Counting and enumeration complexity with application to multicriteria scheduling

Annals of Operations Research

Volumn 153, Issue 1, 2007, Pages 215-234

  T'Kindt, Vincent ^a   Bouibede Hocine, Karima ^a   Esswein, Carl ^a  

^a UNIVERSITÉ DE TOURS   (France)

Author keywords

Complexity; Counting; Enumeration; Multicriteria scheduling

Indexed keywords

EID: 34250223388     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1007/s10479-007-0175-3     Document Type: Article

References (85)

1. Almeida, M. T., & Centeno, M. (1998). A composite heuristic for the single machine early/tardy job scheduling problem. Computers and Operations Research, 25(7-8), 625-635.
2. Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., & Protasi, M. (1999). Complexity and approximation: combinatorial optimization problems and their approximability properties. Heidelberg: Springer.
3. Azizoglu, M., & Webster, S. (1997). Scheduling job families about an unrestricted common due date on a single machine. International Journal of Production Research, 35, 1321-1330.
4. Azizoglu, M., Kondakci, S. K., & Kirca, O. (1991). Bicriteria scheduling problem involving total tardiness and total earliness penalties. International Journal of Production Economics, 23, 17-24.
5. Azizoglu, M., Kondakci, S. K., & Koksalan, M. (1997). Bicriteria scheduling: minimizing flowtime and maximum earliness on a single machine. In J. Climaco (Ed.), Multicriteria analysis (pp. 279-288). Heidelberg: Springer.
6. Bansal, S. P. (1980). Single machine scheduling to minimize weighted sum of completion times with secondary criterion - a branch and bound approach. European Journal of Operational Research, 5(3), 177-181.
7. Brucker, P. (2004). Scheduling algorithms. Berlin: Springer.
8. Burns, R. N. (1976). Scheduling to minimize the weighted sum of completion times with secondary criteria. Naval Research Logistics Quarterly, 23(1), 125-129.
9. Chand, S., & Schneeberger, H. (1984). Single machine scheduling to minimize weighted completion time with maximum allowable tardiness. Technical report, University of Purdue, U.S.A.
10. Chand, S., & Schneeberger, H. (1986). A note on the single machine scheduling problem with minimum weighted completion time and maximum allowable tardiness. Naval Research Logistics Quarterly, 33(3), 551-557.
11. Chand, S., & Schneeberger, H. (1988). Single machine scheduling to minimize weighted earliness subject to no tardy jobs. European Journal of Operational Research, 34(2), 221-230.
12. Chen, C.-L., & Bulfin, R. L. (1990). Scheduling unit processing time jobs on a single machine with multiple criteria. Computers and Operations Research, 17(1), 1-7.
13. Chou, F. D., & Lee, C. Y. (1999). Two-machine flowshop scheduling with bicriteria problem. Computers and Industrial Engineering, 36(3), 549-564.
14. Daniels, R. L., & Chambers, R. J. (1990). Multiobjective flow-shop scheduling. Naval Research Logistics, 37, 981-995.
15. Deckro, R. F., Herbert, J. E., & Winkofsky, E. P. (1982). Multiple criteria job-shop scheduling. Computers and Operations Research, 9(4), 279-285.
16. Dileepan, P., & Sen, T. (1991). Bicriterion jobshop scheduling with total flowtime and sum of squared lateness. Engineering Costs and Production Economic, 21, 295-299.
17. Ehrgott, M. (2000). Approximation algorithms for combinatorial multicriteria optimization problems. International Transactions in Operations Research, 7, 5-31.
18. Emmons, H. (1975). One machine sequencing to minimize mean flow time with minimum number tardy. Naval Research Logistics Quarterly, 22(4), 585-592.
19. Fry, T. D., & Blackstone, R. H. (1988). Planning for idle time: a rationale for underutilization of capacity. International Journal of Production Research, 26(12), 1853-1859.
