presents product information while the other category shows the contact information if visitors want to contact the company or distributors, or if visitors want to become distributors.
Intuitively, we expect visits to pages of contact information to be more informative. Indeed, there is a lot of variation in terms of whether these contact-information pages were visited or not and we use indicator variables to account for this variation. In particular, the variables contact me, contact distributor, become distributor, reach thanks page keep track of detailed clickstream information.
(industrial door) with low order frequency per buyer for whom the matching of identified clicks with orders was easy.
Additionally, there is no censoring problem in the matching given that we have the entire sales records for matching with the clickstream data.
Third, given that new customers may derive more informational value from web browsing than existing customers, we have "historical order information" about each visitor and the dummy variable historical order is used to indicate whether this is an existing customer (i.e., a web visitor who has purchased before visiting the website). Historical order amount denotes the cumulative amount in U.S. dollars of previous orders.
Finally, some "company demographics variables," i.e., industry control variables, are at our disposal. We include company industry type variables to control for the heterogeneity in the latent probability of ordering the products. The variables, chemistry, food, distribution, manufacturing, pharmaceutical, transportation, and automobile are used as controls for industry types. Obviously there are companies not belonging to any of these industries. It should be recognized that these control variables take into account the heterogeneity among visitors to some degree, given that all companies in the same industry are treated as homogenous. Given that our data does not allow us to pick up the customized features to individual customers, we can only treat the products as homogenous. However, the industry type controls for the heterogeneity to a certain degree. Table   1 presents the summary statistics of our data after preprocessing. From Table 1, we can indeed observe significant variations among the ordering behavior variables.

Econometric Model
We We refer readers to Hui and Fader (2009) for a comprehensive literature review. The closest to ours is the seminal work by Moe and Fader (2004) who propose a conversion model and compare with several alternative models such as the logit model, duration models, Beta-Binomial, and historical conversion rates. To facilitate the comparison of the performance of the logit model versus the alternatives, we actually used their data 7 , and found that the logit model can perform "better" than the conversion model, even using their model evaluation criterion in their setting.
To stay focused on the operational value of clickstreams, we relegate the detailed analysis to the Online Supplement. Moreover, as argued elsewhere (Van den Poel et al. 2005 for instance), the typical benefits of logit modeling are: (i) Logit modeling is well-known, simple (due to its closedform expression) and extensively used in the literature; see, for example, Cachon et al. (2008), Jain (2005, 2006), Train (2003) and Van den Poel et al. (2005). (ii) The ease of interpretation of logit is an important advantage over other methods. For example, the logit model can be interpreted as choices made by boundedly rational decision makers (cf. Huang et al. 2012 and references therein). For justifications and limitations of logit models, readers are referred to Cheu et al. (2009). (iii) Levin and Zahavi (1998) have shown that logit modeling provides good and robust results in general comparison studies.
We thus adopt a logit model as our prediction function f , which stems from the random utility model where we assume customer i's outside option has normalized utility zero while purchasing yields utility: where X i = [Y i , Z i ] is a vector representing customer i's observed attributes or characteristics.
Conceptually and purely for pedagogical purposes and convenience, we can decompose the customer attributes to two categories: The vector Y i includes its general attributes, such as its economic characteristics, the industry it belongs to (which affects the relative usefulness of product), its size, the experiences/history of using the product and so on. In our setting, Y i includes a set of variables to capture the customer's historical ordering behavior and a dummy variable to denote which industry it belongs to.
The vector Z i includes the attributes of customer i's customized needs; for example, a customer may need the product specialized to its business setting, and this kind of product may only be some particular firms' specialization and not others'. In our setting, Z i is "approximated" by a set of clickstream variables defined in the previous section. To incorporate (pick up) potential nonlinear effects, we also use squares of these variables. The vector Γ denotes the coefficients of X i and is to be estimated.
