The consecutive multiprocessor job scheduling problem

We study a variant of the multiprocessor job scheduling problem, where jobs are processed by several identical machines. The machines are ordered in a sequence, and each job is processed by several consecutive machines simultaneously. The jobs are characterized by their processing time, the number of required consecutive machines, and their ready time. The objective function is to minimize the sum of general functions defined over the completion time of each job. This study is motivated by a real problem in the semiconductor industry. We present a time-indexed integer programming and a constraint programming formulations for the problem and demonstrate their applicability through an extensive numerical study and an industrial case study.