Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Averbakh, I. (2010). Online integrated production-distribution scheduling problems with capacitated deliveries. European Journal of Operational Research, 200, 377–384.

    Article  Google Scholar 

  • Averbakh, I., & Baysan, M. (2012). Semi-online two-level supply chain scheduling problems. Journal of Scheduling, 15(3), 381–390.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Averbakh, I., & Baysan, M. (2013b). Batching and delivery in semi-online distribution systems. Discrete Applied Mathematics, 161, 28–42.

    Article  Google Scholar 

  • Averbakh, I., & Xue, Z. (2007). On-line supply chain scheduling problems with preemption. European Journal of Operational Research, 181(1), 500–504.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Briand, C., Ourari, S., & Bouzouia, B. (2010). An efficient ilp formulation for the single machine scheduling problem. RAIRO-Operations Research, 44, 61–71.

    Article  Google Scholar 

  • Carlier, J. (1982). The one-machine sequencing problem. European Journal of Operational Research, 11(1), 42–47.

    Article  Google Scholar 

  • Chen, Z. L. (2010). Integrated production and outbound distribution scheduling: Review and extensions. Operations Research, 58(1), 130–148.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Chen, Z. L., & Pundoor, G. (2009). Integrated order scheduling and packing. Production and Operations Management, 18(6), 672–692.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Dror, M., & Trudeau, P. (1989). Savings by split delivery routing. Transportation Science, 23(2), 141–145.

    Article  Google Scholar 

  • 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.

  • 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.

  • 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.

    Article  Google Scholar 

  • Garey, M., & Johnson, D. (1979). Computers and intractability: A guide to the theory of NP-completeness. New York: W.H Freeman.

    Google Scholar 

  • Gharbi, A., & Haouari, M. (2002). Minimizing makespan on parallel machines subject to release dates and delivery times. Journal of Scheduling, 5(4), 329–355.

    Article  Google Scholar 

  • 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 

  • 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).

  • 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.

    Article  Google Scholar 

  • Hall, N., & Potts, C. (2005). The coordination of scheduling and batch deliveries. Annals of Operations Research, 135(1), 41–64.

    Article  Google Scholar 

  • Hall, N. G., & Potts, C. N. (2003). Supply chain scheduling: Batching and delivery. Operations Research, 51(4), 566–584.

    Article  Google Scholar 

  • Horn, W. A. (1974). Some simple scheduling algorithms. Naval Research Logistics Quarterly, 21(1), 177–185.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Jackson, J. R. (1955). Scheduling a production line to minimize maximum tardiness. Technical report, University of California, Los Angeles.

  • 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.

    Article  Google Scholar 

  • Kaminsky, P. (2003). The effectiveness of the longest delivery time rule for the flow shop delivery time problem. Naval Research Logistics, 50, 257–272.

    Article  Google Scholar 

  • Lawler, E. L. (1973). Optimal sequencing of a single machine subject to precedence constraints. Management Science, 19(5), 544–546.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Leung, J. Y. T., & Chen, Z. L. (2013). Integrated production and distribution with fixed delivery departure dates. Operations Research Letters, 41(3), 290–293.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Liu, P., & Lu, X. (2011). An improved approximation algorithm for single machine scheduling with job delivery. Theoretical Computer Science, 412(3), 270–274.

    Article  Google Scholar 

  • Liu, Z., & Cheng, T. (2002). Scheduling with job release dates, delivery times and preemption penalties. Information Processing Letters, 82(2), 107–111.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Mastrolilli, M. (2003). Efficient approximation schemes for scheduling problems with release dates and delivery times. Journal of Scheduling, 6(6), 521–531.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Potts, C. N. (1980). Analysis of a heuristic for one machine sequencing with release dates and delivery times. Operations Research, 28(6), 1436–1441.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • Russel, R., Chaing, W. C., & Zepeda, D. (2008). Integrating multi-product production and distribution in newspaper logistics. Computers and Operations Research, 35, 1576–1588.

    Article  Google Scholar 

  • Selvarajah, E., Steiner, G., & Zhang, R. (2013). Single machine batch scheduling with release times and delivery costs. Journal of Scheduling, 16(1), 69–79.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Ullrich, C. A. (2013a). Issues in supply chain scheduling and contracting. Berlin: Springer.

    Google Scholar 

  • Ullrich, C. A. (2013b). Integrated machine scheduling and vehicle routing with time windows. European Journal of Operational Research, 227(1), 152–165.

    Article  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • Wang, H., & Lee, C. Y. (2005). Production and transport logistics scheduling with two transport mode choices. Naval Research Logistics, 52(8), 796–809.

    Article  Google Scholar 

  • Zdrzaka, S. (1994). Preemptive scheduling with release dates, delivery times and sequence independent setup times. European Journal of Operational Research, 76(1), 60–71.

    Article  Google Scholar 

  • Zhong, W., Chen, Z. L., & Chen, M. (2010). Integrated production and distribution scheduling with committed delivery dates. Operations Research Letters, 38(2), 133–138.

    Article  Google Scholar 

  • Zhong, X., & Jiang, D. (2016). Integrated scheduling of production and distribution with release dates and capacitated deliveries. Mathematical Problems in Engineering, 2016, 9315197.

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. CNRS, LAMSADE UMR 7243, PSL, Université Paris-Dauphine, 75775, Paris Cedex 16, France

    Liang-Liang Fu & Mohamed Ali Aloulou

  2. LAAS-CNRS, Université de Toulouse, CNRS, Toulouse, France

    Christian Artigues

Authors
  1. Liang-Liang Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamed Ali Aloulou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christian Artigues
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liang-Liang Fu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fu, LL., Aloulou, M.A. & Artigues, C. Integrated production and outbound distribution scheduling problems with job release dates and deadlines. J Sched 21, 443–460 (2018). https://doi.org/10.1007/s10951-017-0542-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-017-0542-0

Keywords

Search

Navigation