Abstract
In this paper, a dry kiln scheduling problem from the furniture manufacturing industry is considered. Factory-specified due dates for orders, kiln availability, kiln capacity, and travel time from the kilns to the factories are all incorporated in a model which is formulated as an integer linear program. The objective of the formulation is to minimize the maximum tardiness of orders arriving at the plants by solving a special case of scheduling n independent jobs on m non-identical parallel machines. Because of the computational complexity, and the fact that standard integer programming packages appear to perform very poorly on the problem, a heuristic approach is developed. Computational experience is provided which indicates that the heuristic gives very high quality solutions to problems in near real-time.
Similar content being viewed by others
References
McNaughton, R. (1959) Scheduling with deadlines and loss functions. Management Science, 6(1), 1–12.
Dogramaci, A. (1984) Production scheduling of independent jobs on parallel identical processors. International Journal of Production Research, 22, 535–548.
Dogramaci, A. and Surkis, J. (1979) Evaluation of a heuristic for scheduling independent jobs on parallel identical processors. Management Science, 25, 1208–1216.
Root, J.G. (1965) Scheduling with deadlines and lost functions on k parallel machines. Management Science, 11, 460–475.
Arthanari, T.S. and Ramamurthi, K.G. (1970) A branch and bound algorithm for sequencing n jobs on m parallel processors. Opsearch, 7, 147–156.
Elmaghraby, S.E. and Park, S.H. (1974) Scheduling jobs on a number of identical machines. AIIE Transactions, 6(1), 1–13.
Barnes, W.J. and Brennan, J.J. (1977) An improved algorithm for scheduling independent jobs on identical machines. AIIE Transactions, 9(1), 25–31.
Cheng, T.C.E. and Sin, C.C.S. (1990) A state-of-the-art review of parallel-machine scheduling research. European Journal of Operational Research, 47, 271–292.
Guinet, A., Echalier, F. and Dussauchoy, A. (1992) Scheduling jobs on parallel machines: a survey. Technical Report, Laboratorie d'Informatique des Systems de Production Industriels, Bat.710, Universite Claude Bernard, Villeurbanne, France.
Davis, E. and Jaffe, J.M. (1981) Algorithms for scheduling tasks on unrelated processors. Journal of the Association for Computing Machinery, 28(4), 721–736.
Elmaghraby, S.E. and Elimam, S.A. (1980) Knapsack-based approaches to the makespan problem on multiple processors. AIIE Transactions, 12(1), 87–96.
Graham, R.L. (1969) Bounds on multiprocessing timing anomalies. SIAM Journal of Applied Mathematics, 17(2), 416–429.
Hu, T.C. (1961) Parallel scheduling and assembly line problems. Operations Research, 9, 841–848.
Huang, J.C.-C. (1995) Decision support system for lumber procurement and dry kiln scheduling: a fuzzy system theory application. Industrial Engineering Department, Unpublished Ph.D. dissertation. North Carolina State University, Raleigh, NC.
Panwalkar, S.S. and Iskander, W. (1977) A survey of scheduling rules. Operations Research, 25, 45–61.
Potts, C.N. (1985) Analysis of a linear programming heuristic for scheduling unrelated parallel machines. Discrete Applied Mathematics, 10, 155–164.
Sahni, S. and Cho, Y. (1980) Scheduling independent tasks with due time on a uniform processor system. Journal of the Association for Computing Machinery, 27, 550–563.
Baker, K.R. and Su, Z.-S. (1974) Sequencing with due dates and early start times to minimize maximum tardiness. Naval Research Logistics Quarterly, 21, 171–176.
Blazewicz, J. (1987) Selected topics in scheduling theory. Annals of Discrete Mathematics, 31, 1–60.
Hall, N.G. and Rhee, W.T. (1986) Average and worst-case analysis of heuristics for the maximum tardiness problem. European Journal of Operational Research, 26, 272–277.
Labetoulle, J. (1984) Preemptive scheduling of uniform machines subject to release dates, in Process in Combinatorial Optimization, Pulleyblank, W.R. (ed.), Academic Press, New York.
Li, C.-L. and Lee, C.-Y. (1997) Scheduling with agreeable release times and due dates on a batch processing machine. European Journal of Operational Research, 96, 564–569.
Suresh, V. and Chaudhuri, D. (1994) Minimizing maximum tardiness for unrelated parallel machines. International Journal of Production Economics, 34, 223–229.
Garey, M.R. and Johnson, D.S. (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman and Company, New York.
Suresh, V. and Chaudhuri, D. (1996) Scheduling of unrelated parallel machines when machine availability is specified. Production Planning and Control, 7(4), 393–400.
Lin, S. and Kernighan, B.W. (1973) An effective heuristic algorithm for the traveling-salesman problem. Operations Research, 21(2), 498–516.
Yaghubian, A.R. (1998)Decision support for dry kiln scheduling in the furniture industry: a local improvement heuristic approach. Unpublished Ph.D. dissertation, Industrial Engineering Department, North Carolina State University, Raleigh, NC.
Demirkol, E., Mehta, S. and Uzsoy, R. (1996)Benchmarking for shop scheduling problems. Technical Report, Industrial Engineering, Purdue University.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yaghubian, A.R., Hodgson, T.J., Joines, J.A. et al. Dry kiln scheduling in furniture production. IIE Transactions 31, 733–738 (1999). https://doi.org/10.1023/A:1007602127881
Issue Date:
DOI: https://doi.org/10.1023/A:1007602127881