Active demand management for substitute products through price optimisation

This paper presents a systematic mathematical programming approach for active demand management in process industries. The proposed methodology aims to determine optimal pricing policies as well as output levels for substitute products, while taking into consideration manufacturing costs, resource availability, customer demand elasticity, outsourcing and market competition. First, profit maximisation analytical formulae are derived for determining Nash equilibrium in prices for a duopolistic market environment where each company produces only one product. An iterative algorithm is then proposed so as to determine the decision-making process by solving a series of non-linear mathematical programming (NLP) models before determining the Nash equilibrium in prices for the competing companies. The proposed algorithm is extended in order to accommodate the case of multi-product companies, each one selling a set of substitute products at different prices. The applicability of the proposed methodology is demonstrated by a number of illustrative examples.