Abstract
We investigate a generalization of classical shop scheduling where n jobs are located at the vertices of a general undirected graph and m machines must travel between the vertices to process the jobs. The aim is to minimize the makespan. For the open shop problem, we develop an O(logmloglogm)-approximation algorithm that significantly improves upon the best known \(O(\sqrt{m})\)-approximation algorithm. For the flow shop problem, we present an O(m 2/3)-approximation algorithm that improves upon the best known \(\max\{\frac{m+1}{2},\rho\}\)-approximation algorithm, where ρ is the approximation factor for metric TSP.
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References
Afrati, F., Cosmadakis, S., Papadimitriou, C.H., Papageorgiou, G., Papakostantinou, N.: The complexity of the traveling repairman problem. Informatique Theorique et Applications 20(1), 79–87 (1986)
Allahverdi, A., Ng, C.T., Cheng, T.C.E., Kovalyov, M.Y.: A survey of scheduling problems with setup times or costs. European Journal of Operational Research 187, 985–1032 (2008)
Allahverdi, A., Soroush, H.M.: The significance of reducing setup times/setup costs. European Journal of Operational Research 187, 978–984 (2008)
Augustine, J.E., Seiden, S.: Linear time approximation schemes for vehicle scheduling problems. Theoretical Computer Science 324, 147–160 (2004)
Averbakh, I., Berman, O.: Routing two-machine flowshop problems on networks with special structure. Transportation Science 30, 303–314 (1996)
Averbakh, I., Berman, O.: A simple heuristic for m-machine flow-shop and its applications in routing-scheduling problems. Operations Research 47, 165–170 (1999)
Averbakh, I., Berman, O., Chernykh, I.D.: A 6/5-approximation algorithm for the two-machine routing open-shop problem on a 2-node network. European Journal of Operational Research 166, 3–24 (2005)
Averbakh, I., Berman, O., Chernykh, I.D.: The routing open-shop problem on a network: complexity and approximation. European Journal of Operational Research 173, 531–539 (2006)
Bhattacharya, B., Carmi, P., Hu, Y., Shi, Q.: Single Vehicle Scheduling Problems on Path/Tree/Cycle Networks with Release and Handling Times. In: Hong, S.-H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC 2008. LNCS, vol. 5369, pp. 800–811. Springer, Heidelberg (2008)
Chernykh, I., Dryuck, N., Kononov, A., Sevastyanov, S.: The Routing Open Shop Problem: New Approximation Algorithms. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 75–85. Springer, Heidelberg (2010)
Christofides, N.: Worst-case analysis of a new heuristic for the traveling salesman problem. Technical Report, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA (1976)
Czumaj, A., Scheideler, C.: A new algorithmic approach to the general Lovász local lemma with applications to scheduling and satisfiability problems. In: The Proceeding of the 32nd Symposium on Theory of Computing, pp. 38–47 (2000)
Gaur, D.R., Gupta, A., Krishnamurti, R.: A \(\frac{5}{3}\)-approximation algorithm for scheduling vehicles on a path with release and handling times. Information Processing Letters 86, 87–91 (2003)
Hoogeveen, J.A.: Analysis of Christofide’s heuristic: some paths are more difficult than cycles. Operations Research Letters 10, 291–295 (1991)
Karuno, Y., Nagamochi, H.: 2-Approximation algorithms for the multi-vehicle scheduling problem on a path with release and handling times. Discrete Applied Mathematics 129, 433–447 (2003)
Karuno, Y., Nagamochi, H.: An approximability result of the multi-vehicle scheduling problem on a path with release and handling times. Theoretical Computer Science 312, 267–280 (2004)
Karuno, Y., Nagamochi, H., Ibaraki, T.: Vehicle scheduling on a tree with release and handling time. Annals of Operations Research 69, 193–207 (1997)
Karuno, Y., Nagamochi, H., Ibaraki, T.: Better approximation ratios for the single-vehicle scheduling problems on line-shaped networks. Networks 39, 203–209 (2002)
Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: Sequencing and scheduling: algorithms and complexity. In: Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, P. (eds.) Handbooks in Operations Research and Management Science. Logistics of Production and Inventory, vol. 4, pp. 445–522. North-Holland, Amsterdam (1993)
Nagarajan, V., Sviridenko, M.: Tight Bounds for Permutation Flow Shop Scheduling. In: Lodi, A., Panconesi, A., Rinaldi, G. (eds.) IPCO 2008. LNCS, vol. 5035, pp. 154–168. Springer, Heidelberg (2008)
Shmoys, D., Stein, C., Wein, J.: Improved approximation algorithms for shop scheduling problems. SIAM Journal on Computing 23(3), 617–632 (1994)
Tsitsiklis, J.N.: Special cases of traveling salesman and repairman problems with time windows. Networks 22, 263–282 (1992)
Yu, W., Liu, Z.: Single-vehicle scheduling problems with release and service times on a line. Networks 57, 128–134 (2011)
Yu, W., Liu, Z., Wang, L., Fan, T.: Routing open shop and flow shop scheduling problems. European Journal of Operational Research 213, 24–36 (2011)
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Yu, W., Zhang, G. (2011). Improved Approximation Algorithms for Routing Shop Scheduling. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_5
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DOI: https://doi.org/10.1007/978-3-642-25591-5_5
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