JOB SHOP
Best lower and upper bounds known, from OR-Lib (27.10.97).
Update 27.1.99 including Brinkkoetter’s optimal solutions.
Update 30. 6. 99 including Schilham’s new upper bounds
Update 4.5.0 including Henning’s new upper bounds
Update 11.7.0 including Schilham’s new lower bounds
Update 27.9.01 including Nowicki and Smutnicki new upper bounds
Update 30.8.02 including Henning new upper bounds
Update 20.10.02 including Nowicki and Smutnicki new upper bounds
Update 10.3.03 including Caldeira new upper bound
Update 23.11.05 including Zhang new upper bounds
Update 29.10.09/23.11.09 including Nasiri and Kianfar new upper bounds
Update 10.09.2011 including Beck, Feng and Watson new upper bounds
Update 31.10.2011 including Gon鏰lves & Resende new upper bounds and Gharbi & Labidi new lower bounds
Update 17.06.2013 including Yuichi Nagata and Isao Ono new upper bounds
ta01-05 1231 | 1244 | 1218 | 1175 | 1224
15 x 15 Ta1 Ta1 | VA NS | B BV | B We | B B
ta06-10 1238 | 1227 | 1217 | 1274 | 1241
| 15 x 15 B B | B B | B BV | B BV | VA BV |
|---|---|---|---|---|
| ta11-15 1323-1357 | 1351-1367 | 1282-1342 | 1345 | 1304-1339 |
| 20 x 15 S BFW | S BV | S H2 | VA NS | S ZLGR |
| ta16-20 1304-1360 | 1462 | 1369-1396 | 1304-1332 | 1318-1348 |
| 20 x 15 GL H | S NSc | VA BV | GL BFW | S ZLGR |
| ---------------------- | ----------- | ----------- | ----------- | ---------- |
| ta21-25 1573-1642 | 1542-1600 | 1474-1557 | 1606-1644 | 1518-1595 |
| 20 x 20 GL BFW | GL NSb | GL NSb | GL BFW | GL NSd |
| ta26-30 1558-1643 | 1617-1680 | 1591-1603 | 1525-1625 | 1485-1584 |
| 20 x 20 GL BFW | GL NSb | VA ZLGR | GL Aa | GL NSb |
| ---------------------- | ----------- | ----------- | ----------- | ---------- |
| ta31-35 1764 | 1774-1785 | 1778-1791 | 1828-1829 | 2007 |
| 30 x 15 Ta1 AHLS | Ta1 GR | VA ZLGR | Ta1 NSb | VA Ta1 |
| ta36-40 1819 | 1771 | 1673 | 1795 | 1631-1669 |
| 30 x 15 VA AHLS | Ta1 ZLGR | Ta1 H | VA AHLS | VA GR |
| ---------------------- | ----------- | ----------- | ----------- | ---------- |
| ta41-45 1876-2005 | 1867-1937 | 1809-1848 | 1927-1979 | 1997-2000 |
| 30 x 20 GL NO | VA GR | VA NK | VA NO | VA NSb |
| ta46-50 1940-2004 | 1789-1894 | 1912-1943 | 1915-1961 | 1807-1924 |
| 30 x 20 Ta1 GR | VA GR | VA GR | VA NO | VA BFW |
| ---------------------- | ----------- | ----------- | ----------- | ---------- |
| ta51-55 2760 | 2756 | 2717 | 2839 | 2679 |
| 50 x 15 Ta1 Ta1 | Ta1 Ta1 | Ta1 Ta1 | Ta1 Ta1 | Ta1 NS |
| ta56-60 2781 | 2943 | 2885 | 2655 | 2723 |
| 50 x 15 Ta1 Ta1 | Ta1 Ta1 | Ta1 Ta1 | Ta1 Ta1 | Ta1 Ta1 |
| ---------------------- | ----------- | ----------- | ----------- | ---------- |
| ta61-65 2868 | 2869 | 2755 | 2702 | 2725 |
| 50 x 20 Ta1 NS | VA JPC | Ta1 NS | BV NS | Ta1 NS |
| ta66-70 2845 | 2825 | 2784 | 3071 | 2995 |
| 50 x 20 Ta1 NS | VA AHLS | BV NS | Ta1 NS | Ta1 NS |
| ---------------------- | ----------- | ----------- | ----------- | ---------- |
| ta71-75 5464 | 5181 | 5568 | 5339 | 5392 |
| 100 x 20 Ta1 Ta1 | Ta1 Ta1 | Ta1 Ta1 | Ta1 Ta1 | Ta1 Ta1 |
| ta76-80 5342 | 5436 | 5394 | 5358 | 5183 |
| 100 x 20 Ta1 Ta1 | Ta1 Ta1 | Ta1 Ta1 | Ta1 Ta1 | Ta1 NS |
Aa:
E. Aarts (1996),
Personal communication.
(a parallel taboo search algorithm)
AHLS:
E. Aarts, Huub ten Eikelder, J.K. Lenstra, R. Schilham (23.6.1999)
Personnal communication.
(An adaptive memory programme embedding a taboo search algorithm with
NS neighbourhood and constant time Ta )
B:
Wolfgang Brinkkoetter (27.1.1999),
Personal communication.
(The method combines ideas of Carlier and Pinson with an
efficient way of propagating release/queue-time adjustments
in a simulation of parallel preemptive machines.
The method is described in:
Wolfgang Brinkkoetter (1997),
Erzeugung hochwertiger Loesungen fuer das Job Shop Scheduling Problem
mit Schwerpunkt auf dem Qualitaetsnachweis,
University of Paderborn, Paderborn, Germany).
c.f. also:
W. Brinkkoetter, P. Brucker
Solving open benchmarks problems for the job shop problem,
(1999)
BFW:
J. Christopher Beck, T. K. Feng, Jean-Paul Watson
Combining Constraint Programming and Local Search for Job-Shop Scheduling
INFORMS Journal on Computing 23(1): 1-14 (2011)
BV:
E. Balas, A. Vazacopoulos (1995),
Guided local search with shifting bottleneck for job shop scheduling,
Management Science Research Report #MSRR-609? [revised version],
Graduate School of Industrial Administration, Carnegie-Mellon University,
Pittsburgh, Pennsylvania.
BV’:
E. Balas, A. Vazacopoulos (1996),
Personal communication.
GL:
A. Gharbi, L. Labidi (6.6.2011)
Personal communication. Results obtained with method desribed in:
Anis Gharbi, Mohamed Labidi (2010),
“Extending the single machine-based relaxation scheme for the job shop scheduling problem”,
Electronic Notes in Discrete Mathematics, Volume 36, pp. 1057?064.
GR:
JOS?FERNANDO GON茿LVES AND MAURICIO G. C. RESENDE (2011)
A BIASED RANDOM-KEY GENETIC ALGORITHM FOR JOB-SHOP SCHEDULING
AT&T Labs Research Techhnical Report.
H:
Andre Henning (2000)
Private communication (5.4.0)
(Interactive method including various local searches and parameters)
H2:
Andr?Henning (2002)
Practical job shop scheduling problems (in german)(to be submitted)
Department of Mathematics and Computer Science
Friedrich-Schiller-University Jena
07740 Jena, Germany
JPC: Jo鉶 Paulo Caldeira (2003)
Private communication, 30.1.2003
Private communication, 10.3.2003
(hybrid evolutionary-tabu algorithm)
NK:
Nasiri and Kianfar (2009)
A pseudo杙ath relinking algorithm for the job shop problem
Private communications, 28.20.2009/23.11.2009
NO:
Yuichi Nagata and Isao Ono (2013)
Guided Constructive Local Search for the Job Shop Scheduling Problem
Technical report submitted for publication
27.02.2013
NS:
E. Nowicki, C. Smutnicki (1993),
A fast taboo search algorithm for the job shop problem,
Preprinty nr 8/93,
Institute of Engineering Cybernetics, Technical University of Wroclaw,
Wroclaw, Poland.
NSb:
E.Nowicki, C.Smutnicki, (2001)
New Ideas in TS for Job Shop Scheduling
Preprinty nr 50/2001
Institute of Engineering Cybernetics, Technical University of Wroclaw,
Wroclaw, Poland.
(A method that combines path relinking with NS’s fast taboo search)
NSc: Same method as NSb, Personal communication (7.5.2002)
NSd:
E.Nowicki, C.Smutnicki, (2002)
“Some New Tools to Solve the Job Shop Problem”
Technical Report 60/2002, Institute of Engineering Cybernetics, Technical University of Wroclaw,
Wroclaw, Poland.
S: R. Schilham (11.7.2000)
Personnal communication. (see below)
Ta1:
E. D. Taillard, (1994)
Parallel taboo search techniques for the job shop scheduling problem,
ORSA Journal on Computing 6, 108 ?117.
Results also reported in:
E. D. Taillard (1993),
Benchmarks for basic scheduling problems,
EJOR 64, 278-285.
VA:
R.J.M. Vaessens (1995),
Personal communication.
(lower bounds found using Applegate & Cook’s algorithm `edge-finder’)
VAAa:
R.J.M. Vaessens (1996),
Personal communication.
(upper bounds found using Applegate & Cook’s algorithm `shuffle’ with
initial solutions of B. Aarts (1996))
VABV:
R.J.M. Vaessens (1996),
Personal communication.
(upper bounds found using Applegate & Cook’s algorithm `shuffle’ with
initial solutions of E. Balas and A. Vazacopoulos (1995))
VAWe:
R.J.M. Vaessens (1995),
Personal communication.
(upper bounds found using Applegate & Cook’s algorithm `shuffle’ with
initial solutions of M. Wennink (1995))
We:
M. Wennink (1995),
Personal communication.
