American Institute of Mathematical Sciences

Advanced
January  2017, 13(1): 223-235. doi: 10.3934/jimo.2016013

Talent hold cost minimization in film production

Tai Chiu Edwin Cheng 1, , Bertrand Miao-Tsong Lin 2,, and  Hsiao-Lan Huang 2,

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

* Corresponding author: B. M. T. Lin

Received  May 2015 Revised  December 2015 Published  March 2016

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.

Keywords: Scheduling, talent hold cost, lower bound.
Mathematics Subject Classification: Primary: 590B35; Secondary: 80M50.
Citation: Tai Chiu Edwin Cheng, Bertrand Miao-Tsong Lin, Hsiao-Lan Huang. Talent hold cost minimization in film production. Journal of Industrial & Management Optimization, 2017, 13 (1) : 223-235. doi: 10.3934/jimo.2016013
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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[7]

G. Laporte, Solving a family of permutation problems on 0-1 matrices, RAIRO (Operations Research), 21 (1987), 65-85.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[7]

G. Laporte, Solving a family of permutation problems on 0-1 matrices, RAIRO (Operations Research), 21 (1987), 65-85.   Google Scholar

[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

Figure 1.  Day-out-of-days matrix
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  Areas resolved by different lower bounds
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3.  Partial schedule with days d2, d3, d6, d7 fixed
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4.  Illustration of Lemma 3.1
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 5.  Illustration of Max-w-matching(Φ(P))
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 6.  Analysis of xi1, i2, i3 in Lemma 4.1
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 7.  Analysis of yi1, i2, i3 in Lemma 4.1
Figure Options

Download full-size image

Download as PowerPoint slide

Table 1.  Development of xi1, i2, i3 in Lemma 4.1
ArrangementMinimum hold cost
x-1: $\beta_{\widetilde{i_1},{i_2},{i_3}}---\beta_{\widetilde{i_1},{i_2},{i_3}}$$c_{i_2}|\beta_{{i_1},\widetilde{i_2},{i_3}}|+c_{i_3}|\beta_{{i_1},{i_2},\widetilde{i_3}}|$
x-2: $\beta_{{i_1},\widetilde{i_2},{i_3}}---\beta_{{i_1},\widetilde{i_2},{i_3}}$$c_{i_1}|\beta_{\widetilde{i_1},{i_2},{i_3}}|+c_{i_3}|\beta_{{i_1},{i_2},\widetilde{i_3}}|$
x-3: $\beta_{{i_1},{i_2},\widetilde{i_3}}---\beta_{{i_1},{i_2},\widetilde{i_3}}$$c_{i_1}|\beta_{\widetilde{i_1},{i_2},{i_3}}|+c_{i_2}|\beta_{{i_1},\widetilde{i_2},{i_3}}|$
x-4: $\beta_{\widetilde{i_1},{i_2},{i_3}}---\beta_{{i_1},\widetilde{i_2},{i_3}}$$c_{i_3}|\beta_{{i_1},{i_2},\widetilde{i_3}}|$
x-5: $\beta_{\widetilde{i_1},{i_2},{i_3}}---\beta_{{i_1},{i_2},\widetilde{i_3}}$$c_{i_2}|\beta_{{i_1},\widetilde{i_2},{i_3}}|$
x-6: $\beta_{{i_1},\widetilde{i_2},{i_3}}---\beta_{{i_1},{i_2},\widetilde{i_3}}$$c_{i_1}|\beta_{\widetilde{i_1},{i_2},{i_3}}|$
$\displaystyle x_{i_1,i_2,i_3}=\min\Big\{c_{i_1}|\beta_{\widetilde{i_1},{i_2},{i_3}}|,c_{i_2}|\beta_{{i_1},\widetilde{i_2},{i_3}}|,c_{i_3}|\beta_{{i_1},{i_2},\widetilde{i_3}}|\Big\}$
Table Options

