Optimization Beyond Prediction: Prescriptive Price Optimization
  This paper addresses a novel data science problem, prescriptive price optimization, which derives the optimal price strategy to maximize future profit/revenue on the basis of massive predictive formulas produced by machine learning. The prescriptive price optimization first builds sales forecast formulas of multiple products, on the basis of historical data, which reveal complex relationships between sales and prices, such as price elasticity of demand and cannibalization. Then, it constructs a mathematical optimization problem on the basis of those predictive formulas. We present that the optimization problem can be formulated as an instance of binary quadratic programming (BQP). Although BQP problems are NP-hard in general and computationally intractable, we propose a fast approximation algorithm using a semi-definite programming (SDP) relaxation, which is closely related to the Goemans-Williamson's Max-Cut approximation. Our experiments on simulation and real retail datasets show that our prescriptive price optimization simultaneously derives the optimal prices of tens/hundreds products with practical computational time, that potentially improve 8.2% of gross profit of those products. 
Shinji Ito and Ryohei Fujimaki
math.OC cs.LG stat.ML