Purchase Timing Decisions Research Articles

A Time Series Based Monitoring Methodology to Optimize Purchase Timing Decisions

Businesses as well as consumers utilize price comparison portals prior to purchasing. Usually such systems provide price time series, but the transformation of the embedded information to select an appropriate purchase time is unknown. We present a methodology to forecast the probability of user customizable sufficient price change events. Four main methodological contributions are presented: (i) an economically meaningful definition of user specified price decreases, (ii) the modification of a bootstrap based ARIMA-GARCH volatility forecasting method to predict the probability of the defined events, (iii) the dynamic statistical evaluation of the forecasting accuracy and (iv) the measurement of the economic utility of the buying recommendation procedure using gain functions. Beyond this, the technique is applied to two distinct forecasting situations, which clearly show the dominance of the proposed decision theoretic framework in comparison to naive purchase strategies like always delaying or always buying immediately.

Decision support system for purchasing management of seasonal products: A capital-constrained retailer perspective

With a random price-dependent demand, this paper investigates the capital-constrained retailer's integrated purchase timing, quantity and financing decisions towards seasonal products. Results show that at both purchase moments (i.e. early-purchasing at the beginning of lead time and late-purchasing at the beginning of selling season), there always exists a critical value, and when the retailer's internal capital level is less than the critical value, it will borrow from the bank to purchase a larger quantity; otherwise, it will not borrow and just use up its internal capital for purchasing. The capital-constrained retailer can get an “information bonus” from late-purchasing only when its internal capital level is relatively low, so it needs a trade-off between the “conditional information bonus” and the “inevitable cost loss” brought by late-purchasing and then makes an optimal purchase timing decision. A specific multi-parameter-based method is highlighted to solve the timing decision problem. Based on above findings, this paper designs a simple intelligent purchasing decision support system for small retailers. The proposed system integrates two main functions of purchasing and financing to help small retailers, especially those with limited working capital, make more scientific and intelligent purchasing decisions.

Contingent Preannounced Pricing Policies with Strategic Consumers

Companies in diverse industries must decide the pricing policy of their inventories over time. This decision becomes particularly complex when customers are forward looking and may defer a purchase in the hope of future discounts and promotions. With such uncertainty, many customers may end up not buying or buying at a significantly lower price, reducing the firm’s profitability. Recent studies show that a way to mitigate this negative effect caused by strategic consumers is to use a posted or preannounced pricing policy. With that policy, firms commit to a price path that consumers use to evaluate their purchase timing decision. In this paper, we propose a class of preannounced pricing policies in which the price path corresponds to a price menu contingent on the available inventory. We present a two-period model, with a monopolist selling a fixed inventory of a good. Given a menu of prices specified by the firm and beliefs regarding the number of units to be sold, customers decide whether to buy upon arrival, buy at the clearance price, or not to buy. The firm determines the set of prices that maximizes revenues. The solution to this problem requires the concept of equilibrium between the seller and the buyers that we analyze using a novel approach based on ordinary differential equations. We show existence of equilibrium and uniqueness when only one unit is on sale. However, if multiple units are offered, we show that multiple equilibria may arise. We develop a gradient-based method to solve the firm’s optimization problem and conduct a computational study of different pricing schemes. The results show that under certain conditions the proposed contingent preannounced policy outperforms previously proposed pricing schemes. The source of the improvement comes from the use of the proposed pricing policy as a barrier to discourage strategic waiting and as a discrimination tool for those customers waiting.

Forecasting Gasoline Prices in the Presence of Edgeworth Price Cycles

Forecasting is a central theme in economics. The ability to forecast prices enables economic agents to make optimal decisions for the present and future. In this article, we investigate if and how gasoline prices can be forecast in retail gasoline markets that are subject to high-frequency, asymmetric price cycles known as Edgeworth price cycles. We examine a series of purchase timing decision rules and a series of feasible forecasting algorithms for updating those rules over time. We find that, in the presence of cycles, agents in our five Australian markets can systematically reduce purchase prices below market average the equivalent of 11 to 15 U.S. cents per gallon, using simple decision rules and feasible forecasting algorithms.

Forecasting gasoline prices in the presence of Edgeworth Price Cycles

Forecasting is a central theme in economics. The ability to forecast prices enables economic agents to make optimal decisions for the present and future. In this article, we investigate if and how gasoline prices can be forecast in retail gasoline markets that are subject to high-frequency, asymmetric price cycles known as Edgeworth Price Cycles. We examine a series of purchase timing decision rules and a series of feasible forecasting algorithms for updating those rules over time. We find that, in the presence of cycles, agents in our five Australian markets can systematically reduce purchase prices below market average the equivalent of 11 to 15 U.S. cents per gallon, using simple decision rules and feasible forecasting algorithms.

