Abstract
We consider the routing open shop problem being a generalization of the open shop and the metric travelling salesman problems. The jobs are located at nodes of some transportation network, and the machines travel on the network to execute the jobs in the open shop environment. The machines are initially located at the same node (depot) and must return to the depot after completing all the jobs. It is required to find a non-preemptive schedule that minimizes the makespan. The problem is NP-hard even on a two-node network with two machines. We present new polynomial-time approximation algorithms with worst-case performance guarantees.
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References
Averbakh, I., Berman, O.: Routing Two-Machine Flowshop Problems on Networks with Special Structure. Transportation Science 30(4), 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(1), 165–170 (1999)
Averbakh, I., Berman, O., Chernykh, I.: A \(\frac 65\)-approximation algorithm for the two-machine routing open shop problem on a 2-node network. European Journal of Operational Research 166(1), 3–24 (2005)
Averbakh, I., Berman, O., Chernykh, I.: The Routing Open-Shop Problem on a Network: Complexity and Approximation. European Journal of Operational Research 173(2), 521–539 (2006)
Bárány, I., Fiala, T.: Többgépes ütemezési problémà k közel optimális megoldása. Szigma-Mat.-Közgazdasági Folyóirat 15, 177–191 (1982)
Christofides, N.: Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem, Report 388, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA (1976)
Desrosiers, J., Dumas, Y., Solomon, M., Soumis, F.: Time Constrained Routing and Scheduling. In: Ball, M.O., Magnanti, T.L., Monma, C.L., Nemhauser, G.L. (eds.) Handbooks in Operations Research and Management Science, Network Routing, North-Holland, vol. 8, pp. 35–139 (1995)
Fischetti, M., Laporte, G., Martello, S.: The Delivery Man Problem and Cumulative Matroids. Operations Research 41(6), 1055–1064 (1993)
Garey, M., Johnson, D.: Computers and Intractability, A Guide to the theory of NP-completeness. W.H. Freemann and Company, San Francisco (1979)
Gilmore, P.C., Lawler, E.L., Shmoys, D.B.: Well-solved s pecial cases. In: Lawler, E.L., Lenstra, J.K., Rinnoy Kan, A.H.G., Shmoys, D.B. (eds.) The Travelling Salesman Problem. John Wiley & Sons Ltd, Chichester (1985)
Gonzalez, T., Sahni, S.: Open Shop Scheduling to Minimize Finish Time. J. Assoc. Comp. Math. 23, 665–679 (1976)
Karuno, Y., Nagamochi, H., Ibaraki, T.: Vehicle Scheduling on a Tree with Release and Handling Times. Annals of Operations Research 69, 193–207 (1997)
Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: Sequencing and Scheduling: Algorithms and Complexity. In: Handbooks in Operations Research and Management Science. Logistics of Production and Inventory, vol. 4, pp. 445–522. North Holland, Amsterdam (1993)
Serdyukov, A.: On some extremal routes in graphs. Upravlyaemye Sistemy 17, 76–79 (1978) (in Russian)
Strusevich, V.A.: A Heuristic for the Two-Machine Open Shop Scheduling Problem with Transportation Times. Discrete Applied Mathematics 93, 287–304 (1999)
Williamson, D.P., Hall, L.A., Hoogeveen, J.A., Hurkens, C.A.J., Lenstra, J.K., Sevastianov, S.V., Shmoys, D.B.: Short shop schedules. Oper.Res. 45(2), 288–294 (1997)
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Chernykh, I., Dryuck, N., Kononov, A., Sevastyanov, S. (2010). The Routing Open Shop Problem: New Approximation Algorithms. In: Bampis, E., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2009. Lecture Notes in Computer Science, vol 5893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12450-1_7
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DOI: https://doi.org/10.1007/978-3-642-12450-1_7
Publisher Name: Springer, Berlin, Heidelberg
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