The error terms ε i represent the un-explained variation from X i . Under the assumption that the error terms in (2) are independently and identically distributed with the type-I extreme value distribution, the probability P i that customer i purchases from the firm is given by the logit demand formula (McFadden 1974(McFadden , 2001: The simple logit model has limitations in our setting in that all visitors within each industry share the same coefficients for click variables, although we used demographic variables to take into account visitor heterogeneity.
among the coefficients of click variables even within each industry by adopting a random-coefficient logit model. 8 Specifically, the utility U i for individual i can be written as U i = β i X i + i , where β i is a vector of coefficients that is unobserved for each individual i and varies randomly over each individual representing each individual's "tastes," and i is an unobserved random term that is

Hypothesis Testing
In this subsection, we conduct hypothesis testing to investigate how the clickstream data can be useful for demand forecasting. Then, we present the empirical results.
The first hypothesis is to test whether the clickstream data can be used as advance demand information: HYPOTHESIS 1: Visitor online behavior, as defined by the general clickstream measures and the detailed clickstream measures, is significantly correlated with offline ordering probability/propensity. Demand/order lead time plays an important role in operations management. While past research almost exclusively focused on predicting purchase probabilities, we also investigate whether we can use clickstream data as advance demand information to predict the timing of purchase. Knowing the order lead time (i.e., the time difference between the time of ordering and the most recent time of clicking) is beneficial for cost reduction in operations management. From a psychological 8 Random-coefficient logit models generalize the standard logit model by allowing coefficients to vary randomly over individuals rather than being fixed. The models do not exhibit the restrictive independence of irrelevant alternatives (IIA) property of the standard logit. As shown in McFadden and Train (2000), any pattern of substitution can be represented arbitrarily closely by a random-coefficient logit model. Random-coefficient logit models can take different forms in different applications, and their commonality arises in the integration of the logit formula over the distribution of unobserved random parameters (Train andRevelt 1998, Train 2003).
perspective, a more frequent visitor would be more anxious to place orders to satisfy her need.
Hence, we want to test our second hypothesis: HYPOTHESIS 2: Order lead time is negatively and significantly correlated with cumulative visits.
We are also interested in whether click information is useful for predicting the ordering amount as well: HYPOTHESIS 3: Online clicking behavior is significantly correlated with offline ordering amount. Now we present our regression results. Table 2 shows the logit regression results. From the Wald test result, our logit regression model is significant at level 0.00%. Some of the general click variables and detailed page-specific variables are statistically significant, which indicates that we fail to reject HYPOTHESIS 1, i.e., visitor online click behavior is indeed providing the firm useful information to predict future ordering probabilities.
We find that cumulative visits is positively significant at 1% level. More frequently visiting the website indeed reveals higher probability of ordering.
Table 2 also shows that the detailed click variable, contact distributor, is significant for predicting ordering probability. We conclude that detailed click behavior, besides general click behavior, is also useful for predicting ordering probability.
Intuitively, how long a customer has been searching may affect or reflect her purchasing propensity. We create a new age factor variable to keep track of how long a customer has been searching: Searching time length. This variable measures the time difference between the most recent time of clicking and the first time of clicking (in terms of days) as a proxy for the elapsed time in product searching. As shown in Table 3, it is not statistically significant (P-value=0.786). This finding may appear surprising. However, it might be explained as follows: Cumulative visits measures the depth of searching, which is indeed statistically significant. Searching time length measures the time breadth of searching. A customer may spend a long time in searching without visiting frequently; or she may visit frequently within a short period of time. In our setting, the data suggests that the former behavior tends to suggest this customer is more likely to purchase, i.e., visiting depth rather than visiting time breadth matters more. Table 4, not only does cumulative visits convey useful information about ordering probability, it also provides relevant information about the timing of future orders. Indeed, if a visitor frequently visits the website, this visitor may be anxious to buy some products in the near future. Hence, her order lead time may be shorter than others', ceteris paribus. Table 4 shows the Tobit regression results using order lead time as the non-negative dependent variable and all the other variables as explanatory variables, from which we can see cumulative visits and square of From Table 5, we can see cumulative visits, square of cumulative visits, contact distributor, and historical order amount are significantly and positively associated with order amount. 9 Intuitively, more expensive ordering is associated with more frequent visits. In sum, we can use cumulative visits to predict both ordering probability, amount and the timing. These empirical findings confirm that clickstream data provides advance demand information.

