Product‐line pricing with dual objective of profit and consumer surplus

In this paper, we consider an assortment optimization problem in which a platform must choose pairwise disjoint sets of assortments to offer across a series of T stages. Arriving customers begin their search process in the first stage, and progress sequentially through the stages until their patience expires, at which point they make a multinomial logit–based purchasing decision from among all products they have viewed throughout their search process. The goal is to choose the sequential displays of product offerings to maximize expected revenue. Additionally, we impose stage‐specific constraints that ensure that as each customer progresses farther and farther through the T stages, there is a minimum level of “desirability” met by the collections of displayed products. We consider two related measures of desirability: purchase likelihood and expected utility derived from the offered assortments. In this way, the offered sequence of assortments must be both high earning and well liked, which breaks from the traditional assortment setting, where customer‐centric considerations are generally not explicitly accounted for. We show that our assortment problem of interest is strongly NP‐Hard, thus ruling out the existence of a fully polynomial‐time approximation scheme (FPTAS). From an algorithmic standpoint, as a warm‐up, we develop a simple constant factor approximation scheme in which we carefully stitch together myopically selected assortments for each stage. Our main algorithmic result consists of a polynomial‐time approximation scheme (PTAS), which combines a handful of structural results related to the make‐up of the optimal assortment sequence within an approximate dynamic programming framework. We also provide an additional approximation scheme, which, under mild assumptions, can handle a cardinality constraint that enforces that an exact number of new products are introduced at each stage. Using an extensive set of numerical experiments, we demonstrate that both algorithms exhibit excellent practical performance, producing sequences of assortments that are, on average, always within 2% of optimal.

Section: Beyond Revenue Maximizationmentioning

confidence: 99%

“…They provide a parametric linear programming–based approach to solve their problem optimally. Huh and Li (2022) extend this framework to a game‐theoretical setting in which multiple firms compete to balance revenues and consumer surplus. Asadpour et al.…”

Section: Related Literaturementioning

confidence: 99%

Display optimization under the multinomial logit choice model: Balancing revenue and customer satisfaction

Feldman

Jiang

2023

Retailer Information Sharing With Upstream Product Line Flexibility

Ji,

Wu,

Chen

et al. 2024

With the rise of the digital economy, many firms are enhancing product line flexibility (i.e., the ability to adjust product line length or depth) to better manage demand uncertainties brought about by disruptive technologies. Concurrently, the booming digital economy has widened the information gap in supply chains. Retailers/platforms can now gather more detailed data to predict demand, but such data remains unavailable to manufacturers. This paper studies how a manufacturer's product line flexibility influences a retailer's incentive to voluntarily share private demand information. We show that upstream product line flexibility encourages a retailer to voluntarily share information when product substitutability is low and the product line extension fee is moderate. This insight challenges the conventional belief that retailers should keep demand information private to maintain an advantage over manufacturers. Our work is the first to suggest that upstream product line flexibility can significantly motivate retailer information sharing. Additionally, we show that, although a social planner might prefer to withhold demand information from the manufacturer in the absence of product line flexibility, sharing this information becomes preferable when the manufacturer can adjust the product line length. The retailer's decision on information sharing can align with the social planner's in such scenarios. Furthermore, we demonstrate that, given upstream product line flexibility, except when product substitutability is not sufficiently high and the product line extension fee is moderate, the retailer's information sharing decision is unaffected by whether the manufacturer determines the product line design before or after demand is realized and shared accordingly.

Joint Assortment and Price Optimization With Multiple Purchases

Luan,

Wang,

et al. 2024

In this paper, we incorporate the effects of multi-unit purchases into consumer choice models and investigate the associated joint assortment and pricing problems. Under the proposed two-stage choice framework, consumers first form a consideration set, and then select a product with the optimal quantity from the consideration set to maximize their utility. For the joint assortment and pricing problem with homogeneous consumers, we find that a multi-purchase-willingness-ordered assortment is optimal under certain technical conditions, and propose a polynomial-time algorithm to find the optimal assortment and prices for general cases. We further show that the optimal prices and assortment size are not monotone in multi-purchase preference and multi-purchase resistance. For the joint assortment and pricing problem with heterogeneous consumers, we first prove that this problem is NP-hard. We then consider a scenario with discrete prices and we develop a fully polynomial-time approximation scheme by considering a finite number of consumer segments and nested consideration sets. We conduct an empirical study on the JD.com dataset and show that the new choice framework can improve model fitting and prediction accuracy compared with existing choice models with multiple purchases. We reveal that our model is especially suitable for datasets exhibiting a strong diminishing marginal effect for product variety. We further extend our analysis to price competition and establish the existence and uniqueness of a Nash equilibrium. For the joint optimization with fixed costs, we develop an algorithm that can find a solution guaranteeing at least half the optimal expected profit.