Empirical risk minimization for big data driven prescriptive analytics: An exploration of two-stage stochastic programs with recourse

In the operations research literature, data driven analyses using big data are receiving more and more interest and attention. However, big data driven operational analyses are still limited in scope, with only unconstrained big data driven problems, e.g. the newsvendor problem, being comprehensively explored. If big data driven analyses are to become a core part of operations research and practice, one must be able to formulate and solve constrained big data driven models. We therefore propose a direct empirical risk minimization (DERM) method for formulating and solving a class of constrained big data driven operation research problems. In big data driven problems, relevant operational prescriptions are dependent on a set of observed features. In this paper, we assume linear feature relationships, which enable us to fundamentally base the DERM method on linear stochastic programming. The assumption of linear feature relationships is also seen in the literature on big data driven newsvendor models. We prove that if a big data driven solution exists, the DERM method will always, for the class of constrained problems we study, arrive at a feasible solution of the initial opera tional problem. Moreover, we exemplify the DERM method by formulating and solving two specific big data driven operational problems. In the numerical study of the two operational problems, we show, that under linear demand, the DERM method outperforms, with regard to cost, two benchmark methods and a big data driven method from literature. • We contribute to the emerging area of big data driven operations research. • We introduce a method that can solve a class of constrained big data driven problems. • We show that the method will construct feasible in-sample results for the operational problem. • We show two problems where the method on average outperforms benchmark methods. • We discuss the relative strengths of each big data driven method in an industrial context.