The production planning problem: Clearing functions, variable lead times, delay equations and partial differential equations

Determining the production rate of a factory as a function of current and previous states is at the heart of the production planning problem. Different approaches to this problem presented in this book are reviewed and their relationship is discussed. Necessary conditions for the success of a clearing function as a quasi steady approximation are presented and more sophisticated approaches allowing the prediction of outflow in transient situations are discussed. Open loop solutions to the deterministic production problem are introduced and promising new research directions are outlined.