A truncated column generation algorithm for the parallel batch scheduling problem to minimize total flow time

Abstract

In this paper, we present a column generation based decomposition method for the parallel batch scheduling of jobs on identical parallel machines. Jobs have different release dates, processing times and sizes while machines have limited capacity. The objective is the minimization of total flow time, i.e., sum of completion times of all processed jobs. The straightforward mixed integer linear programming model of the problem is efficient for small size instances. To deal with larger instances, we develop a time indexed column generation model in which each column represents the set of jobs processed together in the same batch and the time instant for the beginning of batch processing. We obtain approximate solutions with a rounding technique followed by another mathematical model to schedule batches on machines. Numerical test results show that the proposed model is able to return high quality solutions within short computation times.