Exact Logit-Based Product Design

References

• Allenby GM, Ginter JL (1995) Using extremes to design products and segment markets. J. Marketing Res. 32(4):392–403.Crossref, Google Scholar
• Anderson SP, De Palma A, Thisse J-F (1988) A representative consumer theory of the logit model. Internat. Econom. Rev. 29(3):461–466.Crossref, Google Scholar
• Anderson R, Huchette J, Ma W, Tjandraatmadja C, Vielma JP (2020) Strong mixed-integer programming formulations for trained neural networks. Math. Program. 183:3–39.Crossref, Google Scholar
• Aouad A, Farias V, Levi R, Segev D (2018) The approximability of assortment optimization under ranking preferences. Oper. Res. 66(6):1661–1669.Link, Google Scholar
• Atamtürk A, Berenguer G, Shen Z-JM (2012) A conic integer programming approach to stochastic joint location-inventory problems. Oper. Res. 60(2):366–381.Link, Google Scholar
• Balakrishnan PV, Jacob VS (1996) Genetic algorithms for product design. Management Sci. 42(8):1105–1117.Link, Google Scholar
• Belloni A, Freund R, Selove M, Simester D (2008) Optimizing product line designs: Efficient methods and comparisons. Management Sci. 54(9):1544–1552.Link, Google Scholar
• Benson HY, Sağlam Ü (2013) Mixed-integer second-order cone programming: A survey. Topaloglu H, ed. Theory Driven by Influential Applications, TutORials in Operations Research (INFORMS, Catonsville, MD), 13–36.Link, Google Scholar
• Bertsimas D, Mišić VV (2017) Robust product line design. Oper. Res. 65(1):19–37.Link, Google Scholar
• Bertsimas D, Mišić VV (2019) Exact first-choice product line optimization. Oper. Res. 67(3):651–670.Link, Google Scholar
• Bezanson J, Edelman A, Karpinski S, Shah VB (2017) Julia: A fresh approach to numerical computing. SIAM Rev. 59(1):65–98.Crossref, Google Scholar
• Boyd SP, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Camm JD, Cochran JJ, Curry DJ, Kannan S (2006) Conjoint optimization: An exact branch-and-bound algorithm for the share-of-choice problem. Management Sci. 52(3):435–447.Link, Google Scholar
• Chen KD, Hausman WH (2000) Mathematical properties of the optimal product line selection problem using choice-based conjoint analysis. Management Sci. 46(2):327–332.Link, Google Scholar
• Chen L, He L, Zhou YH (2023) An exponential cone programming approach for managing electric vehicle charging. Oper. Res. 72(5):2215–2240.Google Scholar
• Coey C, Lubin M, Vielma JP (2020) Outer approximation with conic certificates for mixed-integer convex problems. Math. Program. Comput. 12:249–293.Crossref, Google Scholar
• Davis JM, Gallego G, Topaloglu H (2014) Assortment optimization under variants of the nested logit model. Oper. Res. 62(2):250–273.Link, Google Scholar
• Désir A, Goyal V, Zhang J (2022) Capacitated assortment optimization: Hardness and approximation. Oper. Res. 70(2):893–904.Link, Google Scholar
• Dunning I, Huchette J, Lubin M (2017) JuMP: A modeling language for mathematical optimization. SIAM Rev. 59(2):295–320.Crossref, Google Scholar
• Feldman JB, Topaloglu H (2017) Revenue management under the Markov chain choice model. Oper. Res. 65(5):1322–1342.Link, Google Scholar
• Feng G, Li X, Wang Z (2017) On the relation between several discrete choice models. Oper. Res. 65(6):1516–1525.Link, Google Scholar
• Ferreira KJ, Lee BHA, Simchi-Levi D (2016) Analytics for an online retailer: Demand forecasting and price optimization. Manufacturing Service Oper. Management 18(1):69–88.Link, Google Scholar
• Gallego G, Topaloglu H (2019) Assortment optimization. Revenue Management and Pricing Analytics (Springer, New York), 129–160.Crossref, Google Scholar
• Garey MR, Johnson DS (1979) Computers and Intractability (W. H. Freeman, New York).Google Scholar
• Gorissen BL, den Hertog D, Reusken M (2022) Hidden convexity in a class of optimization problems with bilinear terms. Preprint, submitted July 3, https://optimization-online.org/2022/07/8973/.Google Scholar
• Green PE, Krieger AM, Wind Y (2004) Buyer Choice Simulators, Optimizers, and Dynamic Models (Springer US, Boston), 169–199.Crossref, Google Scholar
• Hainmueller J, Hopkins DJ, Yamamoto T (2014) Causal inference in conjoint analysis: Understanding multidimensional choices via stated preference experiments. Polit. Anal. 22(1):1–30.Crossref, Google Scholar
• Hastad J (1996) Clique is hard to approximate within n1−ϵ. Proc. 37th Conf. Foundations Comput. Sci. (IEEE, Piscataway, NJ), 627–636.Google Scholar
• Håstad J (2001) Some optimal inapproximability results. J. ACM 48(4):798–859.Crossref, Google Scholar
• Hofbauer J, Sandholm WH (2002) On the global convergence of stochastic fictitious play. Econometrica 70(6):2265–2294.Crossref, Google Scholar
• Huchette J, Vielma JP (2017) Nonconvex piecewise linear functions: Advanced formulations and simple modeling tools. Preprint, submitted July 31, https://arxiv.org/abs/1708.00050v1.Google Scholar
• Jagabathula S, Subramanian L, Venkataraman A (2020) A conditional gradient approach for nonparametric estimation of mixing distributions. Management Sci. 66(8):3635–3656.Link, Google Scholar
