Abstract
We consider a single-machine scheduling problem which arises as a subproblem in a job-shop environment where the jobs have to be transported between the machines by a single transport robot. The robot scheduling problem may be regarded as a generalization of the traveling salesman problem with time windows, where additionally generalized precedence constraints (minimal time-lags) have to be respected. The objective is to determine a sequence of all nodes and corresponding starting times in the given time windows in such a way that all generalized precedence relations are respected and the sum of all traveling and waiting times is minimized.
We calculate lower bounds for this problem using constraint propagation techniques and a linear programming formulation which is solved by a column generation procedure. Computational results are presented for test data arising from job-shop instances with a single transport robot and some modified traveling salesman instances.
Similar content being viewed by others
References
N. Ascheuer, Hamiltonian path problems in the on-line optimization of flexible manufacturing systems, Ph.D. Thesis, Technische Universität Berlin (1995).
P. Baptiste, C. Le Pape and W. Nuijten, Constraint-Based Scheduling: Applying Constraint Programming to Scheduling Problems (Kluwer, Dordrecht, 2001).
J. Blazewicz, W. Domschke and E. Pesch, The job shop scheduling problem: conventional and new solution techniques, European Journal of Operational Research 93 (1996) 1-33.
P. Brucker and O. Thiele, A branch and bound method for the general-shop problem with sequence dependent setup-times, OR Spektrum 18 (1996) 145-161.
Y. Crama, V. Kats, J. van de Klundert and E. Levner, Cyclic scheduling in robotic flowshops, Annals of Operations Research 96 (2000) 97-124.
J. Desrosiers, Y. Dumas, M. Solomon and F. Soumis, Time constrained routing and scheduling, in: Handbooks in Operations Research and Management Science, Vol. 8, eds. M.O. Ball et al. (Elsevier, Amsterdam, 1995) pp. 35-139.
U. Dorndorf, T. Phan Huy and E. Pesch, A survey of interval capacity consistency tests for timeand resource-constrained scheduling, in: Handbook on Recent Advances in Project Scheduling, ed. J. Waglarz (Kluwer, Dordrecht, 1998).
Y. Dumas, J. Desrosiers and E. Gelinas, An optimal algorithm for the traveling salesman problem with time windows, Operations Research 43 (1995) 367-371.
F. Focacci and W. Nuijten, A constraint propagation algorithm for scheduling with sequence dependent setup times, in: Proceedings of the 2nd International Workshop, CP-AI-OR'00, Paderborn, Germany (2000).
R. Graham, E.L. Lawler, J.K. Lenstra and A.H.G. Rinnooy-Kan, Optimization and approximation in deterministic sequencing and scheduling: a survey, Annals of Discrete Mathematics 5 (1979) 287-326.
J. Hurink and S. Knust, Tabu search algorithms for job-shop problems with a single transport robot, Osnabrücker Schriften zur Mathematik, Reihe P, Nr. 231, 2001.
J. Hurink and S. Knust, A tabu search algorithm for scheduling a single robot in a job-shop environment, Discrete Applied Mathematics 119 (2002) 181-203.
A.S. Jain and S. Meeran, Deterministic job-shop scheduling: past, present and future, European Journal of Operational Research 113 (1999) 390-434.
R. Klein and A. Scholl, Computing lower bounds by destructive improvement-an application to resource-constrained project scheduling, European Journal of Operational Research 112 (1999) 322-346.
S. Knust, Shop-scheduling problems with transportation, Ph.D. Thesis, Universität Osnabrück, Fachbereich Mathematik/Informatik (1999).
P.B. Martin, A time-oriented approach to computing optimal schedules for the job shop scheduling problem, Ph.D. Thesis, Graduate School of Cornell University, USA (1996).
K. Marriott and P. Stuckey, Programming with Constraints: An Introduction (MIT Press, Cambridge, MA, 1998).
K. McAloon and C. Tretkoff, Optimization and Computational Logic (Wiley, New York, 1996).
A. Mingozzi, L. Bianco and S. Ricciardelli, Dynamic programming strategies for the traveling salesman problem with time window and precedence constraints, Operations Research 45 (1997) 365-377.
J.F. Muth and G.L. Thompson, Industrial Scheduling (Prentice-Hall, Englewood Cliffs, NJ, 1963).
M. Queyranne and A. Schulz, Polyhedral approaches to machine scheduling, Preprint No. 408, TU Berlin (1994).
S. Seibert, Untere Schranken für das Traveling Salesman Problem mit Zeitfenstern und verallgemeinerten Nachfolgebeziehungen, Diplomarbeit, Universität Osnabrück, Fachbereich Mathematik/Informatik (2000).
E.P.K. Tsang, Foundations of Constraint Satisfaction (Academic Press, New York, 1993).
J.M. Van den Akker, C.A.J. Hurkens and M.W.P. Savelsbergh, Time-indexed formulations formachine scheduling problems: column generation, INFORMS Journal on Computing 12 (2000) 111-124.
Van P. Hentenryck, Constraint Satisfaction in Logic Programming (MIT Press, Cambridge, MA, 1989).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Brucker, P., Knust, S. Lower Bounds for Scheduling a Single Robot in a Job-Shop Environment. Annals of Operations Research 115, 147–172 (2002). https://doi.org/10.1023/A:1021149204501
Issue Date:
DOI: https://doi.org/10.1023/A:1021149204501