More interestingly, from
Table 2 also shows that the average time length stayed online is not significant for predicting ordering probability. This finding is somewhat counterintuitive. Suppose we see two visitors online,  one staying very long with just a few visits, and the other visiting many times, but with short staying time each visit. Who has a higher probability of ordering ceteris paribus? Our results simply suggest that the second visitor is more likely to order in the future. However, as will be discussed, for the sub-population of new customers, average time length is significant, as shown in Table 3. Table 2 shows the results for new customers and existing customers separately. One implication is that these two classes of customers indeed should be treated differently, in terms of linking their click behavior to their ordering probability. For new customers, average time length stayed online is significant to predict ordering probability. In addition, the relationship takes a quadratic form, i.e., the positive relationship trend stops at some critical point above which the relationship changes to be negatively significant. This finding confirms our intuition: Staying long online is not necessarily a good sign. For existing customers, however, there is no such significant relationship.
The reason could be explained as follows: Compared to new customers, existing customers have already ordered some products before, and thus may already know enough information about the firm and the products. Hence, they probably do not need to spend much time online to collect information for purchasing decision-making. Existing customers may have different motivations to visit the website. While new customers visit for information searching, existing customers may visit to get after-sales service. We can also see that cumulative visits is just marginally significant (significant at level 10%) from Table 2.
To include more customer heterogeneity, we also estimate the random coefficient logit model.
Assuming the coefficients of click variables are normally distributed, we conduct the simulated maximum likelihood estimation using KNITRO-MATLAB and report the results in Table 6. The click variables are jointly significant, suggesting that click information indeed provides useful information for predicting purchase probabilities even if visitor heterogeneity is taken care of. Furthermore, we have the same signs for these click variables as in the standard logit. From Table 6, we can also Yes Yes Notes. Standard errors are reported in parentheses. * p < 0.10; * * p < 0.05; * * * p < 0.01. see that there is indeed some heterogeneity among visitors, but such heterogeneity is not significant for the majority of the click variables such as cumulative visits.
To further examine predictive validity of the clickstream data for demand, we also estimate the logit model using only the randomly selected first half of the data set. Then, we apply the estimated regression equation to the holdout sample (i.e., the second half of the data) and obtain the predicted average purchasing probability (also called conversion rate) 15.61%. Lastly, we compare the predicted average purchasing probability with the actual purchasing probability 14.65%, and get the prediction error in percentage: 6.49% (=(15.61%-14.65%)/14.65%). This demonstrates that the predictive power of the clickstream data is fairly good.
We highlight a few findings that are novel compared with those in e-commerce: First, we include more detailed webpage-specific variables which are typically absent in the e-commerce literature (cf. Moe and Fader 2004), and we find that visiting the contact-distributor page or not is useful for predicting future demand. Second, we find differences between new customers and existing customers (e.g., average time length is significant for new customers but not for existing customers).
Third, we have the ordering amount information which is also absent in the literature.

Operational Value of Clickstream Data
In the previous section, we have provided affirmative statistical evidence that the clickstream data is useful for operational forecasting in terms of advance demand information. In this section, we will discuss what predictors from the clickstream data companies should track, and evaluate the operational value of the clickstream data based on the theoretical model in §2 and empirical analysis in §3.
Which predictors should be tracked? Although the findings here are only for a specific company, the methods do generalize. In general, companies should first conduct a similar empirical study and estimate the statistical significance of both general click measures and detailed click measures as we did. This will reveal which predictors are most statistically significant for the specific setting during that specific time period. (Indeed, if seasonality is perceived to be significant, the empirical study and any parametric estimation should be performed repeatedly per season.) For example, in our setting, cumulative visits, average time length and contact distributor are three key predictors from Table 2. This suggests that the company we have interacted with should definitely track these measures.