Latent Homophily or Social Influence? An Empirical Analysis of Purchase Within a Social Network

Consumers who are close to one another in a social network often make similar purchase decisions. This similarity can result from latent homophily or social influence, as well as common exogenous factors. Latent homophily means consumers who are connected to one another are likely to have similar characteristics and product preferences. Social influence refers to the ability of one consumer to directly influence another consumer's decision based upon their communication. We present an empirical study of purchases of caller ring-back tones using data from an Asian mobile network that predicts consumers' purchase timing and choice decisions. We simultaneously measure latent homophily and social influence, while also accounting for exogenous factors. Identification is achieved due to our dynamic, panel data structure and the availability of detailed communication data. We find strong influence effects and latent homophily effects in both the purchase timing and product choice decisions of consumers.This paper was accepted by Sandra Slaughter, information systems.

Predicting Purchase Timing, Product Choice, and Purchase Amount for a Firm's Adoption of a Radically Innovative Information Technology: An Analysis of Cloud Computing Services

Cloud computing is a radically innovative information technology (IT) that has been widely commercialized, but understanding its adoption by a firm has been a mystery. Cloud computing offerings include servers, storage and data product services, and desktop cloud solutions for small businesses. Because prior knowledge about cloud computing adoption is quite limited, this paper attempts to fill the gap in the adoption–provider framework by identifying the drivers that help a firm adopt a radical innovation in a business-to-business scenario. We developed an integrated model that links the purchase timing, product choice, and purchase amount decisions of the different types of cloud computing services. The theory of relationship marketing consisting of “commitment” and “trust” constructs has been extended to include the “need” construct to explain the adoption behavior of the cloud computing services. We empirically tested the proposed framework using data from a large IT company. Results indicate that the proposed model predicts the purchase timing with an accuracy of 78%, type of choice with an accuracy of 81%, and purchase amount with a mean absolute percentage error of 28% for the cloud computing services. The paper highlights the contribution, limitations, and future research for both researchers and practitioners.

Contingent Preannounced Pricing Policies with Strategic Consumers

Companies in diverse industries have to decide the pricing policy of their inventory over time. This decision becomes particularly complex when customers accommodate their purchase decision in the hope of future discounts and promotions. With such uncertainty, many of these customers may end up not buying even when the price decreases, leaving a substantial amount of unsold items and reducing the firm’s profitability. Recent studies show that a way to mitigate this negative effect caused by strategic consumers is to use a posted or preannounced pricing policy. With that policy, firms commit to a price path that consumers use to evaluate their purchase timing decision. In this paper, we propose a general class of contingent preannounced pricing policies and derive the corresponding equilibrium properties. Firms using this policy commit to a preannounced price path that is, in addition, contingent on the available inventory. We present a two-period model, with a monopolist selling a fixed inventory of a good. Given a menu of prices specified by the firm, arriving customers observe the price path and decide to buy now, wait until next period, or not to buy. The firm determines the set of prices that maximize revenues. The solution to this problem requires the concept of equilibrium among the seller and the buyers. We show existence of equilibrium and uniqueness when only one unit is on sale. However if multiple units are offered, we show that multiple equilibria may arise. We conduct a computational study of different pricing schemes which shows the better performance of the proposed contingent preannounced policy. The source of the improvement comes from the use of the proposed pricing policy as a barrier to discourage strategic waiting and a discrimination tool for those customers waiting.

Accommodating taste heterogeneity in railway passenger choice models based on internet booking data

This paper presents an application of advanced econometric techniques to railway passenger choices in the context of revenue management. Three modeling approaches; multinomial logit, latent class, and mixed logit models are applied to ticket purchase timing decisions and to three market segments. The analysis, based on internet booking data with limited individual variables, investigates heterogeneous characteristics of passenger behavior across railway markets that differ by the length of haul.The results quantify the importance of fare, advanced booking, departure time of day, and day of week in purchase timing decision. It shows that mixed logit model provides the best statistical fit for the long and medium distance markets, while the latent class model provides the best statistical fit for the short distance market. On the other hand, the latent class model is found to be superior to mixed logit model in term of prediction capability. Results also show that segmenting price sensitivity by booking period is more appropriate for this choice model application than segmenting by socioeconomic information. This research contributes to existing literature on revenue management by demonstrating that complex demand models successfully recover random heterogeneity when limited socio-demographic information is available. The results, coupled with an optimization algorithm, can be used by railway operators to support revenue management policies such as fare pricing or seat allocation.

