A column generation heuristic for complex job shop multiple orders per job scheduling

Scheduling in semiconductor manufacturing is a challenging task due to inherent complexities like assignment of multiple customer orders to front opening unified pods (FOUPs), batch processing in multiple toolgroups with parallel machines, and re-entrant flow. A disjunctive–network-flow mixed integer program (DNF) and a column generation heuristic are presented to minimize the sum of weighted customer order completion times in a complex job shop environment. In addition, a lower bound estimation approach for the complex job shop problem is presented. The column generation heuristic obtains solutions that are very close to that of the time constrained DNF formulation for problem instances with zero order ready times. However, column generation’s performance differs considerably for problem instances with non-zero order ready times and is able to solve large problem instances in a matter of minutes.