Abstract
This paper deals with job‐shop scheduling with stochastic precedenceconstraints given by so‐called OR networks. At first, a job‐shop problem withstochastic OR network precedence constraints is described, where the expected makespan isto be minimized. Next, the concept of an aggregate schedule is discussed, which represents a deterministic staticscheduling policy for our stochastic problem. The construction of an appropriate aggregatedisjunctive graph permits us to adapt the shifting bottleneck heuristic. After that,a priority‐rulemethod is proposed for finding an approximate aggregate schedule. An experimentalperformance analysis shows that both heuristics provide good approximate solutions. Finally,we briefly discuss a flow‐shop problem with OR network precedence constraints and thecase of cyclic OR networks.
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References
J. Adams, E. Balas and D. Zawack, The shifting bottleneck procedure for job shop scheduling, Management Science 34(1988)391-401.
R.K. Ahuja, T.L. Magnanti and J.B. Orlin, Network Flows, Prentice-Hall, Englewood Cliffs, 1993.
E. Balas, J.K. Lenstra and A. Vazacopoulos, One machine scheduling with delayed precedence constraints, Management Science 41(1995)94-109.
J. Błażewicz, K.H. Ecker, E. Pesch, G. Schmidt and J. Włglarz, Scheduling Computer and Manufacturing Processes, Springer, Berlin, 1996.
P. Brucker, Scheduling Algorithms, Springer, Berlin, 1995.
P. Brucker, B. Jurisch and B. Sievers, A branch and bound algorithm for the job shop scheduling problem, Discrete Applied Mathematics 49(1994)107-127.
M. Bücker, Time complexity of single machine scheduling with stochastic precedence constraints, ZOR — Mathematical Methods of Operations Research 36(1992)211-225.
M. Bücker, K. Neumann and T. Rubach, Algorithms for single-machine scheduling with stochastic outtree precedence relations to minimize expected weighted flowtime or maximum expected lateness, ZOR — Mathematical Methods of Operations Research 39 (1994)321-348.
J. Carlier and E. Pinson, An algorithm for solving the job shop problem, Management Science 35(1989)164-176.
S. Dauzère-Péres and J.-B. LasserreAn Integrated Approach in Production Planning and Scheduling, Lecture Notes in Economics and Mathematical Systems 411, Springer, Berlin, 1994.
B. Giffler and G.L. Thompson, Algorithms for solving production-scheduling problems, Operations Research 8(1960)487-503.
R. Haupt, A survey of priority-rule based scheduling, OR Spektrum 11(1989)3-16.
J.K. Lenstra, A.H.G. Rinnooy Kan and P. Brucker, Complexity of machine scheduling problems, Annals of Discrete Mathematics 1(1977)343-362.
K. Neumann, Stochastic Project Networks, Lecture Notes in Economics and Mathematical Systems 344, Springer, Berlin, 1990.
K. Neumann, Produktions-und Operations-Management, Springer, Berlin, 1996.
K. Neumann and W.G. Schneider, Job-shop and flow-shop scheduling with OR network precedence constraints: Structural questions and heuristic procedures, Report WIOR498, Universität Fridericiana zu Karlsruhe, Karlsruhe, 1997.
K. Neumann and J. Zimmermann, Heuristic procedures for parallel-machine scheduling problems with stochastic precedence constraints, Annals of Operations Research 83(1998)115-136.
M. Pinedo, Scheduling: Theory, Algorithms, and Systems, Prentice-Hall, Englewood Cliffs, 1995.
M. Pinedo and L. Schrage, Stochastic job scheduling: A survey, in: Deterministic and Stochastic Scheduling, eds. M.A.H. Dempster, J.K. Lenstra and A.H.G. Rinnooy Kan, D. Reidel, Dordrecht, 1982, pp. 181-196.
W.G. Schneider, Job Shop Scheduling with Stochastic Precedence Constraints, Shaker, Aachen, 1997.
V.A. Strusevich, Shop scheduling problems under precedence constraints, Annals of Operations Research 69(1997)351-377.
J. Zimmermann, Mehrmaschinen-Schedulingprobleme mit GERT-Anordnungsbeziehungen, Ph.D. Thesis, Universität Fridericiana zu Karlsruhe, Karlsruhe, 1995.
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Neumann, K., Schneider, W. Heuristic algorithms for job‐shop scheduling problemswith stochastic precedence constraints. Annals of Operations Research 92, 45–63 (1999). https://doi.org/10.1023/A:1018955319343
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DOI: https://doi.org/10.1023/A:1018955319343