Integrated production and outbound distribution scheduling problems with job release dates and deadlines

  • Liang-Liang Fu
  • Mohamed Ali Aloulou
  • Christian Artigues
Article
First Online:
  • 81 Downloads

Abstract

In this paper, we study an integrated production and outbound distribution scheduling model with one manufacturer and one customer. The manufacturer has to process a set of jobs on a single machine and deliver them in batches to the customer. Each job has a release date and a delivery deadline. The objective of the problem is to issue a feasible integrated production and distribution schedule minimizing the transportation cost subject to the production release dates and delivery deadline constraints. We consider three problems with different ways how a job can be produced and delivered: non-splittable production and delivery (NSP–NSD) problem, splittable production and non-splittable delivery problem and splittable production and delivery problem. We provide polynomial-time algorithms that solve special cases of the problem. One of these algorithms allows us to compute a lower bound for the NP-hard problem NSP–NSD, which we use in a branch-and-bound (B&B) algorithm to solve problem NSP–NSD. The computational results show that the B&B algorithm outperforms a MILP formulation of the problem implemented on a commercial solver.

Keywords

Single machine scheduling Production and delivery Release dates Deadlines Transportation costs Branch-and-bound 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

This work was partially funded by ANR, the French National research agency (ATHENA project, reference ANR-13-BS02-0006).

