Algorithms for Marketing-Mix Optimization

Algorithms for determining quality/cost/price tradeoffs in saturated markets are consid-3 ered. A product is modeled by d real-valued qualities whose sum determines the unit cost of producing4 the product. This leads to the following optimization problem: given a set of n customers, each of5 whom has certain minimum quality requirements and a maximum price they are willing to pay, design6 a new product and select a price for that product in order to maximize the resulting profit.7 An O(n log n) time algorithm is given for the case, d = 1, of products having a single quality,8 and O(n(log n)d+1) time approximation algorithms are given for products with any constant number,9 d, of qualities. To achieve the latter result, an O(nkd−1) bound on the complexity of an arrangement10 of homothetic simplices in Rd is given, where k is the maximum number of simplices that all contain11 a single points.12 ½ ÁÒØÖÓ Ù Ø ÓÒ13 Revealed preference theory [13] is a method of determining a co...

• Type: Journal
• Year: 2011
• Where: ALGORITHMICA
• Authors: Joachim Gudmundsson, Pat Morin, Michiel H. M. Smid
• Keywords: ALGORITHMICA 2011, Algorithms, Optimization Problem, Time Algorithm, Time Approximation Algorithms