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Scheduling Parallel Machines for the Customer Order Problem with Fixed Batch Sequence  

Yang, Jaehwan (LG CNS Ltd.)
Publication Information
Journal of Korean Institute of Industrial Engineers / v.29, no.4, 2003 , pp. 304-311 More about this Journal
Abstract
This paper considers a new variation of scheduling problems where jobs are dispatched in batches. The variation is the case where the batch sequence is fixed. The objective is to minimize the sum of the completion times of the batches. This simple environment has a variety of real world applications such as part kitting and customer order scheduling. We show that this problem is binary NP-complete when there exist two machines. For the same problem, we develop an optimal dynamic programming (DP) algorithm which runs in pseudo-polynomial time. We finally prove the optimality of the DP algorithm.
Keywords
batch scheduling; kitting; customer order scheduling; computational complexity; dynamic programming;
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1 Blocher, J. D., and Cbhajed D. (1996), The Cm-iomer Order Lead Time Problem on Parallel Machines. Naval Res. Logist. 43. 629-654.   DOI   ScienceOn
2 Daganzo. C. F. (1989), The Crane Scheduling Problem, Transpn. Res. -B23B, 159-175.
3 Garey, M. R. and Johnson D. S. (1979), Computers and Intractability: A Guide to the Theory of NP-Complete ness, W.H.Freeman & Co., New York
4 Gerodimos. A. E., Glass C. A., and Potts C. N. (2000), Scheduling the Production of Two-Component Jobs on a Single Machine, Euro. J. Opnl. Res. 120, 250-259.
5 Graham. R.L.. Lawler E.L., Lenstra 1.K.. and Rinnooy Kan A.H.G. (1979), Optimiz.ation and Approximation in Deterministic Machine Scheduling: A Survey. Annals of Discrete Mathematics 5, 287-326.
6 Peterkofsky, R. I., and Daganzo C. F. (1990) A Branch and Bound Solution Method for the Cmne Scheduling Problem, Transpn. Res. -B 24B. 159-172.
7 Vickson. R. G., Magazine M. 1.. and Santos, C. A. (1993), Batching and Sequencing of Components at a Single Facility, llE Trans. 25, 65-70.
8 Baker, K. R. (1988), Scheduling the Production of Components at a Common Facility. HE Trans. 20, 32-35.
9 Coffman, E. G., Nozari A.. and Yannakakis M. (1989), Optimal Scheduling of Products with Two Subassemblies on a Single Machine, Opns. Res. 37, 426-436.
10 Graham, R. L. (1966), Bounds for Certain Multiprocess Anomalies Bell Sys. Tech. 145. 1563-1581.
11 Bruno, J. D., Coffman E. G., and Sethi R. (1974), Scheduling independent Tasks to Reduce Mean Finishing Time, Communications of the ACM17, 382-387.
12 Mason, A. J. and Anderson E. J. (1991). Minimizing Flow Time on a Single Machine with Job Classes and Setup Times, Naval Res. Logist. 38. 333-350.
13 Yang, J. and Posner, M. E. (2003), Scheduling Parallel Machines for the Customer Order Problem, Working Paper, Department of Industrial Welding and Systems Engineering, The Ohio State University.
14 Gupta. J. N. D., Ho J. C .. and van der Veen A. A. (1997), Single Machine Hierarchical Scheduling with Customer Orders and Multiple Job Classes. Ann. Oper. Res 70, 127-143.
15 Potts. C. N., and Van Wassenhove L. N. (1992), Integmting Scheduling with Batching and Lot-sizing: a Review of Algorithm and Complexity . .I. Opnl. Res. Soc. 43, 395-406.
16 Potts. C. N. (1991) Scheduling Two Job Classes on a Single Machine. Compo and Opns. Res.18, 411-415.
17 Webster, C. and Baker, K. R. (1995), Scheduling Groups of Jobs on a Single Machine, Opns. Res. 43, 692-703.
18 Blocher, J. D. , Cbhajed, D. and Leung M. (1998), Customer Order Scheduling in a Genemi Job Shop Environment, Dec. Sci. 29, 951-981.
19 Monrna. C. L., and Potts C. N. (1989), On the Complexity of Scheduling With Batch Setup Times, Opns. Res. 37, 798-804.
20 Santos, C., and Magazine M. (1985) Batching in Single Operation Manufacturing Systems, OR Lett. 4, 99-103.
21 Jordan, C. (1996), Batching and Scheduling: Models and Methods for Several Problem Classes, Springer, New York.
22 Julien, F. M .. and Magazine M. J. (1990), Scheduling Customer Orders: An Alternative Production Scheduling Approach. J. Mfg. Oper. Mgt. 3,177-199.