The Future of Retail Operations

Retailing consists of all the activities associated with the selling of goods to the final consumer. In this article, we review the research on retail operations published in Manufacturing & Service Operations Research (M&SOM) since 1999. We then discuss the current retail landscape and the new research directions it offers, in which M&SOM can play a prominent role

Assortment optimisation under a general discrete choice model: A tight analysis of revenue-ordered assortments

The assortment problem in revenue management is the problem of deciding which subset of products to offer to consumers in order to maximise revenue. A simple and natural strategy is to select the best assortment out of all those that are constructed by fixing a threshold revenue $\pi$ and then choosing all products with revenue at least $\pi$. This is known as the revenue-ordered assortments strategy. In this paper we study the approximation guarantees provided by revenue-ordered assortments when customers are rational in the following sense: the probability of selecting a specific product from the set being offered cannot increase if the set is enlarged. This rationality assumption, known as regularity, is satisfied by almost all discrete choice models considered in the revenue management and choice theory literature, and in particular by random utility models. The bounds we obtain are tight and improve on recent results in that direction, such as for the Mixed Multinomial Logit model by Rusmevichientong et al. (2014). An appealing feature of our analysis is its simplicity, as it relies only on the regularity condition. We also draw a connection between assortment optimisation and two pricing problems called unit demand envy-free pricing and Stackelberg minimum spanning tree: These problems can be restated as assortment problems under discrete choice models satisfying the regularity condition, and moreover revenue-ordered assortments correspond then to the well-studied uniform pricing heuristic. When specialised to that setting, the general bounds we establish for revenue-ordered assortments match and unify the best known results on uniform pricing.Comment: Minor changes following referees' comment

Static Pricing Problems under Mixed Multinomial Logit Demand

Price differentiation is a common strategy for many transport operators. In this paper, we study a static multiproduct price optimization problem with demand given by a continuous mixed multinomial logit model. To solve this new problem, we design an efficient iterative optimization algorithm that asymptotically converges to the optimal solution. To this end, a linear optimization (LO) problem is formulated, based on the trust-region approach, to find a "good" feasible solution and approximate the problem from below. Another LO problem is designed using piecewise linear relaxations to approximate the optimization problem from above. Then, we develop a new branching method to tighten the optimality gap. Numerical experiments show the effectiveness of our method on a published, non-trivial, parking choice model

Assortment and Pricing Optimisation under non-conventional customer choice models

Nowadays, extensive research is being done in the area of revenue management, with applications across industries. In the center of this area lays the assortment problem, which amounts to find a subset of products to offer in order to maximise revenue, provided that customers follow a certain model of choice. Most studied models satisfy the following property: whenever the offered set is enlarged, then the probability of selecting a specific product decreases. This property is called regularity in the literature. However, customer behaviour often shows violations of this condition such as the decoy effect, where adding extra options sometimes leads to a positive effect for some products, whose probabilities of being selected increase relative to other products (e.g., including a medium size popcorn slightly cheaper than the large one, with the purpose of making the latter more attractive by comparison). We study two models of customer choice where regularity violations can be accommodated (hence the non-conventionality), and show that the assortment optimisation problem can still be solved in polynomial time. First we analyse the Sequential Multinomial Logit (SML). Under the SML model, products are partitioned into two levels, to capture differences in attractiveness, brand awareness and, or visibility of the products in the market. When a consumer is presented with an assortment of products, she first considers products on the first level and, if none of them is purchased, products in the second level are considered. This model is a special case of the Perception-Adjusted Luce Model (PALM) recently proposed by Echenique et al.(2018). It can explain many behavioural phenomena such as the attraction, compromise, similarity effects and choice overload which cannot be explained by the Multinomial Logit (MNL) model or any discrete choice model based on random utility. We show that the concept of revenue-ordered assortment sets, which contain an optimal assortment under the MNL model, can be generalized to the SML model. More precisely, we show that all optimal assortments under the SML are revenue-ordered by level, a natural generalization of revenue-ordered assortments that contains, at most, a quadratic number of assortments. As a corollary, assortment optimization under the SML is polynomial-time solvable Secondly, the Two-Stage Luce model (2SLM), is a discrete choice model introduced by Echenique and Saito (2018) that generalizes the standard multinomial logit model (MNL). The 2SLM does not satisfy the Independence of Irrelevant Alternatives (IIA) property nor regularity, and to model customer behaviour, each product has an intrinsic utility, and uses a dominance relation between products. Given a proposed assortment S, consumers first discard all dominated products in S before using an MNL model on the remaining products. As a result, the model can capture behaviour that cannot be replicated by any discrete choice model based on random utilities. We show that the assortment problem under the 2SLM is polynomially-solvable. Moreover, we prove that the capacitated assortment optimization problem is NP-hard and present polynomial-time algorithms for the cases where (1) the dominance relation is attractiveness correlated and (2) its transitive reduction is a forest. The proofs exploit a strong connection between assortments under the 2SLM and independent sets in comparability graphs. The third and final contribution is an in-depth study of the pricing problem under the 2SLM. We first note that changes in prices should be reflected in the dominance relation if the differences between the resulting attractiveness are large enough. This is formalised by solving the joint assortment and pricing problem under the Threshold Luce model, where one product dominates another if the ratio between their attractiveness is greater than a fixed threshold. In this setting, we show that this problem can be solved in polynomial time

Product Line Design, Pricing and Framing under General Choice Models

This thesis handles fundamental problems faced by retailers everyday: how do consumers make choices from an enormous variety of products? How to design a product portfolio to maximize the expected profit given consumers’ choice behavior? How to frame products if consumers’ choices are influenced by the display location? We solve those problems by first, constructing mathematical models to describe consumers’ choice behavior from a given offer set, i.e., consumer choice models; second, by designing efficient algorithms to optimally select the product portfolio to maximize the expected profit, i.e., assortment optimization. This thesis consists of three main parts: the first part solves assortment optimization problem under a consideration set based choice model proposed by Manzini and Mariotti (2014) [Manzini, Paola, Marco Mariotti. 2014. Stochastic choice and consideration sets. Econometrica 82(3) 1153-1176.]; the second part proposes an approximation algorithm to jointly optimize products’ selection and display; the third part works on optimally designing a product line under the Logit family choice models when a product’s utility depends on attribute-level configurations

Assortment Optimization Under Consider-then-Choose Choice Models

Consider-then-choose models, borne out by empirical literature in marketing and psychology, explain that customers choose among alternatives in two phases, by first screening products to decide which alternatives to consider, before then ranking them. In this paper, we develop a dynamic programming framework to study the computational aspects of assortment optimization under consider-then-choose premises. Although non-parametric choice models generally lead to computationally intractable assortment optimization problems, we are able to show that for many empirically vetted assumptions on how customers consider and choose, our resulting dynamic program is efficient. Our approach unifies and subsumes several specialized settings analyzed in previous literature. Empirically, we demonstrate the predictive power of our modeling approach on a combination of synthetic and real industry data sets, where prediction errors are significantly reduced against common parametric choice models. In synthetic experiments, our algorithms lead to practical computation schemes that outperform a state-of-the-art integer programming solver in terms of running time, in several parameter regimes of interest