Dynamic-programming-based heuristic for multi-objective operating theater planning

Ya Liu; Zhaojin Li

doi:10.3934/jimo.2020145

Previous Article
A novel risk ranking method based on the single valued neutrosophic set
JIMO Home
This Issue
Next Article
Incentive contract design for supplier switching with considering learning effect

doi: 10.3934/jimo.2020145

Dynamic-programming-based heuristic for multi-objective operating theater planning

Ya Liu and Zhaojin Li ^,

School of Management, Xi'an Jiaotong University, 710049, NO.28 Xianning Road, Xi'an Shaanxi, China

^* Corresponding author: Zhaojin Li

Received December 2018 Revised August 2020 Published September 2020

This study focuses on the assignment of surgical operations to operating room (OR) blocks to minimize not only the utilization cost of the OR blocks but also the number of patterns generated. We propose a dynamic-programming-based heuristic to solve this problem. Using an iterative formulation, we separate the patterns individually. The computational results show that the proposed heuristic is efficient. Compared with "quasi-optimal" plans, the average cost gap ranges from 0.022 to 0.066 for various scenarios. A lower bound based on column generation procedure is developed. Results show that the average absolute difference of three scenarios are respectively 0.045, 0.081 and 0.115. According to evaluations based on performance indicators from the extant literature, the utilization ratio of the operating theater (OT) varies from 1% underutilization to 2% overutilization in the solutions yielded by the proposed heuristic. This study deals with a multi-objective optimization problem, the second objective of which plays a significant role in reducing the preparation cost, error probability, and staff fatigue in medical systems, where security and human issues are far more emphasized than in other sectors. To the best of our knowledge, our study is the first to investigate such a real-world multi-objective OT planning problem.

Keywords: Healthcare, dynamic programming, operating theater, heuristic, multi-objective optimization.

Mathematics Subject Classification: Primary: 90BXX; Secondary: 90B50.

Citation: Ya Liu, Zhaojin Li. Dynamic-programming-based heuristic for multi-objective operating theater planning. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020145

References:

[1]	I. Adan, J. Bekkers, N. Dellaert, J. Jeunet and J. Vissers, Improving operational effectiveness of tactical master plans for emergency and elective patients under stochastic demand and capacitated resources, European Journal of Operational Research, 213 (2011), 290-308. doi: 10.1016/j.ejor.2011.02.025. Google Scholar
[2]	J. Ansarifar, R. Tavakkoli-Moghaddam, F. Akhavizadegan and S. Hassanzadeh Amin, Multi-objective integrated planning and scheduling model for operating rooms under uncertainty, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 232 (2018), 930-948. doi: 10.1177/0954411918794721. Google Scholar
[3]	J. Belien and E. Demeulemeester, Building cyclic master surgery schedules with leveled resulting bed occupancy, European Journal of Operational Research, 176 (2007), 1185-1204. doi: 10.1016/j.ejor.2005.06.063. Google Scholar
[4]	B. Cardoen, E. Demeulemeester and J. Belien, Optimizing a multiple objective surgical case senquencing problem, International Journal of Production Economics, 119 (2009), 354-366. Google Scholar
[5]	B. Cardoen, E. Demeulemeester and J. Belien, Operating room planning and scheduling: A literature review, European Journal of Operational Research, 201 (2010), 921-932. Google Scholar
[6]	H. F. M. Association et al., Achieving operating room efficiency through process integration., Healthcare Financial Management: Journal of the Healthcare Financial Management Association, 57 (2003), suppl 1–7. Google Scholar
[7]	C. Chu and J. Antonio, Approximation algorithms to solve real-life multicriteria cutting stock problems, Operations Research, 47 (1999), 495-508. doi: 10.1287/opre.47.4.495. Google Scholar
[8]	N. Dellaert, E. Cayiroglu and J. Jeunet, Assessing and controlling the impact of hospital capacity planning on the waiting time, International Journal of Production Research, 54 (2016), 2203-2214. doi: 10.1080/00207543.2015.1051668. Google Scholar
[9]	N. Dellaert and J. Jeunet, A variable neighborhood search algorithm for the surgery tactical planning problem, Computers & Operations Research, 84 (2017), 216-225. doi: 10.1016/j.cor.2016.05.013. Google Scholar
[10]	F. Dexter, A. Macario, R. D. Traub, M. Hopwood and D. A. Lubarsky, An operating room scheduling strategy to maximize the use of operating room block time: computer simulation of patient scheduling and survey of patients' preferences for surgical waiting time, Anesthesia Analgesia, 89 (1999), 7-20. doi: 10.1097/00000539-199907000-00003. Google Scholar
[11]	H. Fei, C. Chu and N. Meskens, Solving a tactical operating room planning problem by a column-generation-based heuristic procedure with four criteria, Annals of Operations Research, 166 (2009), 91-108. doi: 10.1007/s10479-008-0413-3. Google Scholar
[12]	H. Fei, C. Chu, N. Meskens and A. Artiba, Solving surgical cases assignment problem by a branch-and-price approach, International Journal of Production Economics, 112 (2008), 96-108. doi: 10.1016/j.ijpe.2006.08.030. Google Scholar
[13]	H. Fei, N. Meskens and C. Chu, A planning and scheduling problem for an operating theatre using an open scheduling strategy, Computers and Industrial Engineering, 58 (2010), 221-230. doi: 10.1016/j.cie.2009.02.012. Google Scholar
[14]	P. C. Gilmore and R. E. Gomory, A linear programming approach to the cutting-stock problem, Operations Research, 9 (1961), 849-859. doi: 10.1287/opre.9.6.849. Google Scholar
[15]	F. Guerriero and R. Guido, Operational research in the management of the operating theatre: a survey, Health Care Management Science, 14 (2011), 89-114. doi: 10.1007/s10729-010-9143-6. Google Scholar
[16]	R. Guido and D. Conforti, A hybrid genetic approach for solving an integrated multi-objective operating room planning and scheduling problem, Computers & Operations Research, 87 (2017), 270-282. doi: 10.1016/j.cor.2016.11.009. Google Scholar
[17]	A. Guinet and S. Chaabane, Operating theatre planning, International Journal of Production Economics, 85 (2003), 69-81. doi: 10.1016/S0925-5273(03)00087-2. Google Scholar
[18]	E. Hans, G. Wullink, M. V. Houdenhoven and G. Kazemier, Robust surgery loading, European Journal of Operational Research, 185 (2008), 1038-1050. doi: 10.1016/j.ejor.2006.08.022. Google Scholar
[19]	A. Jebali, A. H. Alouane and P. Ladet, Operating rooms scheduling, International Journal of Production Economics, 99 (2006), 52-62. doi: 10.1016/j.ijpe.2004.12.006. Google Scholar
[20]	A. Jebali and A. Diabat, A stochastic model for operating room planning under capacity constraints, International Journal of Production Research, 53 (2015), 7252-7270. doi: 10.1080/00207543.2015.1033500. Google Scholar
[21]	M. A. Kamran, B. Karimi and N. Dellaert, Uncertainty in advance scheduling problem in operating room planning, Computers & Industrial Engineering, 126 (2018), 252-268. doi: 10.1016/j.cie.2018.09.030. Google Scholar
[22]	M. A. Kamran, B. Karimi, N. Dellaert and E. Demeulemeester, Adaptive operating rooms planning and scheduling: A rolling horizon approach, Operations Research for Health Care, 22 (2019), 100200. doi: 10.1016/j.orhc.2019.100200. Google Scholar
[23]	P. Kuo, R. Schroeder, S. Mahaffey and R. R. Bollinger, Optimization of operating room allocation using linear programming technique, The American College of Surgeon, 197 (2003), 889-895. doi: 10.1016/j.jamcollsurg.2003.07.006. Google Scholar
[24]	E. Litvak and M. Long, Cost and quality under managed care: Irreconcilable differences, American Journal of Managed Care, 6 (2000), 305-312. Google Scholar
[25]	Y. Liu, C. Chu and K. Wang, A new heuristic algorithm for the operating room scheduling problem, Computers and Industrial Engineering, 61 (2011), 865-871. doi: 10.1016/j.cie.2011.05.020. Google Scholar
[26]	E. Marcon, S. Kharraja and G. Simonnet, The operating theatre planning by the follow-up of the risk of no realization, International Journal of Production Economics, 85 (2003), 83-90. doi: 10.1016/S0925-5273(03)00088-4. Google Scholar
[27]	A. Testi and E. Tanfani, A pre-assignment heuristic algorithm for the master surgical schedule problem(mssp), Annals of Operations Research, 178 (2010), 105-119. doi: 10.1007/s10479-009-0568-6. Google Scholar
[28]	M. M. Vali-Siar, S. Gholami and R. Ramezanian, Multi-period and multi-resource operating room scheduling under uncertainty: A case study, Computers & Industrial Engineering, 126 (2018), 549-568. doi: 10.1016/j.cie.2018.10.014. Google Scholar
[29]	C. Van Riet and E. Demeulemeester, Trade-offs in operating room planning for electives and emergencies: A review, Operations Research for Health Care, 7 (2015), 52-69. Google Scholar
[30]	F. Vanderbeck, Exact algorithm for minimising the number of setups in the one-dimensional cutting stock problem, Operations Research, 48 (2000), 915-926. doi: 10.1287/opre.48.6.915.12391. Google Scholar
[31]	A. Weinbroum, P. Ekstein and T. Ezri, Efficiency of the operating room suite, The American Journal of Surgery, 185 (2003), 244-250. doi: 10.1016/S0002-9610(02)01362-4. Google Scholar
[32]	W. Xiang, A multi-objective aco for operating room scheduling optimization, Natural Computing, 16 (2017), 607-617. doi: 10.1007/s11047-016-9607-9. Google Scholar
[33]	S. Zhu, W. Fan, S. Yang, J. Pei and P. M. Pardalos, Operating room planning and surgical case scheduling: A review of literature, Journal of Combinatorial Optimization, 37 (2019), 757-805. doi: 10.1007/s10878-018-0322-6. Google Scholar

show all references

References:

[1]	I. Adan, J. Bekkers, N. Dellaert, J. Jeunet and J. Vissers, Improving operational effectiveness of tactical master plans for emergency and elective patients under stochastic demand and capacitated resources, European Journal of Operational Research, 213 (2011), 290-308. doi: 10.1016/j.ejor.2011.02.025. Google Scholar
[2]	J. Ansarifar, R. Tavakkoli-Moghaddam, F. Akhavizadegan and S. Hassanzadeh Amin, Multi-objective integrated planning and scheduling model for operating rooms under uncertainty, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 232 (2018), 930-948. doi: 10.1177/0954411918794721. Google Scholar
[3]	J. Belien and E. Demeulemeester, Building cyclic master surgery schedules with leveled resulting bed occupancy, European Journal of Operational Research, 176 (2007), 1185-1204. doi: 10.1016/j.ejor.2005.06.063. Google Scholar
[4]	B. Cardoen, E. Demeulemeester and J. Belien, Optimizing a multiple objective surgical case senquencing problem, International Journal of Production Economics, 119 (2009), 354-366. Google Scholar
[5]	B. Cardoen, E. Demeulemeester and J. Belien, Operating room planning and scheduling: A literature review, European Journal of Operational Research, 201 (2010), 921-932. Google Scholar
[6]	H. F. M. Association et al., Achieving operating room efficiency through process integration., Healthcare Financial Management: Journal of the Healthcare Financial Management Association, 57 (2003), suppl 1–7. Google Scholar
[7]	C. Chu and J. Antonio, Approximation algorithms to solve real-life multicriteria cutting stock problems, Operations Research, 47 (1999), 495-508. doi: 10.1287/opre.47.4.495. Google Scholar
[8]	N. Dellaert, E. Cayiroglu and J. Jeunet, Assessing and controlling the impact of hospital capacity planning on the waiting time, International Journal of Production Research, 54 (2016), 2203-2214. doi: 10.1080/00207543.2015.1051668. Google Scholar
[9]	N. Dellaert and J. Jeunet, A variable neighborhood search algorithm for the surgery tactical planning problem, Computers & Operations Research, 84 (2017), 216-225. doi: 10.1016/j.cor.2016.05.013. Google Scholar
[10]	F. Dexter, A. Macario, R. D. Traub, M. Hopwood and D. A. Lubarsky, An operating room scheduling strategy to maximize the use of operating room block time: computer simulation of patient scheduling and survey of patients' preferences for surgical waiting time, Anesthesia Analgesia, 89 (1999), 7-20. doi: 10.1097/00000539-199907000-00003. Google Scholar
[11]	H. Fei, C. Chu and N. Meskens, Solving a tactical operating room planning problem by a column-generation-based heuristic procedure with four criteria, Annals of Operations Research, 166 (2009), 91-108. doi: 10.1007/s10479-008-0413-3. Google Scholar
[12]	H. Fei, C. Chu, N. Meskens and A. Artiba, Solving surgical cases assignment problem by a branch-and-price approach, International Journal of Production Economics, 112 (2008), 96-108. doi: 10.1016/j.ijpe.2006.08.030. Google Scholar
[13]	H. Fei, N. Meskens and C. Chu, A planning and scheduling problem for an operating theatre using an open scheduling strategy, Computers and Industrial Engineering, 58 (2010), 221-230. doi: 10.1016/j.cie.2009.02.012. Google Scholar
[14]	P. C. Gilmore and R. E. Gomory, A linear programming approach to the cutting-stock problem, Operations Research, 9 (1961), 849-859. doi: 10.1287/opre.9.6.849. Google Scholar
[15]	F. Guerriero and R. Guido, Operational research in the management of the operating theatre: a survey, Health Care Management Science, 14 (2011), 89-114. doi: 10.1007/s10729-010-9143-6. Google Scholar
[16]	R. Guido and D. Conforti, A hybrid genetic approach for solving an integrated multi-objective operating room planning and scheduling problem, Computers & Operations Research, 87 (2017), 270-282. doi: 10.1016/j.cor.2016.11.009. Google Scholar
[17]	A. Guinet and S. Chaabane, Operating theatre planning, International Journal of Production Economics, 85 (2003), 69-81. doi: 10.1016/S0925-5273(03)00087-2. Google Scholar
[18]	E. Hans, G. Wullink, M. V. Houdenhoven and G. Kazemier, Robust surgery loading, European Journal of Operational Research, 185 (2008), 1038-1050. doi: 10.1016/j.ejor.2006.08.022. Google Scholar
[19]	A. Jebali, A. H. Alouane and P. Ladet, Operating rooms scheduling, International Journal of Production Economics, 99 (2006), 52-62. doi: 10.1016/j.ijpe.2004.12.006. Google Scholar
[20]	A. Jebali and A. Diabat, A stochastic model for operating room planning under capacity constraints, International Journal of Production Research, 53 (2015), 7252-7270. doi: 10.1080/00207543.2015.1033500. Google Scholar
[21]	M. A. Kamran, B. Karimi and N. Dellaert, Uncertainty in advance scheduling problem in operating room planning, Computers & Industrial Engineering, 126 (2018), 252-268. doi: 10.1016/j.cie.2018.09.030. Google Scholar
[22]	M. A. Kamran, B. Karimi, N. Dellaert and E. Demeulemeester, Adaptive operating rooms planning and scheduling: A rolling horizon approach, Operations Research for Health Care, 22 (2019), 100200. doi: 10.1016/j.orhc.2019.100200. Google Scholar
[23]	P. Kuo, R. Schroeder, S. Mahaffey and R. R. Bollinger, Optimization of operating room allocation using linear programming technique, The American College of Surgeon, 197 (2003), 889-895. doi: 10.1016/j.jamcollsurg.2003.07.006. Google Scholar
[24]	E. Litvak and M. Long, Cost and quality under managed care: Irreconcilable differences, American Journal of Managed Care, 6 (2000), 305-312. Google Scholar
[25]	Y. Liu, C. Chu and K. Wang, A new heuristic algorithm for the operating room scheduling problem, Computers and Industrial Engineering, 61 (2011), 865-871. doi: 10.1016/j.cie.2011.05.020. Google Scholar
[26]	E. Marcon, S. Kharraja and G. Simonnet, The operating theatre planning by the follow-up of the risk of no realization, International Journal of Production Economics, 85 (2003), 83-90. doi: 10.1016/S0925-5273(03)00088-4. Google Scholar
[27]	A. Testi and E. Tanfani, A pre-assignment heuristic algorithm for the master surgical schedule problem(mssp), Annals of Operations Research, 178 (2010), 105-119. doi: 10.1007/s10479-009-0568-6. Google Scholar
[28]	M. M. Vali-Siar, S. Gholami and R. Ramezanian, Multi-period and multi-resource operating room scheduling under uncertainty: A case study, Computers & Industrial Engineering, 126 (2018), 549-568. doi: 10.1016/j.cie.2018.10.014. Google Scholar
[29]	C. Van Riet and E. Demeulemeester, Trade-offs in operating room planning for electives and emergencies: A review, Operations Research for Health Care, 7 (2015), 52-69. Google Scholar
[30]	F. Vanderbeck, Exact algorithm for minimising the number of setups in the one-dimensional cutting stock problem, Operations Research, 48 (2000), 915-926. doi: 10.1287/opre.48.6.915.12391. Google Scholar
[31]	A. Weinbroum, P. Ekstein and T. Ezri, Efficiency of the operating room suite, The American Journal of Surgery, 185 (2003), 244-250. doi: 10.1016/S0002-9610(02)01362-4. Google Scholar
[32]	W. Xiang, A multi-objective aco for operating room scheduling optimization, Natural Computing, 16 (2017), 607-617. doi: 10.1007/s11047-016-9607-9. Google Scholar
[33]	S. Zhu, W. Fan, S. Yang, J. Pei and P. M. Pardalos, Operating room planning and surgical case scheduling: A review of literature, Journal of Combinatorial Optimization, 37 (2019), 757-805. doi: 10.1007/s10878-018-0322-6. Google Scholar

