TY - JOUR

T1 - Heuristics for multimachine minmax scheduling problems with general earliness and tardiness costs

AU - Federgruen, Awi

AU - Mosheiov, Gur

PY - 1997/4

Y1 - 1997/4

N2 - We consider the problem of scheduling N jobs on M parallel machines so as to minimize the maximum earliness or tardiness cost incurred for each of the jobs. Earliness and tardiness costs are given by general (but job-independent) functions of the amount of time a job is completed prior to or after a common due date. We show that in problems with a nonrestrictive due date, the problem decomposes into two pans. Each of the M longest jobs is assigned to a different machine, and all other jobs are assigned to the machines so as to minimize their makespan. With these assignments, the individual scheduling problems for each of the machines are simple to solve. We demonstrate that several simple heuristics of low complexity, based on this characterization, are asymptotically optimal under mild probabilistic conditions. We develop attractive worst-case bounds for them. We also develop a simple closed-form lower bound for the minimum cost value. The bound is asymptotically accurate under the same probabilistic conditions. In the case where the due date is restrictive, the problem is more complex only in the sense that the set of initial jobs on the machines is not easily characterized. However, we extend our heuristics and lower bounds to this general case as well. Numerical studies exhibit that these heuristics perform excellently even for small- or moderate-size problems both in the restrictive and nonrestrictive due-date case.

AB - We consider the problem of scheduling N jobs on M parallel machines so as to minimize the maximum earliness or tardiness cost incurred for each of the jobs. Earliness and tardiness costs are given by general (but job-independent) functions of the amount of time a job is completed prior to or after a common due date. We show that in problems with a nonrestrictive due date, the problem decomposes into two pans. Each of the M longest jobs is assigned to a different machine, and all other jobs are assigned to the machines so as to minimize their makespan. With these assignments, the individual scheduling problems for each of the machines are simple to solve. We demonstrate that several simple heuristics of low complexity, based on this characterization, are asymptotically optimal under mild probabilistic conditions. We develop attractive worst-case bounds for them. We also develop a simple closed-form lower bound for the minimum cost value. The bound is asymptotically accurate under the same probabilistic conditions. In the case where the due date is restrictive, the problem is more complex only in the sense that the set of initial jobs on the machines is not easily characterized. However, we extend our heuristics and lower bounds to this general case as well. Numerical studies exhibit that these heuristics perform excellently even for small- or moderate-size problems both in the restrictive and nonrestrictive due-date case.

UR - http://www.scopus.com/inward/record.url?scp=0031117556&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1520-6750(199704)44:3<287::AID-NAV4>3.0.CO;2-4

DO - 10.1002/(SICI)1520-6750(199704)44:3<287::AID-NAV4>3.0.CO;2-4

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AN - SCOPUS:0031117556

SN - 0894-069X

VL - 44

SP - 287

EP - 299

JO - Naval Research Logistics

JF - Naval Research Logistics

IS - 3

ER -