(upper bounds found by a taboo search algorithm)
WHW
Jean-Paul Watson, Adele E. Howeb and L. Darrell Whitley
Deconstructing Nowicki and Smutnicki’s i-TSAB tabu search algorithm for the job-shop scheduling problem
Volume 33, Issue 9, September 2006, Pages 2623-2644
ZLGR:
ChaoYong Zhang, PeiGen Li, ZaiLin Guan, YunQing Rao (2005)
A Tabu Search Algorithm with a New Neighborhood Structure for the Job Shop Scheduling Problem
and
A Very Fast TS/SA Algorithm for the Job Shop Scheduling Problem
School of Mechanical Science & Engineering, Huazhong University of Science & Technology,
Wuhan, 430074, P.R. China
NK - Nasiri and Kianfar, private communication, 28.20.2009
Tai_20_15_1
1358
13 8 2 11 7 6 12 14 3 17 5 10 15 1 9 4 20 19 16 18
8 10 7 4 11 5 6 14 12 13 2 9 1 19 15 17 20 16 3 18
12 7 8 18 3 5 19 9 16 4 13 6 11 1 14 2 15 17 20 10
11 15 6 12 4 14 17 1 2 19 13 10 8 3 18 7 9 5 16 20
9 8 10 4 14 12 2 13 16 11 5 7 1 3 19 17 20 15 18 6
16 9 20 2 12 15 6 8 5 4 14 3 7 19 17 11 10 1 18 13
12 20 16 15 9 6 13 7 18 11 5 8 14 2 19 10 17 1 4 3
12 13 8 9 17 7 6 11 4 2 1 3 15 18 14 10 16 5 19 20
4 5 18 12 13 7 16 2 11 6 17 8 19 10 3 9 20 14 15 1
9 20 14 11 13 5 4 12 16 15 3 18 8 7 6 2 19 17 1 10
18 7 11 4 20 9 6 13 5 17 10 12 14 1 2 3 8 15 19 16
20 18 1 8 6 16 13 4 12 17 10 7 5 11 3 19 2 9 14 15
14 7 13 16 19 5 8 2 9 3 11 6 15 1 17 12 10 20 18 4
4 8 20 18 15 19 7 6 12 13 5 10 9 17 16 14 2 11 3 1
5 20 16 13 15 12 4 1 7 11 18 3 17 2 10 8 19 6 14 9
Tai30_20_1
2010
10 22 28 6 9 24 11 12 4 17 2 20 14 25 19 18 16 29 3 26 23 30 7 21 1 27 15 5 13 8
6 11 23 26 19 15 27 2 10 13 18 30 14 16 17 5 9 12 22 3 25 7 21 8 20 24 4 28 1 29
7 10 2 21 5 27 13 6 12 3 9 22 17 30 14 18 16 8 23 19 25 1 26 24 28 20 4 29 15 11
7 9 10 18 14 22 16 2 30 19 12 13 1 4 8 29 5 3 21 24 6 28 15 20 26 27 17 25 11 23
16 15 23 11 2 14 20 13 8 6 10 5 29 27 17 3 4 19 30 1 9 12 22 25 24 21 26 28 7 18
1 12 23 13 24 3 2 18 6 16 17 27 19 15 10 5 22 20 30 26 4 25 14 21 28 9 7 8 29 11
12 5 25 18 23 21 22 2 20 30 13 10 6 19 1 15 9 4 29 16 3 26 8 11 17 14 24 28 27 7
22 21 9 20 18 2 27 12 23 6 19 17 4 26 5 25 30 3 1 8 15 29 10 13 24 28 14 7 11 16
5 3 20 15 4 10 28 2 14 16 23 6 12 22 17 29 8 7 27 1 25 11 21 26 30 18 19 13 9 24
19 16 18 12 10 23 2 14 27 15 28 29 30 5 20 22 26 1 7 24 25 21 8 11 4 13 6 17 9 3
9 23 6 14 17 12 26 27 8 11 15 19 7 10 22 13 2 25 1 24 20 5 16 28 4 3 29 18 21 30
25 19 13 29 15 27 23 5 4 24 12 16 17 9 14 30 8 20 3 11 22 28 6 7 1 18 26 21 2 10
8 22 2 23 26 10 6 17 5 12 28 21 7 14 18 1 16 20 13 15 30 3 24 25 9 29 11 27 19 4
2 6 26 18 13 4 20 5 17 19 1 23 10 12 7 27 22 15 8 11 29 28 24 9 16 25 14 30 3 21
9 15 24 27 25 13 2 17 18 29 16 3 4 21 12 23 6 1 8 11 7 19 20 26 30 14 5 22 10 28
2 15 13 16 5 27 18 7 6 1 10 11 14 28 24 22 17 19 29 8 20 30 3 23 4 25 12 9 21 26
30 22 7 21 5 25 18 27 10 16 6 19 15 17 20 29 28 9 12 11 3 26 1 14 8 13 2 23 24 4
21 20 17 19 18 9 7 16 14 8 6 15 3 25 28 5 23 12 2 10 22 24 26 1 11 13 4 29 27 30
26 23 16 29 25 28 17 3 6 18 30 22 2 20 15 14 4 19 9 7 21 13 8 24 27 5 12 11 1 10
18 13 16 27 17 9 22 6 2 14 10 5 1 12 7 28 8 24 15 11 4 25 20 23 19 21 3 30 29 26
Tai30_20_2
1945
13 9 25 15 22 5 19 8 16 27 12 1 14 21 20 11 29 26 18 17 3 23 28 10 6 30 24 4 2 7
15 5 10 2 21 24 4 22 8 7 27 29 3 19 28 17 1 25 12 14 6 18 20 30 26 13 16 9 23 11
13 16 2 18 7 4 15 5 14 26 25 9 21 22 24 6 29 8 12 27 28 1 11 19 17 3 10 20 23 30
25 5 26 7 1 2 29 16 10 15 12 17 28 11 14 6 30 21 27 22 19 18 23 9 4 20 3 24 8 13
1 7 29 26 14 25 24 23 17 16 19 9 6 20 22 12 8 4 11 13 10 27 21 18 15 3 28 2 30 5
12 13 1 29 25 21 11 26 30 27 9 17 14 6 24 28 22 2 3 10 19 23 8 16 15 18 7 4 5 20
2 12 26 18 23 15 10 25 1 17 8 24 29 19 5 14 6 22 11 7 3 30 21 27 4 16 13 20 28 9
23 4 5 26 17 9 7 8 21 19 15 2 11 13 22 18 20 29 27 1 16 25 30 14 12 6 10 24 3 28
21 26 29 17 14 1 3 30 22 25 20 6 11 19 7 27 28 4 18 23 10 16 15 12 13 8 9 24 5 2
24 10 12 16 9 15 25 13 26 29 17 6 19 21 20 22 4 30 7 3 28 27 1 11 23 5 2 14 8 18
5 14 1 25 11 8 22 27 2 15 19 10 3 20 7 29 26 17 13 12 23 18 24 21 28 9 30 16 6 4
29 10 19 30 2 21 25 24 17 11 27 1 26 20 9 5 8 22 7 13 6 14 16 12 28 15 18 4 3 23
25 14 1 10 2 12 17 16 24 27 5 29 21 30 6 20 22 8 7 28 9 3 19 15 23 18 11 26 13 4
26 7 18 2 22 29 11 14 17 28 27 10 16 25 3 1 15 5 30 19 9 21 20 6 4 12 24 23 13 8
25 11 16 30 18 2 12 22 24 29 23 15 10 3 28 19 9 1 17 4 7 14 8 13 26 6 27 20 5 21
19 7 3 15 25 22 1 12 14 28 23 21 8 24 30 16 17 2 4 13 29 27 10 5 11 18 9 6 20 26
30 15 22 10 28 16 21 24 3 8 14 5 7 11 4 26 1 2 20 18 25 12 23 6 27 19 17 29 13 9
7 9 17 3 5 15 12 20 14 24 8 21 29 22 23 4 30 16 25 1 2 28 6 27 13 10 26 19 18 11
12 11 13 29 17 5 8 15 22 18 26 25 2 9 19 6 1 30 20 16 10 14 4 3 7 28 24 23 27 21
11 19 7 15 13 17 21 28 26 1 14 30 2 22 16 12 29 27 23 6 10 20 9 18 3 4 5 8 25 24
Tai30_20_6
2014
30 7 15 19 14 12 18 20 13 29 9 24 23 22 28 6 16 2 25 17 5 8 21 10 1 26 11 4 27 3
11 15 23 16 26 28 5 19 4 12 1 27 13 8 24 7 18 14 25 2 22 6 3 29 10 20 21 30 17 9
14 12 18 5 22 27 20 17 11 15 25 4 28 16 13 30 7 29 19 24 10 23 9 26 21 8 1 2 3 6
5 20 16 18 8 13 30 19 27 10 4 12 24 14 15 28 21 6 9 3 2 17 23 1 11 25 7 29 26 22
19 23 18 14 16 30 8 12 26 22 5 7 27 15 4 24 9 10 25 17 21 11 28 29 13 2 3 1 6 20
18 15 7 16 19 8 13 9 29 12 20 24 10 2 23 5 25 30 22 17 11 14 21 3 1 26 27 4 6 28
13 14 29 24 19 26 20 6 11 28 7 8 15 27 25 2 9 23 17 12 3 10 30 18 5 16 4 22 1 21
30 15 12 19 1 18 6 26 16 22 14 11 8 7 20 29 17 5 10 24 3 21 28 2 9 13 27 25 23 4
30 19 7 5 26 15 27 9 13 12 18 23 2 28 10 25 20 6 29 14 1 24 16 22 8 21 3 4 11 17
15 19 7 26 25 10 22 4 6 13 30 20 8 18 29 24 28 9 12 14 27 3 16 5 17 11 23 1 2 21
7 2 16 1 18 5 20 11 9 14 26 15 24 4 12 23 8 19 3 29 28 6 17 21 10 30 22 27 13 25
12 16 6 15 24 13 1 25 18 4 9 2 11 8 30 27 5 19 17 28 22 21 23 26 3 14 7 10 20 29
23 1 14 9 8 7 19 15 10 26 13 17 20 18 28 30 5 11 12 25 27 6 4 21 3 22 29 24 16 2
24 19 21 4 25 16 13 7 29 8 28 20 6 26 10 15 11 30 17 12 9 5 22 2 27 18 23 3 1 14
16 29 25 20 1 12 8 18 4 13 27 11 23 7 6 15 17 24 19 30 9 3 21 10 2 26 5 14 22 28
7 3 18 1 12 10 27 8 11 16 21 19 15 5 6 23 2 25 30 28 24 17 22 14 9 13 26 29 20 4
20 14 21 26 29 24 19 18 2 8 10 15 12 6 11 9 17 5 27 3 23 22 28 7 16 4 25 30 13 1
29 21 12 14 19 22 28 1 24 18 11 7 9 25 16 26 27 17 8 10 23 30 2 5 3 4 6 20 13 15
23 26 11 7 29 4 6 30 8 15 13 22 24 10 14 19 25 16 12 20 1 2 27 3 28 17 21 18 5 9
30 12 1 6 8 7 11 28 27 9 18 23 15 4 24 13 29 19 10 3 2 22 17 16 20 25 14 26 5 21
Tai30_20_7
1899
16 12 20 9 24 27 26 2 29 25 5 15 3 8 19 17 21 13 14 30 4 1 22 11 10 28 7 18 6 23
17 18 8 29 9 19 15 24 16 27 2 4 3 26 1 7 5 28 11 30 13 14 23 12 20 21 10 25 22 6
4 21 7 29 28 9 24 19 5 3 23 10 17 27 22 2 13 15 1 12 20 25 6 26 30 11 18 8 14 16
13 18 29 16 14 12 25 3 30 19 5 10 9 8 27 11 17 2 26 6 15 21 23 22 1 7 4 28 24 20
28 15 13 16 24 7 2 19 27 9 5 8 22 12 26 4 29 21 6 3 17 14 25 18 23 11 10 1 30 20
14 6 29 25 8 23 13 20 17 19 12 2 24 7 4 27 26 30 16 9 10 3 21 22 18 5 1 15 28 11
29 25 4 8 10 14 13 6 22 9 7 5 19 21 2 11 30 18 24 20 1 26 23 17 28 16 3 12 15 27
15 8 13 19 1 18 28 21 11 16 25 17 7 14 12 24 22 30 5 27 6 20 10 3 4 2 23 26 9 29
5 22 7 15 19 2 13 16 24 27 8 14 6 25 10 18 1 12 29 9 4 17 28 21 23 3 26 20 30 11
22 26 20 21 19 7 29 16 6 13 5 3 4 11 8 18 25 28 30 10 15 9 23 17 14 27 12 2 24 1
30 19 15 3 5 25 24 14 16 6 12 11 8 17 10 29 2 13 1 28 26 23 4 18 20 22 7 21 9 27
19 1 17 15 12 16 11 25 30 3 26 10 4 2 7 5 8 20 29 9 6 13 27 28 23 21 22 24 14 18
11 14 9 18 19 15 8 4 29 1 13 3 17 2 5 6 26 30 21 27 20 22 16 10 25 24 28 7 23 12
21 20 15 28 10 16 6 14 4 13 3 24 19 2 29 12 7 8 18 5 17 1 23 26 22 30 27 25 9 11
21 14 16 3 4 29 9 26 8 20 10 24 22 5 11 6 13 30 7 12 27 1 15 2 18 23 17 28 19 25
4 19 16 18 28 13 15 12 20 29 8 21 27 14 6 25 5 24 2 22 10 30 11 1 23 26 3 17 9 7
22 8 21 15 1 5 27 10 6 9 16 23 4 19 29 18 24 3 28 2 20 17 25 14 12 30 7 13 26 11
5 22 16 27 28 10 29 4 17 30 2 11 13 19 14 20 15 9 21 8 26 24 25 12 6 3 7 1 18 23
26 11 29 12 15 27 17 10 24 21 8 22 3 14 13 4 19 16 1 2 30 6 7 5 28 18 23 25 20 9
17 3 1 7 4 19 5 21 29 2 10 15 6 22 23 9 24 26 11 27 12 18 8 13 25 30 20 16 14 28
NK - Nasiri and Kianfar, private communication, 23.11.2009
tai30_15_2
1790
1 19 13 11 23 4 12 17 7 28 5 14 2 25 29 20 27 6 18 30 9 8 10 24 21 15 26 3 16 22
16 24 5 4 11 26 18 7 19 8 3 1 21 27 15 12 28 2 17 30 10 25 23 29 13 22 20 14 6 9
27 16 25 1 7 15 17 5 28 12 29 13 8 4 14 22 18 23 19 11 24 3 20 2 30 10 9 6 21 26
19 15 7 27 5 8 28 12 21 2 10 29 4 3 18 30 25 6 26 9 13 11 22 20 24 14 1 23 16 17
28 10 20 6 7 4 19 29 1 8 15 5 12 16 17 13 14 2 27 3 26 23 25 11 22 9 30 21 18 24
19 20 7 14 5 10 16 11 6 8 15 17 29 1 27 25 12 4 3 30 22 13 9 23 24 26 28 18 21 2
10 23 16 30 20 19 15 1 17 11 22 28 9 5 4 14 8 18 21 29 3 26 2 25 6 24 12 27 13 7
8 5 16 23 20 19 2 4 14 7 15 30 27 26 13 28 24 11 17 10 29 12 22 6 18 9 3 25 21 1
23 7 14 18 1 5 22 26 16 28 17 30 27 13 2 4 29 20 25 24 19 10 9 15 21 8 3 6 11 12
15 18 7 29 19 8 16 24 13 28 14 23 22 17 20 1 25 21 10 5 6 11 12 4 2 9 30 27 3 26
20 21 1 19 15 14 27 16 3 9 8 12 18 17 23 5 26 6 30 2 4 29 22 25 28 11 24 10 13 7
23 6 20 13 30 17 11 15 7 16 12 1 21 28 3 5 4 27 18 10 14 2 8 19 29 25 26 22 9 24
19 12 3 7 4 1 29 22 5 27 13 24 11 8 2 14 10 23 15 21 20 9 30 25 28 6 26 17 18 16
1 4 19 17 12 14 27 11 7 22 5 25 23 3 2 13 21 30 29 9 8 10 24 28 15 26 6 18 20 16
