Abstract
This work contemplates the optimal scheduling of multi-tasking production environments where the processing tasks are subject to uncertain success rates. Such problems arise in many industrial applications that have the potential to yield non compliant products, which must then be reprocessed. We address this problem by mapping the multi-tasking sequential recipe into a State-Task Network representation that includes suitably defined recycle streams to accommodate the option for reprocessing. This allows us to utilize a variant of an established global-event continuous time scheduling formulation to model the overall problem, as well as to employ an Adjustable Robust Optimization framework to account for the uncertainty in the production yields associated with each processing task. We assess the computational performance of the proposed approach via a comprehensive study that involves a large database of multi-tasking scheduling benchmark problems, and we demonstrate that instances involving more than 100 uncertain parameters can be addressed within reasonable computational times. Our results also help elucidate the expected amount of cost premium to insure against various levels of uncertainty in the production success rates.
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Notes
Note that, typically, these states do not correspond to actual storage facilities, and thus, are not subject to storage capacity constraints. If actual storage limitations apply, these can be easily incorporated as upper bounds on the variables that shall represent the state levels.
Note how this calls for augmenting sets \({\mathcal {I}}^{p}_{i,k}\) and \({\mathcal {S}}^{p}_{i,k}\) in the deterministic model.
We remark that these constants could in principle depend on the specific task and/or event point, but for ease of exposition we will consider them in the remainder of this work as common across all (i, n) combinations.
In this context, the production yield towards the main recipe path can be viewed as the task’s success rate.
Obviously, such variable fixings can be simply implemented by not including these variables in the summations of Eq. 23, alleviating the need to clutter the model with additional variables.
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Acknowledgements
C.E.G. and N.H.L. gratefully acknowledge support from the National Science Foundation (Grant No. CBET-1510787). N.H.L. further acknowledges support from the University of Patras via an Andreas Mentzelopoulos scholarship. L.R. and R.F. gratefully acknowledge the support provided by the Natural Sciences and Engineering Research Council of Canada. The authors would also like to acknowledge the support provided by a collaborating company in the scientific services sector.
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Appendices
Appendix 1: Deterministic model nomenclature
Indices | |
n | Event points |
i | Processing tasks |
j | Processing units |
k | Orders |
s | States |
Sets | |
\({\mathcal {N}} \equiv \left\{ 1, 2, \ldots , N\right\} \) | Event points |
\({\mathcal {N}}_n^- \equiv \left\{ n-\delta n, \ldots , n-1\right\} \) | Event points in the immediate past of event point n |
\({\mathcal {N}}_n^+ \equiv \left\{ n+1, \ldots , n+\delta n\right\} \) | Event points in the immediate future of event point n |
\({\mathcal {I}}\) | Processing tasks |
\({\mathcal {J}}\) | Processing units |
\({\mathcal {K}}\) | Orders |
\({\mathcal {S}}\) | States |
\({\mathcal {I}}_j \subseteq {\mathcal {I}}\) | Processing tasks compatible with unit j |
\({\mathcal {I}}^{p}_{k,s} \subseteq {\mathcal {I}}\) | Processing tasks producing state s for order k |
\({\mathcal {I}}^{c}_{k,s} \subseteq {\mathcal {I}}\) | Processing tasks consuming state s for order k |
\({\mathcal {K}}_{i} \subseteq {\mathcal {K}}\) | Orders that are to be processed by task i |
\({\mathcal {S}}^{p}_{i,k} \subseteq {\mathcal {S}}\) | States storing material produced by task i for order k |
\({\mathcal {S}}^{c}_{i,k} \subseteq {\mathcal {S}}\) | States storing material consumed by task i for order k |
\({\mathcal {S}}_{k} \equiv \bigcup \limits _{i\in {\mathcal {I}}} \left( {\mathcal {S}}^{p}_{i,k} \cup {\mathcal {S}}^{c}_{i,k} \right) \) | States relevant to order k (“sub-states (k, s)”) |
Variables | |
z | Objective value (epigraph variable) |
\(T_n\) | Time of event point n |
\(SO_{k,s,n}\) | Level of state s of order k (“sub-state (k, s)”) at event point n |
\(BO_{i,k,n,n^{\prime }}\) | Batch size of task i for order k that starts at event point n and finishes by event point \(n^{\prime }\) |
\(G_{j,n}\) | [pseudo-binary]: 1, if unit j is utilized at event point n;0, otherwise |
\(W_{i,n,n^{\prime }}\) | [binary]: 1, if task i starts exactly at event point n andfinishes by (but no later than) event point \(n^{\prime }\); 0, otherwise |
Parameters | |
N | Total number of event points |
\(\delta n\) | Maximum allowed event-point span for all processing tasks |
\(\alpha _{i}\) | Fixed processing time for task i |
\(\beta _{i}\) | Batch size-dependent processing time for task i |
\(\rho ^{p}_{i,k,s}\) | Production yield of task i towards sub-state (k, s) |
\(\rho ^{c}_{i,k,s}\) | Consumption yield of task i from sub-state (k, s) |
\(B^{max}_i\) | Maximum batch size (total across all orders) for task i |
\(B^{min}_i\) | Minimum batch size (total across all orders) for task i |
\(SO_{k,s,0}\) | Initial storage level for sub-state (k, s) |
\(D_{k,s}\) | Demand for sub-state (k, s) (only for Min Makespan) |
\(P_{k,s}\) | Price of sub-state (k, s) (only for Max Profit) |
H | Horizon (only for Max Profit) |
Appendix 2: Benchmark instances
See Figs. 7, 8, 9, 10, 11, 12, 13, 14 and 15.
Operations figure for benchmark P1
Operations figure for benchmark P2
Operations figure for benchmark P3
Operations figure for benchmark P4
Operations figure for benchmark P5
Operations figure for benchmark P6
Operations figure for benchmark P7
Operations figure for benchmark P8
Operations figure for benchmark P9
Appendix 3: Input data
Data related to specific machines, such as maximum batch sizes and fixed processing times, are shown below. Note that the minimum batch sizes, \(B^{min}_i\), and batch size-dependent processing times, \(\beta {i}\), are zero in all cases.
Data related to specific orders, such as initial storage levels for each order’s initial sub-state (initial material inputs) and unit prices for each order’s final sub-state (final material outputs), are shown below. Note that the orders are referenced in the same sequence as shown in the operations figures of “Appendix 2”. Every non-initial sub-state has an initial storage level of zero.
Finally, for the objective of maximization of profit, the horizon H is set to 8 h in all instances. Furthermore, since the objective of makespan minimization was not considered in the original benchmark problems, we imposed a demand for each order’s final sub-state, \(D_{k,{\text {out}}}\), as being equal to 70% of the initial storage level of the corresponding order’s initial sub-state, divided by the number of processing steps required for this order to reach the final sub-state. The number of processing steps for each order can be inferred from “Appendix 2”.
