Research Papers

Market-System Design Optimization With Consider-Then-Choose Models

[+] Author and Article Information
W. Ross Morrow

Assistant Professor
Mechanical Engineering,
Iowa State University,
Ames, Iowa 50011
e-mail: wrmorrow@iastate.edu

Minhua Long

Mechanical Engineering,
Iowa State University,
Ames, Iowa 50011
e-mail: mhlong@iastate.edu

Erin F. MacDonald

Assistant Professor
Mechanical Engineering,
Iowa State University,
Ames, Iowa 50011
e-mail: erinmacd@iastate.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 12, 2012; final manuscript received November 19, 2013; published online January 10, 2014. Assoc. Editor: Wei Chen.

J. Mech. Des 136(3), 031003 (Jan 10, 2014) (13 pages) Paper No: MD-12-1452; doi: 10.1115/1.4026094 History: Received September 12, 2012; Revised November 19, 2013

Design optimization in market system research commonly relies on Discrete choice analysis (DCA) to forecast sales and revenues for different product variants. Conventional DCA, which represents consumer choice as a compensatory process through maximization of a smooth utility function, has proven to be reasonably accurate at predicting choice and interfaces easily with engineering models. However, the marketing literature has documented significant improvement in modeling choice with the use of models that incorporate both noncompensatory (descriptive) and compensatory (predictive) components. This noncompensatory component can, for example, model a “consider-then-choose” process in which potential customers first narrow their decisions to a small set of products using noncompensatory screening rules and then employ a compensatory evaluation to select from within this consideration set. This article presents solutions to a design optimization challenge that arises when demand is modeled with a consider-then-choose model: the choice probabilities are no longer continuous or continuously differentiable. We examine two different classes of methods to solve optimal design problems–genetic algorithms (GAs) and nonlinear programming (NLP) relaxations based on complementarity constraints–for consider-then-choose models whose screening rules are based on conjunctive (logical “and”) rules.

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Grahic Jump Location
Fig. 1

Contours of profits optimal solutions to Eqs. (15) and (16). Green denotes profits that are nearly, or exactly, zero.

Grahic Jump Location
Fig. 2

Results for Scenario (3). Left: Optimal vehicle designs for Eq. (18) as η varies. Arrow indicates direction of increasing η. Right: Fraction of successful solves of Eq. (18) versus the distance of the optimal solution to the solution from Scenario (2).

Grahic Jump Location
Fig. 3

Non-compensatory (left) and relaxed (right) choice probabilities for Eq. (4) based on Example 1, Sec. 2.

Grahic Jump Location
Fig. 4

Vehicle design solutions for the three methods across two cases; note the different scales on the vertical axis in left and right figures. Gray lines on the left figure denote the budget curves Rip+mipGg=Bi. Best vehicle portfolio profits, per vehicle sold, found by each method are in parentheses.

Grahic Jump Location
Fig. 5

Empirical CDF of solution profits found relative to the best-known profit in two cases: (J,I) = (5,10) (left) and (J,I)=(10,50) (right).

Grahic Jump Location
Fig. 6

Solution times for Eq. (33) for two population sizes. Means plotted with dashed lines, with solid lines illustrating one standard deviation above and below the mean.

Grahic Jump Location
Fig. 7

Function evaluation counts for Eq. (33) for two population sizes. Means plotted with dashed lines, with solid lines illustrating one standard deviation above and below the mean.




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