Channel Interactions in a Vertically Differentiated Channel Structure: The Case of Factory Outlet Stores

This study develops and estimates a model of multi-channel customer purchase behavior in a vertically differentiated channel structure. In recent years many retailers have added exclusively sourced factory outlet stores into their channel mix to achieve market expansion and customer segmentation. However, there are two main concerns for retailers who offer a lower quality alternative channel under the same brand name: cannibalization and the impact of the adoption of the lower quality channel on total spending with the retailer. The current literature has two conflicting predictions regarding the impact of adoption of the outlet channel on total spending with the retailer. Multichannel customer behavior research suggests that customer interaction using more channels would be beneficial for the retailer and lead to increased spending. Brand extension research, on the other hand, suggests that adoption of the lower quality channel might run the risk of brand dilution and lead to decreased spending. Using an individual level customer transaction data set from a large specialty apparel retailer, we investigate the impact of adoption of the outlet channel. We jointly model customer purchase timing, channel choice and expenditure decisions. Our results show that on average, overall spending with the retailer increases after the adoption of the outlet channel due to increased purchase frequency. More surprisingly, in addition to incremental spending at the outlet channel, there is a positive spillover that results in increased spending at the retail store channel. Ours is the first empirical study investigating multichannel customer behavior in a vertically differentiated channel structure. Our results showcase the effectiveness of this channel structure in customer segmentation. We find that by offering the lower quality, lower price channel the retailer is able to significantly increase the purchase frequency and spending of the customers on the lower end of the pre-outlet adoption expenditure distribution with no cannibalization on the higher end.

Key Variables Affecting Decisions of Bus Replacement Age and Total Costs

Recent budget and fiscal constraints make optimal fleet management more imperative than ever for transit agencies. Fleet data have consistently shown that bus operations and maintenance (O&M) costs per mile increase as buses age. From a purely economic perspective, there is a cost trade-off between the lower O&M costs of newer fleets and their higher initial capital costs. This trade-off has a significant impact on the optimal timing of purchase and replacement decisions. Realistic cost data and an optimization modeling framework were used to analyze the impact of purchase timing decisions on fleet costs per mile. The results indicate that (a) increases in diesel prices do not affect total bus fleet costs as much as increases in maintenance costs, (b) increases in maintenance costs and utilization per year reduce the optimal replacement age, (c) increases in utilization and fuel economy have a similar impact in terms of total fleet costs, and (d) bus purchase-price changes have a significant impact on the optimal replacement age. Given uncertain and hard-to-forecast market variables, a thorough sensitivity analysis is presented to ascertain the key variables that affect bus transit replacement timing.

Do Price Charts Provided by Online Shopbots Influence Price Expectations and Purchase Timing Decisions?

Online price comparison sites (shopbots) like PriceGrabber.com are the most powerful tools for consumers to easily compare prices and find offers for desired products. Besides providing distributions of actual prices in price comparison tables, shopbots like NexTag.com have recently introduced price charts (line charts) displaying a product's full price history. Price charts should support consumers in forming expectations about future prices. Nevertheless, it is currently unclear how price charts influence consumer price expectations and purchase decisions. The results of this study show that the provision of past prices leads to strong adjustments of price expectations depending on price chart characteristics. In particular, the trend, variance and range of past prices in the chart strongly affect price expectations and purchase timing decisions. Furthermore, in the case of a strong downward trend and high variance in past prices, results show that nearly 50% of the total effect is caused by the visualization of the price history.

The Importance of Modeling Temporal Dependence of Timing and Quantity in Direct Marketing

The analysis of customer value in direct marketing typically combines customer timing and quantity data into a single statistic that is used to compute lifetime values, rank-order customers for differential action, and identify prospects for cross-selling. However, current models assume that purchase timing and quantity decisions are independently realized (i.e., uncorrelated) over time given individual-level parameters. In this article, the authors show that customer value calculations can be severely biased in these models when timing and quantity are dependently related. The authors propose alternative models that lead to substantial gains in profitability in two direct-marketing data sets. The results indicate that the commonly held assumption of independence leads to an overvaluation of customer value.