Appendix 4: Detailed computational results
Problem | Obj. type | \(\xi \) | \(\phi \) | # Ev. points | # Uncert. Param. | # Bin. Var. | # Cont. Var. | # Constraints | Root node Rlx. | Rel. Obj. Val. | Obj. Val. | Opt. Gap% | # Nodes | CPU time (s) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
P1 | Max P | 0.00 | 0.00 | 6 | 0 | 72 | 288 | 343 | 1640.0 | 1640.0 | 1640.0 | 0.0 | 23 | < 0.1 |
P1 | Max P | 0.10 | 0.00 | 6 | 60 | 72 | 105,380 | 57,883 | 1640.0 | 1640.0 | 1640.0 | 0.0 | 0 | < 0.1 |
P1 | Max P | 0.10 | 0.25 | 6 | 60 | 72 | 105,380 | 57,883 | 1501.5 | 1342.2 | 1342.2 | 0.0 | 251 | 3.1 |
P1 | Max P | 0.10 | 0.50 | 6 | 60 | 72 | 105,380 | 57,883 | 1371.8 | 1196.5 | 1196.5 | 0.0 | 232 | 2.7 |
P1 | Max P | 0.10 | 0.75 | 6 | 60 | 72 | 105,380 | 57,883 | 1250.5 | 1151.8 | 1151.8 | 0.0 | 117 | 1.7 |
P1 | Max P | 0.10 | 1.00 | 6 | 60 | 72 | 105,380 | 57,883 | 1137.2 | 1137.2 | 1137.2 | 0.0 | 85 | 1.3 |
P1 | Max P | 0.20 | 0.00 | 6 | 60 | 72 | 105,380 | 57,883 | 1640.0 | 1640.0 | 1640.0 | 0.0 | 0 | < 0.1 |
P1 | Max P | 0.20 | 0.25 | 6 | 60 | 72 | 105,380 | 57,883 | 1371.8 | 1120.1 | 1120.1 | 0.0 | 290 | 3.3 |
P1 | Max P | 0.20 | 0.50 | 6 | 60 | 72 | 105,380 | 57,883 | 1137.2 | 852.5 | 852.5 | 0.0 | 728 | 6.5 |
P1 | Max P | 0.20 | 0.75 | 6 | 60 | 72 | 105,380 | 57,883 | 933.5 | 778.2 | 778.2 | 0.0 | 264 | 3.0 |
P1 | Max P | 0.20 | 1.00 | 6 | 60 | 72 | 105,380 | 57,883 | 757.8 | 757.8 | 757.8 | 0.0 | 38 | 0.7 |
P1 | Max P | 0.30 | 0.00 | 6 | 60 | 72 | 105,380 | 57,883 | 1640.0 | 1640.0 | 1640.0 | 0.0 | 0 | < 0.1 |
P1 | Max P | 0.30 | 0.25 | 6 | 60 | 72 | 105,380 | 57,883 | 1250.5 | 964.6 | 964.6 | 0.0 | 224 | 2.4 |
P1 | Max P | 0.30 | 0.50 | 6 | 60 | 72 | 105,380 | 57,883 | 933.5 | 621.3 | 621.3 | 0.0 | 1760 | 11.4 |
P1 | Max P | 0.30 | 0.75 | 6 | 60 | 72 | 105,380 | 57,883 | 679.6 | 546.4 | 546.4 | 0.0 | 417 | 4.3 |
P1 | Max P | 0.30 | 1.00 | 6 | 60 | 72 | 105,380 | 57,883 | 480.2 | 480.2 | 480.2 | 0.0 | 0 | 1.2 |
P2 | Max P | 0.00 | 0.00 | 7 | 0 | 60 | 267 | 289 | 2232.4 | 1281.7 | 1281.7 | 0.0 | 247 | < 0.1 |
P2 | Max P | 0.10 | 0.00 | 7 | 84 | 60 | 60,263 | 75,581 | 2232.4 | 1260.0 | 1260.0 | 0.0 | 3217 | 3.0 |
P2 | Max P | 0.10 | 0.25 | 7 | 84 | 60 | 60,263 | 75,581 | 2224.9 | 1256.5 | 1256.5 | 0.0 | 2996 | 2.0 |
P2 | Max P | 0.10 | 0.50 | 7 | 84 | 60 | 60,263 | 75,581 | 2217.4 | 1253.0 | 1253.0 | 0.0 | 2620 | 2.5 |
P2 | Max P | 0.10 | 0.75 | 7 | 84 | 60 | 60,263 | 75,581 | 2210.0 | 1249.5 | 1249.5 | 0.0 | 2504 | 2.3 |
P2 | Max P | 0.10 | 1.00 | 7 | 84 | 60 | 60,263 | 75,581 | 2202.5 | 1246.0 | 1246.0 | 0.0 | 1258 | 1.6 |
P2 | Max P | 0.20 | 0.00 | 7 | 84 | 60 | 60,263 | 75,581 | 2232.4 | 1260.0 | 1260.0 | 0.0 | 3263 | 3.0 |
P2 | Max P | 0.20 | 0.25 | 7 | 84 | 60 | 60,263 | 75,581 | 2217.4 | 1253.0 | 1253.0 | 0.0 | 2708 | 2.1 |
P2 | Max P | 0.20 | 0.50 | 7 | 84 | 60 | 60,263 | 75,581 | 2202.5 | 1246.0 | 1246.0 | 0.0 | 1311 | 1.5 |
P2 | Max P | 0.20 | 0.75 | 7 | 84 | 60 | 60,263 | 75,581 | 2187.6 | 1239.0 | 1239.0 | 0.0 | 897 | 1.1 |
P2 | Max P | 0.20 | 1.00 | 7 | 84 | 60 | 60,263 | 75,581 | 2172.7 | 1232.0 | 1232.0 | 0.0 | 666 | 1.0 |
P2 | Max P | 0.30 | 0.00 | 7 | 84 | 60 | 60,263 | 75,581 | 2232.4 | 1260.0 | 1260.0 | 0.0 | 3047 | 2.7 |
P2 | Max P | 0.30 | 0.25 | 7 | 84 | 60 | 60,263 | 75,581 | 2210.0 | 1249.5 | 1249.5 | 0.0 | 3481 | 2.6 |
P2 | Max P | 0.30 | 0.50 | 7 | 84 | 60 | 60,263 | 75,581 | 2187.6 | 1239.0 | 1239.0 | 0.0 | 967 | 1.4 |
P2 | Max P | 0.30 | 0.75 | 7 | 84 | 60 | 60,263 | 75,581 | 2165.2 | 1228.5 | 1228.5 | 0.0 | 756 | 1.0 |
P2 | Max P | 0.30 | 1.00 | 7 | 84 | 60 | 60,263 | 75,581 | 2143.0 | 1218.0 | 1218.0 | 0.0 | 851 | 1.0 |
P3 | Max P | 0.00 | 0.00 | 8 | 0 | 90 | 453 | 466 | 3700.0 | 3700.0 | 3700.0 | 0.0 | 0 | < 0.1 |
P3 | Max P | 0.10 | 0.00 | 8 | 40 | 90 | 88,366 | 67,586 | 3700.0 | 3700.0 | 3700.0 | 0.0 | 0 | < 0.1 |
P3 | Max P | 0.10 | 0.25 | 8 | 40 | 90 | 88,366 | 67,586 | 3615.9 | 3613.5 | 3613.5 | 0.0 | 521 | 9.0 |
P3 | Max P | 0.10 | 0.50 | 8 | 40 | 90 | 88,366 | 67,586 | 3564.1 | 3558.7 | 3558.7 | 0.0 | 242 | 4.9 |
P3 | Max P | 0.10 | 0.75 | 8 | 40 | 90 | 88,366 | 67,586 | 3511.0 | 3505.0 | 3505.0 | 0.0 | 35 | 2.3 |
P3 | Max P | 0.10 | 1.00 | 8 | 40 | 90 | 88,366 | 67,586 | 3456.0 | 3456.0 | 3456.0 | 0.0 | 0 | < 0.1 |
P3 | Max P | 0.20 | 0.00 | 8 | 40 | 90 | 88,366 | 67,586 | 3700.0 | 3700.0 | 3700.0 | 0.0 | 0 | < 0.1 |
P3 | Max P | 0.20 | 0.25 | 8 | 40 | 90 | 88,366 | 67,586 | 3531.2 | 3522.8 | 3522.8 | 0.0 | 420 | 7.7 |