28 4 8 27 22 7 6 14 19 3 21 1 9 16 26 30 2 10 5 23 12 25 15 13 24 29 17 18 11 20
tai30_15_10
1673
26 23 19 20 22 7 28 12 30 13 18 9 11 3 29 17 27 4 24 25 6 21 10 15 16 5 14 1 2 8
10 24 18 22 16 20 21 1 4 12 28 14 6 29 25 2 11 19 23 15 8 9 30 7 27 5 3 26 13 17
7 17 18 28 9 12 6 29 13 27 30 3 19 23 11 5 10 2 20 22 16 8 24 1 14 15 25 26 4 21
14 25 7 19 29 26 28 21 30 18 11 13 12 16 17 3 1 27 15 22 23 4 9 20 24 10 6 8 5 2
11 27 6 25 18 14 22 21 30 2 24 16 23 17 1 28 19 13 7 9 10 29 20 5 8 4 3 12 15 26
25 12 30 24 5 8 1 17 23 28 6 11 14 16 4 7 27 15 20 21 2 9 13 19 29 3 18 22 10 26
10 11 17 13 8 7 23 29 1 26 9 16 15 3 6 12 14 27 28 24 30 20 21 19 18 2 5 4 25 22
19 11 24 27 10 14 12 21 5 22 7 17 16 28 9 18 25 23 30 1 4 29 13 8 3 26 2 15 6 20
27 25 2 8 21 23 19 11 29 14 5 24 6 18 28 9 17 16 30 4 3 12 20 7 22 10 26 15 1 13
3 12 18 21 23 25 1 29 11 9 30 2 28 22 8 20 6 5 27 24 14 10 7 13 26 15 17 4 16 19
16 22 30 21 29 5 10 14 9 11 13 6 17 12 15 3 25 23 19 24 8 2 1 20 26 27 18 28 4 7
2 21 6 23 30 11 1 18 29 20 16 7 27 28 13 24 15 3 12 4 10 22 14 5 25 9 8 17 19 26
21 28 24 14 13 4 5 12 6 26 25 18 27 11 30 23 2 7 3 15 22 1 20 19 17 16 29 9 8 10
9 18 16 12 21 11 24 29 25 22 28 17 27 4 3 23 30 1 15 20 7 19 5 10 2 14 6 13 26 8
18 8 27 26 21 10 6 22 12 23 7 28 17 20 11 16 4 5 9 3 13 24 30 14 1 15 29 19 2 25
tai30_20_1
2006
10 22 28 6 9 24 11 12 4 17 2 20 25 14 18 19 16 29 3 26 23 30 7 21 1 27 15 5 13 8
6 11 23 26 19 15 27 2 18 13 10 30 16 14 17 5 22 12 9 3 25 21 7 8 1 24 4 28 20 29
7 10 2 21 5 27 13 6 12 9 3 17 22 30 18 14 16 8 25 23 1 26 28 24 20 4 19 29 15 11
7 9 10 18 14 22 16 2 30 19 12 13 8 1 4 29 5 3 21 6 24 28 15 20 26 27 25 17 11 23
16 15 23 11 2 14 20 13 8 6 5 10 29 27 17 3 30 4 1 9 22 12 25 21 24 19 26 28 7 18
12 23 13 1 24 3 2 18 6 16 17 27 19 15 5 22 20 30 26 10 4 25 14 21 28 7 9 8 29 11
12 5 25 18 23 21 22 2 20 30 13 10 6 19 1 15 9 29 4 16 3 26 8 11 14 24 17 28 27 7
22 21 9 20 18 2 27 12 23 6 19 17 4 26 5 25 30 3 1 8 15 29 10 13 24 28 7 14 11 16
5 3 20 15 4 10 28 2 14 16 23 6 12 22 17 29 7 8 1 27 25 11 21 26 30 18 13 19 9 24
19 16 18 12 10 2 23 14 27 29 15 28 30 5 20 22 26 1 7 25 24 21 8 11 13 4 6 17 3 9
9 23 6 14 17 12 26 27 8 11 15 7 19 22 10 13 25 1 2 24 20 5 16 28 4 3 21 29 30 18
25 19 13 29 15 27 5 23 4 24 12 16 17 9 8 30 14 11 20 3 22 28 6 7 1 21 26 18 2 10
8 22 2 23 26 10 6 17 5 12 28 21 7 13 14 1 16 20 15 30 3 24 25 18 29 11 27 9 4 19
2 6 26 18 13 4 20 5 17 19 1 23 10 12 27 7 22 15 8 11 28 29 16 24 9 25 30 14 3 21
24 9 15 27 25 13 2 17 18 29 16 3 4 6 12 21 1 23 8 11 7 20 26 30 22 14 19 5 10 28
2 15 13 16 5 27 18 6 7 1 10 11 28 22 24 17 14 8 29 20 30 3 25 4 19 12 9 21 23 26
30 22 7 21 5 25 18 27 10 16 6 19 15 17 20 29 28 9 12 11 3 26 1 14 8 13 2 24 4 23
21 20 17 19 18 7 9 16 14 8 6 3 15 28 25 5 23 2 12 22 10 26 24 1 11 4 13 29 27 30
26 23 16 29 25 28 17 3 6 18 30 22 20 15 13 4 2 14 7 21 9 12 8 24 27 5 19 1 11 10
18 13 16 27 17 22 9 6 2 14 5 10 1 12 7 28 8 24 15 4 11 25 20 23 21 3 30 29 19 26
tai30_20_3
1848
13 27 22 11 18 10 16 9 3 29 19 28 24 8 25 7 21 6 30 26 2 4 15 17 5 12 14 1 23 20
10 12 4 6 11 3 24 7 14 2 20 29 25 19 27 9 15 16 8 1 22 18 17 23 28 5 13 21 26 30
7 24 18 10 13 4 12 5 8 17 29 16 11 27 6 19 23 15 9 26 14 2 30 3 21 20 1 28 22 25
18 29 1 20 9 4 11 14 16 15 28 26 27 12 24 13 22 30 17 10 2 7 5 21 19 8 3 25 6 23
27 26 7 4 12 18 13 23 10 9 20 25 5 3 2 24 15 19 30 16 8 6 21 1 11 17 28 22 29 14
5 27 23 6 29 14 7 1 10 22 9 18 8 11 3 26 28 16 15 4 21 30 17 24 12 25 2 20 13 19
26 7 20 25 23 17 10 16 18 6 3 9 28 19 8 27 29 5 2 13 1 30 15 4 21 22 11 24 12 14
30 7 26 10 28 2 25 8 14 20 27 12 5 21 13 11 17 4 23 16 1 22 24 9 3 15 6 19 29 18
26 8 22 27 2 21 16 9 29 28 5 23 1 24 20 11 17 10 18 3 4 15 7 13 6 19 25 14 12 30
11 6 13 16 29 27 22 24 18 28 17 20 9 2 12 5 7 3 21 10 1 23 30 4 14 15 8 26 19 25
5 13 1 10 26 27 8 23 18 7 16 4 14 30 24 15 25 22 28 20 9 19 6 11 12 2 3 21 17 29
29 14 4 12 3 16 6 27 18 25 24 28 5 21 13 30 8 19 15 26 17 2 10 11 7 1 9 20 23 22
17 7 29 2 27 3 10 1 23 14 12 8 11 13 28 19 16 9 4 24 21 5 15 25 26 18 22 20 30 6
24 8 5 7 20 11 22 17 29 27 10 6 26 16 23 9 18 4 14 28 3 12 13 21 25 15 19 1 30 2
23 7 12 8 3 1 25 27 17 16 9 14 2 28 18 11 10 6 21 4 26 24 5 13 30 15 20 22 29 19
22 4 18 29 5 7 26 25 27 9 23 14 28 10 16 3 2 1 13 15 6 19 24 21 12 17 20 30 8 11
30 6 23 7 29 8 17 5 11 25 18 27 20 12 9 22 4 10 14 24 19 3 26 21 2 1 28 16 13 15
17 23 14 1 24 10 29 4 2 9 19 18 5 7 13 30 16 25 3 20 6 22 12 15 21 26 27 8 28 11
30 3 17 28 27 20 26 5 21 23 1 10 18 24 19 16 4 7 14 9 12 11 6 25 8 29 13 22 15 2
24 10 23 20 29 5 15 8 2 28 26 16 17 27 11 18 25 6 7 14 9 3 13 21 19 30 22 4 1 12
tai30_20_6
2008
30 7 15 19 12 20 14 24 9 18 29 23 13 22 28 2 25 16 6 17 5 8 21 1 10 26 11 4 27 3
11 15 23 16 27 26 28 19 4 5 12 1 24 14 8 7 13 25 3 2 22 29 18 6 20 10 21 30 17 9
27 12 14 18 22 5 17 20 25 11 15 4 16 28 19 7 29 24 30 13 23 10 9 26 21 8 1 3 2 6
5 20 8 16 27 18 13 30 19 4 10 14 24 12 3 28 21 9 7 6 2 17 23 1 25 15 11 29 26 22
19 23 18 8 16 30 14 27 12 26 22 7 5 24 4 9 15 25 10 17 21 29 28 13 11 3 2 1 6 20
18 15 7 8 16 19 24 9 13 12 20 29 23 2 10 27 25 5 14 22 3 17 30 21 11 1 26 4 6 28
13 24 29 14 19 20 26 27 6 11 7 28 8 25 15 9 2 3 23 17 12 10 30 5 4 16 18 22 1 21
30 15 12 19 1 16 18 26 6 22 11 14 8 7 20 27 29 3 17 24 5 10 21 28 2 9 13 25 23 4
27 30 19 7 26 15 5 9 23 12 2 13 28 14 25 10 18 20 29 24 6 1 16 22 8 21 3 4 11 17
15 10 19 7 26 25 4 22 6 30 13 27 20 8 24 29 14 9 28 3 18 12 16 5 17 23 11 1 2 21
7 2 16 20 18 1 5 11 9 24 14 26 19 3 15 4 23 8 12 29 27 28 17 21 6 10 30 22 13 25
12 16 24 15 6 25 27 13 1 4 9 2 11 18 8 19 5 30 17 28 22 21 23 26 3 14 7 10 20 29
23 9 1 8 14 7 19 10 15 27 26 20 17 13 28 5 25 30 18 12 11 6 4 21 3 29 22 24 16 2
24 19 21 4 25 16 7 8 13 20 27 28 29 10 11 9 26 15 17 6 12 5 22 2 30 23 18 3 1 14
16 29 20 25 8 12 27 1 4 18 23 13 11 7 24 17 6 19 15 9 30 3 21 26 10 5 2 14 28 22
7 3 27 10 18 12 1 8 16 11 19 21 5 15 23 2 25 6 24 30 28 17 22 14 26 9 29 13 20 4
20 21 24 26 14 19 29 27 2 8 10 7 9 12 18 6 17 3 5 11 23 28 22 15 16 4 25 30 13 1
29 21 12 24 19 22 14 28 27 1 7 11 16 9 25 18 8 17 23 26 10 2 30 5 3 4 6 20 13 15
23 26 11 7 4 30 29 6 8 27 14 24 19 22 10 15 13 16 25 20 1 2 28 3 17 12 18 21 5 9
8 12 27 30 1 7 6 11 28 9 24 23 18 4 3 19 15 29 10 2 13 22 17 16 20 14 25 26 5 21
tai30_20_7
1897
16 24 20 12 9 27 26 2 29 5 15 3 25 8 19 17 21 13 14 30 4 1 22 11 10 28 7 18 6 23
17 18 8 29 9 19 24 27 4 2 15 16 3 26 1 7 5 28 11 30 13 14 23 12 20 21 10 25 22 6
4 21 7 29 9 28 24 19 3 5 23 17 10 15 27 22 2 13 1 12 20 25 8 26 6 11 30 18 14 16
13 18 29 16 14 12 25 3 30 19 5 10 9 8 27 11 17 2 26 6 21 15 23 22 1 7 4 28 24 20
24 28 15 16 13 7 2 19 27 9 8 5 22 12 26 4 29 21 6 3 17 14 25 18 23 11 10 1 30 20
14 6 23 29 25 8 20 13 17 19 12 2 24 4 7 27 26 16 30 9 10 3 21 22 18 5 1 15 11 28
29 25 10 14 8 4 6 13 22 9 7 19 21 5 2 11 30 18 20 24 1 26 23 17 3 28 16 12 15 27
15 8 19 13 18 21 28 1 11 16 14 17 7 25 12 24 22 30 5 27 6 20 10 3 4 2 26 23 9 29
22 5 7 19 2 15 13 24 16 27 8 6 14 25 10 18 1 12 9 29 4 17 28 21 23 26 3 20 30 11
22 26 20 21 19 7 29 6 16 13 5 3 4 11 8 18 25 28 30 9 10 15 23 17 14 27 12 2 24 1
30 19 3 15 24 25 5 14 16 6 12 8 11 17 29 10 2 13 1 28 26 23 4 18 20 22 7 21 9 27
19 1 17 30 15 16 11 12 25 3 26 4 10 2 7 5 8 20 9 29 6 13 27 28 23 21 22 24 14 18
11 14 9 18 19 8 15 4 29 1 13 17 2 3 5 6 26 30 21 27 20 22 16 10 25 24 28 7 23 12
21 20 15 28 10 16 6 14 4 13 3 24 19 2 29 12 7 8 18 5 17 1 23 26 30 22 27 25 9 11
21 14 3 16 4 29 9 26 8 20 10 24 22 5 11 6 13 30 7 12 27 1 15 2 18 23 17 19 28 25
4 19 16 18 28 12 13 15 20 29 8 21 27 14 6 25 5 24 2 22 10 30 11 26 1 23 17 3 9 7
22 8 21 1 15 27 5 10 6 9 23 16 4 19 29 18 24 3 28 2 20 17 25 14 12 26 7 30 13 11
22 16 5 27 28 10 29 4 17 30 2 11 13 19 20 15 14 9 21 8 26 24 25 12 6 3 7 1 18 23
26 11 29 12 15 27 17 24 10 21 8 22 3 14 13 4 16 19 1 2 30 6 7 5 28 18 23 25 20 9
17 3 1 7 19 4 29 21 2 10 5 6 15 23 22 9 24 26 11 27 12 18 8 13 25 30 20 16 14 28
tai30_20_8
1945
25 14 23 19 3 17 16 10 12 5 13 6 26 30 9 18 15 22 8 1 28 21 4 20 11 24 7 29 2 27
29 27 17 15 9 25 5 23 24 3 6 13 10 11 8 21 28 20 14 19 4 18 30 22 1 2 12 16 7 26
14 11 2 13 6 24 30 8 7 28 25 20 4 27 23 16 9 26 22 1 3 15 18 29 12 21 19 17 5 10
18 10 5 17 28 14 9 6 3 26 21 16 13 15 4 8 29 7 19 25 22 20 11 30 2 24 1 27 12 23
9 17 26 25 29 11 2 5 16 28 20 19 13 8 6 24 14 10 4 30 21 22 3 18 1 15 23 12 27 7
27 28 15 18 12 30 5 8 25 4 19 13 24 21 29 20 16 1 10 7 17 23 3 6 11 22 2 14 26 9
30 25 6 26 28 12 24 29 1 23 21 10 18 14 9 22 11 7 19 3 4 27 13 5 16 20 2 8 17 15
23 13 5 7 20 12 11 3 27 29 18 25 30 24 14 19 28 22 15 17 4 10 21 8 2 26 1 9 6 16
5 29 14 6 28 25 10 30 21 8 18 9 26 11 19 4 15 24 22 1 7 17 12 3 20 23 16 27 2 13
4 8 26 23 12 5 6 27 10 15 25 9 30 24 21 20 13 7 19 28 1 3 17 22 18 2 14 29 16 11
17 27 22 24 14 13 4 10 29 21 8 5 30 26 23 19 28 18 6 15 9 11 1 25 16 20 12 3 7 2
12 2 19 26 18 27 9 23 20 5 13 25 8 4 29 15 30 10 14 6 1 24 28 21 7 11 16 22 17 3
25 13 24 7 18 2 5 19 3 14 27 4 16 6 26 9 10 15 17 29 20 23 28 30 1 8 22 21 11 12
12 13 2 30 18 3 6 14 5 27 29 8 7 28 24 19 26 25 10 1 20 15 4 21 17 9 11 23 16 22
19 10 23 29 3 27 15 5 13 6 4 30 28 14 20 16 8 11 2 18 22 25 21 17 7 24 9 1 12 26
24 11 18 10 9 28 29 5 13 25 16 21 6 20 27 30 3 1 26 23 7 14 12 19 17 8 15 4 2 22
9 13 18 24 3 7 16 11 27 12 2 5 28 14 10 20 19 29 25 6 8 21 26 15 22 30 1 4 17 23