A Model of the Joint Distribution of Purchase Quantity and Timing

Prediction of purchase timing and quantity decisions of a household is an important element for success of any retailer. This is especially so for an online retailer, as the traditional brick-and-mortar retailer would be more concerned with total sales. A number of statistical models have been developed in the marketing literature to aid traditional retailers in predicting sales and analyzing the impact of various marketing activities on sales. However, there are two important differences between traditional retail outlets and the increasingly important online retail/delivery companies, differences that prevent these firms from using models developed for the traditional retailers: (1) the profits of the online retailer/delivery company depend on purchase frequency and on purchase quantity, whereas the profits of traditional retailers are simply tied to total sales, and (2) customers in the tails of the frequency distribution are more important to the delivery company than to the retail outlet. Both of these differences are due to the fact that the delivery companies incur a delivery cost for each sale, whereas customers themselves travel to retail outlets when buying from traditional retailers. These differences in costs translate directly into needs that a model must address. For a model intended to be useful to online retailers, the dependent variable should be a bivariate distribution of frequency and quantity, and the frequency distribution must accurately represent consumers in the tails. In this article we develop such a model and apply it to predicting the consumer's joint decision of when to shop and how much to spend at the store. Our approach is to model the marginal distribution of purchase timing and the distribution of purchase quantity co nditional on purchase timing. We propose a hierarchical Bayes model that disentangles the weekly and daily components of the purchase timing. The daily component has a dependence on the weekly component, thereby accounting for strong observed periodicity in the data. For the purchase times, we use the Conway-Maxwell-Poisson distribution, which we find useful to fit data in the tail regions (extremely frequent and infrequent purchasers).

The Proportional Hazard Model for Purchase Timing

We use the proportional hazard model (PHM) to study purchase-timing behavior of households in two product categories: laundry detergents and paper towels. The PHM decomposes a household's instantaneous probability of buying the product at a point of time into two components: the baseline hazard that captures the household's intrinsic purchase pattern over time and the covariate function that captures the effects of marketing variables on the household's purchase timing decision. We compare the continuoustime and discrete-time PHMs, where the latter explicitly accounts for households' shopping trips that do not involve purchase of the product. We find that the discrete-time PHM empirically outperforms the continuous-time PHM in terms of explaining the observed purchase outcomes. We compare five different parametric specifications of the baseline hazard, and find that the three-parameter expo-power specification outperforms the exponential, Erlang-2, Weibull, and log-logistic specifications. We use a causespecific, competing-risks PHM to distinguish between two types of purchase events that differ in terms of whether or not they were preceded by a shopping trip that involved purchase of the product. Such a cause-specific, competing-risks PHM is shown to outperform the traditional discrete-time PHM. We then estimate a nonparametric version of the PHM and find that it does not offer any additional insights compared to the parsimonious parametric PHM. Finally, we accommodate unobserved heterogeneity across households by allowing all of the parameters of the PHM to follow a discrete distribution across households whose locations and supports are nonparametrically estimated from the data. We find evidence for substantial unobserved heterogeneity in the data, both in the parameters of marketing variables and in the baseline hazards. This study will be a useful reference to researchers hoping to use the PHM to study event times.

A segment‐level hazard approach to studying household purchase timing decisions

AbstractThe increasing availability of customer‐level data and the willingness of marketers to customize the timing of their offers to consumers makes the accurate segment‐level description of household purchase timing decisions a compelling issue. In this paper we employ a finite mixture accelerated failure time model to identify and characterize household segments in terms of their purchasing rates and their propensity to accelerate purchases due to marketing mix activities. Such an approach also promises to alleviate possible aggregation problems arising from the use of a common hazard rate for all households. An application to household panel data suggested that infrequent buyers show higher propensity to accelerate than frequent buyers do, and that positive duration effects are underestimated when not accounting for segment‐specific hazard rates. Copyright © 2002 John Wiley & Sons, Ltd.

The impact of firm introductory strategies on consumers’ perceptions of future product introductions and purchase decisions

