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TABLE 3. Statistics for 10,000 attempted solves of Eqn. (21) using SNOPT for various values of I. For each value of I, a single set of samples of ι i ,r i ,m i ,B i and the random utility coefficients are drawn as specified in the text. Different trials for each I are started at randomly drawn initial conditions, using the same set of samples. Number of Individuals (I) 5 10 15 20 25 30 35 40 45 50 Collections of Choice Sets (#) 10 1.5 10 3 10 4.5 10 6 10 7.5 10 9 10 10.5 10 12 10 13.5 10 15.1 Statistics from 100,000 solves of Eqn. (23) starting at randomly drawn initial conditions using SNOPT Feasible Collections of Choice Sets (#) 10 26 48 77 108 133 158 207 257 327 Locally Optimal Solutions (#) 2 4 7 9 8 10 13 11 11 10 Optimal Profits (10 4 $) 1.60 1.38 1.15 1.16 1.22 1.19 1.10 1.10 1.15 1.10 “Volume” of Optimal Consideration Set (%) 50.1 12.7 6.8 6.6 6.1 3.1 1.9 1.9 1.9 1.5 Statistics from 10,000 attempted solves of Eqn. (21) starting at randomly drawn initial conditions using SNOPT Number of Problem Variables (#) 32 62 92 122 152 182 212 242 272 302 Number of Problem Constraints (#) 36 71 106 141 176 211 246 281 316 351 Number of Local Solutions Computed (#) 5 6 9 11 13 13 15 16 19 17 Maximum Profits Computed (10 4 $) 1.60 1.38 1.15 1.16 1.22 1.19 1.10 1.10 1.15 1.08 Average Compute Time (all runs) (µs) 4.1 9.3 10.9 15.4 18.6 23.8 26.6 33.3 40.8 49.5 Successful Solves (%) 99.7 99.4 96.6 95.8 97.7 97.4 97.9 96.6 97.3 92.9 Terminated at a Trivial KKT Point (%) 0.03 0.03 0.20 0.19 0.12 0.16 0.07 0.16 0.11 0.26 Solver Failed to Converge (%) 0.19 0.52 3.10 3.91 2.06 2.28 1.81 1.94 2.19 6.43 [14] Kumar, D., Hoyle, C., Chen, W., Wang, N., Gomex-Levi, G., and Koppelman, F., 2009. “A Hierarchical Choice Modeling Approach for Incorporating Customer Preferences in Vehicle Package Design”. International Journal of Product Development, 8(3), pp. 228–251. [15] MacDonald, E., Whitefoot, K., Allison, J., Papalambros, P. Y., and Gonzalez, R., 2010. “An Investigation of Sustainability, Preference, and Profitability in Design Optimization”. In Proceedings of the ASME 2010 International Design Engineering Technical Conferences. [16] Frischknecht, B. D., Whitefoot, K., and Papalambros, P. Y., 2010. “On the Suitability of Econometric Demand Models in Design for Market Systems”. Journal of Mechanical Design, 132, pp. 1–11. [17] Simon, H. A., 1957. Models of Man. Wiley. [18] Coombs, C. H., 1964. A Theory of Data. Wiley. [19] Dawes, R. M., 1964. “Social selection based on multidimensional criteria”. Journal of Abnormal and Social Psychology, 68, pp. 104–109. [20] Einhorn, H. J., 1970. “The use of nonlinear, noncompensatory models in decision making”. Psychological Bulletin, 73, pp. 211–230. [21] Tversky, A., 1972. “Elimination by Aspects: A Theory of Choice”. Psychological Review, 79(4), pp. 281–299. [22] Simon, H. A., 1986. “Rationality in psychology and economics”. The Journal of Business, 59(4), pp. S209–S224. [23] Hauser, J. R., and Wernerfelt, B., 1990. “An Evaluation Cost Model of Consideration Sets”. Journal of Consumer Research, 16, p. 393=408. [24] Hauser, J. R., Forthcoming. “Consideration Set Heuristics”. Journal of Business Research. [25] Hauser, J. R., 1978. “Testing the Accuracy, Usefulness and Significance of Probabilistic Models: An Information- Theoretic Approach”. Operations Research, 26(3), pp. 406–421. [26] Payne, J. W., 1976. “Task Complexity and Contingent Processing in Decision Making: An Information Search”. Organizational Behavior and Human Performance, 16, 14 Copyright c○ 2012 by ASME
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Page 1 and 2: Proceedings of the ASME 2012 Intern
Page 3 and 4: j ∈ {1,...,J} is given by ⎧ ⎪
Page 5 and 6: TABLE 1. Optimal solutions to Eqns.
Page 7 and 8: over the assumed collection of cons
Page 9 and 10: y either relaxing the constraints c
Page 11 and 12: also has different compensatory pre
Page 13: Vehicle Fuel Economy (mpg) 50 45 40
Page 17 and 18: This formula is a modified version

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