Download as excel

ArrangementMinimum hold cost
x-1: $\beta_{\widetilde{i_1},{i_2},{i_3}}---\beta_{\widetilde{i_1},{i_2},{i_3}}$$c_{i_2}|\beta_{{i_1},\widetilde{i_2},{i_3}}|+c_{i_3}|\beta_{{i_1},{i_2},\widetilde{i_3}}|$
x-2: $\beta_{{i_1},\widetilde{i_2},{i_3}}---\beta_{{i_1},\widetilde{i_2},{i_3}}$$c_{i_1}|\beta_{\widetilde{i_1},{i_2},{i_3}}|+c_{i_3}|\beta_{{i_1},{i_2},\widetilde{i_3}}|$
x-3: $\beta_{{i_1},{i_2},\widetilde{i_3}}---\beta_{{i_1},{i_2},\widetilde{i_3}}$$c_{i_1}|\beta_{\widetilde{i_1},{i_2},{i_3}}|+c_{i_2}|\beta_{{i_1},\widetilde{i_2},{i_3}}|$
x-4: $\beta_{\widetilde{i_1},{i_2},{i_3}}---\beta_{{i_1},\widetilde{i_2},{i_3}}$$c_{i_3}|\beta_{{i_1},{i_2},\widetilde{i_3}}|$
x-5: $\beta_{\widetilde{i_1},{i_2},{i_3}}---\beta_{{i_1},{i_2},\widetilde{i_3}}$$c_{i_2}|\beta_{{i_1},\widetilde{i_2},{i_3}}|$
x-6: $\beta_{{i_1},\widetilde{i_2},{i_3}}---\beta_{{i_1},{i_2},\widetilde{i_3}}$$c_{i_1}|\beta_{\widetilde{i_1},{i_2},{i_3}}|$
$\displaystyle x_{i_1,i_2,i_3}=\min\Big\{c_{i_1}|\beta_{\widetilde{i_1},{i_2},{i_3}}|,c_{i_2}|\beta_{{i_1},\widetilde{i_2},{i_3}}|,c_{i_3}|\beta_{{i_1},{i_2},\widetilde{i_3}}|\Big\}$
Table 2.  Analysis of yi1, i2, i3 for actors ai1, ai2, and ai3
ArrangementLower bound of costs
y-1: $\beta_{{i_1},{i_2},{i_3}}---\beta_{{i_1},{i_2},{i_3}}$$c_{i_1}(|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|+|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|)+ c_{i_2}(|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|+|\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|)$
$c_{i_3}(|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|+|\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|)$
y-2: $\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}---\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}$$c_{i_3}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}\cup \beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|$
y-3: $\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}---\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}$$c_{i_2}|\beta_{\widetilde{i_1},\widetilde{i_2}{i_3}}\cup \beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|$
y-4: $\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}---\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}$$c_{i_1}|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}\cup \beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|$
y-5: $\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}---\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}$$\min\{c_{i_2},c_{i_3}\}|\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|$, if $|\beta_{{i_1},{i_2},{i_3}}|>0$; 0, otherwise.
y-6: $\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}---\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}$$\min\{c_{i_1},c_{i_3}\}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|$, if $|\beta_{{i_1},{i_2},{i_3}}|>0$; 0, otherwise.
y-7: $\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}---\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}$$\min\{c_{i_1},c_{i_2}\}|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|$, if $|\beta_{{i_1},{i_2},{i_3}}|>0$; 0, otherwise.
y-8: $\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}---\beta_{{i_1},{i_2}{i_3}}$$\min\{c_{i_1}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|, c_{i_2}|\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|\}+c_{i_3}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}\cup \beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|$
y-9: $\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}---\beta_{{i_1},{i_2},{i_3}}$$\min\{c_{i_1}|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|, c_{i_3}|\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|\}+c_{i_2}|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}\cup \beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|$
y-10: $\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}---\beta_{{i_1},{i_2},{i_3}}$$\min\{c_{i_3}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|, c_{i_2}|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|\}+ c_{i_1}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}\cup \beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|$
$\displaystyle y_{i_1,i_2,i_3}=\min\Big\{\min\{c_{i_2},c_{i_3}\}|\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|, \min\{c_{i_1},c_{i_3}\}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|, \min\{c_{i_1},c_{i_2}\}|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|\Big\}$
Table Options