In this research, we develop and test a model of the consumer’s decision to immediately purchase a technologically advanced product or to delay such a purchase until a future generation of the product is released. We propose that for technologically advancing products, consumers consider both performance lag (how far behind am I now) and expected performance gain (how far ahead will I be if I wait to buy a future expected release) in their purchase decisions. Furthermore, we hypothesize that a firm’s past product introductory strategy can significantly influence consumer perceptions of performance lag, performance gain, and the rate at which a product is advancing technologically. We also propose that these perceptions of lag, gain and rate of technological change influence purchase action and ultimately determine whether or not a consumer will delay or immediately purchase a firm’s current technological offering. We investigate the above relationships by introducing a model of consumer purchase behavior that incorporates the effects of a firm’s frequency and pattern of next generation product introduction, and test the impact of different introductory strategies on performance lag, gain, rate of change perceptions, and purchase action. In our first study we test our model in a monopolistic setting and show that, holding all else fixed, infrequent product upgrades and/or increasing intergenerational release times result in consumers perceiving larger performance lags and gains. We also show that, holding all else fixed, consumers with larger performance lags and/or gains are less likely to delay their purchases of the currently best available product. In our second study we test our model in a competitive setting and show that, holding all else fixed, a firm’s past pattern of new product introduction can influence consumers’ perceptions of the firm’s product’s rate of technological change. We also find that consumers are more likely to purchase products which they perceive to have higher rates of technological change. The key insight from this research is that firms have a strategic tool at their disposal that has been overlooked—the pattern of introduction of next generation products. Our findings suggest that a change in the frequency and/or pattern of introduction, in and of themselves, can influence consumers’ perceptions of future product introductions, and ultimately influence their purchase actions. Specifically, we demonstrate that by better understanding consumers’ purchase timing decisions, firms may be able to induce purchase on the basis of introductory frequency and pattern alone. Additionally, we demonstrate that by strategically managing consumer expectations of future product introductions, firms may be able to decrease the purchase likelihoods of competing products. Implications of our research and its application to the pattern and timing of preannouncements for new products are also explored.

The Impact of Heterogeneity in Purchase Timing and Price Responsiveness on Estimates of Sticker Shock Effects

The notion that individuals have an internal reference price against which they compare observed prices is well supported by several psychological theories. Empirically, several papers in the marketing literature, employing scanner panel data, have modeled the impact of reference prices on brand choice via the sticker shock formulation, in which consumers evaluate choice alternatives using differences between shelf prices and reference prices. Most of the studies reported thus far have not accounted for heterogeneity in price response among consumers and have typically imputed reference prices from the shelf prices of brands that a consumer is supposed to have “observed” on previous purchases in the category. Since category marketing activity can differentially affect the purchase timing of households, we argue that this measure of reference price may follow certain systematic patterns across consumers and, when combined with unaccounted for price response heterogeneity, may result in a spurious sticker shock effect. Specifically, we show that estimates of sticker shock are biased upward if households that are price-sensitive in the brand choice decision are also more responsive to category promotion activity in their purchase timing decision. We discuss some general conditions under which the bias occurs and conduct a simulation experiment to confirm our specific hypotheses. Our simulation results show that changes in purchase timing are a critical determinant of the bias in the sticker shock effect. We also show that unaccounted for price response heterogeneity can in itself result in a biased sticker shock parameter; however, this requires very large differences in price sensitivities across consumers, far greater than what is normally observed. We develop a hierarchical Bayes version of the nested logit model, which models heterogeneity via individual-level parameters in a continuous random effects framework. We estimate the model on scanner panel data from the yogurt and ketchup categories. We find, in both categories, that the 95% probability interval of the posterior distribution of the mean sticker shock coefficient contains the value zero. Therefore, at least for the data used in this study, there is no evidence for the sticker shock effect at the aggregate level. In contrast, the corresponding coefficient from a standard model (which ignores this heterogeneity) is highly significant and supports the existence of a (possibly spurious) sticker shock effect. Consistent with our explanation of the underlying cause of the bias, households that are more price-sensitive in the choice decision are also found to be more responsive to category promotion activity in their decision to purchase in the category. The results highlight the measurement problems associated with imputing reference prices from past prices. Since the frequency, duration, and price level of a retailer's promotional program depend on its size and prevalence, accurate estimates of the sticker shock effect are essential for formulating optimal promotion strategies. An adequate accounting of consumer heterogeneity is critical to this effort.

Household cost effects on purchase timing decisions: do demographics matter?

Previous research has rarely considered purchase acceleration as a measure of consumer deal‐proneness. Also recent studies have found that the effect of demographics either on brand choice or purchase timing is marginal. Examines the effects of demographics on household propensity to accelerate. Selects demographic variables are selected based on theoretical arguments and the results show that their effect is significant. The study found the effects of female head employment status to be the most persistent, followed by income and household size effects. Also found demographics were also found to discriminate between deal‐only and price sensitive households, a difference observed in previous studies.

An Empirical Investigation of the “Dynamic McFadden” Model of Purchase Timing and Brand Choice: Implications for Market Structure

Purchase timing and brand-choice decisions of households are jointly investigated using the “dynamic McFadden” model of Heckman and Singer. The hazard of brand purchase is decomposed into the category purchase hazard and the probability of brand choice conditional on category purchase. The former is modeled using the hazard-function approach and the latter using a logit model. Unobserved heterogeneity in brand preferences, marketing effects, and baseline hazard parameters is accounted for in the empirical analysis. The distribution of preference heterogeneity identifies the locations of brands in multiattribute perceptual space and the distribution of attribute importance weights across households.