Figure 1. Average number of patterns generated in different cases (n = 5, 6, 7)

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2. UROR for different cases (n = 5, 6, 7)

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3. Average accumulated overtime for different cases (n = 5, 6, 7)

Figure Options

Download full-size image

Download as PowerPoint slide

Table 1. Notations

$ Parameters: $
$ n $	number of OR block types;
$ m $	number of operation types;
$ C^{0} $	set of OR blocks available during the planning horizon;
$ B^{0} $	set of operations to be assigned;
$ T_{i} $	the regular opening time of OR block with type $ i $;
$ OT_{i} $	the maximum overtime of OR block with type $ i $;
$ c_{i}^{0} $	number of OR blocks with type $ i $;
$ \omega_{k} $	number of mandatory operations with type $ k $;
$ b_{k}^{0} $	number of operations to be assigned with type $ k $;
$ l_{k} $	the duration of operation with type $ k $;
$ p_{i} $	number of all feasible patterns using block of type $ i $;
$ \rho_{ij} $	utilization cost of pattern $ (i, j) $;
$ a_{ijk} $	number of operations of type $ k $ assigned under pattern $ (i, j) $;
$ \beta $	cost for preparing a pattern;
$ M $	an arbitrarily large number;
$ Decision \quad Variables: $
$ x_{ij} $	the number of occurrences of pattern $ (i, j) $;
$ z_{ij} $	1, if pattern $ (i, j) $ occurs at least once in the solution; 0, otherwise.

Table Options

Download as excel

$ Parameters: $
$ n $	number of OR block types;
$ m $	number of operation types;
$ C^{0} $	set of OR blocks available during the planning horizon;
$ B^{0} $	set of operations to be assigned;
$ T_{i} $	the regular opening time of OR block with type $ i $;
$ OT_{i} $	the maximum overtime of OR block with type $ i $;
$ c_{i}^{0} $	number of OR blocks with type $ i $;
$ \omega_{k} $	number of mandatory operations with type $ k $;
$ b_{k}^{0} $	number of operations to be assigned with type $ k $;
$ l_{k} $	the duration of operation with type $ k $;
$ p_{i} $	number of all feasible patterns using block of type $ i $;
$ \rho_{ij} $	utilization cost of pattern $ (i, j) $;
$ a_{ijk} $	number of operations of type $ k $ assigned under pattern $ (i, j) $;
$ \beta $	cost for preparing a pattern;
$ M $	an arbitrarily large number;
$ Decision \quad Variables: $
$ x_{ij} $	the number of occurrences of pattern $ (i, j) $;
$ z_{ij} $	1, if pattern $ (i, j) $ occurs at least once in the solution; 0, otherwise.

Table 2. Comparison with "quasi-optimal", $ n $ = 5

Ex.	$ m $	#Operation	#OR blocks	Scenario 1					Scenario 2					Scenario 3
Ex.	$ m $	#Operation	#OR blocks	$ rc_1 $	$ rc_2 $	Gap	Time		$ rc_1 $	$ rc_2 $	Gap	Time		$ rc_1 $	$ rc_2 $	Gap	Time
Case 1
1	16	113	27	0.047	0.116	0.069	0.50		0.116	0.200	0.084	0.52		0.186	0.281	0.095	0.56
2	20	122	24	0.049	0.065	0.016	0.56		0.122	0.138	0.016	0.56		0.195	0.210	0.015	0.55
3	15	118	24	0.048	0.074	0.026	0.43		0.121	0.146	0.025	0.47		0.194	0.218	0.024	0.45
4	19	165	28	0.043	0.085	0.042	0.70		0.106	0.202	0.096	0.70		0.170	0.323	0.153	0.71
5	16	104	26	0.049	0.051	0.002	0.47		0.125	0.127	0.002	0.53		0.200	0.202	0.002	0.51
6	19	146	28	0.045	0.053	0.008	0.65		0.112	0.120	0.008	0.66		0.179	0.187	0.008	0.67
7	17	133	26	0.044	0.089	0.045	0.53		0.111	0.183	0.072	0.56		0.177	0.246	0.068	0.54
8	19	136	26	0.046	0.070	0.024	0.58		0.115	0.152	0.037	0.58		0.183	0.234	0.051	0.61
9	18	106	26	0.047	0.078	0.032	0.50		0.118	0.158	0.041	0.53		0.188	0.228	0.040	0.54
10	18	121	24	0.052	0.108	0.056	0.47		0.131	0.204	0.073	0.51		0.209	0.280	0.071	0.50
Ave.	17.70	126.40	25.90	0.047	0.079	0.032	0.54		0.118	0.163	0.045	0.56		0.188	0.241	0.053	0.56
Case 2
1	17	114	22	0.050	0.082	0.032	0.41		0.125	0.200	0.075	0.42		0.201	0.307	0.106	0.45
2	19	174	26	0.048	0.080	0.032	0.60		0.120	0.152	0.032	0.64		0.191	0.224	0.032	0.62
3	18	147	25	0.052	0.173	0.121	0.54		0.130	0.280	0.151	0.58		0.207	0.367	0.160	0.58
4	18	122	20	0.052	0.079	0.027	0.36		0.131	0.173	0.043	0.35		0.209	0.252	0.043	0.36
5	17	121	26	0.048	0.122	0.074	0.50		0.121	0.223	0.102	0.55		0.194	0.322	0.128	0.56
6	18	164	27	0.044	0.071	0.027	0.61		0.110	0.138	0.028	0.63		0.177	0.205	0.028	0.65
7	15	114	25	0.044	0.070	0.025	0.46		0.112	0.137	0.025	0.45		0.180	0.204	0.024	0.49
8	16	143	26	0.047	0.076	0.030	0.48		0.117	0.144	0.027	0.53		0.187	0.215	0.028	0.54
9	17	147	26	0.047	0.065	0.018	0.55		0.118	0.135	0.017	0.58		0.188	0.205	0.017	0.57
10	18	123	24	0.045	0.078	0.033	0.47		0.112	0.159	0.046	0.48		0.180	0.234	0.054	0.46
Ave.	17.30	136.90	24.70	0.048	0.090	0.042	0.50		0.120	0.174	0.055	0.52		0.191	0.253	0.062	0.53
Case 3
1	17	147	24	0.047	0.092	0.045	0.50		0.117	0.162	0.044	0.49		0.188	0.231	0.043	0.52
2	17	109	24	0.045	0.129	0.084	0.38		0.112	0.206	0.095	0.41		0.179	0.265	0.086	0.45
3	18	181	27	0.048	0.057	0.009	0.47		0.120	0.129	0.009	0.60		0.192	0.201	0.009	0.61
4	17	141	24	0.049	0.126	0.077	0.47		0.122	0.216	0.094	0.49		0.195	0.316	0.121	0.48
5	17	103	22	0.060	0.107	0.048	0.39		0.149	0.195	0.046	0.43		0.239	0.282	0.043	0.45
6	20	189	26	0.046	0.058	0.012	0.59		0.115	0.136	0.020	0.67		0.185	0.206	0.021	0.68
7	17	123	27	0.043	0.077	0.034	0.52		0.110	0.142	0.033	0.53		0.175	0.207	0.031	0.54
8	16	109	23	0.057	0.133	0.075	0.42		0.144	0.235	0.092	0.44		0.230	0.338	0.108	0.43
9	17	145	24	0.046	0.072	0.026	0.48		0.115	0.169	0.054	0.48		0.184	0.275	0.091	0.50
10	17	164	28	0.045	0.063	0.018	0.61		0.112	0.130	0.018	0.63		0.179	0.197	0.018	0.63
Ave.	17.30	141.10	24.90	0.049	0.091	0.043	0.48		0.122	0.172	0.050	0.52		0.195	0.252	0.057	0.53
Case 4
1	17	157	27	0.038	0.084	0.046	0.58		0.094	0.161	0.067	0.59		0.151	0.228	0.077	0.59
2	19	110	26	0.052	0.065	0.013	0.53		0.130	0.143	0.012	0.57		0.209	0.220	0.012	0.58
3	16	100	24	0.055	0.076	0.020	0.39		0.139	0.168	0.029	0.46		0.222	0.250	0.028	0.51
4	17	136	26	0.046	0.057	0.011	0.57		0.115	0.139	0.024	0.58		0.184	0.213	0.030	0.56
5	19	125	23	0.051	0.073	0.022	0.49		0.130	0.173	0.044	0.52		0.207	0.267	0.059	0.53
6	16	111	25	0.048	0.065	0.018	0.42		0.120	0.137	0.017	0.44		0.191	0.208	0.017	0.45
7	18	117	25	0.047	0.056	0.009	0.51		0.117	0.126	0.009	0.55		0.188	0.197	0.010	0.55
8	17	107	26	0.052	0.090	0.038	0.53		0.130	0.168	0.037	0.55		0.209	0.245	0.036	0.55
9	17	159	26	0.048	0.053	0.005	0.44		0.120	0.126	0.006	0.50		0.192	0.198	0.006	0.52
10	18	105	24	0.050	0.095	0.045	0.45		0.125	0.169	0.044	0.48		0.200	0.242	0.042	0.46
Ave.	17.40	122.70	25.20	0.049	0.071	0.023	0.49		0.122	0.151	0.029	0.52		0.195	0.227	0.032	0.53
Case 5
1	17	155	27	0.039	0.059	0.020	0.61		0.098	0.130	0.031	0.62		0.157	0.200	0.043	0.65
2	17	135	27	0.038	0.104	0.066	0.49		0.095	0.163	0.068	0.54		0.152	0.222	0.069	0.54
3	18	103	24	0.050	0.070	0.020	0.31		0.125	0.146	0.021	0.45		0.200	0.223	0.023	0.46
4	16	168	28	0.040	0.064	0.023	0.61		0.101	0.137	0.036	0.62		0.162	0.210	0.048	0.63
5	18	139	27	0.044	0.051	0.008	0.61		0.110	0.117	0.007	0.61		0.175	0.183	0.007	0.65
6	19	171	24	0.051	0.055	0.004	0.51		0.128	0.132	0.004	0.53		0.205	0.209	0.004	0.55
7	18	147	26	0.045	0.049	0.005	0.58		0.113	0.117	0.005	0.60		0.180	0.184	0.005	0.59
8	20	141	25	0.049	0.093	0.044	0.55		0.122	0.215	0.092	0.62		0.195	0.318	0.122	0.61
9	17	145	26	0.042	0.054	0.013	0.58		0.105	0.190	0.085	0.59		0.168	0.279	0.111	0.63
10	16	111	25	0.045	0.066	0.021	0.45		0.112	0.152	0.040	0.47		0.180	0.234	0.054	0.47
Ave.	17.60	141.50	25.90	0.044	0.066	0.022	0.53		0.111	0.150	0.039	0.56		0.177	0.226	0.049	0.58
Case 6
1	17	125	19	0.054	0.065	0.011	0.31		0.136	0.147	0.011	0.32		0.217	0.228	0.011	0.31
2	17	164	28	0.043	0.080	0.037	0.58		0.108	0.170	0.061	0.62		0.173	0.248	0.074	0.63
3	18	168	27	0.041	0.065	0.024	0.62		0.103	0.153	0.049	0.67		0.166	0.240	0.075	0.65
4	17	138	24	0.053	0.083	0.030	0.47	0.133	0.162	0.029	0.49	0.212	0.240	0.028	0.48
5	18	139	25	0.044	0.064	0.020	0.56	0.110	0.156	0.046	0.57	0.175	0.214	0.038	0.56
6	18	130	25	0.044	0.055	0.011	0.52	0.110	0.122	0.013	0.56	0.175	0.188	0.013	0.53
7	16	130	24	0.054	0.090	0.037	0.49	0.134	0.202	0.068	0.47	0.215	0.314	0.100	0.50
8	17	149	26	0.047	0.069	0.022	0.56	0.119	0.155	0.036	0.57	0.191	0.241	0.050	0.62
9	17	120	27	0.051	0.106	0.055	0.50	0.129	0.186	0.057	0.57	0.207	0.265	0.058	0.58
10	18	124	26	0.046	0.084	0.038	0.53	0.116	0.147	0.031	0.56	0.185	0.240	0.055	0.58
Ave.	17.30	138.70	25.10	0.048	0.076	0.028	0.51	0.120	0.160	0.040	0.54	0.192	0.242	0.050	0.54