16 22 10 12 17 14 5 30 25 13 24 27 29 18 9 8 21 2 23 6 1 7 11 15 26 19 3 28 20 4
24 29 26 3 14 30 2 27 10 18 4 19 21 6 13 11 9 7 28 25 16 23 12 8 22 15 1 5 20 17
14 13 26 18 28 30 10 3 6 20 5 8 11 2 22 21 4 24 23 17 15 1 9 12 25 16 7 19 29 27
tai30_20_9
1966
20 7 28 15 26 16 22 9 29 21 24 25 30 12 4 5 1 17 19 8 11 10 27 2 3 6 13 18 23 14
16 6 12 2 29 30 19 8 7 4 15 27 20 9 21 3 24 1 22 23 18 26 5 13 11 10 25 14 28 17
12 6 2 9 24 17 15 11 23 22 8 13 4 3 14 19 10 1 29 20 5 7 27 30 26 18 21 25 28 16
11 14 12 4 19 30 9 23 20 21 29 1 17 24 15 27 26 2 28 25 8 3 5 16 10 18 13 22 7 6
12 23 21 11 6 27 19 25 17 14 20 24 9 5 3 8 18 28 15 1 22 10 4 13 29 26 2 16 30 7
5 1 26 20 21 17 8 24 28 29 3 23 11 27 14 22 4 9 25 13 19 30 6 7 18 2 15 16 10 12
21 22 25 3 28 24 6 11 12 23 2 9 20 19 4 10 18 15 30 7 5 13 17 26 1 14 16 8 29 27
6 28 15 16 18 30 24 12 10 9 8 25 11 17 20 2 1 19 13 29 3 4 22 26 14 7 21 5 27 23
1 22 23 24 21 9 10 19 12 26 17 14 4 3 8 7 2 27 30 15 6 20 11 18 28 29 16 25 13 5
3 6 10 29 18 23 17 5 2 22 27 9 13 20 15 8 1 24 14 21 11 28 30 16 4 26 7 12 19 25
24 9 1 17 20 19 10 4 13 8 5 22 3 23 15 27 26 6 25 30 2 18 7 14 16 11 29 28 12 21
20 27 18 1 5 8 12 17 24 29 9 4 14 16 28 15 23 10 19 26 3 22 13 21 2 30 7 11 6 25
23 14 18 22 7 21 20 12 10 13 25 9 24 8 29 11 1 26 17 15 28 19 16 3 4 5 2 27 30 6
21 26 3 1 2 23 28 9 30 12 16 24 14 22 27 15 29 18 5 25 10 19 20 17 8 4 7 6 11 13
2 16 22 10 4 8 19 26 13 7 12 24 28 23 29 20 21 1 17 9 27 25 5 3 11 30 18 6 14 15
19 27 24 12 9 11 20 15 25 29 17 5 1 3 8 26 13 18 23 30 10 4 2 22 6 14 28 21 16 7
27 13 23 29 8 28 12 5 30 17 25 2 4 18 19 11 1 16 20 26 9 3 24 10 7 15 21 14 22 6
29 20 19 16 27 17 14 12 1 30 5 28 18 4 24 2 13 26 8 11 22 7 6 25 10 23 15 3 21 9
27 24 28 2 9 15 11 21 8 17 19 4 12 1 5 13 22 29 7 10 26 6 3 14 30 25 20 16 23 18
16 26 9 23 15 13 10 1 18 2 30 12 22 5 4 3 28 24 17 8 29 7 27 19 6 25 11 20 21 14
JPC - Jo鉶 Paulo Caldeira, private communication, 30.1.2003
Ta62, Makespan: 2869
7 121 8 142 45 886 17 326 25 487 14 266 46 908 5 87 13 246 11 209 19 366 40 785 50 988 12 229 38 747 27 526 16 309 39 775 26 514 35 687 29 572 2 28 4 73 49 973 32 628 47 935 10 194 37 735 28 549 34 671 44 870 6 112 42 832 33 655 18 359 48 954 15 294 9 175 36 716 21 419 43 857 31 618 1 17 22 437 41 819 24 477 20 398 30 599 3 60 23 460
50 981 42 822 38 741 17 323 16 301 14 263 26 502 29 562 48 943 34 662 5 85 12 224 47 926 3 43 10 181 28 544 15 283 11 210 32 623 21 410 19 367 25 490 20 388 23 445 49 970 31 610 40 788 39 777 45 894 13 250 2 31 9 170 6 110 36 713 4 77 18 357 1 12 46 918 30 594 43 856 41 818 22 433 35 696 24 473 7 137 37 738 44 876 27 540 33 660 8 159
5 81 31 601 17 322 39 763 38 742 15 281 47 923 2 23 46 905 21 405 27 522 37 727 50 985 7 122 48 945 16 305 33 647 4 64 26 510 23 444 3 46 29 567 30 585 36 706 24 465 6 107 18 349 40 787 42 826 35 690 45 893 22 424 44 869 25 494 8 151 9 171 20 395 43 855 41 817 49 976 10 199 12 235 28 552 34 677 32 639 11 217 13 256 19 380 14 279 1 20
45 882 46 902 11 202 41 803 13 243 39 766 25 485 37 726 48 944 40 783 47 928 10 183 27 524 14 268 6 105 16 308 7 125 44 867 15 289 4 71 21 415 30 589 43 850 33 653 3 52 23 451 42 829 5 94 50 996 36 712 26 519 29 577 49 975 18 358 38 757 17 340 19 377 8 156 34 676 9 176 22 435 31 617 2 40 24 475 35 700 32 640 1 19 28 558 12 240 20 400
29 561 26 501 12 222 32 622 13 244 33 645 16 303 39 769 1 4 44 865 9 163 17 330 45 890 7 123 41 810 5 90 35 686 10 186 20 390 4 69 14 272 8 145 50 992 49 972 21 416 24 466 27 529 46 915 40 793 19 373 37 736 18 356 23 453 38 756 2 35 36 715 47 938 42 834 22 432 3 58 30 596 48 956 15 296 31 619 11 216 34 679 43 860 6 120 25 500 28 560
35 681 49 961 20 383 24 462 19 364 2 25 45 888 5 86 21 408 37 729 41 808 40 784 12 227 44 866 10 184 13 248 1 5 31 609 34 667 4 68 48 948 17 336 16 310 26 515 14 273 3 50 28 545 42 827 43 851 33 654 50 995 8 150 39 780 38 754 29 578 27 532 25 496 9 174 18 360 32 637 46 920 6 116 47 940 23 457 22 438 7 140 30 600 15 300 36 720 11 220
42 821 20 381 13 242 39 764 34 661 6 101 2 24 45 887 29 564 47 927 14 267 43 845 50 987 26 509 5 89 31 608 17 333 8 144 25 491 41 812 37 733 9 168 4 72 23 447 33 652 10 192 21 417 46 914 16 315 22 425 38 753 18 354 40 794 3 55 48 951 32 632 11 214 19 375 28 551 27 533 35 694 30 595 24 472 49 977 12 237 7 138 36 718 1 18 44 874 15 299
43 841 47 921 5 82 14 262 33 642 2 22 50 982 11 204 21 404 26 504 3 42 41 805 30 583 39 771 25 488 31 607 20 386 34 665 37 731 17 332 16 307 49 969 9 166 15 288 29 569 32 625 7 126 8 146 46 912 23 449 28 546 36 711 18 353 22 426 42 831 45 896 40 796 38 755 4 78 10 198 19 376 1 14 35 695 27 537 6 118 12 239 24 479 44 877 48 960 13 260
18 341 23 442 42 823 46 903 17 325 12 223 31 604 44 864 21 407 27 523 9 162 45 889 36 704 37 730 29 565 33 649 39 773 30 584 4 67 41 811 2 26 11 213 49 971 35 688 1 8 16 312 5 93 26 517 40 790 10 193 3 53 43 853 15 291 32 631 47 936 6 113 22 430 24 469 38 758 50 997 7 134 48 955 19 378 28 553 25 497 34 678 8 157 14 278 13 258 20 399
39 761 30 581 45 883 47 922 33 644 46 904 16 302 50 983 14 265 36 703 17 327 49 965 20 384 26 507 9 164 15 285 4 65 29 566 21 411 18 346 3 48 10 187 40 786 43 849 41 814 2 29 8 147 19 371 22 423 38 752 1 9 32 630 27 530 12 230 24 467 34 672 31 611 42 833 35 693 23 454 6 115 13 252 11 215 44 872 28 554 7 139 37 740 48 959 25 499 5 100
17 321 14 261 19 361 49 962 21 401 20 382 4 61 3 41 29 563 26 505 11 207 37 728 24 463 8 143 25 489 33 648 6 104 7 124 43 848 38 748 15 286 47 932 18 347 50 991 9 167 1 7 35 689 46 911 34 668 13 249 39 778 48 949 16 314 30 591 40 791 28 548 10 195 22 428 2 34 12 232 32 633 45 897 27 534 5 98 31 616 36 717 41 820 23 459 42 840 44 879
41 801 46 901 25 481 44 862 39 765 18 342 42 824 31 603 47 924 21 406 38 744 26 506 11 208 12 225 49 966 20 385 13 247 43 846 16 306 27 525 10 185 19 368 17 334 1 6 30 586 23 446 29 571 3 49 33 651 32 626 40 789 50 994 34 669 9 169 6 109 48 950 5 95 36 714 22 429 15 293 2 36 4 79 8 155 7 133 24 474 35 698 37 739 45 900 28 559 14 280
23 441 12 221 40 781 1 2 31 602 38 743 21 403 26 503 43 842 47 925 4 62 18 344 34 663 50 986 39 772 49 967 17 331 11 211 48 947 14 270 29 568 2 27 41 813 20 392 45 892 27 528 36 710 7 129 15 290 35 691 42 830 46 916 10 197 13 251 8 153 19 374 37 737 33 656 24 471 32 636 3 59 6 117 30 598 28 555 9 178 25 498 5 99 22 439 16 319 44 880
2 21 48 941 28 543 11 205 50 984 39 770 33 646 47 930 12 228 20 387 4 66 22 422 37 732 19 369 25 492 17 338 30 588 6 108 7 127 41 815 8 148 29 574 26 518 45 895 3 54 18 355 1 10 21 418 43 854 14 277 5 96 16 317 31 612 32 634 40 798 34 675 46 919 10 200 27 536 38 760 35 697 23 456 49 978 15 297 13 253 42 838 24 478 36 719 44 878 9 180
5 83 36 702 33 643 45 885 37 724 13 245 44 863 46 906 19 365 41 807 17 329 21 409 47 931 35 685 39 774 3 47 24 464 26 513 14 271 18 348 30 587 27 527 29 573 10 191 20 393 4 74 16 313 42 828 28 547 32 629 23 452 49 974 40 795 25 495 48 952 7 132 34 673 2 37 31 614 38 759 1 15 15 295 50 999 22 436 12 238 43 859 6 119 11 218 8 158 9 179
36 701 37 722 21 402 15 282 25 483 39 767 49 964 38 745 18 345 3 44 5 88 46 910 48 946 43 847 33 650 11 212 17 335 6 106 19 370 20 391 16 311 47 934 7 128 30 590 14 274 2 30 44 868 4 76 41 816 22 427 10 196 1 11 9 172 40 797 12 233 34 674 32 635 26 520 29 579 50 998 45 899 27 538 35 699 13 254 23 458 28 556 42 839 31 620 24 480 8 160
45 881 44 861 28 541 37 721 32 621 8 141 49 963 40 782 39 768 25 486 11 206 16 304 17 328 12 226 47 929 41 809 36 705 14 269 15 287 21 413 5 91 38 750 10 190 26 516 18 352 23 450 4 75 19 372 34 670 29 576 35 692 46 917 3 56 1 13 9 173 6 114 20 396 31 615 2 38 7 136 33 657 30 597 42 837 43 858 24 476 48 957 50 1000 27 539 13 259 22 440
33 641 28 542 45 884 17 324 1 3 48 942 25 484 41 804 30 582 46 907 43 843 31 606 10 182 6 103 35 684 32 624 49 968 38 749 26 512 20 389 47 933 29 570 36 708 5 92 18 351 50 993 37 734 39 779 14 275 7 131 16 316 8 152 27 531 44 871 24 468 3 57 22 431 12 234 4 80 42 835 23 455 2 39 9 177 21 420 19 379 13 255 15 298 34 680 11 219 40 800
1 1 13 241 27 521 24 461 11 203 19 363 37 725 35 682 31 605 41 806 46 909 4 63 34 664 23 443 3 45 9 165 50 989 26 511 21 412 36 707 17 337 10 188 39 776 18 350 38 751 32 627 25 493 43 852 7 130 40 792 20 394 14 276 2 33 6 111 15 292 30 593 48 953 8 154 5 97 45 898 22 434 12 236 47 939 42 836 44 873 33 658 28 557 16 318 29 580 49 980
11 201 41 802 39 762 19 362 37 723 25 482 5 84 14 264 18 343 6 102 9 161 43 844 35 683 26 508 42 825 15 284 38 746 34 666 22 421 50 990 45 891 4 70 21 414 10 189 36 709 23 448 3 51 46 913 8 149 29 575 2 32 30 592 17 339 28 550 12 231 47 937 31 613 24 470 40 799 27 535 7 135 1 16 32 638 20 397 48 958 44 875 13 257 33 659 49 979 16 320
=========================================================================
S: R. Schilham (11.7.2000)
Personnal communication. (see below)
(abstract)
Suppose that we have a number of good solutions to a job shop scheduling
problem and are interested in finding a lower bound. We modify the shaving
algorithm, a lower bound technique dus to Martin and Shmoys, in order to take
advantage of the information contained in the solutions. Given these good
solutions, our approach is up to three times faster than Martin and Shmoys’
algorithm. In the worst case, our approach was only slightly slower.
