Hybridizing discrete- and continuous-time models for batch sizing and scheduling problems

This paper proposes a new hybrid technique called ‘partial parameter uniformization’ (hereafter PPU). The technique simplifies problems by ignoring the different values that certain problem parameters can take, which may facilitate the solution of some hard combinatorial optimization problems. PPU is applied to complex batch sizing and scheduling problems. Some information can be obtained from a discrete-time model in which job durations have been made uniform. This information is then exploited by a more detailed continuous-time model to generate feasible solutions and further improve these solutions. Good, or optimal solutions to the Westenberger and Kallrath Benchmark problems have been obtained in this way, at relatively low computational cost, as have solutions to the newer problems of Blömer and Günther.