Algorithms for determining quality/cost/price tradeoffs in saturated markets are considered. A product is modeled by d real-valued qualities whose sum determines the unit cost of producing the product. This leads to the following optimization problem: given a set of n customers, each of whom has certain minimum quality requirements and a maximum price they are willing to pay, design a new product and select a price for that product in order to maximize the resulting profit.
An O(nlog n) time algorithm is given for the case, d=1, of products having a single quality, and O(n(log n)d+1) time approximation algorithms are given for products with any constant number, d, of qualities. To achieve the latter result, an O(nkd−1) bound on the complexity of an arrangement of homothetic simplices in ℝd is given, where k is the maximum number of simplices that all contain a single points.
Erickson, G.M.: Dynamic Models of Advertising Competition: Open- and Closed-Loop Extensions. Kluwer Academic, Boston (1991)
Kotler, P., Lane, K.: Marketing Management. Prentice-Hall, New York (2005)
Naik, P.A., Raman, K., Winer, R.S.: Planning marketing-mix strategies in the presence of interaction effects. Mark. Sci. 24(1), 25–34 (2005)
Thompson, G.L., Teng, J.-T.: Optimal pricing and advertising policies for new product oligopoly models. Mark. Sci. 3(1), 148–168 (1984)
Varian, H.R.: Revealed preference. In: Szenberg, M., Ramrattan, L., Gottesman, A.A. (eds.) Samuelsonian Economics in the 21st Century, pp. 99–115. Oxford University Press, New York (2006)