Reconciling business analytics with graphically initialized subspace clustering for optimal nonlinear pricing

Abstract

The relationship between price and quantity in nonlinear pricing transcends simple proportionality, as conditional rebates and discounts may be contingent upon the quantity of goods or services purchased by consumers. This dynamic introduces significant challenges for both consumers and business operators because incomplete information arises from the inherent uncertainty of consumer behavior. In light of this, the present research elucidates the pursuit of optimal nonlinear pricing strategies by business operators through an innovative data-driven approach. Our contributions encompass two distinctive facets: a novel unsupervised spectral clustering method, termed graphically initialized subspace clustering, and a decision optimization framework. The proposed data-driven method introduces an optimization problem aimed at minimizing subspace partitioning costs, leveraging the efficient utilization of a mixture multivariate skewed t distribution to effectively capture heavy users and to characterize their parametric behavioral patterns. In addition, the decision optimization component builds upon the aforementioned method, employing a convex optimization algorithm to enable seamless modification of attributes in nonlinear pricing, while ensuring revenue consistency during pre- and post-modification. Notably, we substantiate the interpretability and practical applicability of our proposed methodology in the realm of business analytics, through empirical analysis utilizing real-world data obtained from a cellular carrier. The findings of this study confirm the efficacy and viability of our approach in enabling business operators to navigate the complexities of nonlinear pricing optimization with confidence and informed decision-making.