# BIN-PACKING

**DOI:**https://doi.org/10.1007/1-4020-0611-X_75

- 24 Downloads

## PROBLEM DEFINITION

The bin-packing problem is concerned with the determination of the minimum number of bins that are needed to pack a given set of input data items. The problem has numerous applications in operations research, computer science, and engineering, where the items and bins to be packed can be multi-dimensional. These applications include industrial manufacturing, stock cutting, military vehicle loading, television commercial scheduling, job scheduling on multiple processors, integrated circuit manufacturing and fault detection, location testing in linear circuits, and vehicle routing. Since the bin-packing problem is known to be NP-hard, it is of interest to find efficient heuristics that obtain near-optimal solutions to the problem (Garey and Johnson, 1981).

The classical one-dimensional bin-packing problem is defined as follows: Given a positive bin capacity *C* and a list of items *L* = (*p*_{1}, *p*_{2}, ..., *p*_{n}), where *p*_{i} has size *s*(*p*_{i}) satisfying 0 ≤ *s*(*p*_{i}) ≤ *C*, determine the...

## References

- [1]Anderson, R.J., Mayr, E.W., and Warmuth, M.K. (1989). “Parallel Approximation Algorithms for Bin Packing,” Information and Computation, 82, 262–271Google Scholar
- [2]Berkey, J.O. (1990). “The Design and Analysis of Parallel Algorithms for the One-Dimensional Bin Packing Problem,” Ph.D. Dissertation, School of Information and Technology, George Mason University, Fairfax, Virginia.Google Scholar
- [3]Coffman, E.G., Jr., Courcoubetis, C., Garey, M.R., Johnson, D.S., Shor, P.W., Weber, R.R., and Yannakakis, M. (1998). “Bin Packing with Discrete Item Sizes, Part I: Perfect Packing Theorems and the Average Case Behavior of Optimal Packing,” manuscript, Bell Laboratories. Google Scholar
- [4]Coffman, E.G., Jr., Garey, M.R., and Johnson, D.S. (1997a). “Approximation Algorithms for Bin-Packing — A Survey,” in Approximation Algorithms for Bin Packing for NP-Hard Problems, Hochbaum, D.S., ed., 46–93, PWS Publishing Company, Boston.Google Scholar
- [5]Coffman, E.G., Jr., Johnson, D.S., Shor, P.W., and Weber, R.R. (1997b). “Bin Packing with Discrete Item Sizes, Part II: Tight Bounds on First Fit,” Random Structures and Algorithms, 10, 69–101.Google Scholar
- [6]Coffman, E.G., Jr. and Shor, P.W. (1993). “Packing in Two Dimensions: Asymptotic Average-Case Analysis of Algorithms,” Algorithmica 9, 253–277.Google Scholar
- [7]Coffman, E.G., Jr., Courcoubetis, C.A., Garey, M.R., Johnson, D.S., McGeoch, L.A., Shor, P.A., Weber, R.R., and Yannakakis, M. (1991). “Average-Case Performance of Bin Packing Algorithms under Discrete Uniform Distributions,” Proceedings of the 23rd ACM Symposium on the Theory of Computing, 230–241, ACM Press, New York.Google Scholar
- [8]Coffman, E.G., Jr. and Lueker, G.S. (1991). Probabilistic Analysis of Packing and Partitioning Algorithms, John Wiley, New York.Google Scholar
- [9]Coffman, E.G., Jr., Lueker, G.S., and Rinnooy Kan, A.H.G. (1988). “Asymptotic Methods in the Probabilistic Analysis of Sequencing and Packing Heuristics,” Management Science, 34, 266–291.Google Scholar
- [10]Dyckhoff, H. (1990). “Typology of Cutting and Packing Problems,” European Jl. Operational Research, 44, 145–159.Google Scholar
- [11]Fenrich, R., Miller, R., and Stout, Q.F. (1989). “Hyper-cube Algorithms for some NP-Hard Packing Problems,” in Proceedings of the 4th Conference and Hypercubes, Concurrent Computers, and Applications, 769–776, Golden Gate Enterprises, Los Altos, California.Google Scholar
- [12]Gambosi, G., Postiglione, A., and Talamo, M. (1989). “On the On-line Bin-packing Problem,” IASI Report R.263. Google Scholar
- [13]Garey, M.R. and Johnson, D.S. (1981). “Approximation Algorithms for Bin Packing Problems: A Survey,” in Analysis and Design of Algorithms in Combinatorial Optimization, Ausiello, G. and Lucertini, M., eds., 147–172, Springer-Verlag, New York.Google Scholar
- [14]Han, B.T., Dieh, G., and Cook, J.S. (1994). “Multiple Type, Two-Dimensional Bin Packing Problems: Applications and Algorithms,” Annals of Operations Research, 50, 239–261.Google Scholar
- [15]Rhee, W.T. and Talagrand, M. (1988). “Some Distributions that Allow Perfect Packing,” JACM, 35, 564–573.Google Scholar