Heuristic algorithms for unrelated parallel machine scheduling with a common due date, release dates, and linear earliness and tardiness penalties

This paper considers a scheduling problem where each of n jobs has to be processed without interruption on exactly one of m unrelated parallel machines. For each job, a release date and the processing times on each machine are given, and a common due date d is given for all jobs. The objective is to distribute the jobs to the machines and to schedule the jobs assigned to each machine such that the weighted sum of linear earliness and tardiness penalties is minimal. For this problem, we derive some structural properties useful in connection with the search for an approximate solution. Furthermore, we present various constructive and iterative heuristic algorithms which are compared on problems with up to 500 jobs and 20 machines.