P3 | Max P | 0.20 | 0.50 | 8 | 40 | 90 | 88,366 | 67,586 | 3421.3 | 3399.5 | 3399.5 | 0.0 | 280 | 7.7 |
P3 | Max P | 0.20 | 0.75 | 8 | 40 | 90 | 88,366 | 67,586 | 3306.2 | 3286.1 | 3286.1 | 0.0 | 158 | 5.5 |
P3 | Max P | 0.20 | 1.00 | 8 | 40 | 90 | 88,366 | 67,586 | 3184.0 | 3184.0 | 3184.0 | 0.0 | 0 | 0.5 |
P3 | Max P | 0.30 | 0.00 | 8 | 40 | 90 | 88,366 | 67,586 | 3700.0 | 3700.0 | 3700.0 | 0.0 | 0 | < 0.1 |
P3 | Max P | 0.30 | 0.25 | 8 | 40 | 90 | 88,366 | 67,586 | 3445.7 | 3424.8 | 3424.8 | 0.0 | 668 | 12.8 |
P3 | Max P | 0.30 | 0.50 | 8 | 40 | 90 | 88,366 | 67,586 | 3271.5 | 3210.7 | 3210.7 | 0.0 | 230 | 7.4 |
P3 | Max P | 0.30 | 0.75 | 8 | 40 | 90 | 88,366 | 67,586 | 3071.5 | 3027.0 | 3027.0 | 0.0 | 144 | 5.4 |
P3 | Max P | 0.30 | 1.00 | 8 | 40 | 90 | 88,366 | 67,586 | 2786.0 | 2786.0 | 2786.0 | 0.0 | 0 | 0.5 |
P4 | Max P | 0.00 | 0.00 | 8 | 0 | 144 | 672 | 673 | 1100.0 | 1100.0 | 1100.0 | 0.0 | 0 | < 0.1 |
P4 | Max P | 0.10 | 0.00 | 8 | 64 | 144 | 194,660 | 107,921 | 1100.0 | 1100.0 | 1100.0 | 0.0 | 0 | < 0.1 |
P4 | Max P | 0.10 | 0.25 | 8 | 64 | 144 | 194,660 | 107,921 | 1064.0 | 1059.5 | 1059.5 | 0.0 | 3604 | 162.3 |
P4 | Max P | 0.10 | 0.50 | 8 | 64 | 144 | 194,660 | 107,921 | 1028.4 | 1024.7 | 1024.7 | 0.0 | 1993 | 166.7 |
P4 | Max P | 0.10 | 0.75 | 8 | 64 | 144 | 194,660 | 107,921 | 993.2 | 991.3 | 991.3 | 0.0 | 1824 | 354.1 |
P4 | Max P | 0.10 | 1.00 | 8 | 64 | 144 | 194,660 | 107,921 | 958.5 | 958.5 | 958.5 | 0.0 | 0 | < 0.1 |
P4 | Max P | 0.20 | 0.00 | 8 | 64 | 144 | 194,660 | 107,921 | 1100.0 | 1100.0 | 1100.0 | 0.0 | 0 | < 0.1 |
P4 | Max P | 0.20 | 0.25 | 8 | 64 | 144 | 194,660 | 107,921 | 1028.4 | 1019.7 | 1019.7 | 0.0 | 2203 | 266.4 |
P4 | Max P | 0.20 | 0.50 | 8 | 64 | 144 | 194,660 | 107,921 | 958.5 | 954.0 | 954.0 | 0.0 | 1634 | 230.3 |
P4 | Max P | 0.20 | 0.75 | 8 | 64 | 144 | 194,660 | 107,921 | 890.4 | 887.8 | 887.8 | 0.0 | 1465 | 190.7 |
P4 | Max P | 0.20 | 1.00 | 8 | 64 | 144 | 194,660 | 107,921 | 824.0 | 824.0 | 824.0 | 0.0 | 0 | < 0.1 |
P4 | Max P | 0.30 | 0.00 | 8 | 64 | 144 | 194,660 | 107,921 | 1100.0 | 1100.0 | 1100.0 | 0.0 | 0 | < 0.1 |
P4 | Max P | 0.30 | 0.25 | 8 | 64 | 144 | 194,660 | 107,921 | 993.2 | 980.8 | 980.8 | 0.0 | 3155 | 299.9 |
P4 | Max P | 0.30 | 0.50 | 8 | 64 | 144 | 194,660 | 107,921 | 890.4 | 882.5 | 882.5 | 0.0 | 2799 | 335.9 |
P4 | Max P | 0.30 | 0.75 | 8 | 64 | 144 | 194,660 | 107,921 | 791.5 | 785.6 | 785.6 | 0.0 | 4780 | 417.2 |
P4 | Max P | 0.30 | 1.00 | 8 | 64 | 144 | 194,660 | 107,921 | 696.5 | 696.5 | 696.5 | 0.0 | 0 | < 0.1 |
P5 | Max P | 0.00 | 0.00 | 6 | 0 | 84 | 431 | 438 | 1700.0 | 1700.0 | 1700.0 | 0.0 | 0 | < 0.1 |
P5 | Max P | 0.10 | 0.00 | 6 | 42 | 84 | 73,067 | 68,988 | 1700.0 | 1700.0 | 1700.0 | 0.0 | 17 | 0.3 |
P5 | Max P | 0.10 | 0.25 | 6 | 42 | 84 | 73,067 | 68,988 | 1616.7 | 1591.2 | 1591.2 | 0.0 | 118 | 1.0 |
P5 | Max P | 0.10 | 0.50 | 6 | 42 | 84 | 73,067 | 68,988 | 1541.5 | 1489.2 | 1489.2 | 0.0 | 368 | 3.4 |
P5 | Max P | 0.10 | 0.75 | 6 | 42 | 84 | 73,067 | 68,988 | 1483.1 | 1449.0 | 1449.0 | 0.0 | 180 | 1.3 |
P5 | Max P | 0.10 | 1.00 | 6 | 42 | 84 | 73,067 | 68,988 | 1449.0 | 1449.0 | 1449.0 | 0.0 | 12 | 0.3 |
P5 | Max P | 0.20 | 0.00 | 6 | 42 | 84 | 73,067 | 68,988 | 1700.0 | 1700.0 | 1700.0 | 0.0 | 31 | 0.5 |
P5 | Max P | 0.20 | 0.25 | 6 | 42 | 84 | 73,067 | 68,988 | 1541.5 | 1489.2 | 1489.2 | 0.0 | 187 | 1.4 |
P5 | Max P | 0.20 | 0.50 | 6 | 42 | 84 | 73,067 | 68,988 | 1424.9 | 1288.0 | 1288.0 | 0.0 | 482 | 3.7 |
P5 | Max P | 0.20 | 0.75 | 6 | 42 | 84 | 73,067 | 68,988 | 1326.8 | 1255.2 | 1255.2 | 0.0 | 318 | 2.7 |
P5 | Max P | 0.20 | 1.00 | 6 | 42 | 84 | 73,067 | 68,988 | 1248.0 | 1248.0 | 1248.0 | 0.0 | 0 | 0.1 |
P5 | Max P | 0.30 | 0.00 | 6 | 42 | 84 | 73,067 | 68,988 | 1700.0 | 1700.0 | 1700.0 | 0.0 | 15 | 0.4 |
P5 | Max P | 0.30 | 0.25 | 6 | 42 | 84 | 73,067 | 68,988 | 1482.1 | 1387.6 | 1387.6 | 0.0 | 396 | 2.8 |
P5 | Max P | 0.30 | 0.50 | 6 | 42 | 84 | 73,067 | 68,988 | 1318.4 | 1113.7 | 1113.7 | 0.0 | 355 | 3.0 |
P5 | Max P | 0.30 | 0.75 | 6 | 42 | 84 | 73,067 | 68,988 | 1178.7 | 1077.2 | 1077.2 | 0.0 | 255 | 2.2 |
P5 | Max P | 0.30 | 1.00 | 6 | 42 | 84 | 73,067 | 68,988 | 1060.5 | 1060.5 | 1060.5 | 0.0 | 10 | 0.2 |
P6 | Max P | 0.00 | 0.00 | 10 | 0 | 168 | 1027 | 878 | 4950.0 | 4000.0 | 4000.0 | 0.0 | 1653 | 0.8 |
P6 | Max P | 0.10 | 0.00 | 10 | 80 | 168 | 215,189 | 271,198 | 4950.0 | 4000.0 | 4000.0 | 0.0 | 4388 | 528.3 |
P6 | Max P | 0.10 | 0.25 | 10 | 80 | 168 | 215,189 | 271,198 | 4788.3 | 3812.0 | 3812.0 | 0.0 | 13,493 | 874.1 |
