Efficient Algorithms for Dynamic Assortment Optimization under Multinomial Logit Choice Model

מושגי ליבה

We develop a unified algorithmic framework that provides provable approximation guarantees for dynamic assortment optimization problems under the Multinomial Logit choice model, improving upon the state-of-the-art results. Our algorithms address both the dynamic assortment problem without personalization and the dynamic assortment problem with personalization, and can handle uncertainty in the total number of customers.

תקציר

The content discusses dynamic assortment optimization problems, which involve deciding the optimal assortment of products to offer and the inventory levels for each product in the presence of finite inventory and dynamic stockout-based substitution effects.

The authors consider two settings: 1) the dynamic assortment optimization (DA) problem, where customers see all available products, and 2) the dynamic assortment optimization with personalization (DAP) problem, where the seller can choose to offer a subset of available products to each customer.

The authors develop a unified algorithmic framework to address both DA and DAP problems under the Multinomial Logit (MNL) choice model. Key highlights:

1. For DA, the authors improve the best-known approximation ratio from 0.122-ϵ to 0.194-ϵ for distributions with the Increasing Failure Rate (IFR) property. Their algorithm is also significantly faster than prior work.

2. For DAP with deterministic number of customers (T), the authors achieve an approximation ratio of 1/2(1-1/e)-ϵ, surpassing the current best guarantee of 1/4(1-1/e).

3. For DAP with stochastic T following an arbitrary distribution, the authors provide a (0.25-ϵ)-approximation, addressing an open problem.

4. The authors establish novel structural properties of the fluid relaxations, including the submodular order property, which enables the development of efficient threshold-based approximation algorithms.

Overall, the work provides a unified and efficient algorithmic framework for dynamic assortment optimization under the MNL choice model, with improved approximation guarantees compared to prior work.

סטטיסטיקה

None.

ציטוטים

None.

תובנות מפתח מזוקקות מ:

A Unified Algorithmic Framework for Dynamic Assortment Optimization under MNL Choice

by Shuo Sun,Raj... ב- arxiv.org 04-05-2024

https://arxiv.org/pdf/2404.03604.pdf

שאלות מעמיקות

How can the proposed algorithms be extended to handle more complex constraints beyond cardinality and budget constraints

The proposed algorithms can be extended to handle more complex constraints beyond cardinality and budget constraints by incorporating additional constraints into the optimization framework. For example, constraints related to product compatibility, seasonality, or marketing promotions can be integrated into the algorithm design. These constraints can be formulated as additional constraints in the optimization problem, and the algorithm can be modified to accommodate these constraints while maximizing the objective function. By incorporating these complex constraints, the algorithm can provide more tailored and realistic solutions that align with the specific requirements of the business or industry.

What are the implications of the structural properties established for the fluid relaxations, such as the generalized revenue-ordered property and the submodular order property, on other revenue management problems

The structural properties established for the fluid relaxations, such as the generalized revenue-ordered property and the submodular order property, have significant implications for other revenue management problems. These properties provide insights into the optimal inventory allocation strategies and assortment decisions in dynamic assortment optimization. The generalized revenue-ordered property helps in understanding how inventory levels impact revenue generation, while the submodular order property enables efficient optimization under certain conditions.
These structural properties can be leveraged in various revenue management problems beyond dynamic assortment optimization. For example, in pricing optimization, understanding the revenue-ordered structure can guide pricing strategies for different products. In inventory management, the submodular order property can aid in determining optimal stocking levels and assortment decisions. Overall, these properties offer valuable insights and optimization strategies that can be applied to a wide range of revenue management scenarios.

Can the techniques developed in this work be applied to dynamic assortment optimization under choice models other than the Multinomial Logit

The techniques developed in this work can be applied to dynamic assortment optimization under choice models other than the Multinomial Logit (MNL). While the algorithms and frameworks discussed in the context are specifically designed for the MNL choice model, the underlying principles and methodologies can be adapted to accommodate different choice models. By modifying the objective functions, constraints, and optimization strategies to align with the characteristics of alternative choice models, the algorithms can be extended to handle different modeling frameworks.
For instance, choice models like Nested Logit, Mixed Logit, or Random Utility Models can be integrated into the algorithmic framework by adjusting the choice probabilities and utility functions accordingly. The key lies in understanding the specific properties and requirements of the alternative choice models and tailoring the algorithmic approach to suit those characteristics. By customizing the algorithms to different choice models, the framework can be effectively applied to a broader range of dynamic assortment optimization scenarios.