Journal of Scheduling

, Volume 20, Issue 6, pp 681–693 | Cite as

Complexity results for an integrated single machine scheduling and outbound delivery problem with fixed sequence

  • Azeddine Cheref
  • Alessandro Agnetis
  • Christian Artigues
  • Jean-Charles Billaut


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.


Scheduling 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.


  1. Agnetis, A., Aloulou, M. A., & Fu, L.-L. (2014). Coordination of production and interstage batch delivery with outsourced distribution. European Journal of Operational Research, 238(1), 130–142.CrossRefGoogle Scholar
  2. Agnetis, A., Aloulou, M. A., Fu, L.-L., & Kovalyov, M. Y. (2015). Two faster algorithms for coordination of production and batch delivery: A note. European Journal of Operational Research, 241(3), 927–930.CrossRefGoogle Scholar
  3. Armstrong, R., Gao, S., & Lei, L. (2008). A zero-inventory production and distribution problem with a fixed customer sequence. Annals of Operations Research, 159(1), 395–414.CrossRefGoogle Scholar
  4. 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
  5. Chen, B., & Lee, C.-Y. (2008). Logistics scheduling with batching and transportation. European Journal of Operational Research, 189(3), 871–876.CrossRefGoogle Scholar
  6. Chen, Z.-L. (2010). Integrated production and outbound distribution scheduling: Review and extensions. Operations Research, 58(1), 130–148.CrossRefGoogle Scholar
  7. Chen, Z.-L., & Pundoor, G. (2006). Order assignment and scheduling in a supply chain. Operations Research, 54(3), 555–572.CrossRefGoogle Scholar
  8. Chen, Z.-L., & Vairaktarakis, G. L. (2005). Integrated scheduling of production and distribution operations. Management Science, 51(4), 614–628.Google Scholar
  9. 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
  10. 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
  11. 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
  12. Garey, M. R., Tarjan, R. E., & Wilfong, G. T. (1988). One-processor scheduling with symmetric earliness and tardiness penalties. Mathematics of Operations Research, 13(2), 330–348.CrossRefGoogle Scholar
  13. Hall, N. G., Lesaoana, M., & Potts, C. N. (2001). Scheduling with fixed delivery dates. Operations Research, 49(1), 134–144.CrossRefGoogle Scholar
  14. 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
  15. Lee, C.-Y., & Chen, Z.-L. (2001). Machine scheduling with transportation considerations. Journal of Scheduling, 4(1), 3–24.CrossRefGoogle Scholar
  16. 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
  17. Leung, J. Y.-T., & Chen, Z.-L. (2013). Integrated production and distribution with fixed delivery departure dates. Operations Research Letters, 41(3), 290–293.CrossRefGoogle Scholar
  18. Li, C.-L., & Ou, J. (2005). Machine scheduling with pickup and delivery. Naval Research Logistics (NRL), 52(7), 617–630.CrossRefGoogle Scholar
  19. Li, C.-L., Vairaktarakis, G., & Lee, C.-Y. (2005). Machine scheduling with deliveries to multiple customer locations. European Journal of Operational Research, 164(1), 39–51.CrossRefGoogle Scholar
  20. Stecke, K. E., & Zhao, X. (2007). Production and transportation integration for a make-to-order manufacturing company with a commit-to-delivery business mode. Manufacturing & Service Operations Management, 9(2), 206–224.CrossRefGoogle Scholar
  21. Tsirimpas, P., Tatarakis, A., Minis, I., & Kyriakidis, E. (2008). Single vehicle routing with a predefined customer sequence and multiple depot returns. European Journal of Operational Research, 187(2), 483–495.CrossRefGoogle Scholar
  22. Viergutz, C., & Knust, S. (2014). Integrated production and distribution scheduling with lifespan constraints. Annals of Operations Research, 213(1), 293–318.CrossRefGoogle Scholar
  23. Wang, X., & Cheng, T. (2009). Production scheduling with supply and delivery considerations to minimize the makespan. European Journal of Operational Research, 194(3), 743–752.CrossRefGoogle Scholar
  24. Zhong, W., & Chen, Z.-L. (2015). Flowshop scheduling with interstage job transportation. Journal of Scheduling, 18(4), 411–422.CrossRefGoogle Scholar
  25. Zhong, W., Chen, Z.-L., & Chen, M. (2010). Integrated production and distribution scheduling with committed delivery dates. Operations Research Letters, 38(2), 133–138.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Azeddine Cheref
    • 1
    • 2
  • Alessandro Agnetis
    • 3
  • Christian Artigues
    • 2
  • Jean-Charles Billaut
    • 1
  1. 1.Université de Tours, CNRS, LI EA 6300, ERL CNRS 6305ToursFrance
  2. 2.CNRS, LAAS-CNRS, Université de ToulouseToulouseFrance
  3. 3.Dipartimento di Ingegneria dell’InformazioneUniversitá degli Studi di SienaSienaItaly

Personalised recommendations