20. Fry, T. D., & Leong, G. K. (1986). Bi-criterion single-machine scheduling with forbidden early shipments. Engineering Costs and Production Science, 10(2), 133-137.
21. Fry, T. D., Armstrong, R. D., & Blackstone, R. H. (1987a). Minimizing weighted absolute deviation in single machine scheduling. IIE Transactions, 19(4), 445-450.
22. Fry, T. D., Leong, G. K., & Rakes, T. R. (1987b). Single machine scheduling: a comparison of two solution procedures. Omega, 15(4), 277-282.
23. Fry, T. D., Armstrong, R. D., Darby-Dowman, K., & Philipoom, P. R. (1996). A branch and bound procedure to minimize mean absolute lateness on a single processor. Computers and Operations Research, 23(2), 171-182.
24. Fukuda, K. (1996). Note on new complexity classes ENP, EP and CEP - an extension of the classes NP, co-NP and P. http://www.ifor.math.ethz.ch/staff/fukuda/ENP_home/ENP_note.html.
25. Fukuda, K., Liebling, T. M., & Margot, F. (1997). Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron. Computational Geometry, 8, 1-12.
26. Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: a guide to the theory of NP-Completeness. New York: Freeman.
27. Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics, 5, 287-326.
28. Gupta, J. N. D., & Werner, F. (1999). On the solution of 2-machine flow and open shop scheduling problems with secondary criteria. In 15th ISPE/IEE international conference on CAD/CAM, robotics, and factories of the future, Aguas de Lindoia, Sao Paulo, Brasil.
29. Gupta, J. N. D., Palanimuthu, N., & Chen, C.-L. (1999). Designing a tabu search algorithm for the two-stage flowshop problem with secondary criterion. Production Planning and Control, 10(3), 251-265.
30. Gupta, J. N. D., Neppalli, V. R., & Werner, F. (2001). Minimizing total flow time in a two-machine flowshop problem with minimum makespan. International Journal of Production Economics, 69(3), 323-338.
31. Gupta, J. N. D., Hennig, K., & Werner, F. (2002). Local search heuristic for the two-stage flowshop problems with secondary criterion. Computers and Operations Research, 29(2), 113-149.
32. Heck, H., & Roberts, S. (1972). A note on the extension of a result on scheduling with secondary criteria. Naval Research Logistics Quarterly, 19, 59-66.
33. Hoogeveen, J. A. (1992). Single-machine bicriteria scheduling. PhD thesis, CWI, Amsterdam, The Netherlands.
34. Hoogeveen, J. A. (1996a). Minimizing maximum promptness and maximum lateness on a single machine. Mathematics of Operations Research, 21(1), 100-114.
35. Hoogeveen, J. A. (1996b). Single machine scheduling to minimize a function of two or three maximum cost criteria. Journal of Algorithms, 21(2), 415-433.
36. Hoogeveen, J. A., & VandeVelde, S. L. (1995). Minimizing total completion time and maximum cost simultaneously is solvable in polynomial time. Operations Research Letters, 17, 205-208.
37. Huckert, K., Rhode, R., Roglin, O., & Weber, R. (1980). On the interactive solution to a multicriteria scheduling problem. Zeitchriflfur Operations Research, 24, 47-60.
38. James, R. J. W., & Buchanan, J. T. (1997). A neighbourhood scheme with a compressed solution space for the early/tardy scheduling problem. European Journal of Operational Research, 102, 513-527.
39. James, R. J. W., & Buchanan, J. T. (1998). Performance enhancements to tabu search for the early/tardy scheduling problem. European Journal of Operational Research, 106, 254-265.
40. John, T. C. (1989). Tradeoff solutions in single machine production scheduling for minimizing flow time and maximum penalty. Computers and Operations Research, 16(5), 471-479.