In addition, we found new lower bounds to some open benchmark instances:
ta11 -> 1323 (it took 371160 seconds to prove that solutions of cost 1322
cannot exit)
ta12 -> 1351 (it took 145513 seconds to prove that solutions of cost 1350
cannot exit)
ta13 -> 1282 (it took 67181 seconds to prove that solutions of cost 1281
cannot exit)
ta15 -> 1304 (it took 30886 seconds to prove that solutions of cost 1303
cannot exit)
ta16 -> 1302 (it took 69338 seconds to prove that solutions of cost 1301
cannot exit)
ta17 -> 1462 (it took 14295 seconds to prove that solutions of cost 1461
cannot exit)
ta19 -> 1297 (it took 31054 seconds to prove that solutions of cost 1296
cannot exit)
ta20 -> 1318 (it took 282814 seconds to prove that solutions of cost 1317
cannot exit)
All experiments were carried out on a 333 MHz Pentium II. The reported running
times do not include the running times of the local search heuristic that
generated the local optima that were used.
=========================================================================
Few solutions by A. Henning (Personal communication 4.5.0)
In the solutions row i,column k gives the start time
of job i on machine k.
ta13, Makespan: 1349
546 1204 827 1085 942 1043 1060 311 244 248 640 159 56 500 1119
350 658 196 796 608 273 874 1271 945 1168 449 748 1263 666 810
359 1002 99 0 1032 141 102 507 1125 114 526 1164 199 467 605
1267 1125 975 1007 1327 74 1128 225 1094 0 279 1153 754 249 29
633 444 949 261 1117 801 406 988 345 668 1253 1162 975 532 886
1040 666 1253 382 763 886 852 1092 470 945 1189 532 597 530 844
241 418 102 733 258 445 245 594 796 497 854 35 477 798 937
458 322 1007 92 190 418 610 1318 321 879 720 246 0 569 1237
245 488 1186 1175 632 0 576 161 63 1069 797 1252 282 371 704
810 576 439 190 870 716 47 702 406 311 1039 942 658 969 808
66 1039 1279 1189 440 1103 0 1069 624 1059 1030 969 853 821 563
0 763 642 345 246 945 114 1277 525 862 1149 732 1130 1043 1204
1269 992 0 488 704 350 1174 868 1149 99 1105 843 372 734 501
1230 852 1070 522 356 658 472 35 440 594 97 0 1160 897 470
496 897 732 913 1245 1189 793 1201 248 658 361 795 454 321 999
721 913 526 1094 1175 1310 310 249 1043 449 401 289 992 1245 74
870 1128 617 647 561 477 808 97 11 156 924 310 384 60 733
282 159 778 467 1086 63 966 378 0 832 868 99 702 935 11
649 300 1218 832 956 1060 258 463 161 765 605 384 507 1130 597
152 19 922 591 72 372 704 514 853 1263 956 881 803 0 1036
ta16, Makespan: 1360
93 270 0 873 613 1160 506 687 360 437 1237 76 737 210 1028
626 402 1276 336 866 30 1070 799 171 265 1023 529 906 507 752
876 360 76 1085 706 28 435 880 143 500 1161 783 578 286 171
714 944 1167 786 687 1123 926 1297 475 1222 571 873 1261 879 1276
218 166 615 983 1060 381 1199 1245 0 855 752 93 833 527 693
870 841 1222 472 903 982 1183 876 1276 760 1070 0 1156 673 799
457 1118 1049 210 521 359 693 753 979 989 344 262 381 114 625
1226 870 261 412 789 0 112 187 109 1059 472 1028 1300 1133 971
750 1052 874 315 1126 964 379 246 71 109 748 476 0 615 1288
1107 978 854 1197 476 35 1248 918 685 782 650 401 878 874 269
434 108 247 400 412 457 494 315 798 97 0 1125 143 888 1092
314 548 783 654 1213 220 311 98 670 67 958 685 855 1023 426
1028 742 355 578 1275 774 944 1107 1141 654 834 884 507 421 1200
9 774 517 0 1202 1228 593 1034 437 172 884 1252 993 352 1125
197 1192 426 1161 737 120 0 533 286 1263 789 1331 672 236 358
411 621 1117 1248 511 1328 183 485 250 1167 683 657 1034 760 902
1353 200 143 740 1218 1060 838 1141 571 1036 1265 971 797 0 929
879 1263 658 963 262 197 314 34 989 876 379 220 1183 5 497
1197 485 200 670 982 979 753 401 886 0 247 344 1069 1226 577
533 657 964 1060 114 626 1315 511 779 902 1091 166 230 34 840
ta26, Makespan: 1647
845 1639 163 267 381 938 557 300 1153 224 116 1454 497 1314 616 629 1594 1056 414 1398
0 819 224 1457 1393 1288 408 540 315 1499 1230 242 727 1085 141 560 867 1493 793 1207
1130 496 805 1601 638 1331 1576 352 81 1252 917 1010 557 1402 738 903 1104 1216 685 1548
433 1438 959 1493 1327 1119 502 1292 1245 865 269 1181 1429 1191 1556 368 793 1396 783 1050
727 642 883 366 166 247 1482 1314 352 289 0 775 461 1300 510 1086 127 605 33 959
1329 524 429 0 1595 750 1621 876 840 121 621 155 105 679 340 1527 1133 929 1244 238
1052 867 0 1300 968 219 126 43 786 446 715 534 1563 1245 1407 1340 550 1615 965 165
1063 1242 1436 1327 1312 634 1226 441 715 1120 688 1001 148 1603 842 1219 1511 1010 548 594
662 965 728 544 247 289 1414 126 51 608 368 858 81 803 1050 1230 1130 1133 1318 1027
589 1168 481 657 446 141 881 560 970 393 163 318 1594 227 78 1226 1230 0 1100 1576
938 367 4 750 765 881 853 684 1368 164 1181 1104 1230 1548 272 727 1288 78 1025 1454
1429 166 414 461 96 1135 740 281 544 69 40 443 810 608 1181 433 678 848 300 0
97 289 1414 961 873 1453 1393 972 593 1008 1340 1436 367 477 1496 1318 169 379 1147 794
1527 1312 1596 1001 1052 1245 970 221 453 543 866 1191 281 358 1013 1429 848 512 1389 1235
1198 269 291 1086 289 6 341 589 1563 783 227 684 1477 865 429 997 1396 1354 738 1261
1411 727 616 280 0 1001 1242 805 1061 1331 452 915 638 62 605 1163 1436 1549 183 320
775 1085 361 845 1168 165 208 1508 0 911 541 1238 358 1003 623 51 67 1260 1462 127
1386 453 558 179 291 0 152 1167 381 1411 1081 68 139 750 805 917 997 496 512 40
1261 43 1026 1412 685 342 1109 0 1493 1573 70 1379 1329 575 183 1407 326 1429 116 699
169 1027 629 1207 481 1402 1078 728 1306 252 1272 1350 1462 915 1585 805 287 1499 1439 1119
ta38, Makespan: 1673 (optimum solution)
1570 203 63 911 603 1464 1211 1238 346 223 659 836 495 144 1422
183 1286 1657 79 423 1026 67 395 1492 1591 284 985 1550 343 498
709 1052 1418 1439 20 927 71 770 1273 1185 1412 630 292 838 814
605 805 987 1298 174 1089 1646 1523 1057 889 1125 116 1291 1575 302
0 292 1129 1392 398 95 1234 369 1555 1502 1654 174 1591 694 410
867 898 797 720 975 647 1502 1095 1183 1422 1572 566 1057 1275 1341
1630 1130 867 1251 1511 1113 626 689 1590 595 1320 408 1047 1510 1028
1083 1152 607 1370 57 700 763 889 370 1127 1198 278 818 1002 1570
1186 98 243 1660 836 515 1580 423 1300 762 620 1392 338 552 899
1273 1249 1218 1010 1460 1506 1050 672 508 1138 965 370 408 1338 1627
632 1043 226 158 1575 1219 493 342 1383 369 520 911 1442 1511 243
1223 211 1036 944 1331 336 447 1557 535 1270 711 1652 1129 428 1464
368 742 0 1050 1417 299 997 1160 143 336 1492 1246 513 203 1256
1397 1426 1268 835 237 427 1572 606 745 72 129 0 26 79 1529
343 390 1330 396 517 294 269 201 603 450 1010 26 138 129 688
95 489 395 669 1080 823 531 984 974 626 1418 1534 776 883 1163
898 315 962 498 625 1554 1381 1438 66 1537 1055 1113 1204 529 54
1624 669 1510 529 731 643 791 1080 930 1345 647 1173 1298 1429 995
106 328 1249 428 498 1130 1436 1307 975 526 868 733 248 411 618
259 0 489 1412 1057 1490 955 144 835 98 343 507 706 140 566
1426 1548 523 623 318 1309 880 966 1180 1030 866 1256 630 754 1237
1173 1565 495 285 899 1269 362 814 152 669 539 255 475 975 1038
1008 110 955 584 0 1040 180 1340 444 962 377 763 877 1177 1125
1332 396 700 362 1116 25 138 512 215 3 1260 709 72 0 786
1510 972 1642 0 1229 174 1123 278 679 1331 79 261 1345 764 112
514 711 1590 1509 777 1166 689 976 1442 836 1110 1309 606 1253 1152
430 1273 333 1238 678 552 1312 1222 1088 745 197 1608 955 766 866
1146 1534 1024 223 664 866 694 1586 285 140 1269 1470 1088 385 832
955 598 144 1590 1204 742 292 847 1550 1008 437 830 1389 1083 0
1124 531 708 1149 320 259 0 67 884 492 797 1026 201 608 938
Few solutions by A. Henning (H2)
The solutions describe the sequence of jobs on each machine. The first row
shows the schedule on the first machine, the second row the second machine
etc. Please note that the machine and job indexing starts from zero.
