Optimization and analysis of three-part tariff pricing strategies

Service providers usually offer different pricing schemes to consumers, which can simultaneously influence consumers’ tariff choices and their usage of the service and thus greatly affect the profits of the service providers or the utilization of the service system. However, little is known about the optimal design and management of three-part tariff pricing schemes because the models are generally not analytically tractable since the arbitrary population of heterogeneous consumers can yield an extremely complex profit function with multiple local optima. This study investigates how to design three-part tariffs, which are pricing plans that are widely used in transportation or telecommunications industries, by formulating a mixed-integer nonlinear programming optimization model. In particular, numerical analyses using GAMS/BARON and metaheuristic approaches including genetic algorithm, particle swarm optimization algorithm, and sine cosine algorithm were conducted to derive the optimal three-part tariffs under specific conditions and to compare several common tariff structures (e.g., the menus of the three-part tariff, single three-part tariff, two-part tariff, and flat rate). This study successfully identified key factors affecting the performance of the different pricing structures. Guidelines for determining the best timing of the use of different pricing structures were also derived.