Ricardo Montoya

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.

Package Size Decisions

We describe a model examining how a firm might choose the package size and price for a product that deteriorates over time. Our model considers four factors: (1) the usable life of the product, (2) the rates at which consumers use the product, (3) the relation between package size and the variable cost of the product, and (4) the minimum quantities consumers seek to consume for each dollar they spend (we call these reservation quantities). We allow heterogeneity in the usage rates and reservation quantities for the consumers. We show that when the cost increases as a linear or convex function of the package size, the firm should make packages of the smallest possible size. Smaller packages reduce waste and allow consumers to more closely match their purchases with desired consumption. This in turn allows the firm to charge a higher unit price and also sell more unit volume. The results imply that in a market with multiple package sizes (produced by the same or competing firms), at least one of the packages must have the smallest possible size, provided the fixed cost of making the product is sufficiently low. For concave cost functions, the firm may find it optimal to make larger than smallest-size packages.

Linear penalization support vector machines for feature selection

Support Vector Machines have proved to be powerful tools for classification tasks combining the minimization of classification errors and maximizing their generalization capabilities. Feature selection, however, is not considered explicitly in the basic model formulation. We propose a linearly penalized Support Vector Machines (LP-SVM) model where feature selection is performed simultaneously with model construction. Its application to a problem of customer retention and a comparison with other feature selection techniques demonstrates its effectiveness.

The Design of Durable Goods

The use of a durable good is limited by both its physical life and usable life. For example, an electric-car battery can last for five years (physical life) or 100,000 miles (usable life), whichever comes first. We propose a framework for examining how a profit-maximizing firm might choose the usable life, physical life, and selling price of a durable good. The proposed framework considers differences in usage rates and product valuations by consumers and allows for the effects of technological constraints and product obsolescence on a products usable and physical lives. Our main result characterizes a relationship between optimal price, cost elasticities, and opportunity costs associated with relaxing upper bounds on usable and physical lives. We describe conditions under which either usable life or physical life, or both, obtains its maximum possible values; examine why a firm might devote effort to relaxing nonbinding constraints on usable life or physical life; consider when price cuts might be accompanied with product improvements; and examine how a firm might be able to cross-subsidize product improvements.

Advanced conjoint analysis using feature selection via support vector machines

One of the main tasks of conjoint analysis is to identify consumer preferences about potential products or services. Accordingly, different estimation methods have been proposed to determine the corresponding relevant attributes. Most of these approaches rely on the post-processing of the estimated preferences to establish the importance of such variables. This paper presents new techniques that simultaneously identify consumer preferences and the most relevant attributes. The proposed approaches have two appealing characteristics. Firstly, they are grounded on a support vector machine formulation that has proved important predictive ability in operations management and marketing contexts and secondly they obtain a more parsimonious representation of consumer preferences than traditional models. We report the results of an extensive simulation study that shows that unlike existing methods, our approach can accurately recover the model parameters as well as the relevant attributes. Additionally, we use two conjoint choice experiments whose results show that the proposed techniques have better fit and predictive accuracy than traditional methods and that they additionally provide an improved understanding of customer preferences.

Embedded heterogeneous feature selection for conjoint analysis: A SVM approach using L1 penalty

This paper presents a novel embedded feature selection approach for Support Vector Machines (SVM) in a choice-based conjoint context. We extend the L1-SVM formulation and adapt the RFE-SVM algorithm to conjoint analysis to encourage sparsity in consumer preferences. This sparsity can be attributed to consumers being selective about the attributes they consider when evaluating alternatives in choice tasks. Given limited individual data in choice-based conjoint, we control for heterogeneity by pooling information across consumers and shrinking the individual weights of the relevant attributes towards a population mean. We tested our approach through an extensive simulation study that shows that the proposed approach can capture the sparseness implied by irrelevant attributes. We also illustrate the characteristics and use of our approach on two real-world choice-based conjoint data sets. The results show that the proposed method has better predictive accuracy than competitive approaches, and that it provides additional information at an individual level. Implications for product design decisions are discussed.

Simultaneous preference estimation and heterogeneity control for choice-based conjoint via support vector machines

Support vector machines (SVMs) have been successfully used to identify individuals’ preferences in conjoint analysis. One of the challenges of using SVMs in this context is to properly control for preference heterogeneity among individuals to construct robust partworths. In this work, we present a new technique that obtains all individual utility functions simultaneously in a single optimization problem based on three objectives: complexity reduction, model fit, and heterogeneity control. While complexity reduction and model fit are dealt using SVMs, heterogeneity is controlled by shrinking the individual-level partworths toward a population mean. The proposed approach is further extended to kernel-based machines, conferring flexibility to the model by allowing nonlinear utility functions. Experiments on simulated and real-world datasets show that the proposed approach in its linear form outperforms existing methods for choice-based conjoint analysis.