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The finite-time ruin probability for an inhomogeneous renewal risk model
Talent hold cost minimization in film production
1. | Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong |
2. | Institute of Information Management, National Chiao Tung University, Hsinchu 300, Taiwan |
This paper investigates the talent scheduling problem in film production, which is known as rehearsal scheduling in music and dance performances. The first lower bound on the minimization of talent hold cost is based upon the outside-in branching strategy. We introduce two approaches to add extra terms for tightening the lower bound. The first approach is to formulate a maximum weighted matching problem. The second approach is to retrieve structural information and solve a maximum weighted 3-grouping problem. We make two contributions: First, our results can fathom the matrix of a given partial schedule. Second, our second approach is free from the requirement to schedule some shooting days in advance for providing anchoring information as in the other approaches, i.e., a lower bound can be computed once the input instance is given. The lower bound can fit different branching strategies. Moreover, the second contribution provides a state-of-the-art research result for this problem. Computational experiments confirm that the new bounds are much tighter than the original one.
References:
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R. M. Adelson, G. Laporte and J. M. Norman, A dynamic programming formulation with diverse applications, Operations Research Quarterly, 27 (1976), 119-121. Google Scholar |
[2] |
M. G. de la Banda, P. J. Stuckey and G. Chu,
Solving talent scheduling with dynamic programming, INFORMS Journal on Computing, 23 (2011), 120-137.
doi: 10.1287/ijoc.1090.0378. |
[3] |
T. C. E. Cheng, J. E. Diamond and B. M. T. Lin,
Optimal scheduling in film production to minimize talent hold cost, Journal of Optimization Theory and Applications, 79 (1993), 479-492.
doi: 10.1007/BF00940554. |
[4] |
M. Gendreau, A. Hertz and G. Laporte, A generalized insertion algorithm for the serilization problem, Mathematical and Computational Modeling, 19 (1994), 53-59. Google Scholar |
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R. M. Karp,
Mapping the genome: Some combinatorial problems arising in molecular biology, Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing (STOC), (1993), 279-285.
doi: 10.1145/167088.167170. |
[6] |
G. Laporte,
The serialization problem and the travelling salesman problem, Journal of Computational and Applied Mathematics, 4 (1978), 259-268.
doi: 10.1016/0771-050X(78)90024-4. |
[7] |
G. Laporte,
Solving a family of permutation problems on 0-1 matrices, RAIRO (Operations Research), 21 (1987), 65-85.
|
[8] |
G. Laporte and S. Taillefer, An efficient interchange procedure for the archaeological serisation problem, Journal of Archaeological Science, 14 (1987), 283-289. Google Scholar |
[9] |
B. M. T. Lin, A new branch-and-bound algorithm for the film production problem, Journal of Ming Chuan College, 10 (1999), 101-110. Google Scholar |
[10] |
A. L. Nordström and S. Tufekçi, A genetic algorithm for the talent scheduling problem, Computers and Operations Research, 21 (1994), 927-940. Google Scholar |
[11] |
R. S. Singleton, Film Scheduling: Or, How Long Will It Take to Shoot Your Movie? Lone Eagle, Los Angeles, U. S. A., 1997. Google Scholar |
[12] |
B. M. Smith, Constraint Programming in Practice: Scheduling a Rehearsal, Report APES-67-2003, University of Huddersfield, U. K., 2003. Google Scholar |
[13] |
S. Y. Wang, Y. T. Chuang and B. M. T. Lin, Talent scheduling with daily operating capacities, Journal of Production and Industrial Engineering, 33 (2016), 17-31. Google Scholar |
[14] |
M. Wyon, Preparing to perform periodization and dance, Journal of Dance Medicine and Science, 14 (2010), 67-72. Google Scholar |
show all references
References:
[1] |
R. M. Adelson, G. Laporte and J. M. Norman, A dynamic programming formulation with diverse applications, Operations Research Quarterly, 27 (1976), 119-121. Google Scholar |
[2] |
M. G. de la Banda, P. J. Stuckey and G. Chu,
Solving talent scheduling with dynamic programming, INFORMS Journal on Computing, 23 (2011), 120-137.