P6 | Max P | 0.10 | 0.50 | 10 | 80 | 168 | 215,189 | 271,198 | 4660.3 | 3674.7 | 3674.7 | 0.0 | 9286 | 1118.5 |
P6 | Max P | 0.10 | 0.75 | 10 | 80 | 168 | 215,189 | 271,198 | 4548.3 | 3600.0 | 3600.0 | 0.0 | 8516 | 727.6 |
P6 | Max P | 0.10 | 1.00 | 10 | 80 | 168 | 215,189 | 271,198 | 4455.0 | 3600.0 | 3600.0 | 0.0 | 4430 | 232.7 |
P6 | Max P | 0.20 | 0.00 | 10 | 80 | 168 | 215,189 | 271,198 | 4950.0 | 4000.0 | 4000.0 | 0.0 | 4831 | 361.5 |
P6 | Max P | 0.20 | 0.25 | 10 | 80 | 168 | 215,189 | 271,198 | 4626.7 | 3630.0 | 3630.0 | 0.0 | 8239 | 848.1 |
P6 | Max P | 0.20 | 0.50 | 10 | 80 | 168 | 215,189 | 271,198 | 4370.7 | 3364.6 | 3364.6 | 0.0 | 9089 | 793.7 |
P6 | Max P | 0.20 | 0.75 | 10 | 80 | 168 | 215,189 | 271,198 | 4146.7 | 3210.7 | 3210.7 | 0.0 | 17,518 | 1327.0 |
P6 | Max P | 0.20 | 1.00 | 10 | 80 | 168 | 215,189 | 271,198 | 3960.0 | 3200.0 | 3200.0 | 0.0 | 4900 | 490.3 |
P6 | Max P | 0.30 | 0.00 | 10 | 80 | 168 | 215,189 | 271,198 | 4950.0 | 4000.0 | 4000.0 | 0.0 | 4044 | 465.2 |
P6 | Max P | 0.30 | 0.25 | 10 | 80 | 168 | 215,189 | 271,198 | 4465.0 | 3451.0 | 3451.0 | 0.0 | 9349 | 1067.7 |
P6 | Max P | 0.30 | 0.50 | 10 | 80 | 168 | 215,189 | 271,198 | 4081.0 | 3068.2 | 3068.2 | 0.0 | 10,726 | 645.5 |
P6 | Max P | 0.30 | 0.75 | 10 | 80 | 168 | 215,189 | 271,198 | 3745.0 | 2841.0 | 2841.0 | 0.0 | 13,314 | 818.5 |
P6 | Max P | 0.30 | 1.00 | 10 | 80 | 168 | 215,189 | 271,198 | 3465.0 | 2800.0 | 2800.0 | 0.0 | 3537 | 198.6 |
P7 | Max P | 0.00 | 0.00 | 8 | 0 | 180 | 2142 | 1251 | 3157.5 | 2690.0 | 2690.0 | 0.0 | 105 | < 0.1 |
P7 | Max P | 0.10 | 0.00 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3157.5 | 2690.0 | 2690.0 | 0.0 | 508 | 492.3 |
P7 | Max P | 0.10 | 0.25 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3151.6 | 2687.5 | 2687.5 | 0.0 | 5280 | 2013.8 |
P7 | Max P | 0.10 | 0.50 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3145.6 | 2686.7 | 2686.7 | 0.0 | 1721 | 695.3 |
P7 | Max P | 0.10 | 0.75 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3139.7 | 2686.7 | 2686.7 | 0.0 | 1946 | 950.3 |
P7 | Max P | 0.10 | 1.00 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3133.8 | 2686.7 | 2686.7 | 0.0 | 94 | 32.0 |
P7 | Max P | 0.20 | 0.00 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3157.5 | 2690.0 | 2690.0 | 0.0 | 829 | 860.2 |
P7 | Max P | 0.20 | 0.25 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3145.6 | 2685.1 | 2685.1 | 0.0 | 5017 | 1571.4 |
P7 | Max P | 0.20 | 0.50 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3133.8 | 2683.6 | 2683.6 | 0.0 | 2211 | 978.1 |
P7 | Max P | 0.20 | 0.75 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3121.9 | 2683.6 | 2683.6 | 0.0 | 1285 | 351.4 |
P7 | Max P | 0.20 | 1.00 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3110.0 | 2683.6 | 2683.6 | 0.0 | 75 | 37.6 |
P7 | Max P | 0.30 | 0.00 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3157.5 | 2690.0 | 2690.0 | 0.0 | 639 | 820.4 |
P7 | Max P | 0.30 | 0.25 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3139.7 | 2682.9 | 2682.9 | 0.0 | 4047 | 1401.8 |
P7 | Max P | 0.30 | 0.50 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3121.9 | 2680.9 | 2680.9 | 0.0 | 1960 | 516.2 |
P7 | Max P | 0.30 | 0.75 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3101.3 | 2680.9 | 2680.9 | 0.0 | 935 | 319.0 |
P7 | Max P | 0.30 | 1.00 | 8 | 104 | 180 | 1,646,630 | 802,859 | 3063.1 | 2680.9 | 2680.9 | 0.0 | 316 | 69.0 |
P8 | Max P | 0.00 | 0.00 | 9 | 0 | 210 | 2180 | 1665 | 4980.0 | 4295.0 | 4295.0 | 0.0 | 3,646 | 1.7 |
P8 | Max P | 0.10 | 0.00 | 9 | 63 | 210 | 601,724 | 579,528 | 4980.0 | 4295.0 | 4295.0 | 0.0 | 3955 | 1460.3 |
P8 | Max P | 0.10 | 0.25 | 9 | 63 | 210 | 601,724 | 579,528 | 4957.3 | 4190.5 | 4190.5 | 0.0 | 7494 | 2700.7 |
P8 | Max P | 0.10 | 0.50 | 9 | 63 | 210 | 601,724 | 579,528 | 4955.5 | 4163.2 | 4163.2 | 0.0 | 4587 | 2111.1 |
P8 | Max P | 0.10 | 0.75 | 9 | 63 | 210 | 601,724 | 579,528 | 4953.8 | 4163.2 | 4163.2 | 0.0 | 8045 | 2925.9 |
P8 | Max P | 0.10 | 1.00 | 9 | 63 | 210 | 601,724 | 579,528 | 4952.0 | 4163.2 | 4163.2 | 0.0 | 2387 | 427.8 |
P8 | Max P | 0.20 | 0.00 | 9 | 63 | 210 | 601,724 | 579,528 | 4980.0 | 4295.0 | 4295.0 | 0.0 | 3168 | 1611.6 |
P8 | Max P | 0.20 | 0.25 | 9 | 63 | 210 | 601,724 | 579,528 | 4934.5 | 4098.8 | 4098.8 | 0.0 | 6880 | 2800.9 |
P8 | Max P | 0.20 | 0.50 | 9 | 63 | 210 | 601,724 | 579,528 | 4931.0 | 4042.4 | 4042.4 | 0.0 | 4669 | 2767.5 |