ta13, Makespan: 1342
11 10 1 6 19 8 17 4 0 2 7 14 18 15 9 5 16 3 13 12
19 17 4 6 18 7 1 8 9 5 12 11 13 14 15 10 2 3 16 0
1 6 2 12 9 15 16 11 4 14 19 0 3 17 8 13 7 18 5 10
4 2 7 9 5 12 11 19 13 16 6 1 17 18 8 14 3 0 15 10
19 11 6 7 1 10 13 12 16 8 5 9 4 0 18 2 14 15 3 17
8 17 1 3 2 12 16 19 6 7 4 9 13 5 11 0 14 18 10 15
9 10 11 6 2 4 18 15 13 8 19 7 14 5 1 16 12 0 3 17
16 15 8 3 0 13 18 19 2 12 9 6 17 4 10 14 5 11 1 7
17 16 8 0 4 18 14 7 9 5 13 11 10 19 6 12 1 15 3 2
3 16 0 2 12 9 4 15 6 14 13 18 8 11 5 10 17 7 1 19
1 3 13 15 0 14 18 2 8 12 7 6 19 10 4 17 11 5 16 9
6 17 0 16 13 15 7 18 5 12 11 19 1 14 10 9 4 8 3 2
0 7 16 8 12 2 6 18 14 5 9 19 10 4 3 17 15 11 13 1
19 16 3 4 0 8 14 5 12 2 7 1 10 6 13 9 11 18 17 15
17 15 3 12 13 18 4 10 8 2 9 1 5 16 6 14 19 0 11 7
ta15, Makespan: 1340
17 7 2 6 13 14 0 15 1 3 19 4 12 18 8 10 11 16 5 9
12 19 2 1 18 8 6 11 14 15 4 0 16 7 13 5 10 9 3 17
17 4 1 7 6 10 19 15 14 11 0 13 8 3 2 5 12 9 18 16
1 9 0 13 10 11 4 6 17 12 14 19 3 5 7 8 16 18 15 2
13 9 7 17 14 8 1 19 18 11 6 2 12 15 10 3 4 0 5 16
16 8 1 12 15 17 10 19 7 4 0 11 5 9 14 18 3 2 13 6
4 1 0 10 15 19 12 14 18 7 9 8 13 2 16 5 6 11 17 3
0 7 13 12 5 17 11 15 19 8 3 4 14 18 16 6 9 2 10 1
1 15 14 13 9 6 0 16 17 2 18 10 19 12 8 7 4 5 3 11
9 17 1 6 4 14 16 0 15 19 10 18 13 5 8 12 2 7 3 11
13 15 19 4 7 10 17 18 3 11 16 0 14 1 12 9 6 8 2 5
10 8 7 3 14 11 4 6 15 19 16 12 17 1 2 13 18 9 5 0
1 0 12 19 8 4 11 10 17 15 14 5 13 2 16 7 9 18 6 3
15 7 10 19 6 14 13 12 16 3 8 4 5 9 17 18 2 11 0 1
4 6 1 9 15 19 8 13 16 2 11 12 3 14 0 7 10 18 5 17
ta32, Makespan: 1796
0 18 10 11 12 3 22 24 16 4 27 13 1 6 28 19 26 15 5 29 17 8 14 2 23 20 9 25 7 21
15 25 10 4 3 23 2 17 18 6 7 14 26 0 20 11 29 1 27 9 24 22 28 21 12 16 19 13 5 8
26 15 24 0 14 6 4 27 16 11 18 28 12 2 13 22 3 21 10 17 19 7 9 23 1 29 8 5 20 25
18 14 4 26 6 27 7 11 2 1 20 9 28 29 3 24 17 5 25 8 12 21 10 23 19 22 13 15 0 16
27 9 19 5 28 3 6 14 18 0 4 7 11 15 2 12 16 13 1 26 22 25 24 10 21 8 29 20 17 23
18 10 13 19 6 4 9 15 5 28 14 7 24 16 2 0 26 11 3 29 23 22 21 12 8 25 27 17 20 1
9 29 15 22 8 10 14 18 19 0 16 21 2 27 4 13 3 28 17 20 7 25 24 11 5 23 1 26 12 6
7 4 15 19 22 1 18 3 29 14 13 23 25 26 6 12 10 27 11 9 28 21 2 5 16 8 17 20 0 24
13 6 22 25 17 4 0 15 21 16 29 18 27 26 23 12 1 28 19 24 3 9 8 14 2 20 11 5 10 7
14 28 17 6 15 7 18 23 12 27 13 22 24 21 19 16 0 9 20 11 5 10 4 3 29 2 8 1 26 25
19 8 0 2 14 18 13 15 26 20 5 11 17 22 7 29 16 4 25 1 28 21 3 24 27 10 23 9 12 6
22 29 19 5 12 10 16 14 2 15 11 18 0 6 20 27 4 26 3 9 17 1 13 7 28 24 25 21 8 23
18 11 2 6 28 3 0 4 10 21 23 26 12 13 1 22 9 7 15 14 29 19 8 20 24 27 5 25 16 17
0 13 3 18 11 16 10 2 26 24 4 21 6 22 29 1 12 28 20 23 8 9 14 27 7 25 5 17 19 15
27 26 3 2 7 8 21 13 6 5 15 18 20 0 29 25 1 9 22 11 4 14 24 12 23 28 16 17 10 19
ta41, Makespan: 2018
9 21 27 23 10 16 3 11 8 1 19 18 5 2 15 25 17 22 24 29 28 13 20 6 26 0 14 4 12 7
5 10 22 18 14 25 26 1 29 12 15 17 16 21 9 4 2 11 7 20 8 6 13 24 19 23 3 27 0 28
6 9 1 26 20 4 12 2 11 21 16 29 7 5 15 17 8 25 27 0 22 18 24 19 23 13 3 14 28 10
6 9 29 17 21 15 8 18 1 7 11 12 13 0 3 2 4 20 27 28 23 14 26 19 22 25 16 5 10 24
14 15 22 10 1 7 19 12 4 2 13 16 29 26 9 21 28 3 18 0 5 11 20 8 24 23 25 27 6 17
11 2 22 12 23 0 17 1 15 16 18 26 14 21 5 4 19 29 25 9 20 3 24 27 6 8 13 7 28 10
11 4 24 17 22 21 20 29 1 19 12 18 14 0 9 15 2 3 8 7 25 28 10 16 5 23 27 26 13 6
21 20 19 17 1 26 8 22 18 11 16 25 3 2 4 7 29 24 14 0 5 12 9 28 23 27 6 10 15 13
4 2 14 19 3 27 9 1 15 22 21 7 11 16 26 13 6 5 0 28 10 20 24 25 29 12 18 17 8 23
18 15 17 9 11 14 22 1 26 28 29 21 27 4 25 19 13 0 7 20 6 23 24 10 12 3 16 5 8 2
22 8 16 7 26 10 11 25 14 5 18 21 13 6 12 1 0 9 24 19 23 15 27 4 2 20 3 28 29 17
24 18 12 14 26 28 22 3 4 7 15 16 11 10 29 23 2 21 27 19 8 6 13 0 20 5 25 17 1 9
7 21 1 22 16 25 20 9 4 11 27 6 5 12 15 0 14 19 2 29 13 26 23 17 10 24 8 28 18 3
1 5 3 17 12 16 19 25 4 18 22 0 6 26 21 11 9 14 7 27 10 28 23 8 15 29 2 24 13 20
26 14 23 8 24 16 12 17 1 2 15 28 20 3 11 7 0 22 10 18 6 19 21 25 5 29 9 4 13 27
1 14 12 15 10 4 17 26 6 0 27 21 9 5 7 23 18 2 16 19 29 28 22 13 3 20 24 8 11 25
29 21 6 20 26 4 17 15 18 14 16 9 27 24 19 5 2 11 10 8 28 25 7 0 12 22 1 13 23 3
16 20 19 18 17 7 15 6 2 14 8 22 27 4 5 13 24 11 9 21 23 25 10 12 1 0 3 28 26 29
28 22 15 27 25 24 2 16 17 21 29 14 12 19 5 26 3 20 7 18 6 8 23 1 13 4 10 11 9 0
17 12 26 16 15 21 1 7 4 8 0 27 5 11 14 9 6 23 13 10 3 19 24 22 20 18 2 29 28 25
ta44, Makespan: 1989
6 29 0 19 11 4 12 10 27 18 13 20 5 2 22 26 16 23 14 21 3 17 24 25 1 7 8 28 15 9
22 9 3 4 17 20 18 1 2 13 5 26 14 29 8 19 0 23 16 28 7 21 6 10 24 11 27 12 15 25
4 11 22 27 0 25 3 19 13 9 8 17 12 29 1 21 2 10 24 20 18 26 5 23 14 6 28 7 16 15
12 4 15 18 23 13 5 22 19 9 21 0 1 25 29 7 3 2 26 6 14 24 10 28 17 16 11 27 20 8
8 18 21 29 23 20 1 28 0 14 10 25 16 12 5 26 13 9 22 19 17 11 4 24 3 6 7 27 2 15
0 12 13 11 17 21 9 8 5 29 22 16 10 4 18 23 6 26 25 27 19 14 1 7 15 3 2 28 24 20
5 18 24 0 13 29 8 22 27 14 4 19 10 9 26 3 16 25 15 6 1 28 11 7 12 20 21 17 2 23
23 5 10 1 20 9 24 27 18 19 8 22 2 15 16 12 21 0 26 11 29 14 7 25 4 13 6 17 28 3
18 22 7 23 21 24 5 19 9 1 2 12 13 14 16 3 8 20 6 29 28 15 26 10 17 0 4 11 27 25
7 23 24 2 15 13 8 10 9 11 12 21 4 0 17 19 14 6 27 29 5 3 25 26 1 18 20 16 28 22
14 27 19 7 6 0 21 3 1 24 22 13 18 10 5 16 23 4 9 29 20 17 28 26 8 12 15 11 25 2
28 23 18 26 10 29 11 1 5 12 24 6 22 19 13 25 4 15 20 14 17 2 7 9 27 3 16 8 21 0
9 13 18 5 22 12 0 21 19 29 27 17 10 14 26 1 8 16 2 28 6 15 11 4 25 24 3 20 7 23
11 4 3 26 16 13 12 22 7 1 28 29 0 17 20 2 19 21 5 23 14 8 10 18 6 27 25 9 24 15
11 18 21 22 5 19 20 12 26 27 24 1 4 13 6 2 23 17 9 10 25 15 28 7 3 29 8 14 0 16
28 13 2 10 0 17 18 4 6 14 11 26 7 5 12 20 9 19 21 8 25 22 23 16 27 1 3 29 24 15
21 0 13 24 19 25 26 1 11 12 7 20 2 8 15 4 17 5 27 29 10 6 3 14 28 16 18 9 22 23
9 5 10 13 21 20 1 28 24 19 11 18 22 2 6 14 25 26 4 29 17 0 12 8 23 15 7 3 27 16
29 13 16 2 28 5 23 4 22 7 20 17 27 8 24 21 14 11 25 0 18 15 9 12 19 6 26 1 3 10
28 24 4 29 3 5 0 19 8 2 27 14 17 12 21 1 20 9 18 22 13 10 11 25 6 15 16 23 26 7
ta46, Makespan: 2022
29 6 14 13 1 19 8 5 11 17 16 12 22 28 21 18 4 27 15 23 20 9 24 0 25 7 3 10 2 26
10 14 15 25 27 4 3 22 1 11 7 26 2 12 13 0 18 16 5 21 17 24 23 19 9 28 20 6 29 8
13 16 11 17 4 26 19 21 14 10 3 15 27 24 12 8 29 28 1 9 22 25 20 2 18 0 6 23 7 5
4 19 15 29 12 7 17 9 1 26 13 3 5 2 16 11 8 18 20 27 23 14 22 0 24 25 28 10 6 21
17 18 13 15 29 22 25 7 11 4 16 21 8 26 9 3 1 14 6 20 12 24 2 23 27 28 10 0 19 5
17 14 1 15 6 7 8 12 16 19 9 11 28 22 4 2 18 21 23 29 13 24 20 0 26 25 3 10 5 27
13 25 12 5 19 23 1 28 27 7 16 10 2 8 18 26 14 6 24 22 9 11 4 29 3 15 17 21 0 20
29 14 11 5 15 25 0 17 16 13 21 7 1 2 18 19 10 4 9 28 8 12 20 27 6 26 24 23 3 22
29 1 25 6 4 8 14 26 5 12 22 18 9 11 17 27 19 13 24 0 28 21 15 16 2 3 20 23 7 10
14 25 3 9 24 6 5 18 21 29 12 19 7 8 2 16 28 13 27 26 17 4 11 15 23 22 1 0 10 20
1 6 15 19 17 4 8 0 13 2 10 25 16 14 22 5 11 3 23 28 27 18 20 9 7 29 21 12 26 24
11 15 1 5 14 12 24 8 3 23 0 16 17 7 4 26 2 10 29 21 27 20 22 25 18 9 13 19 28 6
8 16 22 13 9 0 7 25 14 19 6 12 5 4 27 17 18 26 29 2 11 24 3 10 20 21 28 15 1 23
23 3 20 24 15 5 16 12 1 7 19 18 27 9 25 8 28 6 4 11 26 21 14 29 10 17 22 2 0 13
15 19 24 11 28 3 7 0 17 5 16 12 26 22 10 2 8 14 1 6 29 20 9 4 25 23 18 13 21 27
6 2 9 17 11 26 1 0 7 5 15 20 4 10 16 14 22 18 8 24 29 27 21 12 13 25 19 28 3 23
19 1 13 25 20 5 28 16 9 7 8 2 23 17 11 4 18 26 14 22 10 21 27 3 15 24 6 12 29 0
20 28 11 13 27 16 21 1 8 0 17 25 15 18 23 2 26 10 9 24 22 4 29 6 3 19 7 5 12 14
25 5 3 22 6 29 10 7 28 1 9 13 21 16 12 14 19 15 2 24 0 26 23 18 27 11 20 4 17 8
29 11 7 5 27 6 0 8 26 1 2 10 22 17 16 3 9 14 12 28 23 21 19 15 18 13 4 24 25 20
ta48, Makespan: 1956
24 13 22 2 18 15 8 4 9 11 5 21 25 16 12 14 0 27 28 20 29 17 23 7 19 3 10 6 26 1
14 28 8 24 26 4 22 23 2 19 5 20 10 12 27 16 7 13 21 9 0 1 3 17 18 11 15 25 29 6
13 10 1 7 19 12 23 5 27 24 22 6 29 21 8 3 0 15 26 28 25 2 14 20 4 11 17 16 18 9
9 4 17 27 13 8 16 20 2 5 15 25 14 21 19 28 6 3 7 24 1 12 23 10 26 18 0 11 29 22
8 19 24 1 28 16 10 4 27 15 25 23 12 5 7 13 20 21 18 3 0 29 9 2 14 22 11 26 17 6
14 27 7 26 11 3 17 4 19 24 29 20 0 23 12 15 6 28 18 21 16 2 5 22 1 25 10 9 8 13
0 24 27 5 29 20 25 23 11 28 21 22 8 13 9 6 10 2 17 4 26 3 18 15 1 19 12 14 7 16
19 12 22 4 11 2 6 10 28 21 24 26 23 13 27 17 29 14 16 20 1 18 25 3 7 5 0 9 8 15