doi: 10.1287/ijoc.1090.0378. |
[3] |
T. C. E. Cheng, J. E. Diamond and B. M. T. Lin,
Optimal scheduling in film production to minimize talent hold cost, Journal of Optimization Theory and Applications, 79 (1993), 479-492.
doi: 10.1007/BF00940554. |
[4] |
M. Gendreau, A. Hertz and G. Laporte, A generalized insertion algorithm for the serilization problem, Mathematical and Computational Modeling, 19 (1994), 53-59. Google Scholar |
[5] |
R. M. Karp,
Mapping the genome: Some combinatorial problems arising in molecular biology, Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing (STOC), (1993), 279-285.
doi: 10.1145/167088.167170. |
[6] |
G. Laporte,
The serialization problem and the travelling salesman problem, Journal of Computational and Applied Mathematics, 4 (1978), 259-268.
doi: 10.1016/0771-050X(78)90024-4. |
[7] |
G. Laporte,
Solving a family of permutation problems on 0-1 matrices, RAIRO (Operations Research), 21 (1987), 65-85.
|
[8] |
G. Laporte and S. Taillefer, An efficient interchange procedure for the archaeological serisation problem, Journal of Archaeological Science, 14 (1987), 283-289. Google Scholar |
[9] |
B. M. T. Lin, A new branch-and-bound algorithm for the film production problem, Journal of Ming Chuan College, 10 (1999), 101-110. Google Scholar |
[10] |
A. L. Nordström and S. Tufekçi, A genetic algorithm for the talent scheduling problem, Computers and Operations Research, 21 (1994), 927-940. Google Scholar |
[11] |
R. S. Singleton, Film Scheduling: Or, How Long Will It Take to Shoot Your Movie? Lone Eagle, Los Angeles, U. S. A., 1997. Google Scholar |
[12] |
B. M. Smith, Constraint Programming in Practice: Scheduling a Rehearsal, Report APES-67-2003, University of Huddersfield, U. K., 2003. Google Scholar |
[13] |
S. Y. Wang, Y. T. Chuang and B. M. T. Lin, Talent scheduling with daily operating capacities, Journal of Production and Industrial Engineering, 33 (2016), 17-31. Google Scholar |
[14] |
M. Wyon, Preparing to perform periodization and dance, Journal of Dance Medicine and Science, 14 (2010), 67-72. Google Scholar |







Arrangement | Minimum hold cost |
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Arrangement | Minimum hold cost |
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Arrangement | Lower bound of costs |
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Arrangement | Lower bound of costs |
y-1: | |
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Density | lower bound | k = 1 | k = 3 | k = 5 | k = 10 | ||||
value | ratio | value | ratio | value | ratio | value | ratio | ||
0.1 | LB1 | 11,413 | 1.00 | 106,365 | 1.00 | 241,830 | 1.00 | 515,424 | 1.00 |
LB2 | 22,297 | 1.95 | 129,686 | 1.22 | 265,002 | 1.10 | 530,076 | 1.03 | |
LB3 | 50,023 | 4.38 | 143,619 | 1.35 | 272,854 | 1.13 | 531,030 | 1.03 | |
