A heuristic algorithm for two‐machine re‐entrant shop scheduling
This paper considers the problem of sequencing n jobs in a two‐machine re‐entrant shopwith the objective of minimizing the maximum completion time. The shop consists of twomachines, M1 and M2 , and each job has the processing route (M1 , M2 , M1 ). An O(n log n)time heuristic is presented which generates a schedule with length at most 4/3 times that ofan optimal schedule, thereby improving the best previously available worst‐case performanceratio of 3/2.
Unable to display preview. Download preview PDF.
- B. Chen, C.N. Potts and V.A. Strusevich, Approximation algorithms for two-machine flow shop scheduling with batch setup times, Math. Progr. 82(1998)255-272.Google Scholar
- B. Chen, C.A. Glass, C.N. Potts and V.A. Strusevich, A new heuristic three-machine flow shop scheduling, Oper. Res. 44(1996)891-898.Google Scholar
- M.R. Garey, D.S. Johnson and R. Sethi, The complexity of flowshop and jobshop scheduling, Math. Oper. Res. 1(1976)117-129.Google Scholar
- T. Gonzalez and S. Sahni, Open shop scheduling to minimize finish time, J. Assoc. Comput. Mach. 23(1976)665-679.Google Scholar
- T. Gonzalez and S. Sahni, Flowshop and jobshop schedules: complexity and approximation, Oper. Res. 26(1978)36-52.Google Scholar
- S.M. Johnson, Optimal two-and three-machine production schedules with setup times included, Naval Res. Log. Quart. 1(1954)61-68.Google Scholar
- D.E. Lane and J.B. Sidney, Batching and scheduling in FMS hubs: Flow time considerations, Oper. Res. 41(1991)1091-1103.Google Scholar
- V. Lev and I. Adiri, V-shop scheduling, Eur. J. Oper. Res. 18(1984)51-56.Google Scholar
- E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys, Sequencing and scheduling: Algorithms and complexity, in: Handbooks in Operations Research and Management Science, Vol. 4, Logistics of Production and Inventory, eds. S.C. Graves, A.H.G. Rinnooy Kan and P.H. Zipkin, North-Holland, Amsterdam, 1993, pp. 455-522.Google Scholar
- D.B. Shmoys, C. Stein and J. Wein, Improved approximation algorithms for shop scheduling problems, SIAM J. Comput. 23(1994)617-632.Google Scholar
- M.Y. Wang, S.P. Sethi and S.L. van de Velde, Minimizing makespan in a class of re-entrant shops, Oper. Res. 45(1997)702-712.Google Scholar
- D.P. Williamson, L.A. Hall, J.A. Hoogeveen, C.A.J. Hurkens, J.K. Lenstra, S.V. Sevast'janov and D.B. Shmoys, Short shop schedules, Oper. Res. 45(1997)288-294.Google Scholar