41. Johnson, D. S., Yannakakis, M., & Papadimitriou, C. H. (1988). On generating all maximal independent sets. Information Processing Letters, 27, 119-123.
42. Johnson, S. M. (1954). Optimal two and three stage production schedules with set-up time included. Naval Research Logistics Quarterly, 1, 61-68.
43. Jozefowska, J., Jurisch, B., & Kubiak, W. (1994). Scheduling shops to minimize the weighted number of late jobs. Operations Research Letters, 10, 27-33.
44. Kim, Y.-D., & Yano, C. A. (1994). Minimizing mean tardiness and earliness in single-machine scheduling problems with unequal due dates. Naval Research Logistics, 41, 913-933.
45. Kondakci, S. K., Emre, E., & Koksalan, M. (1997). Scheduling of unit processing time jobs on a single machine. In G. Fandel & T. Gal (Eds.), Multiple criteria decision making. Lecture notes in economics and mathematical systems (vol. 448, pp. 654-660). Heidelberg: Springer.
46. Koulamas, C. (1996). Single-machine scheduling with time windows and earliness/tardiness penalties. European Journal of Operational Research, 91, 190-202.
47. Kyparisis, G. J., & Koulamas, C. (2000). Open shop scheduling with makespan and total completion time criteria. Computers and Operations Research, 27, 15-27.
48. Li, G. (1997). Single machine earliness and tardiness scheduling. European Journal of Operational Research, 96, 546-558.
49. Liao, C. J., Yu, W. C., & Joe, C. B. (1997). Bicriterion scheduling in the two-machine flowshop. Journal of the Operational Research Society, 48, 929-935.
50. Liaw, C. F. (1999). A branch-and-bound algorithm for the single machine earliness and tardiness scheduling problem. Computers and Operations Research, 26, 679-693.
51. Lin, K. S. (1983). Hybrid algorithm for sequencing with bicriteria. Journal of Optimization Theory and Applications, 39(1), 105-124.
52. Mazzini, R., & Armentano, V. A. (2001). A heuristic for single machine scheduling with early and tardy costs. European Journal of Operational Research, 128, 129-146.
53. Me Cormick, S. T., & Pinedo, M. L. (1995). Scheduling n independent jobs on m uniform machines with both flowtime and makespan objectives: a parametric analysis. ORSA Journal on Computing, 7(1), 63-77.
54. Miyazaki, S. (1981). One machine scheduling problem with dual criteria. Journal of the Operational Research Society of Japan, 24(1), 37-50.
55. Mohri, S., Masuda, T., & Ishii, H. (1999). Bi-criteria scheduling problem on three identical parallel machines. International Journal of Production Economics, 60-61, 529-536.
56. Nagar, A., Heragu, S. S., & Haddock, J. (1995). A branch-and-bound approach for a two-machine flowshop scheduling problem. Journal of the Operational Research Society, 46, 721-734.
57. Nelson, R. T., Sarin, R. K., & Daniels, R. L. (1986). Scheduling with multiple performance measures: the one-machine case. Management Science, 32(4), 464-479.
58. Neppalli, V. R., Chen, C. L., & Gupta, J. N. D. (1996). Genetic algorithms for the two-stage bicriteria flowshop problem. European Journal of Operational Research, 95, 356-373.
59. Ow, P. S., & Morton, T. E. (1988). Filtered beam search in scheduling. International Journal of Production Research, 26(1), 35-62.
60. Ow, P. S., & Morton, T. E. (1989). The single machine early/tardy problem. Management Science, 35(2), 177-190.
61. Papadimitriou, C. H. (1995). Computational complexity, Reading: Addison-Wesley.
62. Pinedo, M. (1995). Scheduling - theory, algorithms, and systems. Englewood Cliffs: Prentice Hall.
63. Rajendran, C. (1992). Two-stage flowshop scheduling problem with bicriteria. Journal of the Operational Research Society, 43(9), 871-884.