P8 | Max P | 0.20 | 0.75 | 9 | 63 | 210 | 601,724 | 579,528 | 4927.5 | 4042.4 | 4042.4 | 0.0 | 6859 | 2458.4 |
P8 | Max P | 0.20 | 1.00 | 9 | 63 | 210 | 601,724 | 579,528 | 4924.0 | 4042.4 | 4042.4 | 0.0 | 4281 | 434.4 |
P8 | Max P | 0.30 | 0.00 | 9 | 63 | 210 | 601,724 | 579,528 | 4980.0 | 4295.0 | 4295.0 | 0.0 | 3926 | 1486.9 |
P8 | Max P | 0.30 | 0.25 | 9 | 63 | 210 | 601,724 | 579,528 | 4911.8 | 4039.2 | 4039.2 | 0.0 | 9714 | 3936.6 |
P8 | Max P | 0.30 | 0.50 | 9 | 63 | 210 | 601,724 | 579,528 | 4906.5 | 3945.2 | 3945.2 | 0.0 | 9816 | 3678.4 |
P8 | Max P | 0.30 | 0.75 | 9 | 63 | 210 | 601,724 | 579,528 | 4901.3 | 3945.2 | 3945.2 | 0.0 | 5906 | 2532.6 |
P8 | Max P | 0.30 | 1.00 | 9 | 63 | 210 | 601,724 | 579,528 | 4896.0 | 3945.2 | 3945.2 | 0.0 | 3772 | 406.5 |
P9 | Max P | 0.00 | 0.00 | 8 | 0 | 198 | 2647 | 1912 | 6752.9 | 4340.0 | 4340.0 | 0.0 | 8454 | 3.8 |
P9 | Max P | 0.10 | 0.00 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6752.9 | 4340.0 | 4340.0 | 0.0 | 8572 | 7710.5 |
P9 | Max P | 0.10 | 0.25 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6694.4 | 4315.3 | 4315.3 | 0.0 | 15,180 | 9355.4 |
P9 | Max P | 0.10 | 0.50 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6688.9 | 4308.0 | 408.0 | 0.0 | 15,373 | 6803.0 |
P9 | Max P | 0.10 | 0.75 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6685.4 | 4308.0 | 4308.0 | 0.0 | 12,204 | 5970.5 |
P9 | Max P | 0.10 | 1.00 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6682.0 | 4308.0 | 4308.0 | 0.0 | 12,986 | 3345.2 |
P9 | Max P | 0.20 | 0.00 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6752.9 | 4340.0 | 4340.0 | 0.0 | 12,623 | 10,066.9 |
P9 | Max P | 0.20 | 0.25 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6688.9 | 4302.0 | 4302.0 | 0.0 | 16,011 | 9336.5 |
P9 | Max P | 0.20 | 0.50 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6682.0 | 4294.0 | 4294.0 | 0.0 | 13,981 | 7134.0 |
P9 | Max P | 0.20 | 0.75 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6675.1 | 4294.0 | 4294.0 | 0.0 | 13,252 | 6304.6 |
P9 | Max P | 0.20 | 1.00 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6668.3 | 4294.0 | 4294.0 | 0.0 | 8233 | 2811.9 |
P9 | Max P | 0.30 | 0.00 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6752.9 | 4340.0 | 4340.0 | 0.0 | 11,676 | 10,948.2 |
P9 | Max P | 0.30 | 0.25 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6685.4 | 4298.0 | 4298.0 | 0.0 | 13,286 | 10,474.5 |
P9 | Max P | 0.30 | 0.50 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6675.1 | 4286.0 | 4286.0 | 0.0 | 13,183 | 8870.5 |
P9 | Max P | 0.30 | 0.75 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6665.2 | 4286.0 | 4286.0 | 0.0 | 11,932 | 5812.3 |
P9 | Max P | 0.30 | 1.00 | 8 | 88 | 198 | 1,492,337 | 980,576 | 6655.5 | 4286.0 | 4286.0 | 0.0 | 8157 | 2332.8 |
P1 | Min MS | 0.00 | 0.00 | 6 | 0 | 72 | 288 | 353 | 3.1 | 5.4 | 5.4 | 0.0 | 84 | < 0.1 |
P1 | Min MS | 0.10 | 0.00 | 6 | 60 | 72 | 113,048 | 61,673 | 1.3 | 5.4 | 5.4 | 0.0 | 106 | 1.5 |
P1 | Min MS | 0.10 | 0.25 | 6 | 60 | 72 | 113,048 | 61,673 | 1.3 | 5.4 | 5.4 | 0.0 | 70 | 1.8 |
P1 | Min MS | 0.10 | 0.50 | 6 | 60 | 72 | 113,048 | 61,673 | 1.3 | 5.4 | 5.4 | 0.0 | 159 | 2.5 |
P1 | Min MS | 0.10 | 0.75 | 6 | 60 | 72 | 113,048 | 61,673 | 1.4 | 5.4 | 5.4 | 0.0 | 72 | 1.5 |
P1 | Min MS | 0.10 | 1.00 | 6 | 60 | 72 | 113,048 | 61,673 | 1.4 | 5.4 | 5.4 | 0.0 | 124 | 1.3 |
P1 | Min MS | 0.20 | 0.00 | 6 | 60 | 72 | 113,048 | 61,673 | 1.3 | 5.4 | 5.4 | 0.0 | 127 | 1.6 |
P1 | Min MS | 0.20 | 0.25 | 6 | 60 | 72 | 113,048 | 61,673 | 1.3 | 5.4 | 5.4 | 0.0 | 87 | 2.0 |
P1 | Min MS | 0.20 | 0.50 | 6 | 60 | 72 | 113,048 | 61,673 | 1.4 | 5.4 | 5.4 | 0.0 | 70 | 1.5 |
P1 | Min MS | 0.20 | 0.75 | 6 | 60 | 72 | 113,048 | 61,673 | 1.5 | 5.4 | 5.4 | 0.0 | 106 | 2.3 |
P1 | Min MS | 0.20 | 1.00 | 6 | 60 | 72 | 113,048 | 61,673 | 1.7 | 5.4 | 5.4 | 0.0 | 45 | 1.3 |
P1 | Min MS | 0.30 | 0.00 | 6 | 60 | 72 | 113,048 | 61,673 | 1.3 | 5.4 | 5.4 | 0.0 | 199 | 2.5 |
P1 | Min MS | 0.30 | 0.25 | 6 | 60 | 72 | 113,048 | 61,673 | 1.4 | 5.4 | 5.4 | 0.0 | 150 | 2.4 |
P1 | Min MS | 0.30 | 0.50 | 6 | 60 | 72 | 113,048 | 61,673 | 1.5 | 5.8 | 5.8 | 0.0 | 333 | 5.9 |
P1 | Min MS | 0.30 | 0.75 | 6 | 60 | 72 | 113,048 | 61,673 | 1.7 | 5.8 | 5.8 | 0.0 | 248 | 4.5 |
P1 | Min MS | 0.30 | 1.00 | 6 | 60 | 72 | 113,048 | 61,673 | 2.0 | 5.8 | 5.8 | 0.0 | 85 | 1.2 |
P2 | Min MS | 0.00 | 0.00 | 8 | 0 | 72 | 316 | 349 | 1.5 | 5.2 | 5.2 | 0.0 | 1118 | 0.1 |
P2 | Min MS | 0.10 | 0.00 | 8 | 96 | 72 | 82,556 | 103,389 | 1.5 | 5.2 | 5.2 | 0.0 | 933 | 1.3 |
