Optimal lot splitting on parallel machines

The control of manufacturing systems consisting of a certain number of parallel machines processing a given number of jobs is addressed in this work. A decentralised scheme composed of two decisional levels is defined in which, at a local level, the optimal control of each single machine is considered, whereas, at a higher level, the performances of a manufacturing system consisting of several machines are optimised. The relevant optimisation problem, with a quadratic cost function and non-linear constraints, is stated and solved as a multistage control problem to which dynamic programming techniques are applied to determine the sequence of optimal control closed-loop policies.