References

  1. Averbakh, I. (2010). Online integrated production-distribution scheduling problems with capacitated deliveries. European Journal of Operational Research, 200, 377–384.CrossRefGoogle Scholar
  2. Averbakh, I., & Baysan, M. (2012). Semi-online two-level supply chain scheduling problems. Journal of Scheduling, 15(3), 381–390.CrossRefGoogle Scholar
  3. Averbakh, I., & Baysan, M. (2013a). Approximation algorithm for the on-line multi-customer two-level supply chain scheduling problem. Operations Research Letters, 41(6), 710–714.CrossRefGoogle Scholar
  4. Averbakh, I., & Baysan, M. (2013b). Batching and delivery in semi-online distribution systems. Discrete Applied Mathematics, 161, 28–42.CrossRefGoogle Scholar
  5. Averbakh, I., & Xue, Z. (2007). On-line supply chain scheduling problems with preemption. European Journal of Operational Research, 181(1), 500–504.CrossRefGoogle Scholar
  6. Baker, K. R., Lawler, E. L., Lenstra, J. K., & Kan, A. H. G. R. (1983). Preemptive scheduling of a single machine to minimize maximum cost subject to release dates and precedence constraints. Operations Research, 31(2), 381–386.CrossRefGoogle Scholar
  7. Briand, C., Ourari, S., & Bouzouia, B. (2010). An efficient ilp formulation for the single machine scheduling problem. RAIRO-Operations Research, 44, 61–71.CrossRefGoogle Scholar
  8. Carlier, J. (1982). The one-machine sequencing problem. European Journal of Operational Research, 11(1), 42–47.CrossRefGoogle Scholar
  9. Chen, Z. L. (2010). Integrated production and outbound distribution scheduling: Review and extensions. Operations Research, 58(1), 130–148.CrossRefGoogle Scholar
  10. Chen, H. K., Hsueh, C. F., & Chang, M. S. (2009). Production scheduling and vehicle routing with time windows for perishable food products. Computers and Operations Research, 36(7), 2311–2319.CrossRefGoogle Scholar
  11. Chen, Z. L., & Pundoor, G. (2009). Integrated order scheduling and packing. Production and Operations Management, 18(6), 672–692.CrossRefGoogle Scholar
  12. Chiang, W. C., Russel, R., Xu, X., & Zepeda, D. (2009). A simulation/metaheuristic approach to newspaper production and distribution supply chain problems. International Journal of Production Economics, 121(2), 752–767.CrossRefGoogle Scholar
  13. Condotta, A., Knust, S., Meier, D., & Shakhlevich, N. V. (2013). Tabu search and lower bounds for a combined production-transportation problem. Computers and Operations Research, 40(3), 886–900.CrossRefGoogle Scholar
  14. Dror, M., & Trudeau, P. (1989). Savings by split delivery routing. Transportation Science, 23(2), 141–145.CrossRefGoogle Scholar
  15. European Commission. (2011). Road Freight Transport Vademecum 2010 Report. Last visited January, 2017 http://ec.europa.eu/transport/sites/transport/files/modes/road/doc/2010-road-freight-vademecum.pdf.
  16. Feng, X., Cheng, Y., Zheng, F., & Xu, Y. (2016). Online integrated production–distribution scheduling problems without preemption. Journal of Combinatorial Optimization, 31(4), 1569–1585.Google Scholar
  17. Fu, B., Huo, Y., & Zhao, H. (2012). Coordinated scheduling of production and delivery with production window and delivery capacity constraints. Theoretical Computer Science, 422, 39–51.CrossRefGoogle Scholar
  18. Garey, M., & Johnson, D. (1979). Computers and intractability: A guide to the theory of NP-completeness. New York: W.H Freeman.Google Scholar
  19. Gharbi, A., & Haouari, M. (2002). Minimizing makespan on parallel machines subject to release dates and delivery times. Journal of Scheduling, 5(4), 329–355.CrossRefGoogle Scholar
  20. Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. In E. J. P. L. Hammer & B. Korte (Eds.), Discrete optimization II, annals of discrete mathematics (Vol. 5, pp. 287–326). Amsterdam: Elsevier.Google Scholar
  21. Hall, L. A., & Shmoys, D. B. (1989). Approximation algorithms for constrained scheduling problems. In Proceedings of the 30th annual symposium on foundations of computer science (pp. 134–140).Google Scholar
  22. Hall, L. A., & Shmoys, D. B. (1992). Jackson’s rule for single-machine scheduling: Making a good heuristic better. Mathematics of Operations Research, 17(1), 22–35.CrossRefGoogle Scholar
  23. Hall, N., & Potts, C. (2005). The coordination of scheduling and batch deliveries. Annals of Operations Research, 135(1), 41–64.CrossRefGoogle Scholar
  24. Hall, N. G., & Potts, C. N. (2003). Supply chain scheduling: Batching and delivery. Operations Research, 51(4), 566–584.CrossRefGoogle Scholar
  25. Horn, W. A. (1974). Some simple scheduling algorithms. Naval Research Logistics Quarterly, 21(1), 177–185.CrossRefGoogle Scholar
  26. Hsiao, H. I., Kemp, R. G. M., & van der Vist, J. G. A. J. (2010). A classification of logistic outsourcing levels and their impact on service performance: Evidence from the food processing industry. International Journal of Production Economics, 124(1), 75–86.CrossRefGoogle Scholar
  27. Jackson, J. R. (1955). Scheduling a production line to minimize maximum tardiness. Technical report, University of California, Los Angeles.Google Scholar
  28. Jamili, N., Ranjbar, M., & Salari, M. (2016). A bi-objective model for integrated scheduling of production and distribution in a supply chain with order release date restrictions. Journal of Manufacturing Systems, 40, 105–118.CrossRefGoogle Scholar
  29. Kaminsky, P. (2003). The effectiveness of the longest delivery time rule for the flow shop delivery time problem. Naval Research Logistics, 50, 257–272.CrossRefGoogle Scholar
