Complexity results for an integrated single machine scheduling and outbound delivery problem with fixed sequence
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In this paper, we consider an integrated production and outbound delivery scheduling problem. In particular, we address the situation in which the scheduling sequence and the delivery sequence are the same and predefined. A set of jobs are processed on a single machine, and finished jobs are delivered to the customers by a single capacitated vehicle. Each job has a processing time, and transportation times between customers are taken into account. Because the sequence is given, the problem consists in forming batches of jobs and our objective is to minimize the sum of the delivery times or general functions of the delivery times. The NP-hardness of the general problem is established, and a pseudopolynomial time dynamic programming algorithm is given. Some particular cases are treated, for which NP-hardness proofs and polynomial time algorithms are given. Finally, a fixed-parameter tractability result is given.
KeywordsScheduling Delivery Batching Complexity Dynamic programming
This work was supported by the financial support of the ANR ATHENA Project, Grant ANR-13-BS02-0006 of the French Agence Nationale de la Recherche.
- Chang, Y.-C., & Lee, C.-Y. (2004). Machine scheduling with job delivery coordination. European Journal of Operational Research, 158(2):470–487. Methodological Foundations of Multi-Criteria Decision Making.Google Scholar
- Chen, Z.-L., & Vairaktarakis, G. L. (2005). Integrated scheduling of production and distribution operations. Management Science, 51(4), 614–628.Google Scholar
- Cheref, A., Agnetis, A., Artigues, C., & Billaut, J.-C. (2017). Complexity results and algorithms for an integrated single machine scheduling and outbound delivery problem with fixed sequence, CNRS, LAAS-CNRS, report no 17126.Google Scholar
- Fan, J., Lu, X., & Liu, P. (2015). Integrated scheduling of production and delivery on a single machine with availability constraint. Theoretical Computer Science, 562, 581–589.Google Scholar
- Gao, S., Qi, L., & Lei, L. (2015). Integrated batch production and distribution scheduling with limited vehicle capacity. International Journal of Production Economics, 160, 13–25.Google Scholar
- Hurink, J., & Knust, S. (2001). Makespan minimization for flow-shop problems with transportation times and a single robot. Discrete Applied Mathematics, 112(13):199–216. Combinatorial Optimization Symposium, Selected Papers.Google Scholar
- Lenté, C., & Kergosien, Y. (2014). Problème de livraison a séquence fixée. In 10ème conférence internationale de modélisation, optimisation et simulation (MOSIM’14), Nancy.Google Scholar