Robust Production Management

The problem of production management can often be cast in the form of a linear program with uncertain parameters and risk constraints. Typically, such problems are treated in the framework of multi-stage Stochastic Programming. Recently, a Robust Counterpart (RC) approach has been proposed, in which the decisions are optimized for the worst realizations of problem parameters. However, an application of the RC technique often results in very conservative approximations of uncertain problems. To tackle this drawback, an Adjustable Robust Counterpart (ARC) approach has been proposed in (Ben-Tal et al. 2003). In ARC, some decision variables are allowed to depend on past values of uncertain parameters. A restricted version of ARC, introduced in (Ben-Tal et al. 2003), which can be efficiently solved, is referred to as Affinely Adjustable Robust Counterpart (AARC). In this paper, we consider an application of the ARC and AARC methodologies to the problem of yearly electricity production management in France. We provide tractable formulations for the AARC of quadratic and of some conic quadratic optimization problems, as well as for the ARC and AARC of the electricity production problem. We then give the quality of robust solutions obtained by using different uncertainty sets estimated using simulated and historical data. Our methodology is finally compared with other management methods.