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 fl??owshop problem where the fi??rst machine is a batching machine that executes the jobs in constant time??.
Keywords and Phrases:?? machine scheduling problems,?? mathematical formulation??, positional completion times??, batching,?? fl??ow shop scheduling,?? total completion time??, Lagrangian relaxation??.