Relation matrices for automated MILP modeling of scheduling problems using temporal constraints

This paper addresses the forming of Mixed Integer Linear Programming (MILP) models for factory scheduling. Relation Matrices using Allen´s temporal relations for qualitative relations between the single operations of each job are developed. Extensions of the basic temporal relations are introduced to model resource constraints for different shops. The MILP model is automatically developed out of the basic information about the duration and the sequence of the operations forming each job and the relations between these operations. For validation purposes the results for standard shop models as Flow Shop or Robotic Cycle Shop are presented as well as for a more complex Filling Shop involving loops in the process sequence as well as buffers.