P2 | Min MS | 0.10 | 0.25 | 8 | 96 | 72 | 82,556 | 103,389 | 1.5 | 5.2 | 5.2 | 0.0 | 1371 | 2.2 |
P2 | Min MS | 0.10 | 0.50 | 8 | 96 | 72 | 82,556 | 103,389 | 1.5 | 5.2 | 5.2 | 0.0 | 729 | 1.6 |
P2 | Min MS | 0.10 | 0.75 | 8 | 96 | 72 | 82,556 | 103,389 | 1.5 | 5.2 | 5.2 | 0.0 | 2123 | 4.2 |
P2 | Min MS | 0.10 | 1.00 | 8 | 96 | 72 | 82,556 | 103,389 | 1.5 | 5.2 | 5.2 | 0.0 | 411 | 1.2 |
P2 | Min MS | 0.20 | 0.00 | 8 | 96 | 72 | 82,556 | 103,389 | 1.5 | 5.2 | 5.2 | 0.0 | 2373 | 3.2 |
P2 | Min MS | 0.20 | 0.25 | 8 | 96 | 72 | 82,556 | 103,389 | 1.5 | 5.2 | 5.2 | 0.0 | 829 | 1.9 |
P2 | Min MS | 0.20 | 0.50 | 8 | 96 | 72 | 82,556 | 103,389 | 1.5 | 5.2 | 5.2 | 0.0 | 657 | 1.7 |
P2 | Min MS | 0.20 | 0.75 | 8 | 96 | 72 | 82,556 | 103,389 | 1.6 | 5.2 | 5.2 | 0.0 | 1506 | 3.3 |
P2 | Min MS | 0.20 | 1.00 | 8 | 96 | 72 | 82,556 | 103,389 | 1.6 | 5.2 | 5.2 | 0.0 | 682 | 1.8 |
P2 | Min MS | 0.30 | 0.00 | 8 | 96 | 72 | 82,556 | 103,389 | 1.5 | 5.2 | 5.2 | 0.0 | 1204 | 2.4 |
P2 | Min MS | 0.30 | 0.25 | 8 | 96 | 72 | 82,556 | 103,389 | 1.5 | 5.2 | 5.2 | 0.0 | 1364 | 2.8 |
P2 | Min MS | 0.30 | 0.50 | 8 | 96 | 72 | 82,556 | 103,389 | 1.6 | 5.2 | 5.2 | 0.0 | 377 | 1.2 |
P2 | Min MS | 0.30 | 0.75 | 8 | 96 | 72 | 82,556 | 103,389 | 1.6 | 5.2 | 5.2 | 0.0 | 935 | 2.3 |
P2 | Min MS | 0.30 | 1.00 | 8 | 96 | 72 | 82,556 | 103,389 | 1.6 | 5.2 | 5.2 | 0.0 | 475 | 1.1 |
P3 | Min MS | 0.00 | 0.00 | 8 | 0 | 90 | 453 | 479 | 1.6 | 3.8 | 3.8 | 0.0 | 501 | < 0.1 |
P3 | Min MS | 0.10 | 0.00 | 8 | 40 | 90 | 93,262 | 70,959 | 1.6 | 3.8 | 3.8 | 0.0 | 606 | 19.6 |
P3 | Min MS | 0.10 | 0.25 | 8 | 40 | 90 | 93,262 | 70,959 | 1.7 | 3.8 | 3.8 | 0.0 | 1069 | 19.2 |
P3 | Min MS | 0.10 | 0.50 | 8 | 40 | 90 | 93,262 | 70,959 | 1.7 | 3.8 | 3.8 | 0.0 | 945 | 33.5 |
P3 | Min MS | 0.10 | 0.75 | 8 | 40 | 90 | 93,262 | 70,959 | 1.7 | 3.8 | 3.8 | 0.0 | 1251 | 39.2 |
P3 | Min MS | 0.10 | 1.00 | 8 | 40 | 90 | 93,262 | 70,959 | 1.8 | 3.8 | 3.8 | 0.0 | 976 | 17.5 |
P3 | Min MS | 0.20 | 0.00 | 8 | 40 | 90 | 93,262 | 70,959 | 1.6 | 3.8 | 3.8 | 0.0 | 598 | 10.4 |
P3 | Min MS | 0.20 | 0.25 | 8 | 40 | 90 | 93,262 | 70,959 | 1.7 | 3.8 | 3.8 | 0.0 | 805 | 25.4 |
P3 | Min MS | 0.20 | 0.50 | 8 | 40 | 90 | 93,262 | 70,959 | 1.8 | 3.8 | 3.8 | 0.0 | 1188 | 43.8 |
P3 | Min MS | 0.20 | 0.75 | 8 | 40 | 90 | 93,262 | 70,959 | 1.8 | 3.8 | 3.8 | 0.0 | 435 | 21.3 |
P3 | Min MS | 0.20 | 1.00 | 8 | 40 | 90 | 93,262 | 70,959 | 1.9 | 3.8 | 3.8 | 0.0 | 427 | 11.8 |
P3 | Min MS | 0.30 | 0.00 | 8 | 40 | 90 | 93,262 | 70,959 | 1.6 | 3.8 | 3.8 | 0.0 | 388 | 11.4 |
P3 | Min MS | 0.30 | 0.25 | 8 | 40 | 90 | 93,262 | 70,959 | 1.7 | 3.9 | 3.9 | 0.0 | 652 | 18.1 |
P3 | Min MS | 0.30 | 0.50 | 8 | 40 | 90 | 93,262 | 70,959 | 1.8 | 3.9 | 3.9 | 0.0 | 714 | 26.5 |
P3 | Min MS | 0.30 | 0.75 | 8 | 40 | 90 | 93,262 | 70,959 | 2.0 | 3.9 | 3.9 | 0.0 | 843 | 28.3 |
P3 | Min MS | 0.30 | 1.00 | 8 | 40 | 90 | 93,262 | 70,959 | 2.1 | 3.9 | 3.9 | 0.0 | 542 | 11.2 |
P4 | Min MS | 0.00 | 0.00 | 6 | 0 | 96 | 460 | 480 | 0.6 | 2.2 | 2.2 | 0.0 | 130 | < 0.1 |
P4 | Min MS | 0.10 | 0.00 | 6 | 48 | 96 | 118,468 | 64,788 | 0.6 | 2.2 | 2.2 | 0.0 | 45 | 1.4 |
P4 | Min MS | 0.10 | 0.25 | 6 | 48 | 96 | 118,468 | 64,788 | 0.6 | 2.2 | 2.2 | 0.0 | 44 | 2.5 |
P4 | Min MS | 0.10 | 0.50 | 6 | 48 | 96 | 118,468 | 64,788 | 0.6 | 2.2 | 2.2 | 0.0 | 54 | 2.8 |
P4 | Min MS | 0.10 | 0.75 | 6 | 48 | 96 | 118,468 | 64,788 | 0.6 | 2.2 | 2.2 | 0.0 | 42 | 2.5 |
P4 | Min MS | 0.10 | 1.00 | 6 | 48 | 96 | 118,468 | 64,788 | 0.7 | 2.2 | 2.2 | 0.0 | 52 | 1.5 |
P4 | Min MS | 0.20 | 0.00 | 6 | 48 | 96 | 118,468 | 64,788 | 0.6 | 2.2 | 2.2 | 0.0 | 108 | 2.3 |
P4 | Min MS | 0.20 | 0.25 | 6 | 48 | 96 | 118,468 | 64,788 | 0.6 | 2.2 | 2.2 | 0.0 | 44 | 2.0 |
P4 | Min MS | 0.20 | 0.50 | 6 | 48 | 96 | 118,468 | 64,788 | 0.7 | 2.2 | 2.2 | 0.0 | 81 | 2.1 |
P4 | Min MS | 0.20 | 0.75 | 6 | 48 | 96 | 118,468 | 64,788 | 0.7 | 2.2 | 2.2 | 0.0 | 291 | 5.6 |
P4 | Min MS | 0.20 | 1.00 | 6 | 48 | 96 | 118,468 | 64,788 | 0.7 | 2.2 | 2.2 | 0.0 | 389 | 3.7 |
P4 | Min MS | 0.30 | 0.00 | 6 | 48 | 96 | 118,468 | 64,788 | 0.6 | 2.2 | 2.2 | 0.0 | 51 | 1.5 |
P4 | Min MS | 0.30 | 0.25 | 6 | 48 | 96 | 118,468 | 64,788 | 0.6 | 2.2 | 2.2 | 0.0 | 243 | 5.0 |
P4 | Min MS | 0.30 | 0.50 | 6 | 48 | 96 | 118,468 | 64,788 | 0.7 | 2.2 | 2.2 | 0.0 | 223 | 3.8 |
P4 | Min MS | 0.30 | 0.75 | 6 | 48 | 96 | 118,468 | 64,788 | 0.7 | 2.2 | 2.2 | 0.0 | 414 | 9.3 |
P4 | Min MS | 0.30 | 1.00 | 6 | 48 | 96 | 118,468 | 64,788 | 0.8 | 2.2 | 2.2 | 0.0 | 544 | 5.7 |
