Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bartels, J.-H., & Zimmermann, J. (2009). Scheduling tests in automotive R&D projects. European Journal of Operational Research, 193(3), 805–819.
Blazewicz, J., Ecker, K., Pesch, E., Schmidt, G., & Weglarz, J. (2007). Handbook on scheduling. Berlin: Springer.
Boysen, N. (2010). Truck scheduling at zero-inventory crossdocking terminals. Computers & Operations Research, 37, 32–41.
Boysen, N., & Fliedner, M. (2010). Cross dock scheduling: classification, literature review and research agenda. Omega, 38, 413–422.
Boysen, N., Briskorn, D., & Tschöke, M. (2010). Truck scheduling in cross docking terminals with fixed outbound departures. Working Paper.
Boysen, N., Fliedner, M., & Scholl, A. (2010). Scheduling inbound and outbound trucks at cross docking terminals. OR Spektrum, 32, 135–161.
Briskorn, D., & Leung, J. (2010). Branch and bound algorithms for minimizing maximum lateness of trucks at a transshipment terminal. Working Paper.
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.
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.
Chen, F., & Song, K. (2009). Minimizing makespan in two-stage hybrid cross docking scheduling problem. Computers & Operations Research, 36, 2066–2073.
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.
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.
Held, M., & Karp, R. (1962). A dynamic programming approach to sequencing problems. SIAM Journal, 10, 196–210.
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).
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.
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.
Mosheiov, G., & Sarig, A. (2009). Scheduling a maintenance activity and due-window assignment on a single machine. Computers & Operations Research, 36, 2541–2545.
Nemhauser, G., & Wolsey, L. A. (1999). Integer and combinatorial optimization. New York: Wiley-Interscience.
Neumann, K., & Schwindt, C. (2002). Project scheduling with inventory constraints. Mathematical Methods of Operations Research, 56, 513–533.
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.
Pinedo, M. (2008). Scheduling: theory, algorithms, and systems. Berlin: Springer.
Schwindt, C., & Trautmann, N. (2000). Batch scheduling in process industries: An application of resource-constrained project scheduling. OR-Spektrum, 22(4), 501–524.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Briskorn, D., Jaehn, F. & Pesch, E. Exact algorithms for inventory constrained scheduling on a single machine. J Sched 16, 105–115 (2013). https://doi.org/10.1007/s10951-011-0261-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-011-0261-x