Minimizing the sum of job completion times on capacitated parallel machines

Abstract

In the classical problem of scheduling jobs on parallel identical machines to minimize the sum of job completion times, the assumption has always been that all the machines are continuously available. In practice, however, we often encounter settings in which some or all of the machines are shut down at some point, for different reasons, e.g., for preventive maintenance procedures. This paper deals with the problem of scheduling n jobs on m parallel machines to minimize the sum of job completion times, under the assumption that some of the machines are available only for prespecified, limited, machine-dependent time intervals. The problem was recently shown to be NP-hard even for two machines, and thus we are focusing on developing an efficient heuristic and a simple lower bound on the optimal cost. Both are shown to be asymptotically optimal as the number of jobs increases. Our extensive numerical study indicates that both produce extremely close-to-optimal results.