P5 | Min MS | 0.00 | 0.00 | 7 | 0 | 105 | 528 | 550 | 1.0 | 6.3 | 6.3 | 0.0 | 404 | < 0.1 |
P5 | Min MS | 0.10 | 0.00 | 7 | 49 | 105 | 105,427 | 99,390 | 1.0 | 6.3 | 6.3 | 0.0 | 435 | 7.8 |
P5 | Min MS | 0.10 | 0.25 | 7 | 49 | 105 | 105,427 | 99,390 | 1.0 | 6.3 | 6.3 | 0.0 | 100 | 4.0 |
P5 | Min MS | 0.10 | 0.50 | 7 | 49 | 105 | 105,427 | 99,390 | 1.1 | 6.3 | 6.3 | 0.0 | 264 | 5.0 |
P5 | Min MS | 0.10 | 0.75 | 7 | 49 | 105 | 105,427 | 99,390 | 1.1 | 6.3 | 6.3 | 0.0 | 112 | 5.8 |
P5 | Min MS | 0.10 | 1.00 | 7 | 49 | 105 | 105,427 | 99,390 | 1.2 | 6.3 | 6.3 | 0.0 | 375 | 4.5 |
P5 | Min MS | 0.20 | 0.00 | 7 | 49 | 105 | 105,427 | 99,390 | 1.0 | 6.3 | 6.3 | 0.0 | 484 | 7.0 |
P5 | Min MS | 0.20 | 0.25 | 7 | 49 | 105 | 105,427 | 99,390 | 1.1 | 6.3 | 6.3 | 0.0 | 312 | 7.7 |
P5 | Min MS | 0.20 | 0.50 | 7 | 49 | 105 | 105,427 | 99,390 | 1.2 | 6.3 | 6.3 | 0.0 | 120 | 6.1 |
P5 | Min MS | 0.20 | 0.75 | 7 | 49 | 105 | 105,427 | 99,390 | 1.3 | 6.3 | 6.3 | 0.0 | 193 | 5.9 |
P5 | Min MS | 0.20 | 1.00 | 7 | 49 | 105 | 105,427 | 99,390 | 1.4 | 6.3 | 6.3 | 0.0 | 380 | 6.1 |
P5 | Min MS | 0.30 | 0.00 | 7 | 49 | 105 | 105,427 | 99,390 | 1.0 | 6.3 | 6.3 | 0.0 | 321 | 4.6 |
P5 | Min MS | 0.30 | 0.25 | 7 | 49 | 105 | 105,427 | 99,390 | 1.1 | 6.3 | 6.3 | 0.0 | 693 | 7.2 |
P5 | Min MS | 0.30 | 0.50 | 7 | 49 | 105 | 105,427 | 99,390 | 1.3 | 6.3 | 6.3 | 0.0 | 292 | 6.5 |
P5 | Min MS | 0.30 | 0.75 | 7 | 49 | 105 | 105,427 | 99,390 | 1.5 | 6.3 | 6.3 | 0.0 | 154 | 4.7 |
P5 | Min MS | 0.30 | 1.00 | 7 | 49 | 105 | 105,427 | 99,390 | 1.8 | 6.3 | 6.3 | 0.0 | 117 | 2.9 |
P6 | Min MS | 0.00 | 0.00 | 10 | 0 | 168 | 1027 | 899 | 1.1 | 5.0 | 5.0 | 0.0 | 17,995 | 5.9 |
P6 | Min MS | 0.10 | 0.00 | 10 | 80 | 168 | 224,869 | 282,419 | 1.1 | 5.0 | 5.0 | 0.0 | 30,820 | 1575.4 |
P6 | Min MS | 0.10 | 0.25 | 10 | 80 | 168 | 224,869 | 282,419 | 1.1 | 5.0 | 5.0 | 0.0 | 27,540 | 1977.7 |
P6 | Min MS | 0.10 | 0.50 | 10 | 80 | 168 | 224,869 | 282,419 | 1.2 | 5.0 | 5.0 | 0.0 | 33,698 | 1879.5 |
P6 | Min MS | 0.10 | 0.75 | 10 | 80 | 168 | 224,869 | 282,419 | 1.2 | 5.0 | 5.0 | 0.0 | 30,618 | 2509.1 |
P6 | Min MS | 0.10 | 1.00 | 10 | 80 | 168 | 224,869 | 282,419 | 1.2 | 5.0 | 5.0 | 0.0 | 28,024 | 1374.0 |
P6 | Min MS | 0.20 | 0.00 | 10 | 80 | 168 | 224,869 | 282,419 | 1.1 | 5.0 | 5.0 | 0.0 | 64,881 | 2740.5 |
P6 | Min MS | 0.20 | 0.25 | 10 | 80 | 168 | 224,869 | 282,419 | 1.2 | 5.0 | 5.0 | 0.0 | 21,780 | 1542.5 |
P6 | Min MS | 0.20 | 0.50 | 10 | 80 | 168 | 224,869 | 282,419 | 1.2 | 5.0 | 5.0 | 0.0 | 22,194 | 1837.4 |
P6 | Min MS | 0.20 | 0.75 | 10 | 80 | 168 | 224,869 | 282,419 | 1.3 | 5.0 | 5.0 | 0.0 | 33,148 | 2394.3 |
P6 | Min MS | 0.20 | 1.00 | 10 | 80 | 168 | 224,869 | 282,419 | 1.4 | 5.0 | 5.0 | 0.0 | 6399 | 260.0 |
P6 | Min MS | 0.30 | 0.00 | 10 | 80 | 168 | 224,869 | 282,419 | 1.1 | 5.0 | 5.0 | 0.0 | 49,342 | 2135.1 |
P6 | Min MS | 0.30 | 0.25 | 10 | 80 | 168 | 224,869 | 282,419 | 1.2 | 5.2 | 5.2 | 0.0 | 201,752 | 12,565.7 |
P6 | Min MS | 0.30 | 0.50 | 10 | 80 | 168 | 224,869 | 282,419 | 1.3 | 5.2 | 5.2 | 0.0 | 54,470 | 3332.5 |
P6 | Min MS | 0.30 | 0.75 | 10 | 80 | 168 | 224,869 | 282,419 | 1.4 | 5.2 | 5.2 | 0.0 | 112,920 | 5821.5 |
P6 | Min MS | 0.30 | 1.00 | 10 | 80 | 168 | 224,869 | 282,419 | 1.6 | 5.2 | 5.2 | 0.0 | 47,898 | 1637.8 |
P7 | Min MS | 0.00 | 0.00 | 8 | 0 | 180 | 2142 | 1311 | 1.1 | 5.3 | 5.3 | 0.0 | 233 | 0.1 |
P7 | Min MS | 0.10 | 0.00 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.1 | 5.3 | 5.3 | 0.0 | 658 | 832.1 |
P7 | Min MS | 0.10 | 0.25 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.1 | 5.3 | 5.3 | 0.0 | 827 | 1149.5 |
P7 | Min MS | 0.10 | 0.50 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.1 | 5.3 | 5.3 | 0.0 | 829 | 857.8 |
P7 | Min MS | 0.10 | 0.75 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.1 | 5.3 | 5.3 | 0.0 | 1947 | 1016.8 |
P7 | Min MS | 0.10 | 1.00 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.2 | 5.3 | 5.3 | 0.0 | 3517 | 1076.5 |
P7 | Min MS | 0.20 | 0.00 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.1 | 5.3 | 5.3 | 0.0 | 445 | 705.0 |
P7 | Min MS | 0.20 | 0.25 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.1 | 5.3 | 5.3 | 0.0 | 1875 | 1101.7 |
P7 | Min MS | 0.20 | 0.50 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.2 | 5.3 | 5.3 | 0.0 | 1709 | 937.5 |
P7 | Min MS | 0.20 | 0.75 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.2 | 5.3 | 5.3 | 0.0 | 765 | 975.4 |
P7 | Min MS | 0.20 | 1.00 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.2 | 5.3 | 5.3 | 0.0 | 1125 | 579.4 |
