Enhancing marketing with engineering: Optimal product line design for heterogeneous markets

Successful product line design and development often require a balance of technical and market tradeoffs. Quantitative methods for optimizing product attribute levels using preference elicitation (e.g., conjoint) data are useful for many product types. However, products with substantial engineering content involve critical tradeoffs in the ability to achieve those desired attribute levels. Technical tradeoffs in product design must be made with an eye toward market consequences, particularly when heterogeneous market preferences make differentiation and strategic positioning critical to capturing a range of market segments and avoiding cannibalization.We present a unified methodology for product line optimization that coordinates positioning and design models to achieve realizable firm-level optima. The approach overcomes several shortcomings of prior product line optimization models by incorporating a general Bayesian account of consumer preference heterogeneity, managing attributes over a continuous domain to alleviate issues of combinatorial complexity, and avoiding solutions that are impossible to realize. The method is demonstrated for a line of dial-readout scales, using physical models and conjoint-based consumer choice data. The results show that the optimal number of products in the line is not necessarily equal to the number of market segments, that an optimal single product for a heterogeneous market differs from that for a homogeneous one, and that the representational form for consumer heterogeneity has a substantial impact on the design and profitability of the resulting optimal product line — even for the design of a single product. The method is managerially valuable because it yields product line solutions efficiently, accounting for marketing-based preference heterogeneity as well as engineering-based constraints with which product attributes can be realized.     

An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs

Davis, Panas, and Zariphopoulou (1993) and Hodges and Neuberger (1989) have presented a very appealing model for pricing European options in the presence of rehedging transaction costs. In their papers the 'maximization of utility' leads to a hedging strategy and an option value. The latter is different from the Black–Scholes fair value and is given by the solution of a three–dimensional free boundary problem. This problem is computationally very time–consuming. In this paper we analyze this problem in the realistic case of small transaction costs, applying simple ideas of asymptotic analysis. The problem is then reduced to an inhomogeneous diffusion equation in only two independent variables, the asset price and time. The advantages of this approach are to increase the speed at which the optimal hedging strategy is calculated and to add insight generally. Indeed, we find a very simple analytical expression for the hedging strategy involving the option's gamma.