4 28 20 24 27 13 5 8 9 21 7 10 29 25 0 14 17 23 3 6 16 18 11 2 19 22 15 26 12 1
3 7 11 25 4 22 5 14 8 19 24 26 20 9 23 27 6 0 28 21 29 2 1 12 16 18 13 17 15 10
16 3 21 23 26 13 20 12 28 9 22 7 4 27 8 25 5 0 29 14 10 15 18 17 24 19 11 2 6 1
1 11 19 8 17 26 22 18 25 4 24 12 28 14 7 13 3 0 23 27 5 20 29 21 6 9 15 10 16 2
24 12 23 1 6 4 2 13 17 8 15 5 28 3 18 25 26 14 16 27 19 21 22 20 0 9 7 10 11 29
11 1 12 2 29 17 5 13 4 28 27 23 6 7 26 19 0 25 24 20 14 18 8 16 3 9 10 22 15 21
18 9 14 2 28 22 19 26 4 12 5 27 13 3 1 15 29 10 21 7 20 23 17 24 6 16 25 8 11 0
23 8 9 10 17 19 27 28 4 20 24 12 15 5 0 2 26 25 22 29 6 11 13 16 21 1 14 7 18 3
8 12 15 23 2 6 17 1 10 19 27 26 4 13 11 28 20 24 21 25 5 9 7 18 14 0 3 16 22 29
15 11 21 13 9 4 1 24 23 8 28 12 20 29 26 22 16 0 7 5 17 25 6 14 10 2 19 18 27 3
23 28 2 25 1 13 26 20 8 29 3 5 9 10 17 27 12 6 18 15 21 24 22 11 14 7 0 4 19 16
13 27 12 19 17 1 2 21 9 25 5 4 29 20 10 23 7 22 28 16 3 14 0 8 11 15 24 6 26 18
ta49, Makespan: 1968
19 6 25 14 27 28 8 21 29 23 20 15 3 11 24 4 0 16 17 7 9 18 26 10 1 5 2 12 13 22
15 29 11 5 28 1 7 18 6 3 17 14 19 26 8 20 21 0 23 2 4 13 25 12 10 9 24 22 27 16
11 5 8 1 23 16 14 10 13 22 21 7 3 12 2 18 9 0 17 19 4 28 6 26 29 20 25 24 27 15
10 3 13 29 11 18 8 22 19 20 16 0 23 28 14 26 17 27 25 1 24 7 15 4 21 12 2 9 6 5
11 22 10 5 20 13 18 16 17 24 19 26 23 8 4 7 2 27 21 3 0 14 28 12 9 29 25 15 1 6
4 25 0 19 7 16 20 23 27 22 28 2 17 13 21 26 3 10 8 12 24 5 29 6 18 1 14 15 9 11
2 20 21 24 5 23 27 11 22 17 10 8 19 1 29 3 9 18 6 14 4 12 16 13 0 25 15 7 28 26
5 29 14 27 17 15 23 11 8 9 7 16 10 19 1 24 0 3 12 21 13 28 2 18 25 6 20 4 26 22
0 22 21 23 8 20 9 13 18 11 16 3 17 2 25 7 6 26 1 19 29 5 10 14 27 28 15 24 12 4
2 9 5 28 22 17 16 8 21 1 4 19 13 14 7 12 0 23 26 27 20 29 10 3 15 25 6 24 18 11
8 23 0 16 19 18 9 7 3 21 4 17 12 22 2 14 29 26 5 25 13 24 6 1 15 28 27 10 11 20
19 17 0 7 26 11 4 16 23 13 28 8 3 27 15 14 9 21 20 2 25 12 22 1 18 29 6 10 5 24
22 13 17 6 21 20 19 11 9 8 23 12 7 24 0 28 16 10 25 27 3 15 14 2 18 4 29 26 1 5
25 20 0 29 22 1 8 27 17 2 13 11 15 23 21 26 14 4 9 28 19 24 16 3 7 18 6 5 10 12
7 3 9 1 15 21 25 18 6 12 23 27 22 11 19 28 20 0 16 17 26 8 24 4 13 29 10 5 2 14
18 11 8 23 19 28 10 14 26 17 16 24 4 0 2 7 12 25 3 9 29 13 21 1 22 20 27 5 15 6
7 28 22 26 29 11 27 17 16 4 12 3 1 24 18 10 0 19 8 15 25 9 20 2 13 6 14 21 23 5
28 19 18 13 29 16 11 0 17 15 4 27 3 23 26 1 12 7 21 25 6 5 10 24 9 8 14 22 20 2
7 8 23 1 27 14 26 20 10 16 18 3 11 0 4 6 21 12 9 28 13 5 25 2 29 19 24 15 22 17
25 8 15 22 17 9 0 14 12 29 1 21 3 4 27 2 11 7 23 16 6 28 26 19 5 24 18 10 20 13
============================================================================
Few optimum solutions by Wolfgang Brinkkoetter
(Personal communication 27.1.1999),
In the solutions row i,column k gives the start time
of job i on machine k.
ta03, 1218 (Optimal Solution)
526 467 1002 301 920 1017 693 0 220 760 1005 82 373 470 588
880 171 507 431 670 688 342 1042 732 324 875 277 0 819 845
202 0 62 256 447 298 1041 771 376 109 623 1050 656 700 561
485 701 204 599 400 532 115 369 609 587 33 436 704 0 273
969 135 628 609 220 460 273 861 171 693 730 872 1105 787 230
760 373 237 1035 543 0 623 1125 1003 730 286 467 243 845 83
256 306 126 1148 1002 83 846 474 333 490 459 422 918 1110 369
1188 222 693 879 0 919 1050 105 531 225 197 781 1117 1105 743
82 1041 1143 703 1202 654 947 1064 882 242 373 69 834 907 0
78 470 755 82 1101 376 516 872 714 0 117 732 256 305 642
1071 225 109 373 619 710 670 69 907 848 1017 1163 306 1005 495
0 920 1101 800 911 242 431 556 78 241 507 636 198 1012 136
816 623 1005 507 688 792 612 1197 0 883 201 239 83 947 412
422 704 243 628 834 911 919 946 1111 1042 561 329 794 33 500
147 62 234 543 286 596 759 654 447 947 239 163 1037 135 1105
================================================
ta04, 1175 (Optimal Solution)
764 556 965 0 488 400 123 72 296 235 521 895 839 1020 204
274 45 801 507 981 353 925 1000 400 716 550 195 895 440 1091
494 748 1076 217 554 856 849 123 224 636 756 355 925 712 900
683 307 288 269 401 151 9 797 646 452 1025 84 550 235 723
1001 0 730 973 1058 558 550 638 601 712 1099 450 680 880 801
410 213 102 554 723 800 510 584 855 550 684 0 158 569 344
360 1058 1065 884 1020 1112 1076 217 671 800 862 336 418 973 0
903 850 670 1054 60 488 824 48 1137 1025 969 572 752 81 530
356 532 556 288 81 947 610 0 440 862 204 770 705 360 134
723 1135 0 135 636 235 199 885 1041 378 70 764 36 507 291
554 756 610 356 521 670 482 445 969 336 884 274 1063 1045 1159
31 170 322 1026 109 1042 746 684 886 296 624 510 997 584 1005
9 418 48 1001 31 900 0 1091 739 134 40 353 355 269 102
636 903 233 1137 395 0 400 308 399 554 135 854 804 142 1026
219 641 195 768 243 291 456 746 532 348 378 151 495 1063 257
================================================
ta05, 1224 (Optimal Solution)
366 40 994 591 136 656 684 1093 508 195 863 441 0 290 755
760 136 630 831 931 0 493 667 573 477 357 1055 531 409 258
873 970 835 423 603 682 336 486 781 744 469 994 1087 573 1036
76 419 171 899 1094 34 1050 19 267 84 0 666 969 156 539
537 224 667 752 1025 390 0 294 916 1084 1114 464 68 968 139
146 800 552 469 22 554 117 36 218 640 673 996 302 224 405
441 625 554 1042 1191 962 237 884 672 336 114 135 815 1052 1145
316 754 405 0 267 114 227 421 237 490 29 593 666 800 357
307 0 37 316 510 427 68 117 292 673 140 803 141 366 219
643 1142 1093 552 562 1015 446 41 835 900 787 863 40 703 493
1174 994 113 29 0 317 564 815 78 1135 632 900 754 142 111
703 1042 317 969 449 294 146 273 630 1119 753 541 227 477 1146
558 397 931 1052 863 744 423 234 142 836 850 1126 41 62 991
798 302 991 656 397 873 531 576 449 994 564 1216 273 885 1087
252 916 421 562 1046 234 634 140 846 591 306 728 1183 1210 1144
================================================
ta06, 1238 (Optimal Solution)
599 617 717 402 674 298 749 39 369 528 866 770 135 501 463
86 426 534 642 474 197 371 979 54 821 709 665 801 292 826
837 333 861 975 717 436 0 270 177 426 1108 906 512 1004 898
167 471 661 665 1108 838 487 333 555 718 1041 587 0 371 260
810 1157 110 632 534 685 979 922 0 361 258 217 206 1070 642
861 1001 1041 1159 1225 1064 177 743 86 436 1028 269 676 9 356
728 120 282 1064 30 1060 603 501 810 1018 929 1068 904 425 916
723 838 1130 475 284 794 558 1052 980 676 388 661 921 613 422
307 19 722 558 120 74 1054 0 270 363 631 975 426 806 194
1041 707 388 0 194 292 118 676 452 599 351 520 487 177 706
953 0 480 1066 421 750 714 474 1118 826 541 1138 638 676 490
0 921 1001 342 866 596 426 28 307 472 826 1039 743 183 80
254 770 983 785 632 919 826 1141 342 1060 187 709 367 528 156
362 674 206 698 9 118 63 831 46 282 1205 423 539 0 721
660 520 80 430 363 568 269 596 723 925 803 491 1018 1157 0
================================================
ta07, 1227 (Optimal Solution)
248 697 737 828 959 345 991 105 1051 385 534 346 86 34 879
380 110 0 1049 1104 527 1138 1015 214 661 884 641 717 294 216
0 208 803 81 345 493 527 282 440 1033 1131 1196 1007 917 469
62 649 1025 959 845 866 616 155 1121 28 719 38 234 697 493
630 1192 542 601 1138 194 744 1049 59 378 300 814 445 142 391
468 369 1159 508 792 268 409 450 601 168 661 1114 0 3 34
155 409 641 461 268 264 391 1131 508 0 1046 578 319 529 386
1051 28 300 899 570 883 183 478 952 110 250 661 3 778 168
534 282 934 1114 142 89 0 597 626 475 746 1053 120 835 419
803 507 778 244 440 346 1042 635 216 732 578 905 1097 763 1163
268 195 44 881 0 1026 660 952 898 534 381 744 840 1015 356
886 805 143 59 168 165 928 732 0 265 456 144 386 86 132
717 569 888 933 661 1133 840 0 739 959 649 1010 747 871 1053
1205 461 926 292 717 934 617 345 142 1131 794 214 542 888 1026
1112 1046 478 793 828 0 335 462 747 367 953 377 588 194 294
================================================
ta08, 1217 (Optimal Solution)
777 492 1061 38 354 966 121 204 696 818 653 1153 572 300 745
647 108 0 271 384 906 1139 838 513 944 730 982 40 250 583
254 1054 606 188 934 417 865 1030 85 475 329 675 1109 571 131
868 838 313 552 207 0 555 757 475 394 513 154 944 85 305
1163 329 212 490 476 85 889 988 425 1068 1190 493 1015 0 248
329 975 80 894 534 165 1047 701 174 622 209 28 1189 796 0
571 868 394 1074 1030 195 693 300 131 729 290 322 190 486 647
948 714 531 403 850 1047 490 49 758 0 552 1085 129 635 841