P7 | Min MS | 0.30 | 0.00 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.1 | 5.3 | 5.3 | 0.0 | 527 | 983.9 |
P7 | Min MS | 0.30 | 0.25 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.1 | 5.3 | 5.3 | 0.0 | 944 | 849.2 |
P7 | Min MS | 0.30 | 0.50 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.2 | 5.3 | 5.3 | 0.0 | 1596 | 1072.4 |
P7 | Min MS | 0.30 | 0.75 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.3 | 5.3 | 5.3 | 0.0 | 1343 | 1330.9 |
P7 | Min MS | 0.30 | 1.00 | 8 | 104 | 180 | 1,745,632 | 845,871 | 1.3 | 5.3 | 5.3 | 0.0 | 593 | 418.1 |
P8 | Min MS | 0.00 | 0.00 | 9 | 0 | 210 | 2180 | 1727 | 1.3 | 5.8 | 5.8 | 0.0 | 12,462 | 6.0 |
P8 | Min MS | 0.10 | 0.00 | 9 | 63 | 210 | 632,834 | 606,491 | 1.3 | 5.8 | 5.8 | 0.0 | 25,348 | 4935.8 |
P8 | Min MS | 0.10 | 0.25 | 9 | 63 | 210 | 632,834 | 606,491 | 1.3 | 5.8 | 5.8 | 0.0 | 12,737 | 4171.0 |
P8 | Min MS | 0.10 | 0.50 | 9 | 63 | 210 | 632,834 | 606,491 | 1.3 | 5.8 | 5.8 | 0.0 | 13,216 | 5605.7 |
P8 | Min MS | 0.10 | 0.75 | 9 | 63 | 210 | 632,834 | 606,491 | 1.3 | 5.8 | 5.8 | 0.0 | 15,062 | 5120.3 |
P8 | Min MS | 0.10 | 1.00 | 9 | 63 | 210 | 632,834 | 606,491 | 1.4 | 5.8 | 5.8 | 0.0 | 17,889 | 2492.0 |
P8 | Min MS | 0.20 | 0.00 | 9 | 63 | 210 | 632,834 | 606,491 | 1.3 | 5.8 | 5.8 | 0.0 | 17,988 | 4791.7 |
P8 | Min MS | 0.20 | 0.25 | 9 | 63 | 210 | 632,834 | 606,491 | 1.3 | 5.8 | 5.8 | 0.0 | 20,727 | 5669.7 |
P8 | Min MS | 0.20 | 0.50 | 9 | 63 | 210 | 632,834 | 606,491 | 1.4 | 5.8 | 5.8 | 0.0 | 18,575 | 5740.9 |
P8 | Min MS | 0.20 | 0.75 | 9 | 63 | 210 | 632,834 | 606,491 | 1.4 | 5.8 | 5.8 | 0.0 | 32,319 | 5474.0 |
P8 | Min MS | 0.20 | 1.00 | 9 | 63 | 210 | 632,834 | 606,491 | 1.4 | 5.8 | 5.8 | 0.0 | 18,075 | 3533.2 |
P8 | Min MS | 0.30 | 0.00 | 9 | 63 | 210 | 632,834 | 606,491 | 1.3 | 5.8 | 5.8 | 0.0 | 17,193 | 5028.9 |
P8 | Min MS | 0.30 | 0.25 | 9 | 63 | 210 | 632,834 | 606,491 | 1.3 | 5.8 | 5.8 | 0.0 | 18,104 | 4919.9 |
P8 | Min MS | 0.30 | 0.50 | 9 | 63 | 210 | 632,834 | 606,491 | 1.4 | 5.8 | 5.8 | 0.0 | 16,753 | 5361.8 |
P8 | Min MS | 0.30 | 0.75 | 9 | 63 | 210 | 632,834 | 606,491 | 1.5 | 5.8 | 5.8 | 0.0 | 15,353 | 4659.3 |
P8 | Min MS | 0.30 | 1.00 | 9 | 63 | 210 | 632,834 | 606,491 | 1.5 | 5.8 | 5.8 | 0.0 | 20,485 | 2437.2 |
P9 | Min MS | 0.00 | 0.00 | 7 | 0 | 165 | 2236 | 1731 | 1.0 | 6.8 | 6.8 | 0.0 | 1706 | 0.3 |
P9 | Min MS | 0.10 | 0.00 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.5 | 6.8 | 6.8 | 0.0 | 759 | 216.7 |
P9 | Min MS | 0.10 | 0.25 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.5 | 6.8 | 6.8 | 0.0 | 865 | 341.7 |
P9 | Min MS | 0.10 | 0.50 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.6 | 6.8 | 6.8 | 0.0 | 1168 | 230.3 |
P9 | Min MS | 0.10 | 0.75 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.6 | 6.8 | 6.8 | 0.0 | 1164 | 310.7 |
P9 | Min MS | 0.10 | 1.00 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.6 | 6.8 | 6.8 | 0.0 | 535 | 155.0 |
P9 | Min MS | 0.20 | 0.00 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.5 | 6.8 | 6.8 | 0.0 | 1175 | 271.7 |
P9 | Min MS | 0.20 | 0.25 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.6 | 6.8 | 6.8 | 0.0 | 1105 | 325.7 |
P9 | Min MS | 0.20 | 0.50 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.6 | 6.8 | 6.8 | 0.0 | 754 | 222.5 |
P9 | Min MS | 0.20 | 0.75 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.6 | 6.8 | 6.8 | 0.0 | 1454 | 435.5 |
P9 | Min MS | 0.20 | 1.00 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.6 | 6.8 | 6.8 | 0.0 | 647 | 192.4 |
P9 | Min MS | 0.30 | 0.00 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.5 | 6.8 | 6.8 | 0.0 | 493 | 174.5 |
P9 | Min MS | 0.30 | 0.25 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.6 | 6.8 | 6.8 | 0.0 | 1328 | 379.2 |
P9 | Min MS | 0.30 | 0.50 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.6 | 6.8 | 6.8 | 0.0 | 1053 | 272.4 |
P9 | Min MS | 0.30 | 0.75 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.6 | 6.8 | 6.8 | 0.0 | 1184 | 388.7 |
P9 | Min MS | 0.30 | 1.00 | 7 | 77 | 165 | 1,222,264 | 794,691 | 0.6 | 6.8 | 6.8 | 0.0 | 615 | 134.0 |
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Lappas, N.H., Ricardez-Sandoval, L.A., Fukasawa, R. et al. Adjustable Robust Optimization for multi-tasking scheduling with reprocessing due to imperfect tasks. Optim Eng 20, 1117–1159 (2019). https://doi.org/10.1007/s11081-019-09461-2
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DOI: https://doi.org/10.1007/s11081-019-09461-2