Optimality conditions for job 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 decentralized scheme is defined in which at a local level, the optimal control of each single machine is considered, whereas, at a higher level, the optimal splitting of jobs on parallel machines is taken into account. At the local level, an optimization problem with quadratic cost function and nonlinear constraints is stated as a multistage control problem and solved by means of dynamic programming techniques.