Hongzhang Shao, Anton J. Kleywegt
arXiv 17 Jul 2020 · Mathematics — Optimization · 1 citations (OpenAlex)
arXiv:2007.09193 · PDF · DOI · OpenAlex · Extracted main text
A fundamental problem in revenue management is to optimally choose the attributes of products, such that the total profit or revenue or market share is maximized. Usually, these attributes can affect both a product's market share (probability to be chosen) and its profit margin. For example, if a smart phone has a better battery, then it is more costly to be produced, but is more likely to be purchased by a customer. The decision maker then needs to choose an optimal vector of attributes for each product that balances this trade-off. In spite of the importance of such problems, there is not yet a method to solve it efficiently in general. Past literature in revenue management and discrete choice models focus on pricing problems, where price is the only attribute to be chosen for each product. Existing approaches to solve pricing problems tractably cannot be generalized to the optimization problem with multiple product attributes as decision variables. On the other hand, papers studying product line design with multiple attributes all result in intractable optimization problems. Then we found a way to reformulate the static multi-attribute optimization problem, as well as the multi-stage fluid optimization problem with both resource constraints and upper and lower bounds of attributes, as a tractable convex conic optimization problem. Our result applies to optimization problems under the multinomial logit (MNL) model, the Markov chain (MC) choice model, and with certain conditions, the nested logit (NL) model.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | James Dong, A Serdar Simsek, and Huseyin Topaloglu (2019) Pricing Problems under the Markov Chain Choice Model | 1.000 | 11 | 4 | 100% |
| 2 | Hongmin Li and Woonghee Tim Huh (2011) Pricing Multiple Products with the Multinomial Logit and Nested Logit Models: Concavity and Implications | 1.000 | 5 | 4 | 100% |
| 3 | Lingxiu Dong, Panos Kouvelis, and Zhongjun Tian (2009) Dynamic Pricing and Inventory Control of Substitute Products | 0.928 | 4 | 4 | 100% |
| 4 | Jing-Sheng Song and Zhengliang Xue (2007) Demand Management and Inventory Control for Substitutable Products | 0.928 | 4 | 4 | 100% |
| 5 | Guillermo Gallego and Huseyin Topaloglu (2014) Constrained Assortment Optimization for the Nested Logit Model | 0.843 | 3 | 3 | 100% |
| 6 | Philipp W Keller, Retsef Levi, and Georgia Perakis (2014) Efficient Formulations for Pricing Under Attraction Demand Models | 0.843 | 3 | 3 | 100% |
| 7 | Heng Zhang, Paat Rusmevichientong, and Huseyin Topaloglu (2018) Multiproduct Pricing under the Generalized Extreme Value Models with Homogeneous Price Sensitivity Parameters | 0.737 | 3 | 2 | 100% |
| 8 | Aharon Ben-Tal and Arkadi Nemirovski (2001) Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications | 0.693 | 6 | 1 | 100% |
| 9 | Jose Blanchet, Guillermo Gallego, and Vineet Goyal (2016) A Markov Chain Approximation to Choice Modeling | 0.644 | 2 | 2 | 100% |
| 10 | James Davis, Guillermo Gallego, and Huseyin Topaloglu (2013) Assortment Planning under the Multinomial Logit Model with Totally Unimodular Constraint Structures | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 33 scored citations.