Abstract
Very often product development is seen as a process where designers iterate through several design cycles until they converge upon a design that satisfies all of the necessary requirements—design within a single generation. If one takes the view that products change (i.e. adapt and evolve), a broader view must be adopted to capture the drivers of design adaptation across multiple product generations. This paper offers a new multi-generation conceptual framework of parametric design adaptation for consumer products, called the Artisan–Patron (AP) framework, and a complementary computational model. The AP framework captures the interaction between manufacturers (the Artisan) and consumers (the Patron) by structuring the various relevant information (e.g., consumer taste, government policy, cost of raw materials, etc.). Additionally, based on this framework, a corresponding computational model is developed, which allows engineers to find optimal settings for the design variables in a dynamic multi-generation environment. The utility of the conceptual framework and the computational model is demonstrated by considering the parametric design adaptation of the automobile with respect to two design parameters—engine horsepower and weight—based on historical automotive industry data.
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Abbreviations
- N :
-
Total number of competitive products (or manufacturers) within a given product segment
- i :
-
Index denoting product (or manufacturer) \({i.i{\in}N}\)
- j :
-
Index denoting competition of i \({(j\neq i)\cdot j{\in} N}\)
- t :
-
Index denoting time period or generation. t ≥ 0
- fe :
-
Fuel economy
- at :
-
0–60 mph acceleration time
- sf :
-
Measure of safety which is related to the fatality rate in two-car crashes
- hp :
-
Vehicle aggregate horsepower
- w :
-
Vehicle weight
- A :
-
Set of critical-to-value attributes (CVA) in a product
- a :
-
A single CVA, \({a\in A}\)
- \({{\bf z}_{i,t}^A}\) :
-
Vector of critical-to-value attributes (CVA) in product i at time \({t: {\bf z}_{i,t}^A =(z_{i,t}^1, {\ldots}, z_{i,t}^a, {\ldots}}\))
- \({{\hat{{\bf z}}}_{i,t}^A}\) :
-
Estimate of \({{\bf z}_{i,t}^A}\) – forecasted performance
- z a,I :
-
Ideal attribute setting where the consumer is unwilling to pay for further improvement
- z a,C :
-
Critical setting for attributes where the consumer is unwilling to purchase the product even if all other attributes are at an ideal setting
- z a,0 :
-
Baseline attribute settings (i.e. for the baseline product)
- \({\hat{{z}}_t^{fe}}\) :
-
Estimated average fuel economy (fe) at time t
- \({\hat{{z}}_t^{at}}\) :
-
Estimated average acceleration time (at) at time t
- \({\hat{{z}}_t^{sf}}\) :
-
Estimated average safety (sf) at time t
- \({z_{t}^{CAFE}}\) :
-
Sales-weighted (car & truck) adjusted fuel economy standard for the manufacturer’s product mix at time t
- \({R\left( {{\bf z}_{i,t}^A}\right)}\) :
-
Reward value based on \({{\bf z}_{i,t}^A }\)
- \({{\hat{{R}}}\left( {{\bf z}_{i,t}^A}\right)}\) :
-
Estimate of \({R\left( {{\bf z}_{i,t}^A}\right)}\)
- B :
-
Set of decision/design variables in a product design
- b :
-
A single decision variable, \({b\in B}\)
- \({{\bf x}_{i,t}^B}\) :
-
Vector of design or decision variables for product i at time t: \({{\bf x}_{i,t}^B}\) = (\({x_{i,t}^1,{\ldots}, x_{i,t}^b , {\ldots})}\)
- \({{\bf x}_{i,t}^{B,U} ({\bf x}_{i,t}^{B,L} )}\) :
-
Upper (and lower) bounds on design variables of product i at time t
- \({x_t^{hp}}\) :
-
Vehicle aggregate horsepower at time t
- \({x_t^w}\) :
-
Vehicle aggregate weight at time t
- \({c_{i,t}^T (\hat{{c}}_{i,t}^T )}\) :
-
Total production cost (estimate) for product i at time t
- \({c_{i,t}^V (\hat{{c}}_{i,t}^V )}\) :
-
Variable cost (estimate) for product i at time t
- \({c_{i,t}^I (\hat{{c}}_{i,t}^I )}\) :
-
Investment cost (estimate) for product i at time t
- \({c_{i,t}^R (\hat{{c}}_{i,t}^R )}\) :
-
Regulation cost (estimate) for product i at time t
- \({\hat{{c}}_t^{\rm weight}}\) :
-
Estimated cost as a function of overall automobile weight at time t (average for all manufacturers)
- \({\hat{{c}}_t^{\rm engine}}\) :
-
Estimated cost associated with delivering engine horsepower at time t (average for all manufacturers)
- \({\hat{{c}}_t^{CAFE}}\) :
-
Estimated CAFE policy penalty formula at time t(average for all manufacturers)
- V 0 :
-
Baseline value (i.e. at reference point)
- V i,t :
-
Value of product i at time t or average maximum willingness-to-pay for product i at time t
- \({\bar{{V}}_t }\) :
-
Average value of all products at time t
- \({v\left( {\hat{{z}}_{i,t}^a}\right)}\) :
-
Value of a single CVA ‘a’ for product i at time t
- p i,t :
-
Price of product i at time t
- p 0 :
-
Baseline price (i.e. at reference point)
- \({\bar{{p}}_t}\) :
-
Average price of all products at time t
- D i,t :
-
Demand for product i at time t
- D T,t :
-
Total market demand (for whole industry) at time t
- D T,0 :
-
Total market demand (for the whole industry) at the reference state (i.e. baseline total market demand)
- π i,t :
-
Profit of a single manufacturer i at time t
- Π t :
-
Profit of the industry (without investment cost) at time t
- \({\gamma_t^a }\) :
-
Measure of attribute ‘a’ importance. % time attribute ‘a’ is experienced by consumer during product use
- η 0 :
-
Price elasticity of demand at the reference state (baseline price elasticity)
- η t (\({\hat{{\eta}}_t )}\) :
-
Price elasticity (estimate) of demand at time t
- K t :
-
Constant-negative slope of the demand curve for the market segment of interest at time t
- ρ t :
-
Time adjusted CAFE penalty, ($) per mpg below standard
- \({\alpha_1^{fe} ,\alpha_2^{fe} ,\alpha_3^{fe}}\) :
-
Regression coefficients used for fuel economy (fe) transfer function
- \({\alpha_1^{at} ,\alpha_2^{at} ,\alpha_3^{at}}\) :
-
Regression coefficients used for acceleration time (at) transfer function
- \({\alpha_1^{sf} ,\alpha_2^{sf} ,\alpha_3^{sf}}\) :
-
Regression coefficients used for fuel economy (sf) transfer function
- β 1,t & β 2,t :
-
Parameters of engine cost
- β 3,t :
-
Cost of automobile raw materials per pound
- β 4,t :
-
Multiplier to account for economic fluctuation
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Yassine, A.A. Parametric design adaptation for competitive products. J Intell Manuf 23, 541–559 (2012). https://doi.org/10.1007/s10845-010-0392-5
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DOI: https://doi.org/10.1007/s10845-010-0392-5