Efficient formulations for pricing under attraction demand models
We propose a modeling and optimization framework to cast a broad range of fundamental multi-product pricing problems as tractable convex optimization problems. We consider a retailer offering an assortment of differentiated substitutable products to a population of customers that are price-sensitive...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2016
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| Online Access: | http://hdl.handle.net/1721.1/103405 https://orcid.org/0000-0002-0888-9030 https://orcid.org/0000-0002-1994-4875 |
| _version_ | 1811095642385154048 |
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| author | Keller, Philipp W. Levi, Retsef Perakis, Georgia |
| author2 | Sloan School of Management |
| author_facet | Sloan School of Management Keller, Philipp W. Levi, Retsef Perakis, Georgia |
| author_sort | Keller, Philipp W. |
| collection | MIT |
| description | We propose a modeling and optimization framework to cast a broad range of fundamental multi-product pricing problems as tractable convex optimization problems. We consider a retailer offering an assortment of differentiated substitutable products to a population of customers that are price-sensitive. The retailer selects prices to maximize profits, subject to constraints on sales arising from inventory and capacity availability, market share goals, bounds on allowable prices and other considerations. Consumers’ response to price changes is represented by attraction demand models, which subsume the well known multinomial logit (MNL) and multiplicative competitive interaction demand models. Our approach transforms seemingly non-convex pricing problems (both in the objective function and constraints) into convex optimization problems that can be solved efficiently with commercial software. We establish a condition which ensures that the resulting problem is convex, prove that it can be solved in polynomial time under MNL demand, and show computationally that our new formulations reduce the solution time from days to seconds. We also propose an approximation of demand models with multiple overlapping customer segments, and show that it falls within the class of demand models we are able to solve. Such mixed demand models are highly desirable in practice, but yield a pricing problem which appears computationally challenging to solve exactly. |
| first_indexed | 2024-09-23T16:22:27Z |
| format | Article |
| id | mit-1721.1/103405 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:22:27Z |
| publishDate | 2016 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1034052022-10-02T07:50:52Z Efficient formulations for pricing under attraction demand models Keller, Philipp W. Levi, Retsef Perakis, Georgia Sloan School of Management Levi, Retsef Perakis, Georgia Keller, Philipp W. We propose a modeling and optimization framework to cast a broad range of fundamental multi-product pricing problems as tractable convex optimization problems. We consider a retailer offering an assortment of differentiated substitutable products to a population of customers that are price-sensitive. The retailer selects prices to maximize profits, subject to constraints on sales arising from inventory and capacity availability, market share goals, bounds on allowable prices and other considerations. Consumers’ response to price changes is represented by attraction demand models, which subsume the well known multinomial logit (MNL) and multiplicative competitive interaction demand models. Our approach transforms seemingly non-convex pricing problems (both in the objective function and constraints) into convex optimization problems that can be solved efficiently with commercial software. We establish a condition which ensures that the resulting problem is convex, prove that it can be solved in polynomial time under MNL demand, and show computationally that our new formulations reduce the solution time from days to seconds. We also propose an approximation of demand models with multiple overlapping customer segments, and show that it falls within the class of demand models we are able to solve. Such mixed demand models are highly desirable in practice, but yield a pricing problem which appears computationally challenging to solve exactly. National Science Foundation (U.S.) (grants CMMI-0846554 (CAREER Award) and DMS-0732175) United States. Air Force Office of Scientific Research (awards FA9550-08-1-0369 and FA9550- 08-1-0369) National Science Foundation (U.S.) (Awards CMMI-0758061, EFRI-0735905, and CMMI-0824674) Solomon Buchsbaum AT&T Research Fund Singapore-MIT Alliance 2016-06-30T20:57:27Z 2016-06-30T20:57:27Z 2013-03 2011-10 2016-05-23T12:11:02Z Article http://purl.org/eprint/type/JournalArticle 0025-5610 1436-4646 http://hdl.handle.net/1721.1/103405 Keller, Philipp W., Retsef Levi, and Georgia Perakis. “Efficient Formulations for Pricing Under Attraction Demand Models.” Math. Program. 145, no. 1–2 (March 29, 2013): 223–261. https://orcid.org/0000-0002-0888-9030 https://orcid.org/0000-0002-1994-4875 en http://dx.doi.org/10.1007/s10107-013-0646-z Mathematical Programming Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Keller, Philipp W. Levi, Retsef Perakis, Georgia Efficient formulations for pricing under attraction demand models |
| title | Efficient formulations for pricing under attraction demand models |
| title_full | Efficient formulations for pricing under attraction demand models |
| title_fullStr | Efficient formulations for pricing under attraction demand models |
| title_full_unstemmed | Efficient formulations for pricing under attraction demand models |
| title_short | Efficient formulations for pricing under attraction demand models |
| title_sort | efficient formulations for pricing under attraction demand models |
| url | http://hdl.handle.net/1721.1/103405 https://orcid.org/0000-0002-0888-9030 https://orcid.org/0000-0002-1994-4875 |
| work_keys_str_mv | AT kellerphilippw efficientformulationsforpricingunderattractiondemandmodels AT leviretsef efficientformulationsforpricingunderattractiondemandmodels AT perakisgeorgia efficientformulationsforpricingunderattractiondemandmodels |