Theoretical Foundations of Multi-Product Prices Optimization Model (Part1)

Abstract

The paper investigates and analyses the technologies and the methods for price optimization in a multi-product environment, where the firms face more difficulties to make an optimal decisions. Multi-Product Prices Optimization (MPPO) problem emerges specific problems, because of both prices and demands, being random variables, may exhibit different covariate relationships, determined by means of substitutional and complimentarity effects. The system of covariate relationships, determined by means of substitution and complimentarity processes, is represented as the system of multivariance regression equations. MPPO problem have been reduced to the maximization problem of the objective function of Total Revenue, which is a quadratic form. In multidimensional cases one faces the problem of absence of local maximum of Total Revenue function. The simple criterion of existing the optimal solution of
the MPPO problem is suggested. In the case of absence of the strict maximum of Total Revenue function, parameters should be calculated on the base of OPPO model, that is on the base of independent paired problems. The represented theory can be used as a basis for development of a relevant software.
Keywords: complementarity, multi-product pricing, price optimization, single-product pricing, substitution, total revenue
JEL: M21