Table Options

Download as excel

Ex.	$ m $	#Operation	#OR blocks	Scenario 1					Scenario 2					Scenario 3
Ex.	$ m $	#Operation	#OR blocks	$ rc_1 $	$ rc_2 $	Gap	Time		$ rc_1 $	$ rc_2 $	Gap	Time		$ rc_1 $	$ rc_2 $	Gap	Time
Case 1
1	16	113	27	0.047	0.116	0.069	0.50		0.116	0.200	0.084	0.52		0.186	0.281	0.095	0.56
2	20	122	24	0.049	0.065	0.016	0.56		0.122	0.138	0.016	0.56		0.195	0.210	0.015	0.55
3	15	118	24	0.048	0.074	0.026	0.43		0.121	0.146	0.025	0.47		0.194	0.218	0.024	0.45
4	19	165	28	0.043	0.085	0.042	0.70		0.106	0.202	0.096	0.70		0.170	0.323	0.153	0.71
5	16	104	26	0.049	0.051	0.002	0.47		0.125	0.127	0.002	0.53		0.200	0.202	0.002	0.51
6	19	146	28	0.045	0.053	0.008	0.65		0.112	0.120	0.008	0.66		0.179	0.187	0.008	0.67
7	17	133	26	0.044	0.089	0.045	0.53		0.111	0.183	0.072	0.56		0.177	0.246	0.068	0.54
8	19	136	26	0.046	0.070	0.024	0.58		0.115	0.152	0.037	0.58		0.183	0.234	0.051	0.61
9	18	106	26	0.047	0.078	0.032	0.50		0.118	0.158	0.041	0.53		0.188	0.228	0.040	0.54
10	18	121	24	0.052	0.108	0.056	0.47		0.131	0.204	0.073	0.51		0.209	0.280	0.071	0.50
Ave.	17.70	126.40	25.90	0.047	0.079	0.032	0.54		0.118	0.163	0.045	0.56		0.188	0.241	0.053	0.56
Case 2
1	17	114	22	0.050	0.082	0.032	0.41		0.125	0.200	0.075	0.42		0.201	0.307	0.106	0.45
2	19	174	26	0.048	0.080	0.032	0.60		0.120	0.152	0.032	0.64		0.191	0.224	0.032	0.62
3	18	147	25	0.052	0.173	0.121	0.54		0.130	0.280	0.151	0.58		0.207	0.367	0.160	0.58
4	18	122	20	0.052	0.079	0.027	0.36		0.131	0.173	0.043	0.35		0.209	0.252	0.043	0.36
5	17	121	26	0.048	0.122	0.074	0.50		0.121	0.223	0.102	0.55		0.194	0.322	0.128	0.56
6	18	164	27	0.044	0.071	0.027	0.61		0.110	0.138	0.028	0.63		0.177	0.205	0.028	0.65
7	15	114	25	0.044	0.070	0.025	0.46		0.112	0.137	0.025	0.45		0.180	0.204	0.024	0.49
8	16	143	26	0.047	0.076	0.030	0.48		0.117	0.144	0.027	0.53		0.187	0.215	0.028	0.54
9	17	147	26	0.047	0.065	0.018	0.55		0.118	0.135	0.017	0.58		0.188	0.205	0.017	0.57
10	18	123	24	0.045	0.078	0.033	0.47		0.112	0.159	0.046	0.48		0.180	0.234	0.054	0.46
Ave.	17.30	136.90	24.70	0.048	0.090	0.042	0.50		0.120	0.174	0.055	0.52		0.191	0.253	0.062	0.53
Case 3
1	17	147	24	0.047	0.092	0.045	0.50		0.117	0.162	0.044	0.49		0.188	0.231	0.043	0.52
2	17	109	24	0.045	0.129	0.084	0.38		0.112	0.206	0.095	0.41		0.179	0.265	0.086	0.45
3	18	181	27	0.048	0.057	0.009	0.47		0.120	0.129	0.009	0.60		0.192	0.201	0.009	0.61
4	17	141	24	0.049	0.126	0.077	0.47		0.122	0.216	0.094	0.49		0.195	0.316	0.121	0.48
5	17	103	22	0.060	0.107	0.048	0.39		0.149	0.195	0.046	0.43		0.239	0.282	0.043	0.45
6	20	189	26	0.046	0.058	0.012	0.59		0.115	0.136	0.020	0.67		0.185	0.206	0.021	0.68
7	17	123	27	0.043	0.077	0.034	0.52		0.110	0.142	0.033	0.53		0.175	0.207	0.031	0.54
8	16	109	23	0.057	0.133	0.075	0.42		0.144	0.235	0.092	0.44		0.230	0.338	0.108	0.43
9	17	145	24	0.046	0.072	0.026	0.48		0.115	0.169	0.054	0.48		0.184	0.275	0.091	0.50
10	17	164	28	0.045	0.063	0.018	0.61		0.112	0.130	0.018	0.63		0.179	0.197	0.018	0.63
Ave.	17.30	141.10	24.90	0.049	0.091	0.043	0.48		0.122	0.172	0.050	0.52		0.195	0.252	0.057	0.53
Case 4
1	17	157	27	0.038	0.084	0.046	0.58		0.094	0.161	0.067	0.59		0.151	0.228	0.077	0.59
2	19	110	26	0.052	0.065	0.013	0.53		0.130	0.143	0.012	0.57		0.209	0.220	0.012	0.58
3	16	100	24	0.055	0.076	0.020	0.39		0.139	0.168	0.029	0.46		0.222	0.250	0.028	0.51
4	17	136	26	0.046	0.057	0.011	0.57		0.115	0.139	0.024	0.58		0.184	0.213	0.030	0.56
5	19	125	23	0.051	0.073	0.022	0.49		0.130	0.173	0.044	0.52		0.207	0.267	0.059	0.53
6	16	111	25	0.048	0.065	0.018	0.42		0.120	0.137	0.017	0.44		0.191	0.208	0.017	0.45
7	18	117	25	0.047	0.056	0.009	0.51		0.117	0.126	0.009	0.55		0.188	0.197	0.010	0.55
8	17	107	26	0.052	0.090	0.038	0.53		0.130	0.168	0.037	0.55		0.209	0.245	0.036	0.55
9	17	159	26	0.048	0.053	0.005	0.44		0.120	0.126	0.006	0.50		0.192	0.198	0.006	0.52
10	18	105	24	0.050	0.095	0.045	0.45		0.125	0.169	0.044	0.48		0.200	0.242	0.042	0.46
Ave.	17.40	122.70	25.20	0.049	0.071	0.023	0.49		0.122	0.151	0.029	0.52		0.195	0.227	0.032	0.53
Case 5
1	17	155	27	0.039	0.059	0.020	0.61		0.098	0.130	0.031	0.62		0.157	0.200	0.043	0.65
2	17	135	27	0.038	0.104	0.066	0.49		0.095	0.163	0.068	0.54		0.152	0.222	0.069	0.54
3	18	103	24	0.050	0.070	0.020	0.31		0.125	0.146	0.021	0.45		0.200	0.223	0.023	0.46
4	16	168	28	0.040	0.064	0.023	0.61		0.101	0.137	0.036	0.62		0.162	0.210	0.048	0.63
5	18	139	27	0.044	0.051	0.008	0.61		0.110	0.117	0.007	0.61		0.175	0.183	0.007	0.65
6	19	171	24	0.051	0.055	0.004	0.51		0.128	0.132	0.004	0.53		0.205	0.209	0.004	0.55
7	18	147	26	0.045	0.049	0.005	0.58		0.113	0.117	0.005	0.60		0.180	0.184	0.005	0.59
8	20	141	25	0.049	0.093	0.044	0.55		0.122	0.215	0.092	0.62		0.195	0.318	0.122	0.61
9	17	145	26	0.042	0.054	0.013	0.58		0.105	0.190	0.085	0.59		0.168	0.279	0.111	0.63
10	16	111	25	0.045	0.066	0.021	0.45		0.112	0.152	0.040	0.47		0.180	0.234	0.054	0.47
Ave.	17.60	141.50	25.90	0.044	0.066	0.022	0.53		0.111	0.150	0.039	0.56		0.177	0.226	0.049	0.58
Case 6
1	17	125	19	0.054	0.065	0.011	0.31		0.136	0.147	0.011	0.32		0.217	0.228	0.011	0.31
2	17	164	28	0.043	0.080	0.037	0.58		0.108	0.170	0.061	0.62		0.173	0.248	0.074	0.63
3	18	168	27	0.041	0.065	0.024	0.62		0.103	0.153	0.049	0.67		0.166	0.240	0.075	0.65
4	17	138	24	0.053	0.083	0.030	0.47	0.133	0.162	0.029	0.49	0.212	0.240	0.028	0.48
5	18	139	25	0.044	0.064	0.020	0.56	0.110	0.156	0.046	0.57	0.175	0.214	0.038	0.56
6	18	130	25	0.044	0.055	0.011	0.52	0.110	0.122	0.013	0.56	0.175	0.188	0.013	0.53
7	16	130	24	0.054	0.090	0.037	0.49	0.134	0.202	0.068	0.47	0.215	0.314	0.100	0.50
8	17	149	26	0.047	0.069	0.022	0.56	0.119	0.155	0.036	0.57	0.191	0.241	0.050	0.62
9	17	120	27	0.051	0.106	0.055	0.50	0.129	0.186	0.057	0.57	0.207	0.265	0.058	0.58
10	18	124	26	0.046	0.084	0.038	0.53	0.116	0.147	0.031	0.56	0.185	0.240	0.055	0.58
Ave.	17.30	138.70	25.10	0.048	0.076	0.028	0.51	0.120	0.160	0.040	0.54	0.192	0.242	0.050	0.54

