Formulating a scheduling problem with almost identical jobs by using positional completion times

Abstract

We present a new type of formulation for scheduling problems where jobs are identical in all aspects but one. This type of formulation is particularly useful for deriving Lagrangian lower and upper bounds for flowshop problems, where the jobs only differ in their processing times. We illustrate the effectiveness of this type of formulation for a two-machine flowshop problem where the first machine is a batching machine.