Proportional lot-sizing and scheduling problem with identical parallel machines

This article addresses mixed integer programming (MIP) models for lot-sizing and scheduling of several products on identical parallel machines. The application of binary variables to such models leads to many solutions which differ only in the numbering of machines. To avoid this symmetry, one can aggregate the machines and use integer variables. We propose such a generalisation of the Proportional Lot-sizing and Scheduling Problem using sequence-dependent change-over variables. Several randomly generated instances of a problem have been solved with the new models using standard MIP procedures. The results confirm that they can be useful for practical applications.