Download as excel

ArrangementLower bound of costs
y-1: $\beta_{{i_1},{i_2},{i_3}}---\beta_{{i_1},{i_2},{i_3}}$$c_{i_1}(|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|+|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|)+ c_{i_2}(|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|+|\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|)$
$c_{i_3}(|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|+|\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|)$
y-2: $\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}---\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}$$c_{i_3}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}\cup \beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|$
y-3: $\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}---\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}$$c_{i_2}|\beta_{\widetilde{i_1},\widetilde{i_2}{i_3}}\cup \beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|$
y-4: $\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}---\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}$$c_{i_1}|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}\cup \beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|$
y-5: $\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}---\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}$$\min\{c_{i_2},c_{i_3}\}|\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|$, if $|\beta_{{i_1},{i_2},{i_3}}|>0$; 0, otherwise.
y-6: $\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}---\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}$$\min\{c_{i_1},c_{i_3}\}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|$, if $|\beta_{{i_1},{i_2},{i_3}}|>0$; 0, otherwise.
y-7: $\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}---\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}$$\min\{c_{i_1},c_{i_2}\}|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|$, if $|\beta_{{i_1},{i_2},{i_3}}|>0$; 0, otherwise.
y-8: $\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}---\beta_{{i_1},{i_2}{i_3}}$$\min\{c_{i_1}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|, c_{i_2}|\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|\}+c_{i_3}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}\cup \beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|$
y-9: $\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}---\beta_{{i_1},{i_2},{i_3}}$$\min\{c_{i_1}|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|, c_{i_3}|\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|\}+c_{i_2}|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}\cup \beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|$
y-10: $\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}---\beta_{{i_1},{i_2},{i_3}}$$\min\{c_{i_3}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|, c_{i_2}|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|\}+ c_{i_1}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}\cup \beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|$
$\displaystyle y_{i_1,i_2,i_3}=\min\Big\{\min\{c_{i_2},c_{i_3}\}|\beta_{{i_1},\widetilde{i_2},\widetilde{i_3}}|, \min\{c_{i_1},c_{i_3}\}|\beta_{\widetilde{i_1},{i_2},\widetilde{i_3}}|, \min\{c_{i_1},c_{i_2}\}|\beta_{\widetilde{i_1},\widetilde{i_2},{i_3}}|\Big\}$
Table 3.  Lower bounds subject to outside-in branching scheme
Densitylower
bound		k = 1k = 3k = 5k = 10
valueratiovalueratiovalueratiovalueratio
0.1LB111,4131.00106,3651.00241,8301.00515,4241.00
LB222,2971.95129,6861.22265,0021.10530,0761.03
LB350,0234.38143,6191.35272,8541.13531,0301.03
0.2LB143,2991.00282,3871.00462,9861.00723,4021.00
LB281,4281.88324,6081.15496,7981.07727,8371.01
LB3112,7492.60333,7101.18498,4861.08727,8371.01
0.3LB1102,5311.00393,9301.00564,1091.00693,1171.00
LB2160,7441.57439,0861.11585,5161.04693,7161.00
LB3188,9081.84442,2291.12585,5161.04693,7161.00
Table Options

Download as excel

Densitylower
bound		k = 1k = 3k = 5k = 10
valueratiovalueratiovalueratiovalueratio
0.1LB111,4131.00106,3651.00241,8301.00515,4241.00
LB222,2971.95129,6861.22265,0021.10530,0761.03
LB350,0234.38143,6191.35272,8541.13531,0301.03
0.2LB143,2991.00282,3871.00462,9861.00723,4021.00
LB281,4281.88324,6081.15496,7981.07727,8371.01
LB3112,7492.60333,7101.18498,4861.08727,8371.01
0.3LB1102,5311.00393,9301.00564,1091.00693,1171.00
LB2160,7441.57439,0861.11585,5161.04693,7161.00
LB3188,9081.84442,2291.12585,5161.04693,7161.00
Table 4.  Lower bounds subject to sequential branching
Densitylower
bound		k = 1k = 3k = 5k = 10
valueratiovalueratiovalueratiovalueratio
0.1LB10N/A7,7641.0022,9181.0087,3581.00
LB26,541N/A26,9953.4851,9912.27127,3061.46
LB337,745N/A49,1036.3267,4352.94132,7591.52
0.2LB10N/A11,7371.0035,6051.0011,71471.00
LB224,446N/A74,2276.32113,4623.19206,2711.76
LB371,501N/A96,4548.22125,3533.52212,2101.81
0.3LB10N/A14,7691.0039,5631.00113,6261.00
LB244,348N/A119,8728.12275,2546.96236,5532.08
LB395,967N/A135,8919.20281,5407.12236,5532.08
Table Options

Download as excel

Densitylower
bound		k = 1k = 3k = 5k = 10
valueratiovalueratiovalueratiovalueratio
0.1LB10N/A7,7641.0022,9181.0087,3581.00
LB26,541N/A26,9953.4851,9912.27127,3061.46
LB337,745N/A49,1036.3267,4352.94132,7591.52
0.2LB10N/A11,7371.0035,6051.0011,71471.00
LB224,446N/A74,2276.32113,4623.19206,2711.76
LB371,501N/A96,4548.22125,3533.52212,2101.81
0.3LB10N/A14,7691.0039,5631.00113,6261.00
LB244,348N/A119,8728.12275,2546.96236,5532.08
LB395,967N/A135,8919.20281,5407.12236,5532.08
[1]

Srimanta Bhattacharya, Sushmita Ruj, Bimal Roy. Combinatorial batch codes: A lower bound and optimal constructions. Advances in Mathematics of Communications, 2012, 6 (2) : 165-174. doi: 10.3934/amc.2012.6.165
[2]