Table 3. Comparison with "quasi-optimal", $ n $ = 6

Ex.	$ m $	#Operation	#OR blocks	Scenario 1					Scenario 2					Scenario 3
Ex.	$ m $	#Operation	#OR blocks	$ rc_1 $	$ rc_2 $	Gap	Time		$ rc_1 $	$ rc_2 $	Gap	Time		$ rc_1 $	$ rc_2 $	Gap	Time
Case 1
1	16	137	28	0.055	0.089	0.034	0.71		0.137	0.198	0.061	0.74		0.220	0.289	0.069	0.75
2	18	133	27	0.053	0.103	0.049	0.71		0.134	0.203	0.068	0.75		0.215	0.284	0.069	0.73
3	17	105	25	0.051	0.077	0.026	0.57		0.128	0.180	0.052	0.60		0.205	0.254	0.050	0.60
4	17	115	27	0.047	0.066	0.019	0.66		0.118	0.140	0.023	0.69		0.188	0.210	0.023	0.72
5	17	148	28	0.050	0.101	0.051	0.75		0.126	0.176	0.050	0.79		0.201	0.249	0.048	0.75
6	16	105	24	0.057	0.108	0.052	0.54		0.143	0.216	0.073	0.63		0.228	0.314	0.086	0.57
7	18	115	24	0.057	0.129	0.072	0.59		0.143	0.217	0.074	0.65		0.228	0.316	0.087	0.62
8	16	122	26	0.059	0.081	0.021	0.62		0.149	0.170	0.021	0.64		0.239	0.259	0.020	0.64
9	18	167	27	0.048	0.088	0.040	0.78		0.119	0.158	0.040	0.79		0.190	0.229	0.039	0.77
10	19	117	26	0.059	0.136	0.077	0.72		0.147	0.242	0.094	0.89		0.236	0.348	0.112	0.76
Ave.	17.20	126.40	26.20	0.054	0.098	0.044	0.67		0.134	0.190	0.056	0.72		0.215	0.275	0.060	0.69
Case 2
1	21	162	24	0.064	0.105	0.041	0.67		0.159	0.214	0.056	0.74		0.254	0.314	0.060	0.72
2	21	124	24	0.062	0.110	0.048	0.69		0.155	0.214	0.059	0.72		0.248	0.305	0.057	0.69
3	18	116	24	0.065	0.189	0.124	0.60		0.163	0.322	0.159	0.63		0.261	0.429	0.169	0.64
4	22	173	27	0.056	0.068	0.012	0.76		0.140	0.152	0.012	0.84		0.224	0.236	0.012	0.81
5	16	136	26	0.048	0.097	0.049	0.61		0.119	0.170	0.051	0.64		0.191	0.241	0.050	0.61
6	22	167	26	0.051	0.072	0.021	0.84		0.127	0.160	0.033	0.86		0.204	0.253	0.049	0.85
7	18	104	25	0.068	0.119	0.051	0.48		0.170	0.220	0.050	0.57		0.272	0.321	0.050	0.60
8	18	137	25	0.058	0.098	0.041	0.62		0.144	0.201	0.058	0.65		0.230	0.302	0.072	0.64
9	19	96	27	0.056	0.113	0.057	0.71		0.139	0.227	0.088	0.82		0.222	0.322	0.100	0.74
10	19	128	28	0.050	0.070	0.020	0.84		0.125	0.159	0.034	0.89		0.200	0.246	0.046	0.88
Ave.	19.40	134.30	25.60	0.058	0.104	0.047	0.68		0.144	0.204	0.060	0.74		0.231	0.297	0.066	0.72
Case 3
1	20	147	23	0.064	0.148	0.084	0.62		0.160	0.257	0.097	0.63		0.255	0.345	0.090	0.62
2	20	136	28	0.051	0.075	0.024	0.71		0.128	0.165	0.036	0.85		0.205	0.253	0.048	0.85
3	22	141	25	0.061	0.096	0.035	0.74		0.153	0.187	0.034	0.80		0.245	0.278	0.033	0.79
4	19	172	26	0.056	0.145	0.089	0.72		0.141	0.291	0.151	0.77		0.225	0.383	0.158	0.75
5	19	138	26	0.052	0.084	0.031	0.73		0.132	0.189	0.058	0.75		0.210	0.295	0.085	0.73
6	21	160	28	0.044	0.056	0.012	0.84		0.109	0.124	0.015	0.89		0.175	0.190	0.014	0.90
7	18	105	18	0.071	0.123	0.052	0.35		0.178	0.255	0.077	0.37		0.284	0.362	0.078	0.37
8	19	143	25	0.062	0.091	0.029	0.62		0.156	0.184	0.028	0.68		0.249	0.277	0.027	0.67
9	18	140	25	0.056	0.065	0.010	0.66		0.141	0.151	0.010	0.68		0.225	0.236	0.011	0.65
10	22	136	23	0.062	0.112	0.050	0.66		0.155	0.239	0.084	0.68		0.248	0.336	0.088	0.67
Ave.	19.80	141.80	24.70	0.058	0.099	0.042	0.67		0.145	0.204	0.059	0.71		0.232	0.295	0.063	0.70
Case 4
1	21	109	24	0.056	0.088	0.032	0.68		0.140	0.187	0.047	0.73		0.224	0.284	0.060	0.70
2	18	123	27	0.053	0.091	0.038	0.72		0.132	0.169	0.037	0.76		0.211	0.247	0.036	0.80
3	21	127	25	0.062	0.077	0.015	0.66		0.156	0.170	0.014	0.71		0.249	0.263	0.014	0.74
4	20	119	25	0.051	0.078	0.027	0.69		0.130	0.177	0.048	0.74		0.208	0.271	0.063	0.71
5	19	126	27	0.051	0.067	0.016	0.74		0.129	0.147	0.018	0.82		0.207	0.224	0.017	0.80
6	21	99	25	0.052	0.131	0.078	0.62		0.131	0.207	0.075	0.67		0.210	0.282	0.072	0.68
7	19	103	24	0.059	0.102	0.043	0.59		0.148	0.206	0.059	0.66		0.236	0.312	0.076	0.65
8	20	150	25	0.058	0.072	0.014	0.74		0.146	0.183	0.036	0.80		0.234	0.286	0.052	0.77
9	21	137	27	0.052	0.056	0.004	0.80		0.131	0.135	0.004	0.89		0.210	0.214	0.004	0.85
10	22	170	28	0.045	0.075	0.030	0.91		0.112	0.141	0.029	0.93		0.180	0.208	0.028	0.93
Ave.	20.20	126.30	25.70	0.054	0.084	0.030	0.72		0.136	0.172	0.037	0.77		0.217	0.259	0.042	0.76
Case 5
1	18	121	23	0.062	0.082	0.019	0.55		0.156	0.175	0.019	0.68		0.249	0.267	0.018	0.56
2	18	186	28	0.047	0.075	0.028	0.83		0.119	0.148	0.029	0.92		0.190	0.218	0.028	0.86
3	22	137	27	0.048	0.089	0.041	0.86		0.119	0.182	0.063	0.96		0.190	0.268	0.077	0.92
4	18	142	26	0.054	0.091	0.037	0.67		0.137	0.191	0.054	0.73		0.220	0.271	0.051	0.70
5	20	138	26	0.050	0.055	0.005	0.75		0.126	0.132	0.005	0.78		0.203	0.208	0.006	0.77
6	18	106	25	0.059	0.111	0.052	0.56		0.150	0.199	0.049	0.62		0.240	0.287	0.047	0.60
7	21	135	27	0.052	0.090	0.038	0.66		0.130	0.165	0.035	0.84		0.208	0.243	0.035	0.83
8	18	140	28	0.046	0.060	0.014	0.74		0.116	0.130	0.014	0.79		0.186	0.199	0.013	0.82
9	19	117	26	0.054	0.081	0.026	0.71		0.136	0.177	0.041	0.72		0.218	0.272	0.055	0.74
10	18	119	27	0.056	0.074	0.018	0.76		0.141	0.174	0.033	0.78		0.226	0.274	0.048	0.81
Ave.	19.00	134.10	26.30	0.053	0.081	0.028	0.71		0.133	0.167	0.034	0.78		0.213	0.251	0.038	0.76
Case 6
1	20	119	25	0.055	0.084	0.029	0.62		0.138	0.185	0.046	0.67		0.220	0.281	0.061	0.69
2	21	162	25	0.049	0.059	0.010	0.71		0.124	0.147	0.023	0.73		0.197	0.221	0.023	0.72
3	20	127	26	0.051	0.071	0.020	0.72		0.128	0.176	0.048	0.76		0.205	0.265	0.060	0.78
4	19	162	28	0.056	0.074	0.019	0.68	0.140	0.159	0.019	0.81	0.224	0.242	0.019	0.82
5	17	116	24	0.056	0.078	0.022	0.52	0.141	0.162	0.021	0.55	0.226	0.246	0.021	0.59
6	18	138	26	0.062	0.166	0.105	0.68	0.154	0.285	0.132	0.70	0.246	0.392	0.146	0.70
7	20	165	28	0.046	0.081	0.035	0.91	0.115	0.186	0.071	0.89	0.184	0.297	0.114	0.89
8	19	117	26	0.049	0.062	0.013	0.66	0.122	0.147	0.026	0.69	0.195	0.226	0.030	0.71
9	18	151	28	0.044	0.087	0.043	0.68	0.111	0.164	0.053	0.75	0.177	0.240	0.063	0.77
10	20	123	26	0.061	0.130	0.069	0.72	0.154	0.253	0.099	0.74	0.246	0.360	0.114	0.81
Ave.	19.20	138.00	26.20	0.053	0.089	0.036	0.69	0.133	0.186	0.054	0.73	0.212	0.277	0.065	0.75

Table Options

Download as excel

Ex.	$ m $	#Operation	#OR blocks	Scenario 1					Scenario 2					Scenario 3
Ex.	$ m $	#Operation	#OR blocks	$ rc_1 $	$ rc_2 $	Gap	Time		$ rc_1 $	$ rc_2 $	Gap	Time		$ rc_1 $	$ rc_2 $	Gap	Time
Case 1
1	16	137	28	0.055	0.089	0.034	0.71		0.137	0.198	0.061	0.74		0.220	0.289	0.069	0.75
2	18	133	27	0.053	0.103	0.049	0.71		0.134	0.203	0.068	0.75		0.215	0.284	0.069	0.73
3	17	105	25	0.051	0.077	0.026	0.57		0.128	0.180	0.052	0.60		0.205	0.254	0.050	0.60
4	17	115	27	0.047	0.066	0.019	0.66		0.118	0.140	0.023	0.69		0.188	0.210	0.023	0.72
5	17	148	28	0.050	0.101	0.051	0.75		0.126	0.176	0.050	0.79		0.201	0.249	0.048	0.75
6	16	105	24	0.057	0.108	0.052	0.54		0.143	0.216	0.073	0.63		0.228	0.314	0.086	0.57
7	18	115	24	0.057	0.129	0.072	0.59		0.143	0.217	0.074	0.65		0.228	0.316	0.087	0.62
8	16	122	26	0.059	0.081	0.021	0.62		0.149	0.170	0.021	0.64		0.239	0.259	0.020	0.64
9	18	167	27	0.048	0.088	0.040	0.78		0.119	0.158	0.040	0.79		0.190	0.229	0.039	0.77
10	19	117	26	0.059	0.136	0.077	0.72		0.147	0.242	0.094	0.89		0.236	0.348	0.112	0.76
Ave.	17.20	126.40	26.20	0.054	0.098	0.044	0.67		0.134	0.190	0.056	0.72		0.215	0.275	0.060	0.69
Case 2
1	21	162	24	0.064	0.105	0.041	0.67		0.159	0.214	0.056	0.74		0.254	0.314	0.060	0.72
2	21	124	24	0.062	0.110	0.048	0.69		0.155	0.214	0.059	0.72		0.248	0.305	0.057	0.69
3	18	116	24	0.065	0.189	0.124	0.60		0.163	0.322	0.159	0.63		0.261	0.429	0.169	0.64
4	22	173	27	0.056	0.068	0.012	0.76		0.140	0.152	0.012	0.84		0.224	0.236	0.012	0.81
5	16	136	26	0.048	0.097	0.049	0.61		0.119	0.170	0.051	0.64		0.191	0.241	0.050	0.61
6	22	167	26	0.051	0.072	0.021	0.84		0.127	0.160	0.033	0.86		0.204	0.253	0.049	0.85
7	18	104	25	0.068	0.119	0.051	0.48		0.170	0.220	0.050	0.57		0.272	0.321	0.050	0.60
8	18	137	25	0.058	0.098	0.041	0.62		0.144	0.201	0.058	0.65		0.230	0.302	0.072	0.64
9	19	96	27	0.056	0.113	0.057	0.71		0.139	0.227	0.088	0.82		0.222	0.322	0.100	0.74
10	19	128	28	0.050	0.070	0.020	0.84		0.125	0.159	0.034	0.89		0.200	0.246	0.046	0.88
Ave.	19.40	134.30	25.60	0.058	0.104	0.047	0.68		0.144	0.204	0.060	0.74		0.231	0.297	0.066	0.72
Case 3
1	20	147	23	0.064	0.148	0.084	0.62		0.160	0.257	0.097	0.63		0.255	0.345	0.090	0.62
2	20	136	28	0.051	0.075	0.024	0.71		0.128	0.165	0.036	0.85		0.205	0.253	0.048	0.85
3	22	141	25	0.061	0.096	0.035	0.74		0.153	0.187	0.034	0.80		0.245	0.278	0.033	0.79
4	19	172	26	0.056	0.145	0.089	0.72		0.141	0.291	0.151	0.77		0.225	0.383	0.158	0.75
5	19	138	26	0.052	0.084	0.031	0.73		0.132	0.189	0.058	0.75		0.210	0.295	0.085	0.73
6	21	160	28	0.044	0.056	0.012	0.84		0.109	0.124	0.015	0.89		0.175	0.190	0.014	0.90
7	18	105	18	0.071	0.123	0.052	0.35		0.178	0.255	0.077	0.37		0.284	0.362	0.078	0.37
8	19	143	25	0.062	0.091	0.029	0.62		0.156	0.184	0.028	0.68		0.249	0.277	0.027	0.67
9	18	140	25	0.056	0.065	0.010	0.66		0.141	0.151	0.010	0.68		0.225	0.236	0.011	0.65
10	22	136	23	0.062	0.112	0.050	0.66		0.155	0.239	0.084	0.68		0.248	0.336	0.088	0.67
Ave.	19.80	141.80	24.70	0.058	0.099	0.042	0.67		0.145	0.204	0.059	0.71		0.232	0.295	0.063	0.70
Case 4
1	21	109	24	0.056	0.088	0.032	0.68		0.140	0.187	0.047	0.73		0.224	0.284	0.060	0.70
2	18	123	27	0.053	0.091	0.038	0.72		0.132	0.169	0.037	0.76		0.211	0.247	0.036	0.80
3	21	127	25	0.062	0.077	0.015	0.66		0.156	0.170	0.014	0.71		0.249	0.263	0.014	0.74
4	20	119	25	0.051	0.078	0.027	0.69		0.130	0.177	0.048	0.74		0.208	0.271	0.063	0.71
5	19	126	27	0.051	0.067	0.016	0.74		0.129	0.147	0.018	0.82		0.207	0.224	0.017	0.80
6	21	99	25	0.052	0.131	0.078	0.62		0.131	0.207	0.075	0.67		0.210	0.282	0.072	0.68
7	19	103	24	0.059	0.102	0.043	0.59		0.148	0.206	0.059	0.66		0.236	0.312	0.076	0.65
8	20	150	25	0.058	0.072	0.014	0.74		0.146	0.183	0.036	0.80		0.234	0.286	0.052	0.77
9	21	137	27	0.052	0.056	0.004	0.80		0.131	0.135	0.004	0.89		0.210	0.214	0.004	0.85
10	22	170	28	0.045	0.075	0.030	0.91		0.112	0.141	0.029	0.93		0.180	0.208	0.028	0.93
Ave.	20.20	126.30	25.70	0.054	0.084	0.030	0.72		0.136	0.172	0.037	0.77		0.217	0.259	0.042	0.76
Case 5
1	18	121	23	0.062	0.082	0.019	0.55		0.156	0.175	0.019	0.68		0.249	0.267	0.018	0.56
2	18	186	28	0.047	0.075	0.028	0.83		0.119	0.148	0.029	0.92		0.190	0.218	0.028	0.86
3	22	137	27	0.048	0.089	0.041	0.86		0.119	0.182	0.063	0.96		0.190	0.268	0.077	0.92
4	18	142	26	0.054	0.091	0.037	0.67		0.137	0.191	0.054	0.73		0.220	0.271	0.051	0.70
5	20	138	26	0.050	0.055	0.005	0.75		0.126	0.132	0.005	0.78		0.203	0.208	0.006	0.77
6	18	106	25	0.059	0.111	0.052	0.56		0.150	0.199	0.049	0.62		0.240	0.287	0.047	0.60
7	21	135	27	0.052	0.090	0.038	0.66		0.130	0.165	0.035	0.84		0.208	0.243	0.035	0.83
8	18	140	28	0.046	0.060	0.014	0.74		0.116	0.130	0.014	0.79		0.186	0.199	0.013	0.82
9	19	117	26	0.054	0.081	0.026	0.71		0.136	0.177	0.041	0.72		0.218	0.272	0.055	0.74
10	18	119	27	0.056	0.074	0.018	0.76		0.141	0.174	0.033	0.78		0.226	0.274	0.048	0.81
Ave.	19.00	134.10	26.30	0.053	0.081	0.028	0.71		0.133	0.167	0.034	0.78		0.213	0.251	0.038	0.76
Case 6
1	20	119	25	0.055	0.084	0.029	0.62		0.138	0.185	0.046	0.67		0.220	0.281	0.061	0.69
2	21	162	25	0.049	0.059	0.010	0.71		0.124	0.147	0.023	0.73		0.197	0.221	0.023	0.72
3	20	127	26	0.051	0.071	0.020	0.72		0.128	0.176	0.048	0.76		0.205	0.265	0.060	0.78
4	19	162	28	0.056	0.074	0.019	0.68	0.140	0.159	0.019	0.81	0.224	0.242	0.019	0.82
5	17	116	24	0.056	0.078	0.022	0.52	0.141	0.162	0.021	0.55	0.226	0.246	0.021	0.59
6	18	138	26	0.062	0.166	0.105	0.68	0.154	0.285	0.132	0.70	0.246	0.392	0.146	0.70
7	20	165	28	0.046	0.081	0.035	0.91	0.115	0.186	0.071	0.89	0.184	0.297	0.114	0.89
8	19	117	26	0.049	0.062	0.013	0.66	0.122	0.147	0.026	0.69	0.195	0.226	0.030	0.71
9	18	151	28	0.044	0.087	0.043	0.68	0.111	0.164	0.053	0.75	0.177	0.240	0.063	0.77
10	20	123	26	0.061	0.130	0.069	0.72	0.154	0.253	0.099	0.74	0.246	0.360	0.114	0.81
Ave.	19.20	138.00	26.20	0.053	0.089	0.036	0.69	0.133	0.186	0.054	0.73	0.212	0.277	0.065	0.75

