State estimation in online batch production scheduling: concepts, definitions, algorithms and optimization models

The goal of this paper is to present concepts and methods that allow us to account for real-time data in online scheduling without embedding a dynamic model. First, we discuss the key role played by the progress status of a batch, the key state in scheduling. Specifically, we show how fractional changes in the progress status necessitate the re-calculation, using real-time data, of parameters used in scheduling models (which have always been thought to be constants). Second, we present algorithms for the calculation of the progress status and the above parameters. Third, we present a state-space resource task network (RTN) formulation employing parameters calculated in real-time and show why, in this context, it should account for delays of batches under execution as optimization decisions. Finally, we show how the proposed methods lead to tractable optimization problems and can be used to address problems that cannot be solved using existing scheduling approaches.