• Jaillet P, Loke GG, Sim M (2018) Strategic manpower planning under uncertainty. Preprint, submitted April 24, https://doi.org/10.2139/ssrn.3168168.Google Scholar
• Kohli R, Krishnamurti R (1987) A heuristic approach to product design. Management Sci. 33(12):1523–1533.Link, Google Scholar
• Kohli R, Krishnamurti R (1989) Optimal product design using conjoint analysis: Computational complexity and algorithms. Eur. J. Oper. Res. 40(2):186–195.Crossref, Google Scholar
• Kohli R, Sukumar R (1990) Heuristics for product-line design using conjoint analysis. Management Sci. 36(12):1464–1478.Link, Google Scholar
• Liu S, Siddiq A, Zhang J (2025) Planning bike lanes with data: Ridership, congestion, and path selection. Management Sci. 71(9):7631–7654.Link, Google Scholar
• Liu M, Pan Z, Xu K, Manocha D (2020) New formulation of mixed-integer conic programming for globally optimal grasp planning. IEEE Robotics Automation Lett. 5(3):4663–4670.Google Scholar
• Lubin M, Dvorkin Y, Roald L (2019) Chance constraints for improving the security of AC optimal power flow. IEEE Trans. Power Systems 34(3):1908–1917.Crossref, Google Scholar
• Lubin M, Vielma JP, Zadik I (2017) Mixed-integer convex representability. Preprint, submitted June 16, https://arxiv.org/abs/1706.05135v1.Google Scholar
• Lubin M, Yamangil E, Bent R, Vielma JP (2018) Polyhedral approximation in mixed-integer convex optimization. Math. Program. 172(1):139–168.Crossref, Google Scholar
• Mak H-Y, Rong Y, Shen Z-JM (2013) Infrastructure planning for electric vehicles with battery swapping. Management Sci. 59(7):1557–1575.Link, Google Scholar
• McBride RD, Zufryden FS (1988) An integer programming approach to the optimal product line selection problem. Marketing Sci. 7(2):126–140.Link, Google Scholar
• Mišić VV (2020) Optimization of tree ensembles. Oper. Res. 68(5):1605–1624.Link, Google Scholar
• Mosek ApS (2021a) Mosek modeling cookbook. Accessed June 1, 2021, https://docs.mosek.com/MOSEKModelingCookbook.pdf.Google Scholar
• Mosek ApS (2021b) Mosek optimization suite. Accessed June 1, 2021, http://www.mosek.com.Google Scholar
• Papadimitriou CH, Yannakakis M (1991) Optimization, approximation, and complexity classes. J. Comput. System Sci. 43(3):425–440.Crossref, Google Scholar
• Rossi PE (2019) bayesm: Bayesian inference for marketing/micro-econometrics. R package version 3.1-4. Accessed June 1, 2021, https://cran.r-project.org/web/packages/bayesm/index.html.Google Scholar
• Rusmevichientong P, Shmoys D, Tong C, Topaloglu H (2014) Assortment optimization under the multinomial logit model with random choice parameters. Production Oper. Management 23(11):2023–2039.Crossref, Google Scholar
• Schmalensee R, Thisse J-F (1988) Perceptual maps and the optimal location of new products: An integrative essay. Internat. J. Res. Marketing 5(4):225–249.Crossref, Google Scholar
• Schön C (2010) On the optimal product line selection problem with price discrimination. Management Sci. 56(5):896–902.Link, Google Scholar
• Şen A, Atamtürk A, Kaminsky P (2018) A conic integer optimization approach to the constrained assortment problem under the mixed multinomial logit model. Oper. Res. 66(4):994–1003.Link, Google Scholar
• Shao H, Kleywegt AJ (2021) Tractable profit maximization over multiple attributes under discrete choice models. Preprint, submitted December 22, https://arxiv.org/abs/2007.09193.Google Scholar
• Sherali HD, Adams WP (1990) A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Discrete Math. 3(3):411–430.Crossref, Google Scholar
• Shi L, Ólafsson S, Chen Q (2001) An optimization framework for product design. Management Sci. 47(12):1681–1692.Link, Google Scholar
• Talluri K, Van Ryzin G (2004) Revenue management under a general discrete choice model of consumer behavior. Management Sci. 50(1):15–33.Link, Google Scholar
• Toubia O, Simester DI, Hauser JR, Dahan E (2003) Fast polyhedral adaptive conjoint estimation. Marketing Sci. 22(3):273–303.Link, Google Scholar
• Train KE (2009) Discrete Choice Methods with Simulation (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Udell M, Boyd S (2013) Maximizing a sum of sigmoids. Working paper, Stanford University, Stanford, CA.Google Scholar
• Vavra TC, Green PE, Krieger AM (1999) Evaluating EZPass. Marketing Res. 11(2):4–16.Google Scholar
• Wang X, Camm JD, Curry DJ (2009) A branch-and-price approach to the share-of-choice product line design problem. Management Sci. 55(10):1718–1728.Link, Google Scholar
• Wind J, Green PE, Shifflet D, Scarbrough M (1989) Courtyard by Marriott: Designing a hotel facility with consumer-based marketing models. Interfaces 19(1):25–47.Link, Google Scholar
• Zhen J, de Moor D, den Hertog D (2021) An extension of the reformulation-linearization technique to nonlinear optimization. Preprint, submitted July 8, https://optimization-online.org/2021/07/8491/.Google Scholar
• Zhen J, Marandi A, de Moor D, den Hertog D, Vandenberghe L (2022) Disjoint bilinear optimization: A two-stage robust optimization perspective. INFORMS J. Comput. 34(5):2410–2427.Link, Google Scholar
• Zhu T, Xie J, Sim M (2022) Joint estimation and robustness optimization. Management Sci. 68(3):1659–1677.Link, Google Scholar