  30. Lawler, E. L. (1973). Optimal sequencing of a single machine subject to precedence constraints. Management Science, 19(5), 544–546.CrossRefGoogle Scholar
  31. Lenstra, J., Rinnooy Kan, A., & Brucker, P. (1977). Complexity of machine scheduling problems. In P. Hammer, E. Johnson, B. Korte, & G. Nemhauser (Eds.), Studies in integer programming, annals of discrete mathematics (Vol. 1, pp. 343–362). Amsterdam: Elsevier.CrossRefGoogle Scholar
  32. 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
  33. Li, K., Jia, Z. H., & Leung, J. Y. T. (2015). Integrated production and delivery on parallel batching machines. European Journal of Operational Research, 247(3), 755–763.CrossRefGoogle Scholar
  34. Liu, P., & Lu, X. (2011). An improved approximation algorithm for single machine scheduling with job delivery. Theoretical Computer Science, 412(3), 270–274.CrossRefGoogle Scholar
  35. Liu, Z., & Cheng, T. (2002). Scheduling with job release dates, delivery times and preemption penalties. Information Processing Letters, 82(2), 107–111.CrossRefGoogle Scholar
  36. Lu, L., Yuan, J., & Zhang, L. (2008). Single machine scheduling with release dates and job delivery to minimize the makespan. Theoretical Computer Science, 393(1–3), 102–108.CrossRefGoogle Scholar
  37. Mastrolilli, M. (2003). Efficient approximation schemes for scheduling problems with release dates and delivery times. Journal of Scheduling, 6(6), 521–531.CrossRefGoogle Scholar
  38. Mazdeh, M. M., Esfahani, A. N., Sakkaki, S. E., & Pilerood, A. E. (2012). Single-machine batch scheduling minimizing weighted flow times and delivery costs with job release times. International Journal of Industrial Engineering Computations, 3(3), 347–364.CrossRefGoogle Scholar
  39. Mazdeh, M. M., Sarhadi, M., & Hindi, K. S. (2008). A branch-and-bound algorithm for single-machine scheduling with batch delivery and job release times. Computers and Operations Research, 35(4), 1099–1111.CrossRefGoogle Scholar
  40. Mensendiek, A., Gupta, J. N., & Herrmann, J. (2015). Scheduling identical parallel machines with fixed delivery dates to minimize total tardiness. European Journal of Operational Research, 243(2), 514–522.CrossRefGoogle Scholar
  41. Moons, S., Ramaekers, K., Caris, A., & Arda, Y. (2017). Integrating production scheduling and vehicle routing decisions at the operational decision level: A review and discussion. Computers and Industrial Engineering, 104, 224–225.CrossRefGoogle Scholar
  42. Ng, C., & Lu, L. (2012). On-line integrated production and outbound distribution scheduling to minimize the maximum delivery completion time. Journal of Scheduling, 15(3), 391–398.CrossRefGoogle Scholar
  43. Potts, C. N. (1980). Analysis of a heuristic for one machine sequencing with release dates and delivery times. Operations Research, 28(6), 1436–1441.CrossRefGoogle Scholar
  44. Pundoor, G., & Chen, Z. L. (2005). Scheduling a production-distribution system to optimize the tradeoff between delivery tardiness and distribution cost. Naval Research Logistics, 52(6), 571–589.CrossRefGoogle Scholar
  45. Queyranne, M., & Schulz, A.S. (1994). Polyhedral approaches to machine scheduling. Technical report, Preprint No. 408/1994, Department of Mathematics, Technical University of Berlin, Germany.Google Scholar
  46. Russel, R., Chaing, W. C., & Zepeda, D. (2008). Integrating multi-product production and distribution in newspaper logistics. Computers and Operations Research, 35, 1576–1588.CrossRefGoogle Scholar
  47. Selvarajah, E., Steiner, G., & Zhang, R. (2013). Single machine batch scheduling with release times and delivery costs. Journal of Scheduling, 16(1), 69–79.CrossRefGoogle Scholar
  48. 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 and Service Operations Management, 9, 206–224.CrossRefGoogle Scholar
  49. Ullrich, C. A. (2013a). Issues in supply chain scheduling and contracting. Berlin: Springer.Google Scholar
  50. Ullrich, C. A. (2013b). Integrated machine scheduling and vehicle routing with time windows. European Journal of Operational Research, 227(1), 152–165.CrossRefGoogle Scholar
  51. Volpe, R., Roeger, E., & Leibtag, E. (2013). How transportation costs affect fresh fruit and vegetable prices. USDA-ERS (Economic Research Service), Economic Research Report 160.Google Scholar
  52. Wang, D. Y., Grunder, O., & Moudni, A. E. (2014). Integrated scheduling of production and distribution operations: a review. International Journal of Industrial and Systems Engineering, 19(1), 94–122.CrossRefGoogle Scholar
  53. Wang, H., & Lee, C. Y. (2005). Production and transport logistics scheduling with two transport mode choices. Naval Research Logistics, 52(8), 796–809.CrossRefGoogle Scholar
  54. Zdrzaka, S. (1994). Preemptive scheduling with release dates, delivery times and sequence independent setup times. European Journal of Operational Research, 76(1), 60–71.CrossRefGoogle Scholar
  55. 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
  56. Zhong, X., & Jiang, D. (2016). Integrated scheduling of production and distribution with release dates and capacitated deliveries. Mathematical Problems in Engineering, 2016, 9315197.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Liang-Liang Fu
    • 1
  • Mohamed Ali Aloulou
    • 1
  • Christian Artigues
    • 2
  1. 1.CNRS, LAMSADE UMR 7243PSL, Université Paris-DauphineParis Cedex 16France
  2. 2.LAAS-CNRSUniversité de Toulouse, CNRSToulouseFrance

Personalised recommendations