Z.G. Feng, K.L. Teo, Y. Zhao. Branch and bound method for sensor scheduling in discrete time. Journal of Industrial & Management Optimization, 2005, 1 (4) : 499-512. doi: 10.3934/jimo.2005.1.499
[3]

Onur Şimşek, O. Erhun Kundakcioglu. Cost of fairness in agent scheduling for contact centers. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021001
[4]

Florent Foucaud, Tero Laihonen, Aline Parreau. An improved lower bound for $(1,\leq 2)$-identifying codes in the king grid. Advances in Mathematics of Communications, 2014, 8 (1) : 35-52. doi: 10.3934/amc.2014.8.35
[5]

Geng Chen, Ronghua Pan, Shengguo Zhu. A polygonal scheme and the lower bound on density for the isentropic gas dynamics. Discrete & Continuous Dynamical Systems - A, 2019, 39 (7) : 4259-4277. doi: 10.3934/dcds.2019172
[6]

Aixian Zhang, Zhengchun Zhou, Keqin Feng. A lower bound on the average Hamming correlation of frequency-hopping sequence sets. Advances in Mathematics of Communications, 2015, 9 (1) : 55-62. doi: 10.3934/amc.2015.9.55
[7]

Pablo Blanc. A lower bound for the principal eigenvalue of fully nonlinear elliptic operators. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3613-3623. doi: 10.3934/cpaa.2020158
[8]

Paolo Gidoni, Alessandro Margheri. Lower bound on the number of periodic solutions for asymptotically linear planar Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 585-606. doi: 10.3934/dcds.2019024
[9]

Sofian De Clercq, Koen De Turck, Bart Steyaert, Herwig Bruneel. Frame-bound priority scheduling in discrete-time queueing systems. Journal of Industrial & Management Optimization, 2011, 7 (3) : 767-788. doi: 10.3934/jimo.2011.7.767
[10]

Lihui Zhang, Xin Zou, Jianxun Qi. A trade-off between time and cost in scheduling repetitive construction projects. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1423-1434. doi: 10.3934/jimo.2015.11.1423
[11]

Daniel N. Dore, Andrew D. Hanlon. Area preserving maps on $\boldsymbol{S^2}$: A lower bound on the $\boldsymbol{C^0}$-norm using symplectic spectral invariants. Electronic Research Announcements, 2013, 20: 97-102. doi: 10.3934/era.2013.20.97
[12]

Christopher S. Goodrich, Benjamin Lyons, Mihaela T. Velcsov. Analytical and numerical monotonicity results for discrete fractional sequential differences with negative lower bound. Communications on Pure & Applied Analysis, 2021, 20 (1) : 339-358. doi: 10.3934/cpaa.2020269
[13]

Marc Briant. Instantaneous exponential lower bound for solutions to the Boltzmann equation with Maxwellian diffusion boundary conditions. Kinetic & Related Models, 2015, 8 (2) : 281-308. doi: 10.3934/krm.2015.8.281
[14]

Claude Carlet, Brahim Merabet. Asymptotic lower bound on the algebraic immunity of random balanced multi-output Boolean functions. Advances in Mathematics of Communications, 2013, 7 (2) : 197-217. doi: 10.3934/amc.2013.7.197
[15]

Nam Yul Yu. A Fourier transform approach for improving the Levenshtein's lower bound on aperiodic correlation of binary sequences. Advances in Mathematics of Communications, 2014, 8 (2) : 209-222. doi: 10.3934/amc.2014.8.209
[16]

Katrin Gelfert. Lower bounds for the topological entropy. Discrete & Continuous Dynamical Systems - A, 2005, 12 (3) : 555-565. doi: 10.3934/dcds.2005.12.555
[17]

Yuzhong Zhang, Chunsong Bai, Qingguo Bai, Jianteng Xu. Duplicating in batch scheduling. Journal of Industrial & Management Optimization, 2007, 3 (4) : 685-692. doi: 10.3934/jimo.2007.3.685
[18]

Mikko Kaasalainen. Dynamical tomography of gravitationally bound systems. Inverse Problems & Imaging, 2008, 2 (4) : 527-546. doi: 10.3934/ipi.2008.2.527
[19]

R. Enkhbat , N. Tungalag, A. S. Strekalovsky. Pseudoconvexity properties of average cost functions. Numerical Algebra, Control & Optimization, 2015, 5 (3) : 233-236. doi: 10.3934/naco.2015.5.233
[20]

Giuseppe Buttazzo, Serena Guarino Lo Bianco, Fabrizio Oliviero. Optimal location problems with routing cost. Discrete & Continuous Dynamical Systems - A, 2014, 34 (4) : 1301-1317. doi: 10.3934/dcds.2014.34.1301

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (134)
  • HTML views (364)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences