A backward algorithm for computing optimal controls for single-stage hybrid manufacturing systems

Abstract

This paper concerns optimal control problems in single-stage manufacturing systems. The control variables comprise parameters of the jobs' processing times, and the cost functional involves measures of both jobs' due dates and products' physical characteristics. The system is configured for processing a finite number of jobs in a given order, and it is modelled as a hybrid dynamical system cast in a deterministic setup. The paper identifies a necessary and sufficient optimality condition having an intuitive geometric appeal, and it develops an efficient, low-complexity algorithm for computing the optimal controls. Numerical experiments testify to the efficacy of the proposed algorithm.