A fractional programming approach for retail category price optimization

Abstract

We present a new mixed-integer programming (MIP) approach to study certain retail category pricing problems that arise in practice. The motivation for this research arises from the need to design innovative analytic retail optimization techniques at Oracle Corporation to not only predict the empirical effect of price changes on the overall sales and revenue of a category, but also to prescribe optimal dynamic pricing recommendations across a category or demand group. A multinomial logit nonlinear optimization model is developed, which is recast as a discrete, nonlinear fractional program (DNFP). The DNFP model employs a bi-level, predictive modeling framework to manage the empirical effects of price elasticity and competition on sales and revenue, and to maximize the gross-margin of the demand group, while satisfying certain practical side-constraints. This model is then transformed by using the Reformulation–Linearization Technique in tandem with a sequential bound-tightening scheme to recover an MIP formulation having a relatively tight underlying linear programming relaxation, which can be effectively solved by any commercial optimization software package. We present sample computational results using randomly generated instances of DNFP having different constraint settings and price range restrictions that are representative of common business requirements, and analyze the empirical effects of certain key modeling parameters. Our results indicate that the proposed retail price optimization methodology can be effectively deployed within practical retail category management applications for solving DNFP instances that typically occur in practice.