Table 4. Comparison with "quasi-optimal", $ n $ = 7

Ex.	$ m $	#Operation	#OR blocks	Scenario 1					Scenario 2					Scenario 3
Ex.	$ m $	#Operation	#OR blocks	$ rc_1 $	$ rc_2 $	Gap	Time		$ rc_1 $	$ rc_2 $	Gap	Time		$ rc_1 $	$ rc_2 $	Gap	Time
Case 1
1	22	127	27	0.054	0.123	0.069	1.04		0.135	0.215	0.080	1.09		0.216	0.296	0.080	1.01
2	20	153	29	0.050	0.092	0.042	1.05		0.125	0.177	0.052	1.06		0.200	0.262	0.063	1.07
3	20	146	29	0.057	0.095	0.038	1.18		0.142	0.205	0.063	1.20		0.227	0.315	0.088	1.22
4	17	144	29	0.061	0.111	0.050	0.92		0.155	0.203	0.048	0.96		0.248	0.294	0.046	0.97
5	19	111	29	0.048	0.058	0.010	0.94		0.121	0.131	0.011	1.17		0.193	0.205	0.011	1.03
6	17	97	27	0.060	0.112	0.052	0.82		0.149	0.211	0.062	0.82		0.239	0.313	0.074	0.80
7	20	105	25	0.068	0.126	0.058	0.67		0.172	0.231	0.059	0.79		0.275	0.333	0.057	0.77
8	18	143	28	0.060	0.118	0.057	0.91		0.150	0.207	0.057	0.97		0.241	0.296	0.055	0.96
9	20	115	26	0.057	0.095	0.038	0.90		0.097	0.161	0.064	0.92		0.230	0.324	0.094	0.92
10	20	136	28	0.053	0.078	0.025	1.03		0.134	0.196	0.062	1.08		0.214	0.289	0.075	1.09
Ave.	19.30	127.70	27.70	0.057	0.101	0.044	0.95		0.138	0.194	0.056	1.01		0.228	0.293	0.064	0.98
Case 2
1	17	110	27	0.056	0.081	0.025	0.82		0.140	0.179	0.039	0.87		0.224	0.263	0.038	0.91
2	24	153	27	0.063	0.120	0.057	1.15		0.157	0.232	0.075	1.18		0.250	0.339	0.088	1.28
3	21	110	26	0.069	0.098	0.029	0.93		0.172	0.203	0.030	0.97		0.275	0.304	0.029	0.99
4	22	115	25	0.074	0.117	0.043	0.88		0.184	0.225	0.041	0.94		0.296	0.335	0.039	1.01
5	12	92	29	0.060	0.066	0.005	0.47		0.152	0.137	-0.015	0.47		0.243	0.201	-0.042	0.48
6	21	135	24	0.061	0.100	0.038	0.77		0.155	0.192	0.037	0.79		0.247	0.282	0.036	0.80
7	19	128	28	0.058	0.081	0.023	0.99		0.145	0.173	0.027	1.00		0.233	0.260	0.026	1.00
8	21	114	27	0.062	0.100	0.037	0.91		0.158	0.208	0.051	1.02		0.252	0.302	0.050	0.98
9	23	101	23	0.065	0.092	0.027	0.72		0.163	0.190	0.027	0.78		0.260	0.287	0.027	0.77
10	20	151	24	0.068	0.119	0.050	0.80		0.172	0.225	0.053	0.81		0.274	0.324	0.050	0.78
Ave.	20.00	120.90	26.00	0.064	0.097	0.034	0.84		0.160	0.196	0.037	0.88		0.256	0.290	0.034	0.90
Case 3
1	21	152	28	0.057	0.079	0.023	1.13		0.143	0.178	0.035	1.13		0.229	0.264	0.035	1.15
2	21	149	27	0.054	0.096	0.042	1.08		0.135	0.184	0.049	1.11		0.216	0.281	0.065	1.05
3	16	117	26	0.060	0.118	0.057	0.72		0.152	0.266	0.113	0.74		0.243	0.369	0.126	0.74
4	21	145	24	0.065	0.108	0.043	0.86		0.162	0.207	0.046	0.84		0.258	0.301	0.043	0.88
5	15	114	28	0.068	0.125	0.057	0.80		0.171	0.239	0.069	0.85		0.273	0.342	0.069	0.84
6	16	158	25	0.057	0.063	0.006	0.73		0.143	0.150	0.007	0.74		0.229	0.236	0.007	0.74
7	19	128	25	0.069	0.150	0.081	0.76		0.174	0.252	0.078	0.79		0.277	0.352	0.075	0.77
8	18	160	26	0.058	0.074	0.016	0.85		0.144	0.160	0.016	0.86		0.230	0.246	0.015	0.84
9	20	134	26	0.064	0.119	0.055	0.89		0.162	0.215	0.053	0.89		0.259	0.310	0.051	0.88
10	21	147	27	0.055	0.083	0.028	0.99		0.139	0.167	0.028	1.01		0.222	0.252	0.029	0.98
Ave.	18.80	140.40	26.20	0.061	0.101	0.041	0.88		0.152	0.202	0.049	0.90		0.244	0.295	0.051	0.89
Case 4
1	23	99	24	0.065	0.097	0.031	0.76		0.163	0.192	0.029	0.85		0.262	0.290	0.028	0.86
2	22	130	28	0.056	0.093	0.037	1.16		0.141	0.179	0.039	1.17		0.225	0.262	0.037	1.18
3	18	115	27	0.061	0.097	0.036	0.82		0.151	0.187	0.036	0.84		0.242	0.278	0.035	0.84
4	24	130	27	0.068	0.111	0.043	1.13		0.171	0.216	0.045	1.19		0.273	0.316	0.043	1.21
5	23	111	25	0.058	0.077	0.019	0.85		0.147	0.166	0.018	0.93		0.235	0.253	0.018	0.95
6	20	128	26	0.056	0.084	0.028	0.88		0.141	0.169	0.028	0.94		0.225	0.252	0.027	0.93
7	20	104	25	0.067	0.099	0.032	0.84		0.167	0.199	0.032	0.85		0.268	0.300	0.032	0.87
8	22	123	24	0.067	0.104	0.038	0.84		0.167	0.220	0.053	0.92		0.267	0.334	0.066	0.87
9	25	133	26	0.064	0.092	0.028	1.09		0.159	0.207	0.047	1.14		0.254	0.301	0.047	1.11
10	19	107	25	0.067	0.087	0.021	0.80		0.167	0.187	0.020	0.91		0.267	0.286	0.019	0.83
Ave.	21.60	118.00	25.70	0.063	0.094	0.031	0.92		0.157	0.192	0.035	0.97		0.252	0.287	0.035	0.96
Case 5
1	23	107	27	0.067	0.151	0.084	0.91		0.168	0.275	0.106	1.04		0.268	0.389	0.121	1.04
2	21	151	28	0.054	0.082	0.028	1.05		0.137	0.180	0.043	1.17		0.219	0.274	0.055	1.11
3	22	136	26	0.058	0.081	0.023	0.97		0.147	0.183	0.037	1.01		0.235	0.285	0.050	1.04
4	18	138	27	0.060	0.092	0.032	0.90		0.151	0.182	0.031	0.92		0.241	0.264	0.023	0.90
5	21	89	26	0.064	0.102	0.038	0.78		0.160	0.196	0.036	0.89		0.257	0.290	0.033	0.92
6	20	123	25	0.068	0.117	0.048	0.84		0.172	0.234	0.061	0.87		0.276	0.352	0.076	0.86
7	19	127	24	0.059	0.073	0.015	0.76		0.148	0.163	0.016	0.77		0.236	0.251	0.015	0.75
8	21	107	25	0.067	0.076	0.010	0.69		0.169	0.179	0.010	0.81		0.270	0.281	0.011	0.79
9	18	137	26	0.068	0.084	0.015	0.78		0.172	0.187	0.015	0.88		0.275	0.291	0.016	0.86
10	24	135	23	0.076	0.096	0.020	0.82		0.191	0.210	0.019	0.87		0.306	0.325	0.019	0.83
Ave.	20.70	125.00	25.70	0.064	0.095	0.031	0.85		0.161	0.199	0.038	0.92		0.258	0.300	0.042	0.91
Case 6
1	21	181	28	0.053	0.081	0.028	1.10		0.133	0.180	0.046	1.11		0.213	0.273	0.059	1.20
2	17	119	25	0.068	0.094	0.025	0.69		0.171	0.196	0.025	0.73		0.274	0.298	0.024	0.79
3	16	138	25	0.069	0.102	0.033	0.67		0.173	0.230	0.056	0.74		0.278	0.337	0.059	0.82
4	24	154	27	0.060	0.088	0.027	1.10	0.152	0.183	0.031	1.13	0.243	0.272	0.030	1.29
5	18	101	25	0.065	0.097	0.032	0.69	0.164	0.199	0.035	0.76	0.263	0.301	0.038	0.83
6	19	155	27	0.053	0.079	0.026	0.87	0.133	0.159	0.025	0.95	0.213	0.238	0.025	0.93
7	21	134	27	0.057	0.076	0.019	1.02	0.142	0.175	0.032	1.09	0.228	0.274	0.046	1.20
8	23	141	26	0.064	0.124	0.060	1.05	0.161	0.218	0.057	1.02	0.257	0.311	0.054	0.98
9	14	126	24	0.079	0.154	0.075	0.57	0.198	0.255	0.057	0.59	0.317	0.371	0.054	0.62
10	20	153	28	0.053	0.085	0.032	1.03	0.132	0.186	0.053	1.05	0.211	0.276	0.065	1.11
Ave.	19.30	140.20	26.20	0.062	0.098	0.036	0.88	0.156	0.198	0.042	0.92	0.250	0.295	0.045	0.98

