Modeling and solving real-time scheduling problems by stochastic integer programming

This contribution deals with scheduling problems of flexible chemical batch processes with a special emphasis on their real-time character. This implies not only the need for sufficiently short response times, but in particular the burden of incomplete knowledge about the future. To solve such problems, the application of two-stage stochastic integer programming techniques on moving horizons is proposed. They reflect the need for immediately applicable decisions and the potential of later recourse actions to cope with realized uncertainties. In addition to the classical expected value objective, simple measures of risk can be included. Motivated by an example process, some essential modeling prerequisites are discussed. As an important first step, the master scheduling problem is studied and a number of master scheduling models are presented. Large mixed-integer linear problems arise, which are well-suited for a dual decomposition approach. Numerical experiments with a problem-specific solution algorithm demonstrate the applicability of the method to real-world problems.