TY - JOUR
T1 - Minimizing the sum of job completion times on capacitated parallel machines
AU - Mosheiov, G.
PY - 1994/9
Y1 - 1994/9
N2 - 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.
AB - 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.
KW - Heuristics
KW - Parallel machines
KW - Scheduling
UR - http://www.scopus.com/inward/record.url?scp=0002574777&partnerID=8YFLogxK
U2 - 10.1016/0895-7177(94)90024-8
DO - 10.1016/0895-7177(94)90024-8
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AN - SCOPUS:0002574777
SN - 0895-7177
VL - 20
SP - 91
EP - 99
JO - Mathematical and Computer Modelling
JF - Mathematical and Computer Modelling
IS - 6
ER -