Product line optimization in the presence of preferences for compromise alternatives

Highlights

• First study considering compromise effects in product line optimization.

• Integration of the compromise variable model from the econometric literature.

• Proposition of a mixed-integer linear programming approach.

• Computational tractability of the approach for practically relevant problem sizes.

• Case study showing mean profit benefits of ca. 23% over the traditional approach.

Abstract

Recent advances in customer choice analysis demonstrated the strong impact of compromise alternatives on the behaviour of decision-makers in a wide range of decision situations. Compromise alternatives are characterized by an intermediate performance on some of the relevant attributes. For instance, price compromises are well known in the sense that customers tend to buy neither the cheapest, nor the most expensive alternative, but the mid-priced one. However, thus far, the literature on product line optimization has not considered such context effects.

In this paper, we propose a model-based approach for optimal product line selection which incorporates customers’ preferences for compromise alternatives. We consider customer choice in a realistic, sophisticated fashion by applying an established utility model that integrates compromise variables into a multinomial logit model. We formulate the resulting optimization problem as a mixed-integer linear program. The challenging feature for modelling – making the formulation substantially more complicated than existing ones without compromises – are the endogenous effects of selected products on other alternatives’ utilities that need to be adequately captured via compromise variables. Based on data we collected by a stated choice experiment in a retail setting, we perform a computational study and demonstrate the superiority of our product line selection approach compared to a reference model that does not take compromises into account. Even under uncertainty of the estimated utility parameters, profit gains of, on average, 23% can be achieved in our experimental setting.

Introduction

To cope with increasing competition and to account for heterogeneous customer needs and preferences, companies today usually offer several versions of the basic goods or services they provide. To obtain these versions, they change the level of at least one characteristic attribute and, most commonly, the price. For example, in the case of a tablet computer, the attribute changes can refer to screen and memory size, or battery life. For a telecommunications tariff, standing and call charges, as well as data volume, might differ. In this context, each of the versions represents a product; the set of all products defines a product line.

Product line decisions are usually made on a strategic or tactical planning level as part of product policy management, because short term adaptions are not feasible due to the necessary ramp-up in production or communication. The main challenge is to make optimal decisions concerning corporate objectives (e.g., maximization of profit) for new products that have never been offered before. Thereby, a multitude of influencing factors, such as mutual effects of the products (e.g., cannibalization effects), have to be taken into account.

In the last few decades, numerous papers have appeared in the academic literature, taking on this challenge by applying quantitative approaches (e.g., Bertsimas & Mišić, 2019, Chen & Hausman, 2000, Kraus & Yano, 2003, Schön, 2010a). In this context, two basic product line optimization approaches are discussed: in Product Line Design (PLD), the products to be offered are configured by choosing a certain level for each attribute, while in the Product Line Selection (PLS) approach there are two steps. First, a set of potential products is preconfigured. Second, the products to be offered are selected from that set within the optimization calculus.

In both these approaches, customer choice behaviour has to be estimated and simulated for the hypothetical products, using some choice model. Such a model describes whether a customer will pick a specific product or choose not to buy at all. Most commonly, utility-based models are proposed in this context (cf., e.g., Schön, 2010a). Here, a scalar expresses a product's attractiveness, i.e., the utility that a customer attempts to maximize by his or her choice. In the context of product line optimization, this scalar is commonly computed using an additive utility function based on the sum of part-worth utilities for each of the product's attributes (e.g., screen or memory size). For each attribute, the part-worth utility expresses the customer's valuation depending on the respective attribute's level. Thereby, the assumption is that the part-worth utility associated with a particular attribute's level is independent of the remaining attributes’ levels, and that the total utility of the product is independent of the remaining products in the line.

However, these assumptions contradict findings of behavioural research, which postulate several sources of bias in decision-making in a wide range of contexts (cf., Huber, Payne & Puto, 1982, Tversky, 1972). One such bias originates from the compromise effect, which states preferences for compromise alternatives (Simonson, 1989). The compromise effect has proven to be particularly strong and robust (Kivetz, Netzer & Srinivasan, 2004). It describes the phenomenon of a product gaining additional market share when it represents a “middle option”. A “middle option” means that, compared to all other products in the product line, the product is characterized by some non-extreme attribute levels. The compromise effect causes the product utility to depend not only on the product-inherent attribute levels, but also on the offered product line in its entirety. Thus, not considering this effect could lead to suboptimal product lines concerning the overall profit. Despite these findings, publications on product line optimization have not considered preferences for compromise alternatives yet.

Our contributions are as follows: this paper is the first to explicitly define and investigate the problem of optimal product line selection under consideration of preferences for compromise alternatives (referred to as the PLSC model). Customer choice behaviour is described following a probabilistic choice model from the econometric and marketing literature based on utilities. The basic idea is not only to consider products’ utilities generated by their attribute levels, but to additionally integrate the utility of compromises into the well-known multinomial logit (MNL) model. For this purpose, we include so-called compromise variables, counting the number of attributes of a product in a line representing a compromise. In this context, an attribute represents a compromise when the line includes at least one product with a higher and lower level for this attribute. The number cannot be calculated exogenously, but has to be computed depending on the products selected in the line.

Based on this choice model, we formulate the PLSC as a mixed-integer linear program. Concerning the constraints, the specific modelling challenge lies in capturing the endogenous effects selected products have on other alternatives' utilities. Taking on this challenge substantially complicates the resulting formulation in comparison to (and different from) existing standard (linear) formulations for product line optimization. Additionally, the objective function is fractional and, thus, nonlinear at first glance. However, it can easily be linearized exactly, by applying existing linearization techniques.

As a basis for the evaluation of our approach, we collected empirical data via a stated choice experiment in a retail setting, i.e., in a market experiment based on hypothetical products with participants representing potential customers. Based on the experiment's results, we estimated appropriate choice model instances, i.e., utility parameters. The econometrical analysis of the estimation outputs provides evidence that the choice model which we use, and which incorporates preferences for compromise alternatives by using compromise variables, has a significantly higher model fit. Thus, it transfers previous findings, e.g., from route choice settings as in Chorus and Bierlaire (2013), to our retail setting with customers choosing from a product line.

Following on from the stated choice experiment, we switched to the seller's perspective and evaluated our product line selection approach by conducting a computational study for which we used the collected data. Compared to a model that does not take preferences for compromise alternatives into account, we show that applying our PLSC model increases the expected profits. Since the choice model's true utility parameters are not known, but estimated on the choice experiment's data, we additionally performed a similar investigation under uncertainty of the parameters. Further, we examined the impact on a restricted product line by imposing cardinality constraints. Finally, to justify the relevance of our model-based approach, we compared the PLSC to applying complete enumeration.

The paper is organized as follows: In §2, we give an overview of the related literature. In §3, we propose a mixed-integer programming formulation for optimal product line selection, taking customers’ preferences for compromise alternatives into account. In §4, we present the stated choice experiment which we conducted. We describe the data collection process, as well as the choice model's parameters estimation and analysis. Based on this, we turn to evaluating the new product line selection approach in §5. We present our evaluation framework and investigate the computational study's results. In §6, we state the central managerial implications of the approach in general, as well as of our computational results in particular. In §7, we conclude the paper and provide future research directions.