Abstract
The problem of scheduling the production and delivery of a supplier to feed the production of F manufacturers is studied. The orders fulfilled by the supplier are delivered to the manufacturers in batches of the same size. The supplier's production line has to be set up whenever it switches from processing an order of one manufacturer to an order of another manufacturer. The objective is to minimize the total setup cost, subject to maintaining continuous production for all manufacturers. The problem is proved to be NP-hard. It is reduced to a single machine scheduling problem with deadlines and jobs belonging to F part types. An O(Nlog F) algorithm, where N is the number of delivery batches, is presented to find a feasible schedule. A dynamic programming algorithm with O(N F/F F−2) running time is presented to find an optimal schedule. If F=2 and setup costs are unit, an O(N) time algorithm is derived.
Similar content being viewed by others
References
A. Allahverdi, J.N.D. Gupta and T. Aldowaisan, A review of scheduling research involving setup considerations, Omega 27 (1999) 219–239.
J. Bruno and P. Downey, Complexity of task sequencing with deadlines, set-up times and changeover costs, SIAM Journal of Computing 7 (1978) 393–404.
T.C.E. Cheng, V.S. Gordon and M.Y. Kovalyov, Single machine scheduling with batch deliveries, European Journal of Operational Research 94 (1996) 277–283.
T.C.E. Cheng, M.Y. Kovalyov and B.M.T. Lin, Single machine scheduling to minimize batch delivery and job earliness penalties, SIAM Journal on Optimization 7 (1997) 547–559.
M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979).
A. Gascon and R.C. Leachman, A dynamic programming solution to the dynamic, multi-item, singlemachine scheduling problem, Operations Research 36 (1988) 50–56.
C.R. Glassey, Minimum change-over scheduling of several products on one machine, Operations Research 16 (1968) 342–352.
N.G. Hall and C.N. Potts, Supply chain scheduling: batching and delivery, in: Seventh International Workshop on Project Management and Scheduling (PMS 2000), Osnabruck, Germany (April 17-19, 2000) pp. 18-21.
J.R. Jackson, Scheduling a production line to minimize maximum tardiness, Research Report 43, Management Science Research Project, University of California, Los Angeles (1955).
C.N. Potts and M.Y. Kovalyov, Scheduling with batching: a review, European Journal of Operational Research 120 (2000) 228–249.
C.N. Potts and L.N. Van Wassenhove, Integrating scheduling with batching and lot-sizing: a review of algorithms and complexity, Journal of the Operational Research Society 43 (1992) 395–406.
D.J. Thomas and P.M. Griffin, Coordinated supply chain management, European Journal of Operations Research 94 (1996) 1–15.
S. Webster and K.R. Baker, Scheduling groups of jobs on a single machine, Operations Research 43 (1995) 692–703.
X. Yang, Scheduling with generalized batch delivery dates and earliness penalties, IIE Transactions (2001) to appear.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cheng, T.E., Kovalyov, M.Y. Single Supplier Scheduling for Multiple Deliveries. Annals of Operations Research 107, 51–63 (2001). https://doi.org/10.1023/A:1014938712999
Issue Date:
DOI: https://doi.org/10.1023/A:1014938712999