Table Options

Download as excel

Ex.	$ m $	#Operation	#OR blocks	Scenario 1					Scenario 2					Scenario 3
Ex.	$ m $	#Operation	#OR blocks	$ rc_1 $	$ rc_2 $	Gap	Time		$ rc_1 $	$ rc_2 $	Gap	Time		$ rc_1 $	$ rc_2 $	Gap	Time
Case 1
1	22	127	27	0.054	0.123	0.069	1.04		0.135	0.215	0.080	1.09		0.216	0.296	0.080	1.01
2	20	153	29	0.050	0.092	0.042	1.05		0.125	0.177	0.052	1.06		0.200	0.262	0.063	1.07
3	20	146	29	0.057	0.095	0.038	1.18		0.142	0.205	0.063	1.20		0.227	0.315	0.088	1.22
4	17	144	29	0.061	0.111	0.050	0.92		0.155	0.203	0.048	0.96		0.248	0.294	0.046	0.97
5	19	111	29	0.048	0.058	0.010	0.94		0.121	0.131	0.011	1.17		0.193	0.205	0.011	1.03
6	17	97	27	0.060	0.112	0.052	0.82		0.149	0.211	0.062	0.82		0.239	0.313	0.074	0.80
7	20	105	25	0.068	0.126	0.058	0.67		0.172	0.231	0.059	0.79		0.275	0.333	0.057	0.77
8	18	143	28	0.060	0.118	0.057	0.91		0.150	0.207	0.057	0.97		0.241	0.296	0.055	0.96
9	20	115	26	0.057	0.095	0.038	0.90		0.097	0.161	0.064	0.92		0.230	0.324	0.094	0.92
10	20	136	28	0.053	0.078	0.025	1.03		0.134	0.196	0.062	1.08		0.214	0.289	0.075	1.09
Ave.	19.30	127.70	27.70	0.057	0.101	0.044	0.95		0.138	0.194	0.056	1.01		0.228	0.293	0.064	0.98
Case 2
1	17	110	27	0.056	0.081	0.025	0.82		0.140	0.179	0.039	0.87		0.224	0.263	0.038	0.91
2	24	153	27	0.063	0.120	0.057	1.15		0.157	0.232	0.075	1.18		0.250	0.339	0.088	1.28
3	21	110	26	0.069	0.098	0.029	0.93		0.172	0.203	0.030	0.97		0.275	0.304	0.029	0.99
4	22	115	25	0.074	0.117	0.043	0.88		0.184	0.225	0.041	0.94		0.296	0.335	0.039	1.01
5	12	92	29	0.060	0.066	0.005	0.47		0.152	0.137	-0.015	0.47		0.243	0.201	-0.042	0.48
6	21	135	24	0.061	0.100	0.038	0.77		0.155	0.192	0.037	0.79		0.247	0.282	0.036	0.80
7	19	128	28	0.058	0.081	0.023	0.99		0.145	0.173	0.027	1.00		0.233	0.260	0.026	1.00
8	21	114	27	0.062	0.100	0.037	0.91		0.158	0.208	0.051	1.02		0.252	0.302	0.050	0.98
9	23	101	23	0.065	0.092	0.027	0.72		0.163	0.190	0.027	0.78		0.260	0.287	0.027	0.77
10	20	151	24	0.068	0.119	0.050	0.80		0.172	0.225	0.053	0.81		0.274	0.324	0.050	0.78
Ave.	20.00	120.90	26.00	0.064	0.097	0.034	0.84		0.160	0.196	0.037	0.88		0.256	0.290	0.034	0.90
Case 3
1	21	152	28	0.057	0.079	0.023	1.13		0.143	0.178	0.035	1.13		0.229	0.264	0.035	1.15
2	21	149	27	0.054	0.096	0.042	1.08		0.135	0.184	0.049	1.11		0.216	0.281	0.065	1.05
3	16	117	26	0.060	0.118	0.057	0.72		0.152	0.266	0.113	0.74		0.243	0.369	0.126	0.74
4	21	145	24	0.065	0.108	0.043	0.86		0.162	0.207	0.046	0.84		0.258	0.301	0.043	0.88
5	15	114	28	0.068	0.125	0.057	0.80		0.171	0.239	0.069	0.85		0.273	0.342	0.069	0.84
6	16	158	25	0.057	0.063	0.006	0.73		0.143	0.150	0.007	0.74		0.229	0.236	0.007	0.74
7	19	128	25	0.069	0.150	0.081	0.76		0.174	0.252	0.078	0.79		0.277	0.352	0.075	0.77
8	18	160	26	0.058	0.074	0.016	0.85		0.144	0.160	0.016	0.86		0.230	0.246	0.015	0.84
9	20	134	26	0.064	0.119	0.055	0.89		0.162	0.215	0.053	0.89		0.259	0.310	0.051	0.88
10	21	147	27	0.055	0.083	0.028	0.99		0.139	0.167	0.028	1.01		0.222	0.252	0.029	0.98
Ave.	18.80	140.40	26.20	0.061	0.101	0.041	0.88		0.152	0.202	0.049	0.90		0.244	0.295	0.051	0.89
Case 4
1	23	99	24	0.065	0.097	0.031	0.76		0.163	0.192	0.029	0.85		0.262	0.290	0.028	0.86
2	22	130	28	0.056	0.093	0.037	1.16		0.141	0.179	0.039	1.17		0.225	0.262	0.037	1.18
3	18	115	27	0.061	0.097	0.036	0.82		0.151	0.187	0.036	0.84		0.242	0.278	0.035	0.84
4	24	130	27	0.068	0.111	0.043	1.13		0.171	0.216	0.045	1.19		0.273	0.316	0.043	1.21
5	23	111	25	0.058	0.077	0.019	0.85		0.147	0.166	0.018	0.93		0.235	0.253	0.018	0.95
6	20	128	26	0.056	0.084	0.028	0.88		0.141	0.169	0.028	0.94		0.225	0.252	0.027	0.93
7	20	104	25	0.067	0.099	0.032	0.84		0.167	0.199	0.032	0.85		0.268	0.300	0.032	0.87
8	22	123	24	0.067	0.104	0.038	0.84		0.167	0.220	0.053	0.92		0.267	0.334	0.066	0.87
9	25	133	26	0.064	0.092	0.028	1.09		0.159	0.207	0.047	1.14		0.254	0.301	0.047	1.11
10	19	107	25	0.067	0.087	0.021	0.80		0.167	0.187	0.020	0.91		0.267	0.286	0.019	0.83
Ave.	21.60	118.00	25.70	0.063	0.094	0.031	0.92		0.157	0.192	0.035	0.97		0.252	0.287	0.035	0.96
Case 5
1	23	107	27	0.067	0.151	0.084	0.91		0.168	0.275	0.106	1.04		0.268	0.389	0.121	1.04
2	21	151	28	0.054	0.082	0.028	1.05		0.137	0.180	0.043	1.17		0.219	0.274	0.055	1.11
3	22	136	26	0.058	0.081	0.023	0.97		0.147	0.183	0.037	1.01		0.235	0.285	0.050	1.04
4	18	138	27	0.060	0.092	0.032	0.90		0.151	0.182	0.031	0.92		0.241	0.264	0.023	0.90
5	21	89	26	0.064	0.102	0.038	0.78		0.160	0.196	0.036	0.89		0.257	0.290	0.033	0.92
6	20	123	25	0.068	0.117	0.048	0.84		0.172	0.234	0.061	0.87		0.276	0.352	0.076	0.86
7	19	127	24	0.059	0.073	0.015	0.76		0.148	0.163	0.016	0.77		0.236	0.251	0.015	0.75
8	21	107	25	0.067	0.076	0.010	0.69		0.169	0.179	0.010	0.81		0.270	0.281	0.011	0.79
9	18	137	26	0.068	0.084	0.015	0.78		0.172	0.187	0.015	0.88		0.275	0.291	0.016	0.86
10	24	135	23	0.076	0.096	0.020	0.82		0.191	0.210	0.019	0.87		0.306	0.325	0.019	0.83
Ave.	20.70	125.00	25.70	0.064	0.095	0.031	0.85		0.161	0.199	0.038	0.92		0.258	0.300	0.042	0.91
Case 6
1	21	181	28	0.053	0.081	0.028	1.10		0.133	0.180	0.046	1.11		0.213	0.273	0.059	1.20
2	17	119	25	0.068	0.094	0.025	0.69		0.171	0.196	0.025	0.73		0.274	0.298	0.024	0.79
3	16	138	25	0.069	0.102	0.033	0.67		0.173	0.230	0.056	0.74		0.278	0.337	0.059	0.82
4	24	154	27	0.060	0.088	0.027	1.10	0.152	0.183	0.031	1.13	0.243	0.272	0.030	1.29
5	18	101	25	0.065	0.097	0.032	0.69	0.164	0.199	0.035	0.76	0.263	0.301	0.038	0.83
6	19	155	27	0.053	0.079	0.026	0.87	0.133	0.159	0.025	0.95	0.213	0.238	0.025	0.93
7	21	134	27	0.057	0.076	0.019	1.02	0.142	0.175	0.032	1.09	0.228	0.274	0.046	1.20
8	23	141	26	0.064	0.124	0.060	1.05	0.161	0.218	0.057	1.02	0.257	0.311	0.054	0.98
9	14	126	24	0.079	0.154	0.075	0.57	0.198	0.255	0.057	0.59	0.317	0.371	0.054	0.62
10	20	153	28	0.053	0.085	0.032	1.03	0.132	0.186	0.053	1.05	0.211	0.276	0.065	1.11
Ave.	19.30	140.20	26.20	0.062	0.098	0.036	0.88	0.156	0.198	0.042	0.92	0.250	0.295	0.045	0.98

Table 5. Comparison with lower bound

Ex.		Scenario 1				Scenario 2				Scenario 3
Ex.		$ rc_2 $	$ rc_3 $	$ Gap_1 $	$ Time_1 $	$ rc_2 $	$ rc_3 $	$ Gap_1 $	$ Time_1 $	$ rc_2 $	$ rc_3 $	$ Gap_1 $	$ Time_1 $
n=5	case1	0.079	0.039	0.040	145.800	0.163	0.096	0.067	132.000	0.241	0.128	0.113	152.610
	case2	0.090	0.042	0.048	116.200	0.174	0.102	0.072	116.300	0.253	0.153	0.100	132.560
	case3	0.091	0.040	0.051	118.200	0.172	0.097	0.075	120.200	0.252	0.155	0.097	118.800
	case4	0.071	0.031	0.040	110.200	0.151	0.072	0.079	116.400	0.227	0.107	0.120	119.600
	case5	0.066	0.038	0.028	94.000	0.150	0.083	0.067	103.800	0.226	0.118	0.108	111.100
	case6	0.076	0.037	0.039	110.600	0.160	0.091	0.069	97.000	0.242	0.130	0.112	119.000
n=6	case1	0.098	0.040	0.058	120.400	0.190	0.089	0.101	132.500	0.275	0.150	0.125	126.800
	case2	0.104	0.054	0.050	127.400	0.204	0.123	0.081	124.100	0.297	0.194	0.103	124.800
	case3	0.099	0.057	0.042	118.500	0.204	0.131	0.073	127.300	0.295	0.195	0.100	120.800
	case4	0.084	0.046	0.038	106.900	0.172	0.089	0.083	119.300	0.259	0.150	0.109	115.700
	case5	0.081	0.036	0.045	120.900	0.167	0.084	0.083	128.000	0.251	0.126	0.125	132.700
	case6	0.089	0.035	0.054	140.100	0.186	0.070	0.116	155.900	0.277	0.105	0.172	157.700
n=7	case1	0.101	0.051	0.050	126.700	0.194	0.111	0.083	145.100	0.293	0.176	0.117	135.900
	case2	0.097	0.051	0.046	109.000	0.196	0.116	0.080	98.400	0.290	0.174	0.116	114.300
	case3	0.101	0.058	0.043	98.000	0.202	0.145	0.057	101.800	0.295	0.218	0.077	103.700
	case4	0.094	0.044	0.050	133.900	0.192	0.096	0.096	138.200	0.287	0.138	0.149	143.200
	case5	0.095	0.056	0.039	100.800	0.199	0.124	0.075	120.800	0.300	0.199	0.101	109.700
	case6	0.098	0.044	0.054	111.500	0.198	0.093	0.105	112.800	0.295	0.162	0.133	117.900
	Average	0.090	0.044	0.045	117.172	0.182	0.101	0.081	121.661	0.270	0.154	0.115	125.382

Table Options

Download as excel

Ex.		Scenario 1				Scenario 2				Scenario 3
Ex.		$ rc_2 $	$ rc_3 $	$ Gap_1 $	$ Time_1 $	$ rc_2 $	$ rc_3 $	$ Gap_1 $	$ Time_1 $	$ rc_2 $	$ rc_3 $	$ Gap_1 $	$ Time_1 $
n=5	case1	0.079	0.039	0.040	145.800	0.163	0.096	0.067	132.000	0.241	0.128	0.113	152.610
	case2	0.090	0.042	0.048	116.200	0.174	0.102	0.072	116.300	0.253	0.153	0.100	132.560
	case3	0.091	0.040	0.051	118.200	0.172	0.097	0.075	120.200	0.252	0.155	0.097	118.800
	case4	0.071	0.031	0.040	110.200	0.151	0.072	0.079	116.400	0.227	0.107	0.120	119.600
	case5	0.066	0.038	0.028	94.000	0.150	0.083	0.067	103.800	0.226	0.118	0.108	111.100
	case6	0.076	0.037	0.039	110.600	0.160	0.091	0.069	97.000	0.242	0.130	0.112	119.000
n=6	case1	0.098	0.040	0.058	120.400	0.190	0.089	0.101	132.500	0.275	0.150	0.125	126.800
	case2	0.104	0.054	0.050	127.400	0.204	0.123	0.081	124.100	0.297	0.194	0.103	124.800
	case3	0.099	0.057	0.042	118.500	0.204	0.131	0.073	127.300	0.295	0.195	0.100	120.800
	case4	0.084	0.046	0.038	106.900	0.172	0.089	0.083	119.300	0.259	0.150	0.109	115.700
	case5	0.081	0.036	0.045	120.900	0.167	0.084	0.083	128.000	0.251	0.126	0.125	132.700
	case6	0.089	0.035	0.054	140.100	0.186	0.070	0.116	155.900	0.277	0.105	0.172	157.700
n=7	case1	0.101	0.051	0.050	126.700	0.194	0.111	0.083	145.100	0.293	0.176	0.117	135.900
	case2	0.097	0.051	0.046	109.000	0.196	0.116	0.080	98.400	0.290	0.174	0.116	114.300
	case3	0.101	0.058	0.043	98.000	0.202	0.145	0.057	101.800	0.295	0.218	0.077	103.700
	case4	0.094	0.044	0.050	133.900	0.192	0.096	0.096	138.200	0.287	0.138	0.149	143.200
	case5	0.095	0.056	0.039	100.800	0.199	0.124	0.075	120.800	0.300	0.199	0.101	109.700
	case6	0.098	0.044	0.054	111.500	0.198	0.093	0.105	112.800	0.295	0.162	0.133	117.900
	Average	0.090	0.044	0.045	117.172	0.182	0.101	0.081	121.661	0.270	0.154	0.115	125.382

Table 6. By performance indicators, $ n = 5 $

Ex.	Scenario 1				Scenario 2				Scenario 3
Ex.	IT	Overtime	UROR		IT	Overtime	UROR		IT	Overtime	UROR
Case 1
1	65	132	1.01		16	250	1.03		16	250	1.03
2	0	71	1.01		0	71	1.01		0	71	1.01
3	0	121	1.01		0	121	1.01		0	121	1.01
4	62	107	1.00		165	216	1.00		71	273	1.02
5	15	0	1.00		15	0	1.00		15	0	1.00
6	60	12	1.00		60	12	1.00		60	12	1.00
7	89	71	1.00		89	71	1.00		207	181	1.00
8	9	64	1.01		9	64	1.01		9	64	1.01
9	67	40	1.00		49	118	1.01		49	118	1.01
10	16	147	1.02		96	279	1.02		96	279	1.02
Ave.	38.30	76.50	1.00		49.90	120.20	1.01		52.30	136.90	1.01
Case 2
1	44	21	1.00		124	18	0.99		124	18	0.99
2	112	108	1.00		112	108	1.00		112	108	1.00
3	25	422	1.04		0	645	1.07		0	645	1.07
4	107	8	0.99		108	1	0.99		89	130	1.01
5	42	182	1.02		43	185	1.02		42	182	1.02
6	147	58	0.99		147	58	0.99		147	58	0.99
7	25	93	1.01		25	93	1.01		25	93	1.01
8	24	110	1.01		18	105	1.01		24	110	1.01
9	15	84	1.01		15	84	1.01		15	84	1.01
10	106	50	0.99		148	21	0.99		194	132	0.99
Ave.	64.70	113.60	1.01		74.00	131.80	1.01		77.20	156.00	1.01
Case 3
1	33	60	1.00		26	196	1.02		26	196	1.02
2	0	259	1.04		0	261	1.04		0	320	1.05
3	13	37	1.00		13	37	1.00		13	37	1.00
4	190	56	0.98		14	203	1.02		14	203	1.02
5	0	191	1.03		0	191	1.03		0	191	1.03
6	26	0	1.00		104	55	1.00		104	55	1.00
7	0	169	1.02		0	169	1.02		0	169	1.02
8	89	164	1.01		89	164	1.01		89	164	1.01
9	64	0	0.99		64	0	0.99		49	55	1.00
10	52	77	1.00		52	77	1.00		52	77	1.00
Ave.	46.70	101.30	1.01		36.20	135.30	1.01		34.70	146.70	1.01
Case 4
1	180	48	0.99		194	120	0.99		413	120	0.97
2	3	51	1.01		3	51	1.01		3	51	1.01
3	35	16	1.00		46	89	1.01		46	89	1.01
4	7	4	1.00		7	4	1.00		42	138	1.01
5	38	27	1.00		53	43	1.00		53	43	1.00
6	12	56	1.01		12	56	1.01		12	56	1.01
7	71	0	0.99		71	0	0.99		71	0	0.99
8	26	146	1.02		26	146	1.02		26	146	1.02
9	52	0	1.00		52	0	1.00		52	0	1.00
10	2	144	1.02		2	184	1.02		2	184	1.02
Ave.	42.60	49.20	1.00		46.60	69.30	1.00		72.00	82.70	1.00
Case 5
1	32	48	1.00		32	48	1.00		32	48	1.00
2	379	117	0.97		379	117	0.97		379	117	0.97
3	115	1	0.98		115	1	0.98		115	1	0.98
4	63	42	1.00		63	42	1.00		63	42	1.00
5	17	30	1.00		17	30	1.00		17	30	1.00
6	31	0	1.00		31	0	1.00		31	0	1.00
7	9	17	1.00		9	17	1.00		9	17	1.00
8	77	65	1.00		156	97	0.99		156	97	0.99
9	2	19	1.00		186	95	0.99		186	95	0.99
10	63	14	0.99		117	1	0.99		117	1	0.99
Ave.	78.80	35.30	0.99		110.50	44.80	0.99		110.50	44.80	0.99
Case 6
1	34	18	1.00		34	18	1.00		34	18	1.00
2	73	48	1.00		116	14	0.99		95	132	1.00
3	59	6	0.99		59	6	0.99		59	6	0.99
4	29	137	1.01	29	137	1.01	29	137	1.01
5	22	0	1.00	19	0	1.00	27	0	1.00
6	20	0	1.00	56	28	1.00	56	28	1.00
7	4	69	1.01	4	69	1.01	4	69	1.01
8	28	41	1.00	28	41	1.00	28	41	1.00
9	234	77	0.98	234	77	0.98	234	77	0.98
10	48	104	1.01	45	120	1.01	3	275	1.03
Ave.	55.10	50.00	1.00	62.40	51.00	1.00	56.90	78.30	1.00