0.2 | LB1 | 43,299 | 1.00 | 282,387 | 1.00 | 462,986 | 1.00 | 723,402 | 1.00 |
LB2 | 81,428 | 1.88 | 324,608 | 1.15 | 496,798 | 1.07 | 727,837 | 1.01 | |
LB3 | 112,749 | 2.60 | 333,710 | 1.18 | 498,486 | 1.08 | 727,837 | 1.01 | |
0.3 | LB1 | 102,531 | 1.00 | 393,930 | 1.00 | 564,109 | 1.00 | 693,117 | 1.00 |
LB2 | 160,744 | 1.57 | 439,086 | 1.11 | 585,516 | 1.04 | 693,716 | 1.00 | |
LB3 | 188,908 | 1.84 | 442,229 | 1.12 | 585,516 | 1.04 | 693,716 | 1.00 |
Density | lower bound | k = 1 | k = 3 | k = 5 | k = 10 | ||||
value | ratio | value | ratio | value | ratio | value | ratio | ||
0.1 | LB1 | 11,413 | 1.00 | 106,365 | 1.00 | 241,830 | 1.00 | 515,424 | 1.00 |
LB2 | 22,297 | 1.95 | 129,686 | 1.22 | 265,002 | 1.10 | 530,076 | 1.03 | |
LB3 | 50,023 | 4.38 | 143,619 | 1.35 | 272,854 | 1.13 | 531,030 | 1.03 | |
0.2 | LB1 | 43,299 | 1.00 | 282,387 | 1.00 | 462,986 | 1.00 | 723,402 | 1.00 |
LB2 | 81,428 | 1.88 | 324,608 | 1.15 | 496,798 | 1.07 | 727,837 | 1.01 | |
LB3 | 112,749 | 2.60 | 333,710 | 1.18 | 498,486 | 1.08 | 727,837 | 1.01 | |
0.3 | LB1 | 102,531 | 1.00 | 393,930 | 1.00 | 564,109 | 1.00 | 693,117 | 1.00 |
LB2 | 160,744 | 1.57 | 439,086 | 1.11 | 585,516 | 1.04 | 693,716 | 1.00 | |
LB3 | 188,908 | 1.84 | 442,229 | 1.12 | 585,516 | 1.04 | 693,716 | 1.00 |
Density | lower bound | k = 1 | k = 3 | k = 5 | k = 10 | ||||
value | ratio | value | ratio | value | ratio | value | ratio | ||
0.1 | LB1 | 0 | N/A | 7,764 | 1.00 | 22,918 | 1.00 | 87,358 | 1.00 |
LB2 | 6,541 | N/A | 26,995 | 3.48 | 51,991 | 2.27 | 127,306 | 1.46 | |
LB3 | 37,745 | N/A | 49,103 | 6.32 | 67,435 | 2.94 | 132,759 | 1.52 | |
0.2 | LB1 | 0 | N/A | 11,737 | 1.00 | 35,605 | 1.00 | 11,7147 | 1.00 |
LB2 | 24,446 | N/A | 74,227 | 6.32 | 113,462 | 3.19 | 206,271 | 1.76 | |
LB3 | 71,501 | N/A | 96,454 | 8.22 | 125,353 | 3.52 | 212,210 | 1.81 | |
0.3 | LB1 | 0 | N/A | 14,769 | 1.00 | 39,563 | 1.00 | 113,626 | 1.00 |
LB2 | 44,348 | N/A | 119,872 | 8.12 | 275,254 | 6.96 | 236,553 | 2.08 | |
LB3 | 95,967 | N/A | 135,891 | 9.20 | 281,540 | 7.12 | 236,553 | 2.08 |
Density | lower bound | k = 1 | k = 3 | k = 5 | k = 10 | ||||
value | ratio | value | ratio | value | ratio | value | ratio | ||
0.1 | LB1 | 0 | N/A | 7,764 | 1.00 | 22,918 | 1.00 | 87,358 | 1.00 |
LB2 | 6,541 | N/A | 26,995 | 3.48 | 51,991 | 2.27 | 127,306 | 1.46 | |
LB3 | 37,745 | N/A | 49,103 | 6.32 | 67,435 | 2.94 | 132,759 | 1.52 | |
0.2 | LB1 | 0 | N/A | 11,737 | 1.00 | 35,605 | 1.00 | 11,7147 | 1.00 |
LB2 | 24,446 | N/A | 74,227 | 6.32 | 113,462 | 3.19 | 206,271 | 1.76 | |
LB3 | 71,501 | N/A | 96,454 | 8.22 | 125,353 | 3.52 | 212,210 | 1.81 | |
0.3 | LB1 | 0 | N/A | 14,769 | 1.00 | 39,563 | 1.00 | 113,626 | 1.00 |
LB2 | 44,348 | N/A | 119,872 | 8.12 | 275,254 | 6.96 | 236,553 | 2.08 | |
LB3 | 95,967 | N/A | 135,891 | 9.20 | 281,540 | 7.12 | 236,553 | 2.08 |
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