Approximation algorithms for Job Scheduling with reconfigurable resources (2401.00419v1)
Abstract: We consider here the MultiBot problem for the scheduling and the resource parametrization of jobs related to the production or the transportation of different products inside a given time horizon. Those jobs must meet known in advance demands. The time horizon is divided into several discrete identical periods representing each the time needed to proceed a job. The objective is to find a parametrization and a schedule for the jobs in such a way they require as less resources as possible. Though this problem derived from the applicative context of reconfigurable robots, we focus here on fundamental issues. We show that the resulting strongly NP-hard Multibot problem may be handled in a greedy way with an approximation ratio of $\frac{4}{3}$.
- Workforce minimization for a mixed-model assembly line in the automotive industry. International Journal of Production Economics, 170:489–500, 2015.
- Multi-mode resource constrained multi-project scheduling and resource portfolio problem. European Journal of Operational Research, 240(1):22–31, 2015.
- Assembly line balancing: What happened in the last fifteen years? European Journal of Operational Research, 301(3):797–814, 2022.
- A framework for the complexity of high-multiplicity scheduling problems. J. Comb. Optim., 9(3):313–323, 2005.
- H. Brinkop and K. Jansen. High multiplicity scheduling on uniform machines in FPT-time. CoRR, abs/2203.01741, 2022.
- M. Chaikovskaia. Optimization of a fleet of reconfigurable robots for logistics warehouses. PhD thesis, Université Clermont Auvergne, France, 2023.
- Sizing of a fleet of cooperative and reconfigurable robots for the transport of heterogeneous loads. In 2022 IEEE 18th International Conference on Automation Science and Engineering, pages 2253–2258, 2022.
- An application of bin-packing to multiprocessor scheduling. SIAM Journal on Computing, 7(1):1–17, 1978.
- Computers and Intractability: A Guide to the theory of NP-completeness. 1979.
- R. L. Graham. Bounds on multiprocessing timing anomalies. SIAM Journal on Applied Mathematics, 17(2):416–429, 1969.
- S. Hartmann and D. Briskorn. An updated survey of variants and extensions of the resource-constrained project scheduling problem. European Journal of operational research, 297(1):1–14, 2022.
- Using dual approximation algorithms for scheduling problems: Theoretical and practical results. In Procs. of FOCS, pages 79–89. IEEE Computer Society, 1985.
- Combinatorial n𝑛nitalic_n-fold integer programming and applications. Math. Program., 184(1):1–34, 2020.
- A polynomial algorithm for multiprocessor scheduling with two job lengths. Mathematics of Operations Research, 26(1):31–49, 2001.
- MecaBotiX. https://www.mecabotix.com/, 2023.
- M. Mnich and R. van Bevern. Parameterized complexity of machine scheduling: 15 open problems. Comput. Oper. Res., 100:254–261, 2018.
- M. Mnich and A. Wiese. Scheduling and fixed-parameter tractability. Math. Program., 154(1-2):533–562, 2015.
- M. Yue. On the exact upper bound for the multifit processor scheduling algorithm. Annals of Operations Research, 24(1):233–259, 1990.