One-machine n-part-type optimal setup scheduling: analytical characterization of switching surfaces

The authors consider optimal setup scheduling of a single reliable machine. Production flow of n different part types and the setup process are described by differential equations. Setup change rates are control variables. Necessary conditions on optimal setup changes are characterized analytically, and optimal setup change times are derived for a given setup change sequence. The linearization of optimal setup switching surfaces is derived, indicating the existence of attractors observed in numerical optimal solutions. The approach developed in this paper establishes a strong basis for studying multimachine production systems and for constructing tractable near-optimal numerical solution techniques.