Probabilistic analysis of a generalized bin packing problem and applications

Operations Research

Volumn 45, Issue 4, 1997, Pages 596-609

  Federgruen, Awi ^a   Van Ryzin, Garrett ^a  

^a Columbia University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HEURISTIC METHODS; OPERATIONS RESEARCH; PROBABILITY; SCHEDULING; STATISTICAL METHODS;

BIN PACKING PROBLEMS; DISCRETE PLANNING PROBLEMS;

PLANNING;

EID: 0031188458     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.45.4.596     Document Type: Article

References (40)

1. BALINSKI, M. AND R. QUANDT. 1964. On an Integer Program for a Delivery Problem. Opns. Res. 12, 300-304.
2. BLAIR, C. AND R. JEROSLOW. 1982. The Value Function of an Integer Program. Math. Programming, 23, 237-273.
3. BUCK, R. C. 1978. Advanced Calculus. Third Edition, McGraw-Hill, New York.
4. BRAMEL, J., E. G. COFFMAN, P. W. SHOR, AND D. SIMCHI-LEVI. 1992. Probabilistic Analysis of the Capacitated Vehicle Routing Problem with Unsplit Demands. Optis. Res. 40, 1095-1106.
5. BRAMEL, J., C. L. LI, AND D. SIMCHI-LEVI. 1993. Probabilistic Analysis of a Vehicle Routing Problem with Time Windows. Amer. J. Math. Mgmt. Sci. 13, 267-322.
6. BRAMEL, J. AND D. SIMCHI-LEVI. 1997. Probabilistic Analysis and Practical Algorithms for the Vehicle Routing Problem with Time Windows Opus. Res. 44, 501-509.
7. COFFMAN, E. G. 1982. An Introduction to Proof Techniques for Bin-Packing Algorithms. In Deterministic and Stochastic Scheduling. M. A. H. Dempster, J. K. Lenstra and A. H. G. Rinnooy Kan (eds.), Dordrecht, Holland.
8. COFFMAN, E. G., M. GAREY, AND D. JOHNSON. 1984. Approximation Algorithms for Bin-Packing: An Updated Survey, In Algorithm Design for Computer System Design. G. Ausiello, M. Lucertini and P. Serafini (eds.), 49-106, Springer-Verlag.
9. COFFMAN, E. G., G. LUEKER, AND A. RINNOOY KAN. 1988. Asymptotic Methods in the Probabilistic Analysis of Sequencing and Packing Heuristics. Mgmt. Sci. 34, 266-290.
10. COFFMAN, E. G. AND G. S. LUEKER. 1991. Probabilistic Analysis of Packing and Partitioning Algorithms. John Wiley, New York.
11. COURCOUBETIS, C. AND R. R. WEBER. 1986. Necessary and Sufficient Conditions for Stability of a Bin Packing System. J. Appl. Probability, 23, 989-999.
12. 1 View. John Wiley, New York.
13. EISEMANN, K. 1957. The Trim Problem. Mgmt. Sci. 3, 279-283.
14. FEDERGRUEN, A. AND G. J. VAN RYZIN. 1994. Probabilistic Analysis of a Generalized Bin Packing Problem and Applications (unabridged version). Working Paper, Columbia Graduate School of Business.
15. FREDERICKSON, G. N. 1980. Probabilistic Analysis for Simple One and Two-Dimensional Bin Packing Algorithms. Information Processing Letters, 11, 156-161.
16. GILMORE, P. C. AND R. E. GOMORY. 1961. A Linear Programming Approach to the Cutting-Stock Problem. Opns. Res. 9, 849-859.
17. GOLDFARB, D. AND M. J. ToDD. 1989. Linear Programming. In Optimization, G. L. Nemhauser, A. H. G. Rinnooy Kan, and M. J. Todd (eds.). Handbooks in Operations Research, Elsevier, Amsterdam.
18. GRÖTSCHEL, M., L. LOVASZ, AND A. SCHRIJVER. 1981. The Ellipsoid Method and its Consequences in Combinatorial Optimization. Combinatorial, 1, 169-197.
