.. Auto-generated by scripts/generate_problem_catalog_docs.py. Do not edit by hand. 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 :doc:`../decision` for the decision family index. Quick Facts ----------- .. list-table:: :header-rows: 1 :widths: 20 80 * - 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 ---------------- .. list-table:: :header-rows: 1 :widths: 25 75 * - 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 .. list-table:: :header-rows: 1 :widths: 10 30 15 20 20 * - 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. .. list-table:: :header-rows: 1 :widths: 10 22 10 13 10 15 20 * - 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. .. list-table:: :header-rows: 1 :widths: 10 22 10 13 10 15 20 * - 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 --------------- .. list-table:: :header-rows: 1 :widths: 25 75 * - Field - Value * - Candidate Kind - discrete-option * - Candidate Count - 3125 * - Competitor Profile Count - 10 * - Total Option Count - 3125 Option Factors ~~~~~~~~~~~~~~ .. list-table:: :header-rows: 1 :widths: 10 20 12 33 25 * - 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 ------- .. list-table:: :header-rows: 1 :widths: 20 80 * - 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 -------------------- .. code-block:: text 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.