64. Ruiz-Torres, A. J., Enscore, E. E., & Barton, R. R. (1997). Simulated annealing heuristics for the average flow-time and the number of tardy jobs bi-criteria identical parallel machine problem. Computers and Industrial Engineering, 33(1-2), 257-260.
65. Sarin, S. C., & Hariharan, R. (2000). A two machine bicriteria scheduling problem. International Journal of Production Economics, 65, 125-139.
66. Serafini, P. (1986). Some considerations about computational complexity for multi objective combinatorial problems. In Lecture notes in economics and mathematical systems (vol. 294, pp. 222-232). Heidelberg: Springer.
67. Serifoglu, F. S., & Ulusoy, G. (1998). A bicriteria two-machine permutation flowshop problem. European Journal of Operational Research, 107, 414-430.
68. Simon, J. (1977). On the difference between the one and the many. In Proceedings ICALP 1977, Lecture Notes in Computer Sciences (vol. 52, pp. 480-491).
69. Smith, W. E. (1956). Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3(1), 59-66.
70. Sundararaghavan, P. S., & Ahmed, M. U. (1984). Minimizing the sum of absolute lateness in single-machine and multimachine scheduling. Naval Research Logistics Quarterly, 31(2), 325-333.
71. Szwarc, W. (1993). Adjacent orderings in single machine scheduling with earliness and tardiness penalties. Naval Research Logistics, 40, 229-243.
72. T'kindt, V., & Billaut, J.-C. (2006). Multicriteria scheduling: theory, models and algorithms (2nd edn.). Berlin: Springer.
73. T'kindt, V., Gupta, J. N. D., & Billaut, J.-C. (2003). Two-machine flowshop scheduling problem with a secondary criterion. Computers and Operations Research, 30(4), 505-526.
74. T'kindt, V., Bouibede-Hocine, K., & Esswein, C. (2005a). Counting and enumeration complexity with application to multicriteria scheduling. 40R, 3(1), 1-21.
75. T'kindt, V., Della Croce, F., & Bouquard, J.-L. (2005b). Enumeration of Pareto optima for a flowshop scheduling problem with two criteria. Submitted for publication, p. 24.
76. Tuzikov, A., Makhaniok, M., & Manner, R. (1998). Bicriterion scheduling of identical processing time jobs by uniform processors. Computers and Operations Research, 25(1), 31-35.
77. Vadhan, S. (1995). The complexity of counting. Thesis of Bachelor of Arts, Harvard College, Cambridge (USA), p. 58.
78. Valiant, L. G. (1979a). The complexity of computing the permanent. Theoretical Computer Science, 8, 189-201.
79. Valiant, L. G. (1979b). The complexity of enumeration and reliability problems. SIAM Journal on Computing, 8(3), 410-421.
80. VandenAkker, M., Hoogeveen, H., & VandeVelde, S. (1998). A combined column generation and Lagrangian relaxation algorithm for common due date scheduling. In 6th workshop on project management and scheduling PMS'98, EURO, Istanbul, Turkey.
81. VanWassenhove, L., & Gelders, L. F. (1978). Four solution techniques for a general one machine scheduling problem: a comparative study. European Journal of Operational Research, 2(4), 281-290.
82. Webster, S., Job, P. D., & Gupta, A. (1998). A genetic algorithm for scheduling job families on a single machine with arbitrary earliness/tardiness penalties and an unrestricted common due date. International Journal of Production Research, 36(9), 2543-2551.
83. Yano, C. A., & Kim, Y. D. (1991). Algorithms for a class of single machine weighted tardiness and earliness problems. European Journal of Operational Research, 52, 167-178.
84. Yeh, W. C. (1999). A new branch-and-bound approach for the n/2/flowshop/a F + bCmax flowshop scheduling problem. Computers and Operations Research, 26, 1293-1310.
85. Zegordi, S. H., Itoh, K., & Enkawa, T. (1995). A knowledgeable simulated annealing scheme for the early/tardy flow shop scheduling problem. International Journal of Production Research, 33(5), 1449-1466.