To illustrate how our approach and the dynamic flow equation (1) works, we now discuss how the operational forecasting process can be simulated based on our data sets. As a simple heuristic and representative example, we classify the visitors based on whether their cumulative visits is more than 4 or not, given that those visitors who visited less than 4 times have a negligible purchasing probability on average according to our data. Hence, we effectively assume J = 2 classes: Visitors who visited the website less than 4 times belong to the first class j = 1 having p t = 0 for any t, and all the others are in class j = 2 having positive p t to be estimated. 10 We can thus omit the "class subscript" j = 2 in the notations for the sake of brevity. We follow two steps: (a) In each period, the new potential demand K from the new clickstreams follows a Poisson distribution 11 with expectation µ K which is estimated from the clickstream data. Given that the total number of visitors from the data during the one year and a half is 325, the average number of new visitors per period (i.e., three months) is approximately µ K = 50. (b) We directly estimate purchasing probabilities p n and indirectly obtain never-purchasing probabilities γ n from the clickstream data using the empirical distribution of the click lead time: The mean purchasing probability for the visitors is 0.1046. There are 69/87 = 79.3% percent of visitors whose click lead time is less than two periods based on the clickstream and sales data. Hence, all new visitors clicking in any given 10 We also did a cluster analysis using the k-means method without a priori committing to a belief of the number of classes. Interestingly, the optimal cluster number turns out to be 2, which, to some degree, justifies our heuristic choice in this particular setting. 11 A Poisson distribution is frequently used in modeling customers arriving at a counter or call centre. Suppose there are N customers in the market, and each customer visits the website with probability p. Then the number of visitors to the website would follow the Binomial distribution B(N ; p). In our setting, N is large and p is small (and so the expectation µK ≡ N p is of intermediate magnitude). Then the distribution can be approximated by the Poisson distribution with mean µK (by the "Law of Rare Events"). period will purchase with probability p 1 = 0.1046 * 79.3% = 0.083 in the next period. Based on the assumption p t = p 1 (1 − p 1 − γ 1 ) t−1 , we have p t = αp t−1 for t = 2, 3, ..., where α ≡ 1 − p 1 − γ 1 . Hence, we can use an ordinary least squares regression (OLS) to estimate α based on the empirical distribution. We estimated that α = 0.129. Therefore, p 2 = 0.129 * 0.083 = 0.011, p 3 = 0.129 * p 2 = 0.001, p 4 = 0.129 * 0.001 = 0.0002 and γ 1 = 1 − 0.083 − 0.129 = 0.788.
Let us apply the model to the current inventory management at the company we studied. As aforementioned, the company keeps inventory for a "patented part" (required for assembling an end product) that is supplied from Europe with a transportation lead time of three months. The company procures this component every period (i.e., three months) using Figure 1 in §2. The supply lead time is one period, and the demand lead time is zero.
Before quantifying the operational value in terms of cost reduction, we can first demonstrate how clickstream data improves operational forecasting by reducing demand uncertainty. We compare the variance of demand when clickstream data is utilized versus when it is not. Without clickstream data, the company can only use its prior demand distribution. Let D L be the lead time demand without clickstream data utilized, then we have ED L = p 1 EZ and V ar(D L ) = p 1 (1 − p 1 )EZ + p 2 1 V ar(Z), where Z is the total number of potential buyers expressed in flow equation (1). Utilizing clickstream data, however, the company can update its demand forecast after observing clickstreams. Let D L1 be the lead time demand with clickstream data utilized, then ED L1 = ED L = p 1 EZ. Invoking the law of total variance, we obtain V ar(D L1 ) = E[V ar(D L1 (Z))|Z] + V ar[E(D L1 (Z))|Z] = p 1 (1−p 1 )EZ +p 2 1 (1−p 1 ) 2 V ar(Z). It is clear that V ar(D L1 ) < V ar(D L ). Using the estimated parameters from our data set, we computed V ar(D L ) ≈ 4.76 and V ar(D L1 ) ≈ 4.04.
