job independent time lags. In other words for all job pairs i, j and a given number ℓ. : job pair dependent arbitrary time lags. Transportation delays : Between the completion of operation of job on machine and the start of operation of job on machine , there is a transportation delay of at least units. : Between the completion of operation of job on machine and the start of operation of job on machine , there is a transportation delay of at least units. : Machine dependent transportation delay. Between the completion of operation of job on machine and the start of operation of job on machine , there is a transportation delay of at least units. : Machine pair dependent transportation delay. Between the completion of operation of job on machine and the start of operation of job on machine , there is a transportation delay of at least units. : Job dependent transportation delay. Between the completion of operation of job on machine and the start of operation of job on machine , there is a transportation delay of at least units. Various constraints rcrc: Recirculation, also called Flexible job shop. The promise on is lifted and for some pairs we might have . no-wait: The operation must start exactly when operation completes. Sometimes also denoted as 'nwt'. no-idle: No machine is ever idle between two executions. : Multiprocessor tasks on identical parallel machines. The execution of job is done simultaneously on parallel machines. : Multiprocessor tasks. Every job is given with a set of machines , and needs simultaneously all these machines for execution. Sometimes also denoted by 'MPT'. : Multipurpose machines. Every job needs to be scheduled on one machine out of a given set . Sometimes also denoted by Mj. Objective functions Usually the goal is to minimize some objective value. One difference is the notation where the goal is to maximize the number of jobs that complete before their deadline. This is also called the throughput. The objective value can be sum, possibly weighted by some given priority weights per job. -: The absence of an objective value is denoted by a single dash. This means that the problem consists simply in producing a feasible scheduling, satisfying all given constraints. : the completion time of job . is the maximum completion time; also known as the makespan. Sometimes we are interested in the