Abstract
We consider shop problems with transportation delays where not only the jobs on the machines have to be scheduled, but also transportation of the jobs between the machines has to be taken into account. Jobs consisting of a given number of operations have to be processed on machines in such a way that each machine processes at most one operation at a time and a job is not processed by more than one machine simultaneously. Transportation delays occur if a job changes from one machine to another. The objective is to find a feasible schedule which minimizes some objective function. A survey of known complexity results for flow-shop and open-shop environments is given and some new complexity results are derived.
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References
Achugbue, J.O. and F.Y. Chin. (1982). “Scheduling the Open Shop to Minimize Mean Flow Time.” SIAM Journal on Computing 11, 709–720.
Brucker, P. (2001). “Scheduling Algorithms.” 3rd ed. Berlin: Springer.
Chretienne, P. and C. Picouleau. (1995). “Scheduling with Communication Delays: A Survey.” In P. Chretiennne, E.G. Coffman, Jr., J.K. Lenstra and Z. Liu (eds.), Scheduling Theory and Its Applications. Chichester: Wiley.
Crama, Y., V. Kats, J. Klundert, and E. van de Levner. (2000). “Cyclic Scheduling in Robotic Flowshops.” Annals of Operations Research 96, 97–124.
Dell'Amico, M. (1996). “Shop Problems with Two Machines and Time Lags.” Operations Research 44, 777–787.
Garey, M.R., D.S. Johnson, and R. Sethi. (1976). “The Complexity of Flowshop and Jobshop Scheduling.” Mathematics of Operations Research 1, 117–129.
Gonzalez, T. and S. Sahni. (1976). “Open Shop Scheduling to Minimize Finish Time.” Journal of the Association for Computing Machinery 23, 665–679.
Graham, R.L., E.L. Lawler, J.K. Lenstra, and A.H.G. Rinnooy Kan. (1979). “Optimization and Approximation in Deterministic Sequencing and Scheduling: A Survey.” Annals of Discrete Mathematics 5, 287–326.
Hardy, G.H., J.E. Littlewood, and G. Polya. (1934, 1952). Inequalities, 1st ed., 2nd ed., London/New York: Cambridge Univ. Press.
Johnson, S.M. (1954). “Optimal Two-and Three-Stage Production Schedules with Setup Times Included.” Naval Research Logistics Quarterly 1, 61–68.
Kise, H. (1991). “On an Automated Two-Machine Flowshop Scheduling Problem with Infinite Buffer.” Journal of the Operations Research Society Japan 34, 354–361.
Knust, S. (1999). “Shop-Scheduling Problems with Transportation.” Ph.D. thesis. Fachbereich Mathematik/ Informatik, Universität Osnabrück.
Lawler, E.L., J.K. Lenstra, and A.H.G. Rinnooy Kan. (1981, 1982). “Minimizing Maximum Lateness in a Two-Machine Open Shop.” Mathematics of Operations Research 6, 153–158; Erratum, Mathematics of Operations Research 7, 635.
Lee, C.-Y. and Z.-L. Chen. (2001). “Machine Scheduling with Transportation Considerations.” Journal of Scheduling 4, 3–24.
Lenstra, J.K., A.H.G. Rinnooy Kan, and P. Brucker. (1977). “Complexity of Machine Scheduling Problems.” Annals of Discrete Mathematics 1, 343–362.
Mitten, L.G. (1958). “Sequencing n Jobs on Two Machines with Arbitrary Time Lags.” Management Science 5, 293–298.
Rayward-Smith, V.J. and D. Rebaine. (1992). “Open Shop Scheduling with Delays.” Theoretical Informatics and Applications 26, 439–448.
Rebaine, D. and V.A. Strusevich. (1999). “Two-Machine Open Shop Scheduling with Special Transportation Times.” Journal of the Operational Research Society 50, 756–764.
Strusevich, V.A. (1999). “A Heuristic for the Two-Machine Open-Shop Scheduling with Transportation Times.” Discrete Applied Mathematics 93, 287–304.
Veltmann, B., B. Lageweg, and J.K. Lenstra. (1990). “Multiprocessor Scheduling with Communication Delays.” Parallel Computing 16, 173–182.
Yu, W. (1996). “The Two-Machine Flow Shop Problem with Delays and the One-Machine Total Tardiness Problem.” Ph.D. thesis. Technische Universiteit Eindhoven.
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Brucker, P., Knust, S., Cheng, T.E. et al. Complexity Results for Flow-Shop and Open-Shop Scheduling Problems with Transportation Delays. Annals of Operations Research 129, 81–106 (2004). https://doi.org/10.1023/B:ANOR.0000030683.64615.c8
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DOI: https://doi.org/10.1023/B:ANOR.0000030683.64615.c8