Hence, clickstream data improves the "accuracy" of demand forecasting. However, to evaluate the operational impact of this improvement, we use the dynamic inventory control model presented in §2.
We used the following parameters: c = 80, h = 0.5c, b = 5c, T = 4 and β 0 = 0.95. We solved the dynamic programming problem based on backward induction, and we found that the annual expected cost reduction is 4.6% for these parameters. Given that these parameters are approximations, to test the robustness of the result with respect to the "accuracy" of these estimated parameters, we performed a numerical study by varying the parameters within a reasonable neighborhood of the values used earlier. Table 7 summarizes the results and suggests that the cost reduction is typically larger than 3%. 12

Discussions and Limitations
Our primary goal of this study is to show how, and to what extent, clickstream data from nontransactional websites can improve operational forecasting and inventory management. We first introduced a dynamic decision support model that includes clickstreams as state variables in inventory management. Second, we conducted an empirical study to identify which clickstream variables are statistically significant for demand forecasting and to estimate the extent to which including these clickstreams reduces operational costs. We found that clickstream data can be used to estimate ordering probability, amount and timing. We also found that advance demand information extracted from the clickstream data can reduce the inventory holding and backordering cost by 3% to 5% in many representative parameter scenarios.
Our study is motivated by practice and is aimed to guide better practice of clickstream tracking in operations management. Our model provides a practical framework to dynamically convert clickstream data into useful advance demand information for inventory management. In practice, firms should develop decision support systems using clickstream data by taking advantage of various statistical and computer science tools, such as data mining and artificial intelligence, to enhance the prediction from the regression equation (e.g., using more sophisticated prediction function f (X i )) and better extract advance demand information from the clickstream data.
Our findings must be interpreted cautiously given the limitations of our study: First, all our hypotheses are about "correlation" rather than "causality." Establishing the causality has been difficult in the literature, and we are not aware of any study that establishes whether clicking causes purchasing or whether it is vice versa. Our data does not allow us to establish such a causal relationship. That requires expensive field experiments for future research. Second, we only used the visitors who are identifiable in our clickstream data set, which can create biases for our empirical study. Companies should consider mechanisms to improve customer identification of clickstreams (e.g., use cookies, let customers sign in and provide more information, etc.). Third, considering the heterogeneity of visitors, our control variables are limited. For example, price is negotiated offline and such information is unobserved by us. While this is the best our data allows, we can take comfort knowing that the random-coefficient logit model further takes care of the heterogeneity to some degree. Fourth, we do not conduct time series analysis due to our limited observations within a short period of time. Availability of large-scale data sets for a long period of time would allow us to investigate the dynamics over time. Fifth, due to analytical tractability and data availability, we cannot incorporate multi-unit demand information for a customer. Hence, this study provides a lower bound for the operational value of the clickstream data. Finally, although our models and methods can be generalized and help build an integrated decision support tool to be applied to other settings of offline sales with informational websites, all the findings herein are based on the data from a particular industrial firm with a fixed period of visiting customers. We hope our study stimulates more research in this important, practice-driven and data-driven area.

Online Supplement for "Clickstream Data and Inventory Management: Model and Empirical Analysis"
This Online Supplement provides partial support and motivation for adopting the logit model in §3.3.
One of our motivations for exploring a visitor economic/behavioral model stems from studying the "conversion model" using clickstream data in Moe and Fader (2004) (from now on MF), a seminal paper of e-commerce clickstreams. Although the setting there is different from ours, we argue that our approach, i.e., the random-utility model, can perform "better" than the conversion model. This result should be treated as a byproduct of our study (which focuses on demonstrating and quantifying the operations value of the clickstream data in an offline setting). For clarity, we first briefly summarize their work, and then demonstrate how a logit model can perform better.
