Numerous studies indicate that the abundance of choices can make decision-making challenging for consumers. Rather than searching for the absolute best option, consumers may choose a ``good enough" option by sequentially evaluating alternatives until they find a satisfactory one, referred to as satisficing. However, while satisficing is often a bounded rational strategy, it may be a rational choice within a game-theoretic framework between sellers and consumers. We show mild conditions under which a seller prefers satisficers over maximizers, making satisficing a Pareto-dominant strategy where both the seller and the consumer may benefit. We study the assortment optimization problem where consumers follow a satisficing approach (SAOP), and demonstrate that it can be solved optimally by offering all products in decreasing order of revenue. However, we show that the problem with a cardinality constraint or with impatient satisficers is APX-hard. For the case where consumers have a homogeneous patience level, we show that the objective function is monotone submodular, so the greedy algorithm has a (1-1/e)-approximation guarantee. For the case with heterogeneous patience levels, we develop a Dynamic Greedy Algorithm (DGA) that provides a constant-factor approximation. We also study the SAOP problem for the latent class multinomial logit (LC-MNL) model and  demonstrate that it is NP-hard. Nevertheless, we propose a fully polynomial-time approximation algorithm for homogeneous consumers and a quasi-polynomial-time approximation algorithm for heterogeneous consumers within this context.

Guilermo Gallego, Mina M. Iravani, Masoud Talebian

In this study, we investigate rationality in the context of discrete choices, focusing on consumer behavior that can help bridge the gap between traditional parametric models and machine learning-based methods. We introduce an axiom, namely strong-rationality (SR), that allows for a new characterization of Random Utility Models (RUMs). We show that any regular choice model that is not a RUM can be written as a convex combination of more primitive discrete choice models (DCMs), at least one of which is not regular. We then propose the class of consideration-set rational (CSR) models. We show that this class is closed under convex combinations and is strictly larger than the class of RUMs, but different from the class of regular models. We show that menu-independent attention-based models, where consumers first consider a subset of options and then select from the subset, can be seen as special cases of consideration-set rational models. We illustrate that various behavioral choices, such as satisficing choice models and more general attention-based choice models, belong to this class. Turning to assortment optimization, we show that CSR models allow for simplified formulas for the expected revenue for consumers that are satisficers instead of utility maximizers and to closed-form upper bounds on the expected revenue from personalized assortments.  

Guilermo Gallego, Mina M. Iravani

In our study, we examine the bundling of subadditive and superadditive products in decentralized supply chains, taking into account the vertical competition between suppliers and retailers. We focus on the ex ante bundling decision, where retailers determine their bundling strategy before observing the supplier's wholesale price, and compare it with the ex post bundling decision. We find that retailers benefit from ex ante bundling in cases of weak subadditivity and weak to medium superadditivity. Conversely, the ex post bundling decision proves advantageous for retailers when dealing with strong superadditivity. This is due to the differential impact of bundling strong superadditive products on retailers and suppliers. While bundling may harm retailers, it can benefit suppliers in cases of strong superadditivity. As a result, the ex post bundling decision leads to a reduction in wholesale prices and improves retailer profits. Furthermore, we illustrate that mixed bundling is not a dominant strategy in decentralized supply chains. Instead, it can lead to lower profits for both retailers and suppliers, as well as reduced consumer surplus, negatively impacting social welfare. Conversely, pure bundling emerges as a strategy that benefits all parties involved and improves social welfare.

Mina M. Iravani, Masoud Talebian, Ying-Ju Chen, Mohammad Reza Akbari Jokar 

This study addresses the challenge of formulating a general heuristic algorithm for bundle pricing, an extensively adopted marketing strategy that offers discounted prices for product bundles. Considering the prevalence of bundle pricing in various industries, there is a clear and pressing need for a heuristic to address the problem associated with different levels of product inter-relatedness. In this paper, we introduce a general heuristic algorithm for bundle pricing, which applicable across a wide range of product inter-relatedness scenarios. Employing a pricing and assignment alternating approach, our algorithm marginally reduces the gap with the optimal solution. Through analytical comparisons and an extensive numerical study, we establish the advantages of our algorithm over existing heuristics, highlighting its potential to enhance seller profits. Our numerical study demonstrates that our algorithm can generate profits up to 56% higher than the best of the previous heuristics for independent products, with this advantage increasing to 64% for the general case. Furthermore, our algorithm exhibits lower sensitivity to cost when compared to prior heuristics. By breaking down the bundle pricing problem into pricing and assignment subproblems, our algorithm provides guidance for future research in bundling. Its flexibility in terms of the initial starting point makes it an appealing tool for consultants seeking to optimize profits. Moreover, the proposed algorithm can be implemented after existing heuristics to further improve the seller's profits. This adaptability allows the our approach to build upon and enhance the results achieved by previous methods, providing an effective means of driving higher seller's profit.

Guillermo Gallego, Mina M. Iravani, Masoud Talebian

This research investigates the environmental and fairness implications of product bundling, a prevalent marketing strategy offering multiple items at a discounted price. While bundling offers economic advantages, it can incentivize overconsumption, leading to resource depletion and waste generation. We analyze the impact of bundling on product access and the environment, focusing on pure bundling (exclusive bundles) and mixed bundling (option for bundles or individual products). Our analysis reveals that pure bundling can lead to increased resource consumption and waste generation, especially when selling substitutable products. However, even with complementary products, waste is not entirely eliminated. We further explore the limitations of mixed bundling in completely curbing waste. To address these limitations, we propose a new bundling approach – the shared-ownership strategy. We demonstrate that this approach surpasses both pure and mixed bundling by eliminating waste, increased fairness (It enables price discrimination, potentially benefiting consumers with low and moderate valuations while still maintaining accessibility to at least one product), enhanced seller profit (Increased profits incentivize sellers to adopt the strategy). The shared-ownership strategy by sharing the benefit of selling in the secondary market and recycling products in the store by consumers can be a win-win-win solution for consumers, sellers, and the environment. This framework offers a more sustainable approach to marketing compared to traditional bundling practices, ensuring economic benefits without compromising environmental well-being.

 

Mina M. Iravani, Ozge Sahin, Ying-Ju Chen

Guillermo Gallego, Mina M. Iravani, Mengqian Lu