19. GRÖTSCHEL, M., L. LOVASZ, AND A. SCHRIJVER. 1988. Geometric Algorithms and Combinatorial Optimization. Springer-Verlag, Berlin.
20. HAIMOVICH, M. AND A. H. G. RINNOOY KAN. 1985. Bounds and Heuristics for Capacitated Routing Problems. Math. O. R. 10, 527-541.
21. KARNIARKAR, N. AND R. M. KARP. 1982. An Efficient Approximation Scheme for the One-Dimensional Bin-Packing Problem. Proc. IEEE 23rd Annual Symposium on the Foundations of Computer Science. Chicago, November 3-5.
22. KARP, R. M. 1972. Reducibility Among Combinatorial Problems. In Complexity of Computer Computations, R. E. Miller and J. W. Thatcher (eds.). 85-103, Plenum Press, New York.
23. KARP, R. M. 1982. Lecture Notes. Computer Science Division EECS, University of California, Berkeley.
24. KARP, R. M., M. LUBY, AND A. MARCHETTI-SPACCAMELA. 1984. A Probabilistic Analysis of Multidimensional Bin Packing Problems. Sixteenth ACM Symposium on the Theory of Computing, Washington, DC, April 30-May 2.
25. KIEFER, J. 1961. On Large Deviations of the empirical D.F. of Vector Chance Variables and a Law of Iterated Logarithm. Pacific J. Math, 11, 649-660.
26. KINGMAN, J. F. C. 1976. Subadditive Processes. Lecture Notes in Mathematics, 539, Springer-Verlag, Berlin.
27. KNODEL, W. 1981. A Bin Packing Algorithm with Complexity O(n log n) and Performance 1 in the Stochastic Limit, published as Mathematical Foundations of Computer Science 1981, Proceedings, 10th Symposium, J. Gruska and M. Chytil, cds., Czechoslovakia, August 31-September 4, 1981. Lecture Notes in Computer Science, 118, 369-378. Springer-Verlag, Berlin, 1981.
28. KOLEN, A., A. RINNOOY KAN, AND H. TRIENEKENS. 1987. Vehicle Routing with Time Windows. Opus. Res. 35, 266-273.
29. LUEKER, G. S. 1982. An Average-Case Analysis of Bin Packing with Uniformly Distributed Item Sizes. Technical Report 181, University of California at Irvine, Department of Information and Computer Science.
30. MAGNANTI, T. 1981. Combinatorial Optimization and Vehicle Fleet Planning: Perspectives and Prospects. Networks, 11, 179-213.
31. MASSART, P. 1986. Rates of Convergence in the Central Limit Theorem for Empirical Processes. Ann. Inst. H. Poincare, 22, 381-423.
32. MCDIARMID, C. 1989. The Method of Bounded Difference Sequences. Surveys in Combinatorics. London Mathematical Society Lecture Notes, 141, Cambridge University Press, Cambridge, 148-188.
33. POLLARD, D. 1984. Convergence of Stochastic Processes. Springer-Verlag, New York.
34. ROYDEN, H. 1968. Real Analysis. MacMillan Company, London.
35. REVESZ, P. 1968. The Laws of Large Numbers. Academic Press, New York.
36. RHEE, W. T. 1993. Personal communication.
37. RHEE, W. T. AND M. TALARAND. 1987. Martingale Inequalities and NP-Complete Problems. Math. O. R. 12, 177-181.
38. RUEE, W. T. AND M. TALAGRAND. 1989a. Optimal Bin Packing with Items of Random Size - II. SLAM J. Comput. 18, 139-498.
39. SERFLING, R. 1986. Approximation Theorems in Mathematical Statistics. John Wiley, New York.
40. SOLOMON, M. M. 1987. Algorithms for Vehicle Routing and Scheduling Problems with Time Window Constraints. Opns. Res. 35, 254-265.