MF adopt the novel idea from Schmittlein and Morrison (2003), who use a "fraction" to model the success probability of in vitro fertilization (IVF). Specifically, Schmittlein and Morrison (2003) denotes the net effect of visits since last purchase, and τ ij denotes the purchasing threshold. MF assume that the vet visit effect, V ij consists of two components: a baseline propensity to buy, v i0 , that applies at every visit, and incremental effects, m ij that accumulate over all visits that have occurred since that last purchase. In a customer's first purchasing cycle, they have V ij = v i0 + m i1 + m i2 + ... + m ij for household i who has made j non-purchase visits. To accommodate different forms of heterogeneity, they assume that the baseline purchasing propensity v i0 is gamma distributed across the customer population with shape parameter r v and scale parameter γ. They also assume that the visit impacts and the purchasing thresholds vary across customers in accordance with a gamma distribution, such that m ij ∼ gamma(µ, γ) and τ ij ∼ gamma(r τ , γ). To take the evolving visiting effects into account, they assume V ij ∼ gamma(r v , γ) + gamma(µ 0 k 1 , γ) + gamma(µ 0 k 2 , γ) + ... + gamma(µ 0 k j , γ), where the parameter k ranges from zero to infinity and characterizes how visit impacts involve as customer familiarity increases.
To incorporate the evolving purchasing thresholds, they assume τ ij ∼ gamma(r τ exp{ψx ij }, γ), where r τ captures the initial purchasing threshold, ψ is a parameter that governs the magnitude and direction of the dynamic process, and x ij is the number of purchases that customer i has made, up to (but not including) visit j. Then, they derive the likelihood function, apply to the observed panel data, and find that their model fits the data better than existing simple models, such as the simple logistic regression. As they argued, ... model the probability of purchasing in each session as a function of: (1) the number of past visits (2) the number of past purchases (3) the number of visits since the last purchase (4) time elapsed (in days) since the last visit (5) time elapsed (in days) since the last purchase. The fit of the model (LL=-4367.79 and BIC=8791.55) is vastly inferior to that of the conversion model...     Note that we have limited information from the data set, given that no detailed click information such as which web pages are visited, etc., is provided. Hence, we question the appropriateness of simply aggregating or summing the past visits and purchases as "attributes" (explanatory variables). Intuitively, the visits and purchases may have a diminishing effect on purchasing as the numbers increase, and we can re-scale or discount the numbers to incorporate such effect to some degree. For example, we can use various functions of the number of visits or purchases to approximate the "attributes." We can easily pick up some discounting functions in our regression. Tables A-3-A-8 show some simple and readily found examples that are no worse than the conversion model in terms of the criterion, LL and BIC, used in MF. Our general two-stage approach would be: (1) Exploring: try different common nonlinear forms of raw data and do maximum likelihood estimation using the logit type model; (2) Exploiting: fix some parameters (to reduce the number of parameters) from the first-stage result, then do logit (or maximum likelihood estimation in general) using the explanatory variables from the first stage. This method can be better than, or at least no worse than the conversion model proposed in MF using their criterion. One of many advantages of using logit-type models is that it is a behavioral model coming from rational utility maximization.
As MF argued and we agree, the conversion model has some compelling features such as allowing the heterogeneity across visitors, heterogenous effects of visits and purchases, and non-stationarity of these effects. However, this model does not explicitly capture each visitor's underlying purchasing decision-making behavior. We know the probability of purchasing for human beings should be fundamentally different from the probability of IVF's success which is mainly determined exogenously out of human-beings' control. As we have shown, the simple logit model can perform as well as the conversion model in terms of LL and BIC if we use carefully-chosen explanatory variables, and the advantage for the logit model is that it is based on the commonly used random utility model, a behavioral model based on utility maximization.