Decision Problem - Student Laptop Design Under Choice-Based Demand

A decision-based design framing for choosing laptop architecture and price to maximize predicted market share as an equal-margin profit proxy in a student market segment under engineering and demand constraints.

See Decision Problem Catalog for the decision family index.

Quick Facts

Field	Value
Problem ID	`decision_laptop_design_profit_maximization`
Problem Family	decision
Implementation	`DecisionProblem`
Capabilities	`bounded-variables`, `citation-backed`, `statement-markdown`
Study Suitability	none
Tags	`decision`, `product-design`, `laptop`, `consumer-choice`, `profit`, `conjoint-analysis`, `market-modeling`

Taxonomy

Formulation: decision_based_design
Convexity: not_guaranteed
Design Variable Type: mixed
Is Dynamic: no
Orientation: engineering-practical
Objective Mode: single
Constraint Nature: hard
Bounds Summary: Six bounded decision variables: five physical design attributes plus price.
Tags: decision, product-design, laptop, consumer-choice, profit, conjoint-analysis, market-modeling
Deliverable Type: recommended-design
Participants: individual
Evaluation Mode: profit-maximization

Statement

Select the specification and selling price of a new laptop targeted at college and graduate students. The decision combines engineering feasibility, estimated production cost, and a conjoint-survey demand model calibrated against ten competitor laptops.

The paper models a single-product launch. The decision is to choose LCD size, body width, body depth, body thickness, battery volume ratio, and price so that the resulting design remains physically reasonable and attractive to the target market.

This packaged representation exposes the continuous engineering-side variables, the discrete conjoint factor levels, the competitor set, one executable discrete part-worth logit evaluator, and the five continuous-design constraint equations from the paper. The evaluator maximizes predicted market share over the explicit conjoint option set under the paper’s equal-margin assumption.

Decision Context

Field	Value
Decision Maker	A laptop producer choosing one new product design for the U.S. student laptop segment.
Market Segment	College and graduate students, modeled as a 1.6 million-unit market segment with ten incumbent competitors.
Decision Scope	Choose one product configuration and price at a single time point, assuming competitor designs and prices remain fixed during the decision.

Decision Variables

LCD size x1 in [10, 17] inches
Body width x2 in [5, 20] inches
Body depth x3 in [5, 20] inches
Body thickness x4 in [0.75, 2.0] inches
Battery volume ratio x5 in [-0.05, 0.20]
Price p in [0, 20] hundred-dollar units

Symbol	Label	Unit	Lower Bound	Upper Bound
x1	LCD size	inch	10	17
x2	Body width	inch	5	20
x3	Body depth	inch	5	20
x4	Body thickness	inch	0.75	2
x5	Battery volume ratio	n/a	-0.05	0.2
p	Price / 100	$100	0	20

Objectives

Maximize predicted market share over the explicit conjoint option set as an equal-margin profit proxy.
Score each discrete option with the Table 8 part-worth logit model against the ten Table 6 competitor profiles.
Convert predicted market share to expected demand using a 1.6 million-unit market-size assumption.

Key	Label	Sense	Domain	Executable	Variables	Expression
market_share_proxy	Discrete part-worth market-share proxy	maximize	discrete-option	yes	`z1`, `z2`, `z3`, `z4`, `z5`	exp(u_new) / (exp(u_new) + sum(exp(u_comp_i)))

Constraints

Expose the five continuous-design constraints from Equations (8) through (12) as typed formulas.
Reserve at least 100 cubic inches for non-battery components in the x-space engineering model.
Ensure the LCD plus a 0.5-inch margin fits within the chosen width and depth in the x-space engineering model.
Provide at least 1 hour of battery life and keep total weight at or below 10 pounds in the x-space engineering model.
Respect all lower and upper bounds taken from observed market offerings for the continuous design variables.

Key	Label	Relation	Domain	Executable	Variables	Expression
g1	Minimum non-battery volume	<=	continuous-design	no	`x2`, `x3`, `x4`, `x5`	100 - (x2 * x3 * x4) * (1 - x5)
g2	LCD width fit	<=	continuous-design	no	`x1`, `x2`	x1 * sqrt(1 + a^(-2)) + 2 * mLCD - x2
g3	LCD depth fit	<=	continuous-design	no	`x1`, `x3`	x1 * sqrt(1 + a^2) / a + 2 * mLCD - x3
g4	Minimum battery life	<=	continuous-design	no	`x2`, `x3`, `x4`, `x5`	1 - (160 * x2 * x3 * x4 * x5 * rB - 5.69) / Pavg
g5	Maximum total weight	<=	continuous-design	no	`x2`, `x3`, `x4`, `x5`	rV * (x2 * x3 * x4) * (1 - x5) + rB * (x2 * x3 * x4) * x5 - 10

Assumptions

The target market is approximated using responses from 18 Carnegie Mellon graduate students.
Competitor products are treated as static alternatives during optimization.
Cost curves for the LCD, battery, and motherboard are simplified empirical regressions.
Brand effects, advertising, distribution, and multi-product line interactions are excluded.

Candidate Space

Field	Value
Candidate Kind	discrete-option
Candidate Count	3125
Competitor Profile Count	10
Total Option Count	3125

Option Factors

Key	Label	Unit	Levels	Part Worths
z1	LCD size	inch	10.4, 12.1, 14.1, 15.4, 17	-1.076, -0.509, 0.231, 0.583, 0.381
z2	Thickness	inch	0.75, 1, 1.25, 1.5, 1.75	0.519, -0.075, -0.249, 0.091, -0.676
z3	Battery life	hour	1, 2, 4, 6, 8	-1.438, -0.687, 0.335, 0.778, 0.622
z4	Weight	lb	2.5, 4.5, 6, 8, 10	1.179, -0.455, 0.069, -0.471, -1.621
z5	Price / 100	$100	7.5, 10, 12.5, 15, 20	0.659, 0.314, 0.279, -0.018, -1.624

Sources

Key	Summary
`shiau_tseng_heutchy_michalek_2007`	Shiau, Tseng, Heutchy, and Michalek (2007). Design optimization of a laptop computer using aggregate and mixed logit demand models with consumer survey data. ASME IDETC/CIE 2007, DETC2007/DAC-34883.

Raw Citation Records

Shiau, Ching-Shin, Ian H. Tseng, Andrew W. Heutchy, and Jeremy Michalek (2007).
Design optimization of a laptop computer using aggregate and mixed logit demand
models with consumer survey data. Proceedings of the ASME 2007 International
Design Engineering Technical Conferences & Computers and Information in
Engineering Conference, DETC2007/DAC-34883.