Table Options

Download as excel

Ex.	Scenario 1				Scenario 2				Scenario 3
Ex.	IT	Overtime	UROR		IT	Overtime	UROR		IT	Overtime	UROR
Case 1
1	65	132	1.01		16	250	1.03		16	250	1.03
2	0	71	1.01		0	71	1.01		0	71	1.01
3	0	121	1.01		0	121	1.01		0	121	1.01
4	62	107	1.00		165	216	1.00		71	273	1.02
5	15	0	1.00		15	0	1.00		15	0	1.00
6	60	12	1.00		60	12	1.00		60	12	1.00
7	89	71	1.00		89	71	1.00		207	181	1.00
8	9	64	1.01		9	64	1.01		9	64	1.01
9	67	40	1.00		49	118	1.01		49	118	1.01
10	16	147	1.02		96	279	1.02		96	279	1.02
Ave.	38.30	76.50	1.00		49.90	120.20	1.01		52.30	136.90	1.01
Case 2
1	44	21	1.00		124	18	0.99		124	18	0.99
2	112	108	1.00		112	108	1.00		112	108	1.00
3	25	422	1.04		0	645	1.07		0	645	1.07
4	107	8	0.99		108	1	0.99		89	130	1.01
5	42	182	1.02		43	185	1.02		42	182	1.02
6	147	58	0.99		147	58	0.99		147	58	0.99
7	25	93	1.01		25	93	1.01		25	93	1.01
8	24	110	1.01		18	105	1.01		24	110	1.01
9	15	84	1.01		15	84	1.01		15	84	1.01
10	106	50	0.99		148	21	0.99		194	132	0.99
Ave.	64.70	113.60	1.01		74.00	131.80	1.01		77.20	156.00	1.01
Case 3
1	33	60	1.00		26	196	1.02		26	196	1.02
2	0	259	1.04		0	261	1.04		0	320	1.05
3	13	37	1.00		13	37	1.00		13	37	1.00
4	190	56	0.98		14	203	1.02		14	203	1.02
5	0	191	1.03		0	191	1.03		0	191	1.03
6	26	0	1.00		104	55	1.00		104	55	1.00
7	0	169	1.02		0	169	1.02		0	169	1.02
8	89	164	1.01		89	164	1.01		89	164	1.01
9	64	0	0.99		64	0	0.99		49	55	1.00
10	52	77	1.00		52	77	1.00		52	77	1.00
Ave.	46.70	101.30	1.01		36.20	135.30	1.01		34.70	146.70	1.01
Case 4
1	180	48	0.99		194	120	0.99		413	120	0.97
2	3	51	1.01		3	51	1.01		3	51	1.01
3	35	16	1.00		46	89	1.01		46	89	1.01
4	7	4	1.00		7	4	1.00		42	138	1.01
5	38	27	1.00		53	43	1.00		53	43	1.00
6	12	56	1.01		12	56	1.01		12	56	1.01
7	71	0	0.99		71	0	0.99		71	0	0.99
8	26	146	1.02		26	146	1.02		26	146	1.02
9	52	0	1.00		52	0	1.00		52	0	1.00
10	2	144	1.02		2	184	1.02		2	184	1.02
Ave.	42.60	49.20	1.00		46.60	69.30	1.00		72.00	82.70	1.00
Case 5
1	32	48	1.00		32	48	1.00		32	48	1.00
2	379	117	0.97		379	117	0.97		379	117	0.97
3	115	1	0.98		115	1	0.98		115	1	0.98
4	63	42	1.00		63	42	1.00		63	42	1.00
5	17	30	1.00		17	30	1.00		17	30	1.00
6	31	0	1.00		31	0	1.00		31	0	1.00
7	9	17	1.00		9	17	1.00		9	17	1.00
8	77	65	1.00		156	97	0.99		156	97	0.99
9	2	19	1.00		186	95	0.99		186	95	0.99
10	63	14	0.99		117	1	0.99		117	1	0.99
Ave.	78.80	35.30	0.99		110.50	44.80	0.99		110.50	44.80	0.99
Case 6
1	34	18	1.00		34	18	1.00		34	18	1.00
2	73	48	1.00		116	14	0.99		95	132	1.00
3	59	6	0.99		59	6	0.99		59	6	0.99
4	29	137	1.01	29	137	1.01	29	137	1.01
5	22	0	1.00	19	0	1.00	27	0	1.00
6	20	0	1.00	56	28	1.00	56	28	1.00
7	4	69	1.01	4	69	1.01	4	69	1.01
8	28	41	1.00	28	41	1.00	28	41	1.00
9	234	77	0.98	234	77	0.98	234	77	0.98
10	48	104	1.01	45	120	1.01	3	275	1.03
Ave.	55.10	50.00	1.00	62.40	51.00	1.00	56.90	78.30	1.00

Table 7. By performance indicators, $ n = 6 $

Ex.	Scenario 1				Scenario 2				Scenario 3
Ex.	IT	Overtime	UROR		IT	Overtime	UROR		IT	Overtime	UROR
Case 1
1	39	66	1.00		39	66	1.00		30	186	1.01
2	66	120	1.01		295	163	0.99		295	163	0.99
3	15	62	1.01		3	214	1.03		3	214	1.03
4	55	12	0.99		22	75	1.01		40	64	1.00
5	27	261	1.02		27	261	1.02		27	261	1.02
6	71	100	1.00		90	163	1.01		90	163	1.01
7	154	129	1.00		69	174	1.01		69	174	1.01
8	24	72	1.01		24	72	1.01		24	72	1.01
9	79	164	1.01		79	164	1.01		79	164	1.01
10	332	123	0.98		332	123	0.98		332	123	0.98
Ave.	86.20	110.90	1.00		98.00	147.50	1.01		98.90	158.40	1.01
Case 2
1	20	145	1.01		20	145	1.01		0	343	1.04
2	31	100	1.01		70	220	1.02		70	220	1.02
3	49	238	1.03		86	482	1.06		86	482	1.06
4	10	65	1.01		10	65	1.01		10	65	1.01
5	108	108	1.00		81	165	1.01		81	165	1.01
6	23	52	1.00		23	52	1.00		35	64	1.00
7	80	125	1.01		80	125	1.01		80	125	1.01
8	52	74	1.00		96	108	1.00		96	108	1.00
9	103	95	1.00		56	239	1.02		56	239	1.02
10	31	0	1.00		18	56	1.00		18	56	1.00
Ave.	50.70	100.20	1.01		54.00	165.70	1.01		53.20	186.70	1.02
Case 3
1	30	219	1.02		0	343	1.04		0	459	1.05
2	26	48	1.00		26	48	1.00		57	23	1.00
3	61	145	1.01		61	145	1.01		61	145	1.01
4	5	298	1.03		11	676	1.07		11	676	1.07
5	91	13	0.99		73	21	0.99		73	21	0.99
6	30	7	1.00		28	53	1.00		28	53	1.00
7	78	64	1.00		208	172	1.00		208	172	1.00
8	31	120	1.01		31	120	1.01		31	120	1.01
9	85	0	0.99		85	0	0.99		85	0	0.99
10	94	81	1.00		51	127	1.01		91	173	1.01
Ave.	53.10	99.50	1.01		57.40	170.50	1.01		64.50	184.20	1.01
Case 4
1	23	46	1.00		10	101	1.01		10	101	1.01
2	47	144	1.01		47	144	1.01		47	144	1.01
3	20	55	1.00		20	55	1.00		20	55	1.00
4	60	10	0.99		11	114	1.01		213	154	0.99
5	33	15	1.00		13	78	1.01		13	78	1.01
6	6	286	1.04		6	286	1.04		6	286	1.04
7	136	10	0.98		206	0	0.97		206	0	0.97
8	32	2	1.00		75	16	0.99		73	23	1.00
9	27	2	1.00		27	2	1.00		27	2	1.00
10	19	148	1.01		19	148	1.01		19	148	1.01
Ave.	40.30	71.80	1.00		43.40	94.40	1.01		63.40	99.10	1.00
Case 5
1	4	78	1.01		4	78	1.01		4	78	1.01
2	35	100	1.01		19	171	1.01		19	171	1.01
3	142	35	0.99		92	53	1.00		120	145	1.00
4	76	0	0.99		6	146	1.02		6	250	1.03
5	42	0	1.00		42	0	1.00		42	0	1.00
6	6	174	1.03		6	174	1.03		6	174	1.03
7	234	0	0.97		91	107	1.00		91	107	1.00
8	3	63	1.01		3	63	1.01		3	63	1.01
9	36	57	1.00		73	38	1.00		73	38	1.00
10	65	0	0.99		65	0	0.99		65	0	0.99
Ave.	64.30	50.70	1.00		40.10	83.00	1.01		42.90	102.6	1.01
Case 6
1	67	0	0.99		91	32	0.99		91	32	0.99
2	37	29	0.99		81	68	1.00		81	68	1.00
3	14	34	1.00		5	16	1.00		8	104	1.01
4	28	34	1.00	26	90	1.01	26	90	1.01
5	17	71	1.01	17	71	1.01	17	71	1.01
6	70	386	1.03	70	386	1.03	21	595	1.06
7	91	22	0.99	91	22	0.99	131	42	0.99
8	27	6	1.00	27	6	1.00	26	118	1.01
9	34	135	1.01	34	135	1.01	34	135	1.01
10	47	160	1.02	162	192	1.00	162	192	1.00
Ave.	47.40	87.70	1.00	60.40	101.80	1.00	59.70	144.70	1.01

Table Options

Download as excel

Ex.	Scenario 1				Scenario 2				Scenario 3
Ex.	IT	Overtime	UROR		IT	Overtime	UROR		IT	Overtime	UROR
Case 1
1	39	66	1.00		39	66	1.00		30	186	1.01
2	66	120	1.01		295	163	0.99		295	163	0.99
3	15	62	1.01		3	214	1.03		3	214	1.03
4	55	12	0.99		22	75	1.01		40	64	1.00
5	27	261	1.02		27	261	1.02		27	261	1.02
6	71	100	1.00		90	163	1.01		90	163	1.01
7	154	129	1.00		69	174	1.01		69	174	1.01
8	24	72	1.01		24	72	1.01		24	72	1.01
9	79	164	1.01		79	164	1.01		79	164	1.01
10	332	123	0.98		332	123	0.98		332	123	0.98
Ave.	86.20	110.90	1.00		98.00	147.50	1.01		98.90	158.40	1.01
Case 2
1	20	145	1.01		20	145	1.01		0	343	1.04
2	31	100	1.01		70	220	1.02		70	220	1.02
3	49	238	1.03		86	482	1.06		86	482	1.06
4	10	65	1.01		10	65	1.01		10	65	1.01
5	108	108	1.00		81	165	1.01		81	165	1.01
6	23	52	1.00		23	52	1.00		35	64	1.00
7	80	125	1.01		80	125	1.01		80	125	1.01
8	52	74	1.00		96	108	1.00		96	108	1.00
9	103	95	1.00		56	239	1.02		56	239	1.02
10	31	0	1.00		18	56	1.00		18	56	1.00
Ave.	50.70	100.20	1.01		54.00	165.70	1.01		53.20	186.70	1.02
Case 3
1	30	219	1.02		0	343	1.04		0	459	1.05
2	26	48	1.00		26	48	1.00		57	23	1.00
3	61	145	1.01		61	145	1.01		61	145	1.01
4	5	298	1.03		11	676	1.07		11	676	1.07
5	91	13	0.99		73	21	0.99		73	21	0.99
6	30	7	1.00		28	53	1.00		28	53	1.00
7	78	64	1.00		208	172	1.00		208	172	1.00
8	31	120	1.01		31	120	1.01		31	120	1.01
9	85	0	0.99		85	0	0.99		85	0	0.99
10	94	81	1.00		51	127	1.01		91	173	1.01
Ave.	53.10	99.50	1.01		57.40	170.50	1.01		64.50	184.20	1.01
Case 4
1	23	46	1.00		10	101	1.01		10	101	1.01
2	47	144	1.01		47	144	1.01		47	144	1.01
3	20	55	1.00		20	55	1.00		20	55	1.00
4	60	10	0.99		11	114	1.01		213	154	0.99
5	33	15	1.00		13	78	1.01		13	78	1.01
6	6	286	1.04		6	286	1.04		6	286	1.04
7	136	10	0.98		206	0	0.97		206	0	0.97
8	32	2	1.00		75	16	0.99		73	23	1.00
9	27	2	1.00		27	2	1.00		27	2	1.00
10	19	148	1.01		19	148	1.01		19	148	1.01
Ave.	40.30	71.80	1.00		43.40	94.40	1.01		63.40	99.10	1.00
Case 5
1	4	78	1.01		4	78	1.01		4	78	1.01
2	35	100	1.01		19	171	1.01		19	171	1.01
3	142	35	0.99		92	53	1.00		120	145	1.00
4	76	0	0.99		6	146	1.02		6	250	1.03
5	42	0	1.00		42	0	1.00		42	0	1.00
6	6	174	1.03		6	174	1.03		6	174	1.03
7	234	0	0.97		91	107	1.00		91	107	1.00
8	3	63	1.01		3	63	1.01		3	63	1.01
9	36	57	1.00		73	38	1.00		73	38	1.00
10	65	0	0.99		65	0	0.99		65	0	0.99
Ave.	64.30	50.70	1.00		40.10	83.00	1.01		42.90	102.6	1.01
Case 6
1	67	0	0.99		91	32	0.99		91	32	0.99
2	37	29	0.99		81	68	1.00		81	68	1.00
3	14	34	1.00		5	16	1.00		8	104	1.01
4	28	34	1.00	26	90	1.01	26	90	1.01
5	17	71	1.01	17	71	1.01	17	71	1.01
6	70	386	1.03	70	386	1.03	21	595	1.06
7	91	22	0.99	91	22	0.99	131	42	0.99
8	27	6	1.00	27	6	1.00	26	118	1.01
9	34	135	1.01	34	135	1.01	34	135	1.01
10	47	160	1.02	162	192	1.00	162	192	1.00
Ave.	47.40	87.70	1.00	60.40	101.80	1.00	59.70	144.70	1.01

