Journal of Scheduling

, Volume 16, Issue 1, pp 105–115 | Cite as

Exact algorithms for inventory constrained scheduling on a single machine

  • Dirk BriskornEmail author
  • Florian Jaehn
  • Erwin Pesch


This paper focuses on single machine scheduling subject to inventory constraints. Jobs add or remove items to or from the inventory, respectively. Jobs that remove items cannot be processed if the required number of items is not available. We consider scheduling problems on a single machine where the objective is to minimize the total weighted completion time. We develop properties of optimal solutions and design a branch and bound algorithm and a dynamic programming algorithm with two extensions. We compare the approaches in our computational study and empirically derive parameter settings leading to instances which are hard to solve.


Machine scheduling Inventory constraints Branch and bound Dynamic programming 


  1. Bartels, J.-H., & Zimmermann, J. (2009). Scheduling tests in automotive R&D projects. European Journal of Operational Research, 193(3), 805–819. CrossRefGoogle Scholar
  2. Blazewicz, J., Ecker, K., Pesch, E., Schmidt, G., & Weglarz, J. (2007). Handbook on scheduling. Berlin: Springer. Google Scholar
  3. Boysen, N. (2010). Truck scheduling at zero-inventory crossdocking terminals. Computers & Operations Research, 37, 32–41. CrossRefGoogle Scholar
  4. Boysen, N., & Fliedner, M. (2010). Cross dock scheduling: classification, literature review and research agenda. Omega, 38, 413–422. CrossRefGoogle Scholar
  5. Boysen, N., Briskorn, D., & Tschöke, M. (2010). Truck scheduling in cross docking terminals with fixed outbound departures. Working Paper. Google Scholar
  6. Boysen, N., Fliedner, M., & Scholl, A. (2010). Scheduling inbound and outbound trucks at cross docking terminals. OR Spektrum, 32, 135–161. CrossRefGoogle Scholar
  7. Briskorn, D., & Leung, J. (2010). Branch and bound algorithms for minimizing maximum lateness of trucks at a transshipment terminal. Working Paper. Google Scholar
  8. Briskorn, D., Choi, B.-C., Lee, K., Leung, J., & Pinedo, M. (2010). Complexity of single machine scheduling subject to nonnegative inventory constraints. European Journal of Operational Research, 207(2), 605–619. CrossRefGoogle Scholar
  9. Chen, F., & Lee, C.-Y. (2009). Minimizing the makespan in a two-machine cross-docking flow shop problem. European Journal of Operational Research, 193, 59–72. CrossRefGoogle Scholar
  10. Chen, F., & Song, K. (2009). Minimizing makespan in two-stage hybrid cross docking scheduling problem. Computers & Operations Research, 36, 2066–2073. CrossRefGoogle Scholar
  11. Chen, J.-S. (2008). Scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan. European Journal of Operational Research, 190, 90–102. CrossRefGoogle Scholar
  12. Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimisation and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics, 5, 236–287. CrossRefGoogle Scholar
  13. Held, M., & Karp, R. (1962). A dynamic programming approach to sequencing problems. SIAM Journal, 10, 196–210. CrossRefGoogle Scholar
  14. Lee, C.-Y. (2004). Machine scheduling with availability constraints. In J. Y.-T. Leung (Ed.), Handbook of scheduling: algorithms, models and performance analysis (pp. 22-1–22-13). Google Scholar
  15. McWilliams, D. L., Stanfield, P. M., & Geiger, C. D. (2005). The parcel hub scheduling problem: A simulation-based solution approach. Computers & Industrial Engineering, 49, 393–412. CrossRefGoogle Scholar
  16. Miao, Z., Lim, A., & Ma, H. (2009). Truck dock assignment with operational time constraint within crossdocks. European Journal of Operational Research, 192(1), 105–115. CrossRefGoogle Scholar
  17. Mosheiov, G., & Sarig, A. (2009). Scheduling a maintenance activity and due-window assignment on a single machine. Computers & Operations Research, 36, 2541–2545. CrossRefGoogle Scholar
  18. Nemhauser, G., & Wolsey, L. A. (1999). Integer and combinatorial optimization. New York: Wiley-Interscience. Google Scholar
  19. Neumann, K., & Schwindt, C. (2002). Project scheduling with inventory constraints. Mathematical Methods of Operations Research, 56, 513–533. CrossRefGoogle Scholar
  20. Neumann, K., Schwindt, C., & Trautmann, N. (2005). Scheduling of continuous and discontinuous material flows with intermediate storage restrictions. European Journal of Operational Research, 165, 495–509. CrossRefGoogle Scholar
  21. Pinedo, M. (2008). Scheduling: theory, algorithms, and systems. Berlin: Springer. Google Scholar
  22. Schwindt, C., & Trautmann, N. (2000). Batch scheduling in process industries: An application of resource-constrained project scheduling. OR-Spektrum, 22(4), 501–524. CrossRefGoogle Scholar
  23. Sun, K., & Li, H. (2010). Scheduling problems with multiple maintenance activities and non-preemptive jobs on two identical parallel machines. International Journal of Production Economics, 124, 151–158. CrossRefGoogle Scholar
  24. Yu, W., & Egbelu, P. J. (2008). Scheduling of inbound and outbound trucks in cross docking systems with temporary storage. European Journal of Operational Research, 184, 377–396. CrossRefGoogle Scholar
  25. Zhao, C.-L., & Tang, H.-Y. (2010). Single machine scheduling with general job-dependent aging effect and maintenance activities to minimize makespan. Applied Mathematical Modelling, 34, 837–841. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Lehrstuhl für Quantitative PlanungUniversität SiegenSiegenGermany
  2. 2.Lehrstuhl für WirtschaftsinformatikUniversität SiegenSiegenGermany

Personalised recommendations