arXiv 19 Dec 2019 · Mathematics — Optimization
arXiv:1912.09552 · PDF · DOI · OpenAlex · Extracted main text
We study robust versions of pricing problems where customers choose products according to a generalized extreme value (GEV) choice model, and the choice parameters are not known exactly but lie in an uncertainty set. We show that, when the robust problem is unconstrained and the price sensitivity parameters are homogeneous, the robust optimal prices have a constant markup over products, and we provide formulas that allow to compute this constant markup by bisection. We further show that, in the case that the price sensitivity parameters are only homogeneous in each partition of the products, under the assumption that the choice probability generating function and the uncertainty set are partition-wise separable, a robust solution will have a constant markup in each subset, and this constant-markup vector can be found efficiently by convex optimization. We provide numerical results to illustrate the advantages of our robust approach in protecting from bad scenarios. Our results hold for convex and bounded uncertainty sets,} and for any arbitrary GEV model, including the multinomial logit, nested or cross-nested logit.
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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 | Heng Zhang, Paat Rusmevichientong, and Huseyin Topaloglu (2018) Multiproduct pricing under the generalized extreme value models with homogeneous price sensitivity parameters | 1.000 | 25 | 6 | 100% |
| 2 | Paat Rusmevichientong and Huseyin Topaloglu (2012) Robust assortment optimization in revenue management under the multinomial logit choice model | 0.874 | 5 | 2 | 100% |
| 3 | Andrew Daly and Michel Bierlaire (2006) A general and operational representation of generalised extreme value models | 0.843 | 3 | 3 | 100% |
| 4 | Daniel McFadden (1978) Modeling the choice of residential location | 0.811 | 4 | 2 | 100% |
| 5 | Aharon Ben-Tal and Arkadi Nemirovski (1998) Robust convex optimization | 0.737 | 3 | 2 | 100% |
| 6 | Mogens Fosgerau, Daniel McFadden, and Michel Bierlaire (2013) Choice probability generating functions | 0.737 | 3 | 2 | 100% |
| 7 | Moshe E Ben-Akiva (1973) Structure of passenger travel demand models | 0.644 | 2 | 2 | 100% |
| 8 | Moshe E Ben-Akiva, Steven R Lerman, and Steven R Lerman (1985) Discrete choice analysis: theory and application to travel demand, volume 9 | 0.644 | 2 | 2 | 100% |
| 9 | Guillermo Gallego and Ming Hu (2014) Dynamic pricing of perishable assets under competition | 0.644 | 2 | 2 | 100% |
| 10 | Guillermo Gallego and Ruxian Wang (2014) Multiproduct price optimization and competition under the nested logit model with product-differentiated price sensitivities | 0.644 | 2 | 2 | 100% |
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