Table 8. By performance indicators, $n = 7$

Ex.	Scenario 1				Scenario 2				Scenario 3
Ex.	IT	Overtime	UROR		IT	Overtime	UROR		IT	Overtime	UROR
Case 1
1	232	171	0.99		247	252	1.00		247	252	1.00
2	81	140	1.01		81	140	1.01		81	140	1.01
3	111	51	0.99		11	49	0.99		111	51	0.99
4	34	243	1.02		34	243	1.02		34	243	1.02
5	81	0	0.99		81	0	0.99		81	0	0.99
6	96	90	1.00		74	130	1.01		74	130	1.01
7	91	116	1.00		87	160	1.01		87	160	1.01
8	50	196	1.02		50	243	1.02		50	243	1.02
9	66	20	0.99		151	66	0.99		53	259	1.02
10	118	24	0.99		223	91	0.99		320	19	0.97
Ave.	96.00	105.10	1.00		103.90	137.60	1.00		113.80	149.70	1.00
Case 2
1	53	7	0.99		43	139	1.01		43	139	1.01
2	28	116	1.01		137	148	1.00		137	148	1.00
3	40	58	1.00		28	117	1.01		28	117	1.01
4	16	171	1.02		16	171	1.02		16	171	1.02
5	6	53	1.01		0	119	1.02		0	119	1.02
6	36	158	1.01		36	158	1.01		36	158	1.01
7	17	64	1.00		9	140	1.01		9	140	1.01
8	37	53	1.00		74	155	1.01		74	155	1.01
9	77	62	1.00		77	62	1.00		77	62	1.00
10	68	163	1.01		6	278	1.03		6	278	1.03
Ave.	37.80	90.50	1.01		42.60	148.70	1.01		42.60	148.70	1.01
Case 3
1	74	38	1.00		90	144	1.01		90	144	1.01
2	59	28	1.00		89	119	1.00		63	164	1.01
3	65	118	1.01		195	245	1.01		195	245	1.01
4	53	108	1.01		23	184	1.02		20	181	1.02
5	6	192	1.02		6	192	1.02		36	294	1.03
6	52	3	0.99		52	3	0.99		52	3	0.99
7	55	243	1.03		55	243	1.03		55	243	1.03
8	15	31	1.00		6	79	1.01		6	79	1.01
9	31	211	1.02		31	211	1.02		31	211	1.02
10	84	91	1.00		84	91	1.00		39	131	1.01
Ave.	49.40	106.30	1.01		63.10	151.10	1.01		58.70	169.50	1.01
Case 4
1	57	88	1.00		22	104	1.01		22	104	1.01
2	21	129	1.01		2	198	1.02		2	198	1.02
3	53	81	1.00		91	92	1.00		91	92	1.00
4	7	216	1.02		20	229	1.02		20	229	1.02
5	17	58	1.01		17	58	1.01		17	58	1.01
6	31	83	1.01		15	138	1.01		15	138	1.01
7	69	82	1.00		69	82	1.00		69	82	1.00
8	76	42	1.00		45	112	1.01		45	112	1.01
9	72	12	0.99		26	120	1.01		27	254	1.02
10	20	71	1.01		20	71	1.01		20	71	1.01
Ave.	42.30	86.20	1.01		32.70	120.40	1.01		32.80	133.80	1.01
Case 5
1	334	44	0.96		376	66	0.96		384	38	0.95
2	38	37	1.00		72	73	1.00		72	73	1.00
3	113	5	0.99		113	5	0.99		113	5	0.99
4	47	139	1.01		47	139	1.01		20	113	1.01
5	67	34	1.00		18	129	1.02		37	110	1.01
6	22	157	1.02		22	157	1.02		5	182	1.02
7	50	2	0.99		26	63	1.00		26	63	1.00
8	48	6	0.99		48	6	0.99		48	6	0.99
9	54	41	1.00		54	41	1.00		54	41	1.00
10	20	74	1.01		20	74	1.01		20	74	1.01
Ave.	79.30	53.90	1.00		79.60	75.30	1.00		77.90	70.50	1.00
Case 6
1	48	0	1.00		194	27	0.98		194	27	0.98
2	19	82	1.01		21	84	1.01		21	84	1.01
3	49	28	1.00		107	71	1.00		6	283	1.03
4	6	90	1.01	0	166	1.02	0	166	1.02
5	202	0	0.97	202	0	0.97	202	0	0.97
6	41	109	1.01	41	109	1.01	41	109	1.01
7	79	0	0.99	79	0	0.99	188	71	0.99
8	9	291	1.03	9	291	1.03	9	291	1.03
9	123	203	1.01	26	207	1.03	26	207	1.03
10	111	77	1.00	118	130	1.00	118	130	1.00
Ave.	68.70	88.00	1.00	79.70	108.50	1.00	80.50	136.80	1.01

Table Options

Download as excel

Ex.	Scenario 1				Scenario 2				Scenario 3
Ex.	IT	Overtime	UROR		IT	Overtime	UROR		IT	Overtime	UROR
Case 1
1	232	171	0.99		247	252	1.00		247	252	1.00
2	81	140	1.01		81	140	1.01		81	140	1.01
3	111	51	0.99		11	49	0.99		111	51	0.99
4	34	243	1.02		34	243	1.02		34	243	1.02
5	81	0	0.99		81	0	0.99		81	0	0.99
6	96	90	1.00		74	130	1.01		74	130	1.01
7	91	116	1.00		87	160	1.01		87	160	1.01
8	50	196	1.02		50	243	1.02		50	243	1.02
9	66	20	0.99		151	66	0.99		53	259	1.02
10	118	24	0.99		223	91	0.99		320	19	0.97
Ave.	96.00	105.10	1.00		103.90	137.60	1.00		113.80	149.70	1.00
Case 2
1	53	7	0.99		43	139	1.01		43	139	1.01
2	28	116	1.01		137	148	1.00		137	148	1.00
3	40	58	1.00		28	117	1.01		28	117	1.01
4	16	171	1.02		16	171	1.02		16	171	1.02
5	6	53	1.01		0	119	1.02		0	119	1.02
6	36	158	1.01		36	158	1.01		36	158	1.01
7	17	64	1.00		9	140	1.01		9	140	1.01
8	37	53	1.00		74	155	1.01		74	155	1.01
9	77	62	1.00		77	62	1.00		77	62	1.00
10	68	163	1.01		6	278	1.03		6	278	1.03
Ave.	37.80	90.50	1.01		42.60	148.70	1.01		42.60	148.70	1.01
Case 3
1	74	38	1.00		90	144	1.01		90	144	1.01
2	59	28	1.00		89	119	1.00		63	164	1.01
3	65	118	1.01		195	245	1.01		195	245	1.01
4	53	108	1.01		23	184	1.02		20	181	1.02
5	6	192	1.02		6	192	1.02		36	294	1.03
6	52	3	0.99		52	3	0.99		52	3	0.99
7	55	243	1.03		55	243	1.03		55	243	1.03
8	15	31	1.00		6	79	1.01		6	79	1.01
9	31	211	1.02		31	211	1.02		31	211	1.02
10	84	91	1.00		84	91	1.00		39	131	1.01
Ave.	49.40	106.30	1.01		63.10	151.10	1.01		58.70	169.50	1.01
Case 4
1	57	88	1.00		22	104	1.01		22	104	1.01
2	21	129	1.01		2	198	1.02		2	198	1.02
3	53	81	1.00		91	92	1.00		91	92	1.00
4	7	216	1.02		20	229	1.02		20	229	1.02
5	17	58	1.01		17	58	1.01		17	58	1.01
6	31	83	1.01		15	138	1.01		15	138	1.01
7	69	82	1.00		69	82	1.00		69	82	1.00
8	76	42	1.00		45	112	1.01		45	112	1.01
9	72	12	0.99		26	120	1.01		27	254	1.02
10	20	71	1.01		20	71	1.01		20	71	1.01
Ave.	42.30	86.20	1.01		32.70	120.40	1.01		32.80	133.80	1.01
Case 5
1	334	44	0.96		376	66	0.96		384	38	0.95
2	38	37	1.00		72	73	1.00		72	73	1.00
3	113	5	0.99		113	5	0.99		113	5	0.99
4	47	139	1.01		47	139	1.01		20	113	1.01
5	67	34	1.00		18	129	1.02		37	110	1.01
6	22	157	1.02		22	157	1.02		5	182	1.02
7	50	2	0.99		26	63	1.00		26	63	1.00
8	48	6	0.99		48	6	0.99		48	6	0.99
9	54	41	1.00		54	41	1.00		54	41	1.00
10	20	74	1.01		20	74	1.01		20	74	1.01
Ave.	79.30	53.90	1.00		79.60	75.30	1.00		77.90	70.50	1.00
Case 6
1	48	0	1.00		194	27	0.98		194	27	0.98
2	19	82	1.01		21	84	1.01		21	84	1.01
3	49	28	1.00		107	71	1.00		6	283	1.03
4	6	90	1.01	0	166	1.02	0	166	1.02
5	202	0	0.97	202	0	0.97	202	0	0.97
6	41	109	1.01	41	109	1.01	41	109	1.01
7	79	0	0.99	79	0	0.99	188	71	0.99
8	9	291	1.03	9	291	1.03	9	291	1.03
9	123	203	1.01	26	207	1.03	26	207	1.03
10	111	77	1.00	118	130	1.00	118	130	1.00
Ave.	68.70	88.00	1.00	79.70	108.50	1.00	80.50	136.80	1.01

[1]	Jian Xiong, Zhongbao Zhou, Ke Tian, Tianjun Liao, Jianmai Shi. A multi-objective approach for weapon selection and planning problems in dynamic environments. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1189-1211. doi: 10.3934/jimo.2016068
[2]	Namsu Ahn, Soochan Kim. Optimal and heuristic algorithms for the multi-objective vehicle routing problem with drones for military surveillance operations. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021037
[3]	Yuan-mei Xia, Xin-min Yang, Ke-quan Zhao. A combined scalarization method for multi-objective optimization problems. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020088
[4]	Xia Zhao, Jianping Dou. Bi-objective integrated supply chain design with transportation choices: A multi-objective particle swarm optimization. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1263-1288. doi: 10.3934/jimo.2018095
[5]	Tien-Fu Liang, Hung-Wen Cheng. Multi-objective aggregate production planning decisions using two-phase fuzzy goal programming method. Journal of Industrial & Management Optimization, 2011, 7 (2) : 365-383. doi: 10.3934/jimo.2011.7.365
[6]	Han Yang, Jia Yue, Nan-jing Huang. Multi-objective robust cross-market mixed portfolio optimization under hierarchical risk integration. Journal of Industrial & Management Optimization, 2020, 16 (2) : 759-775. doi: 10.3934/jimo.2018177
[7]	Shoufeng Ji, Jinhuan Tang, Minghe Sun, Rongjuan Luo. Multi-objective optimization for a combined location-routing-inventory system considering carbon-capped differences. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021051
[8]	Qiang Long, Xue Wu, Changzhi Wu. Non-dominated sorting methods for multi-objective optimization: Review and numerical comparison. Journal of Industrial & Management Optimization, 2021, 17 (2) : 1001-1023. doi: 10.3934/jimo.2020009
[9]	Min Zhang, Gang Li. Multi-objective optimization algorithm based on improved particle swarm in cloud computing environment. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1413-1426. doi: 10.3934/dcdss.2019097
[10]	Liwei Zhang, Jihong Zhang, Yule Zhang. Second-order optimality conditions for cone constrained multi-objective optimization. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1041-1054. doi: 10.3934/jimo.2017089
[11]	Danthai Thongphiew, Vira Chankong, Fang-Fang Yin, Q. Jackie Wu. An on-line adaptive radiation therapy system for intensity modulated radiation therapy: An application of multi-objective optimization. Journal of Industrial & Management Optimization, 2008, 4 (3) : 453-475. doi: 10.3934/jimo.2008.4.453
[12]	Azam Moradi, Jafar Razmi, Reza Babazadeh, Ali Sabbaghnia. An integrated Principal Component Analysis and multi-objective mathematical programming approach to agile supply chain network design under uncertainty. Journal of Industrial & Management Optimization, 2019, 15 (2) : 855-879. doi: 10.3934/jimo.2018074
[13]	Henri Bonnel, Ngoc Sang Pham. Nonsmooth optimization over the (weakly or properly) Pareto set of a linear-quadratic multi-objective control problem: Explicit optimality conditions. Journal of Industrial & Management Optimization, 2011, 7 (4) : 789-809. doi: 10.3934/jimo.2011.7.789
[14]	Lin Jiang, Song Wang. Robust multi-period and multi-objective portfolio selection. Journal of Industrial & Management Optimization, 2021, 17 (2) : 695-709. doi: 10.3934/jimo.2019130
[15]	Dušan M. Stipanović, Claire J. Tomlin, George Leitmann. A note on monotone approximations of minimum and maximum functions and multi-objective problems. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 487-493. doi: 10.3934/naco.2011.1.487
[16]	Hamed Fazlollahtabar, Mohammad Saidi-Mehrabad. Optimizing multi-objective decision making having qualitative evaluation. Journal of Industrial & Management Optimization, 2015, 11 (3) : 747-762. doi: 10.3934/jimo.2015.11.747
[17]	Mahdi Karimi, Seyed Jafar Sadjadi. Optimization of a Multi-Item Inventory model for deteriorating items with capacity constraint using dynamic programming. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2021013
[18]	Alireza Eydi, Rozhin Saedi. A multi-objective decision-making model for supplier selection considering transport discounts and supplier capacity constraints. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020134
[19]	Adriel Cheng, Cheng-Chew Lim. Optimizing system-on-chip verifications with multi-objective genetic evolutionary algorithms. Journal of Industrial & Management Optimization, 2014, 10 (2) : 383-396. doi: 10.3934/jimo.2014.10.383
[20]	Zongmin Li, Jiuping Xu, Wenjing Shen, Benjamin Lev, Xiao Lei. Bilevel multi-objective construction site security planning with twofold random phenomenon. Journal of Industrial & Management Optimization, 2015, 11 (2) : 595-617. doi: 10.3934/jimo.2015.11.595

2019 Impact Factor: 1.366

Tools

Metrics

Tools

Article outline

Figures and Tables

2019 Impact Factor: 1.366

Tools

Figures and Tables

2019 Impact Factor: 1.366

American Institute of Mathematical Sciences

Dynamic-programming-based heuristic for multi-objective operating theater planning

References:

References:

Tools

Metrics

Other articles
by authors

Tools

Tools

Tools

Metrics

Other articles
by authors

American Institute of Mathematical Sciences

Dynamic-programming-based heuristic for multi-objective operating theater planning

References:

References:

Tools

Metrics

Other articlesby authors

Tools

Tools

Tools

Metrics

Other articlesby authors

Other articles
by authors

Other articles
by authors