Abstract
Consider a company that manufactures perishable goods. The company relies on a third party to deliver goods, which picks up delivery products at regular times. At each delivery time, there is a time window that products can be produced to be delivered at that delivery time. Suppose we have a set of jobs with each job specifying its delivery time, processing time and profit. The company can earn the profit of the job if the job is produced and delivered at its specified delivery time. From the company point of view, we are interested in picking a subset of jobs to produce and deliver so as to maximize the total profit. The jobs that are not picked will be discarded without penalty. We consider both the single machine case and the parallel and identical machines case.
In this article we consider two kinds of profits: (1) arbitrary profit, (2) profit proportional to its processing time. In the first case, we give a fully polynomial time approximation scheme (FPTAS) for a single machine with running time \(O(\frac{n^3}{\epsilon})\). In the second case, we give a faster FPTAS for a single machine with running time \(O(\frac{n^2}{\epsilon})\). All of our algorithms can be extended to parallel and identical machines with a degradation of performance ratios.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bar-Noy, A., Guha, S., Naor, J., Schieber, B.: Approximating the throughput of Multiple Machines in Real-Time Scheduling. SIAM J. on Computing 31, 331–352 (2001)
Bilgen, B., Ozkarahan, I.: Strategic Tactical and Operational Production-Distribution Models: A Review. International J. of Technology Management 28, 151–171 (2004)
Chen, Z.-L.: Integrated Production and Distribution Operations: Taxonomy, Models, and Review. In: Simchi-Levi, D., Wu, S.D., Shen, Z.-J. (eds.) Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era. Kluwer Academic Publishers, Dordrecht (2004)
Chen, Z.-L.: Integrated Production and Outbound Distribution Scheduling in a Supply Chain: Review and Extensions. Working paper, Robert H. Smith School of Business, University of Maryland, College Park, MD 20742 (2006)
Coffman Jr., E.G., Leung, J.Y.-T., Ting, D.W.: Bin Packing: Maximizing the Number of Pieces Packed. Acta Informatica 9, 263–271 (1978)
Erenguc, S.S., Simpson, N.C., Vakharia, A.J.: Integrated Production/Distribution Planning in Supply Chains: An Invited Review. European J. of Operational Research 115, 219–236 (1999)
Garcia, J.M., Lozano, S.: Production and Delivery Scheduling Problem with Time Windows. Computers and Industrial Engineering 48, 733–742 (2004)
Garcia, J.M., Lozano, S., Canca, D.: Coordinated Scheduling of Production and Delivery from Multiple Plants. Robotics and Computer-Integrated Manufacturing 20, 191–198 (2004)
Garcia, J.M., Smith, K., Lozano, S., Guerrero, F.: A Comparison of GRASP and an Exact Method for Solving a Production and Delivery Scheduling Problem. In: Proceedings of Hybrid Information Systems: Advances in Soft Computing, pp. 431–447. Physica-Verlag, Heidelberg (2002)
Goetschalckx, M., Vidal, C.J., Dogan, K.: Modeling and Design of Global Logistics Systems: A Review of Integrated Strategic and Tactical Models and Design Algorithms. European J. of Operational Research 143, 1–18 (2002)
Ibarra, O.H., Kim, C.E.: Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems. J. of ACM 22, 463–468 (1975)
Leung, J.Y.-T., Dror, M., Young, G.H.: A Note on an Open-End Bin Packing Problem. Journal of Scheduling 4, 201–207 (2001)
Sarmiento, A.M., Nagi, R.: A Review of Integrated Analysis of Production-Distribution Systems. IIE Transactions 31, 1061–1074 (1999)
Thomas, D.J., Griffin, P.M.: Coordinated Supply Chain Management. European J. of Operational Research 94, 1–15 (1996)
Yang, J., Leung, J.Y.-T.: The Ordered Open-End Bin Packing Problem. Operations Research 51, 759–770 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Huo, Y., Leung, J.Y.T., Wang, X. (2009). Integrated Production and Delivery Scheduling with Disjoint Windows. In: Du, DZ., Hu, X., Pardalos, P.M. (eds) Combinatorial Optimization and Applications. COCOA 2009. Lecture Notes in Computer Science, vol 5573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02026-1_45
Download citation
DOI: https://doi.org/10.1007/978-3-642-02026-1_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02025-4
Online ISBN: 978-3-642-02026-1
eBook Packages: Computer ScienceComputer Science (R0)