Abstract: This paper investigates the joint optimization issue of product production and capacity for manufacturing enterprises in a data-driven context. A notable feature of this issue is that uncertain product demand depends on production decisions. Firstly, the paper utilizes statistical learning models to construct a prediction function for demand based on product decisions and exogenous covariates. Furthermore, based on this prediction model, a decision-dependent data-driven two-stage stochastic production optimization model is constructed. Additionally, in the case of a single production facility, the paper provides an analytical solution for the optimal capacity decision and a pseudo-polynomial time algorithm for solving the optimal production decision. In general cases, an equivalent reformulation of the model as a mixed-integer linear programming is given. Finally, numerical experiments based on real data validate the significance of incorporating decision-dependency modeling and prediction models in enhancing the quality of production decisions.

Key words: production optimization, two-stage stochastic programming, decision-dependent, data-driven, demand uncertainty