0 572 865 1068 77 475 766 675 935 986 1073 669 1212 908 871
944 253 966 1111 520 948 614 149 0 695 847 85 486 418 329
160 211 1169 1187 40 48 159 322 621 531 938 757 0 154 1003
505 766 1149 0 128 290 750 546 315 305 826 879 653 176 38
440 187 248 994 176 1085 988 643 152 910 0 1081 750 894 693
80 246 14 355 305 622 0 478 579 621 417 804 311 714 188
390 478 146 975 669 305 440 463 991 212 89 583 838 271 492
================================================
ta09, 1274 (Optimal Solution)
1020 954 409 42 343 787 574 779 885 514 567 186 652 134 806
88 492 1040 936 170 224 297 612 698 43 887 412 797 0 48
796 118 972 1175 717 932 985 1098 547 1056 593 984 891 465 315
1118 579 984 343 322 315 761 527 1040 817 415 641 952 674 265
734 103 603 819 444 517 134 1012 1168 655 1248 1098 213 118 88
921 864 798 1110 1049 1035 1056 690 786 44 550 123 991 559 413
891 391 1043 0 285 1001 723 42 168 322 672 81 516 1135 921
365 709 541 593 873 316 817 917 514 461 855 760 1146 224 103
501 641 341 221 709 717 1168 845 1100 952 1041 504 932 753 1231
618 377 940 430 517 391 877 1175 972 123 1100 231 746 311 18
504 285 108 1021 213 163 1110 787 593 1153 688 845 18 377 0
432 221 501 133 0 869 541 427 336 409 771 311 1026 50 1108
573 80 269 723 916 819 674 431 93 2 341 0 168 645 199
1174 0 885 415 80 188 224 963 798 430 461 336 1108 1012 1035
698 1020 224 622 369 1119 855 547 682 790 1163 722 444 149 746
================================================
Previous list :
tail01-05 1231 | 1244 | 1206-1218 | 1170-1175| 1210-1228
15 x 15 T T | V N | V B | V W | V W
tail06-10 1210-1240 | 1223-1228 | 1187-1217 | 1247-1274 | 1241
15 x 15 V W | V T | V B | V B | V B
tail11-15 1321-1371 | 1321-1367 | 1271-1350 | 1345 | 1293-1353
20 x 15 V P | V B | V B | V N | V B
tail16-20 1300-1370 | 1458-1478 | 1369-1409 | 1276-1343 | 1316-1353
20 x 15 V P | V B | V B | V W’ | V W
tail21-25 1539-1658 | 1511-1618 | 1472-1563 | 1594-1659 | 1496-1598
20 x 20 V W | V B | V W | V B | V T
tail26-30 1539-1655 | 1616-1697 | 1591-1615 | 1514-1629 | 1468-1612
20 x 20 V W | V W | V B | V N | V B
tail31-35 1764-1766 | 1774-1810 | 1778-1796 | 1828-1836 | 2007
30 x 15 T N | T B | V B | T B | V T
tail36-40 1819-1826 | 1771-1787 | 1673-1681 | 1795-1806 | 1631-1695
30 x 15 V B | T B | T B | V B | V B
tail41-45 1859-2026 | 1867-1974 | 1809-1886 | 1927-2021 | 1997-2021
30 x 20 V B | V B | V B | V B | V P
tail46-50 1940-2047 | 1789-1934 | 1912-1986 | 1905-2013 | 1807-1967
30 x 20 T P | V B | V B | V T | V B
tail51-55 2760 | 2756 | 2717 | 2839 | 2679
50 x 15 T T | T T | T T | T T | T N
tail56-60 2781 | 2943 | 2885 | 2655 | 2723
50 x 15 T T | T T | T T | T T | T T
tail61-65 2868 | 2869-2900 | 2755 | 2702 | 2725
50 x 20 T N | V B | T N | B N | T N
tail66-70 2845 | 2825-2826 | 2784 | 3071 | 2995
50 x 20 T N | V B | B N | T N | T N
tail71-75 5464 | 5181 | 5568 | 5339 | 5392
100 x 20 T T | T T | T T | T T | T T
tail76-80 5342 | 5436 | 5394 | 5358 | 5183
100 x 20 T T | T T | T T | T T | T N
For each instance the character T, N, B, W, W’, V or P refers to the first
person or group of persons who proved the lower bound (character on the
left) or found a solution with the given upper bound (character on the
right). T refers to the reference of Taillard, N to the reference of
Nowicki and Smutnicki, B to the reference of Balas and Vazacopoulos, W
and W’ to the reference of Wennink, and V to the reference of Vaessens
and P to the reference of PEZZELLA, FAGGIOLI, COACCI.
The lower bounds proved by Vaessens were obtained using the codes of the
edgefinder algorithm of Applegate and Cook; the upper bounds of Wennink
that are marked with W are obtained by a taboo search algorithm; the
upper bounds marked with W’ correspond to schedules that were obtained
by the taboo search algorithm of Wennink and already improved upon the
current best known value, but that were still further improved by
Vaessens using the shuffle algorithm of Applegate and Cook.
E. Taillard (1993),
Benchmarks for basic scheduling problems,
EJOR 64, 278-285.
E. Nowicki, C. Smutnicki (1993),
A fast taboo search algorithm for the job shop problem,
Preprinty nr 8/93,
Institute of Engineering Cybernetics, Technical University of Wroclaw,
Wroclaw, Poland.
E. Balas, A. Vazacopoulos (1994),
Guided local search with shifting bottleneck for job shop scheduling,
Management Science Research Report #MSRR-609,
Graduate School of Industrial Administration, Carnegie-Mellon University,
Pittsburgh, Pennsylvania.
M. Wennink (1995),
Personal communication.
R.J.M. Vaessens (1995),
Personal communication.
D. Applegate, W. Cook (1991),
A computational study of the job-shop scheduling problem,
ORSA J. Comput. 3, 149-156.
Ferdinando PEZZELLA, Enrico FAGGIOLI, Gianluca COACCI (1996).
Computer Science Dept.
University of Ancona
Italy
Personal communication.
================================================================================
Solutions found by PEZZELLA, FAGGIOLI, COACCI, where
the makespan and the schedule of each machine is given by a pair
[job, operation], e.g the pair [1, 4] stands for the 4th operation of the
1st job.
FILE: TA11
Makespan = 1371
Machine Sequence
Mch1 =
[13 1] [8 2] [2 2] [11 4] [7 6] [17 5] [14 6] [12 10] [3 4] [10 6] [5 11]
[6 6] [15 8] [1 9] [19 13] [9 12] [20 11] [16 14] [4 13] [18 14]
Mch2 =
[8 1] [10 1] [7 3] [11 3] [4 3] [5 3] [14 5] [2 6] [12 9] [13 10] [9 8]
[19 5] [17 7] [6 3] [1 4] [15 7] [20 8] [16 12] [3 14] [18 15]
Mch3 =
[12 1] [7 1] [19 2] [8 3] [18 3] [5 4] [16 6] [3 1] [9 7] [13 12]
[11 11] [14 10] [1 6] [2 12] [4 9] [15 11] [6 11] [17 15] [10 15] [20 14]
Mch4 =
[11 1] [19 1] [1 1] [17 1] [12 5] [14 2] [2 3] [10 3] [15 1] [4 5]
[13 8] [8 8] [3 2] [6 1] [16 11] [7 12] [18 8] [9 10] [5 13] [20 12]
Mch5 =
[9 1] [10 2] [8 4] [2 5] [14 4] [12 8] [16 7] [4 6] [11 9] [13 11]
[5 8] [7 11] [19 9] [3 8] [17 11] [1 7] [20 9] [15 12] [18 11] [6 15]
Mch6 =
[16 1] [20 3] [9 2] [2 1] [12 6] [15 4] [8 10] [14 9] [6 4] [5 10]
[19 8] [17 9] [3 7] [7 13] [11 13] [4 10] [10 11] [1 11] [18 12] [13 15]
Mch7 =
[20 4] [12 3] [16 3] [9 6] [13 9] [15 3] [7 8] [11 8] [18 6] [14 8]
[2 9] [19 6] [5 9] [6 5] [10 7] [8 11] [17 13] [1 13] [3 15] [4 14]
Mch8 =
[12 2] [13 2] [17 2] [8 5] [9 5] [7 7] [11 10] [2 10] [3 9] [1 8]
[6 8] [15 10] [14 13] [16 13] [18 10] [10 13] [19 15] [4 12] [5 15] [20 15]
Mch9 =
[4 1] [18 2] [12 4] [5 2] [13 4] [2 4] [7 5] [16 5] [11 6] [17 6]
[19 10] [6 7] [3 11] [10 10] [20 10] [14 14] [9 13] [8 14] [15 14] [1 15]
Mch10 =
[9 3] [20 6] [14 3] [11 5] [13 7] [16 8] [5 6] [12 11] [3 5] [15 6]
[4 8] [7 14] [19 11] [2 13] [18 9] [8 13] [17 14] [1 12] [10 14] [6 14]
Mch11 =
[18 1] [7 2] [11 2] [4 2] [20 5] [9 4] [17 3] [13 6] [10 4] [5 5]
[14 7] [12 12] [6 2] [1 5] [2 11] [3 10] [19 14] [15 13] [16 15] [8 15]
Mch12 =
[20 1] [1 2] [18 4] [8 7] [16 9] [13 13] [17 8] [12 14] [10 9] [7 15]
[11 14] [19 12] [3 12] [6 9] [4 11] [5 14] [2 15] [14 15] [9 15] [15 15]
Mch13 =
[14 1] [19 3] [7 4] [13 5] [16 4] [2 7] [8 9] [5 7] [9 9] [3 6]
[11 12] [17 12] [15 9] [12 15] [1 10] [10 12] [6 13] [18 13] [20 13] [4 15]
Mch14 =
[19 4] [4 4] [20 7] [8 6] [18 5] [16 10] [15 5] [7 10] [12 13] [13 14]
[10 8] [17 10] [5 12] [14 12] [9 11] [6 10] [2 14] [3 13] [11 15] [1 14]
Mch15 =
[20 2] [5 1] [16 2] [13 3] [1 3] [12 7] [17 4] [15 2] [11 7] [7 9]
[2 8] [10 5] [3 3] [4 7] [19 7] [18 7] [14 11] [8 12] [6 12] [9 14]
FILE: TA16
Makespan = 1370
Machine Sequence
Mch1 =
[14 2] [1 3] [15 3] [16 3] [6 7] [5 4] [12 5] [7 7] [11 9] [2 8] [20 6] [4 4] [9 10] [18 11] [3 12] [13 11] [10 13] [19 14] [8 14] [17 15]
Mch2 =
[11 3] [17 3] [5 3] [6 6] [1 5] [16 6] [2 5] [19 6] [3 6] [12 7] [13 6] [20 8] [14 8] [8 9] [15 13] [10 12] [4 9] [9 13] [7 15] [18 15]
Mch3 =
[1 1] [17 2] [3 2] [13 1] [19 2] [11 5] [8 5] [15 7] [18 9] [14 6] [5 7] [6 14] [10 8] [12 11] [9 11] [20 12] [7 14] [16 12] [4 11] [2 15]
Mch4 =
[14 1] [6 2] [7 2] [2 4] [9 5] [17 5] [11 7] [13 4] [8 6] [12 8] [19 8] [4 5] [15 12] [1 12] [5 12] [18 12] [20 13] [3 14] [10 14] [16 14]
Mch5 =
[10 4] [16 5] [18 5] [6 9] [20 2] [11 8] [7 8] [1 9] [4 3] [15 10] [8 8] [2 11] [3 10] [17 13] [19 12] [5 13] [14 13] [9 14] [12 15] [13 15]
Mch6 =
[2 1] [10 1] [3 1] [8 1] [15 2] [18 3] [12 3] [7 5] [6 10] [5 5] [11 10]
[13 7] [20 7] [17 11] [19 11] [9 12] [4 10] [1 14] [14 14] [16 15]
Mch7 =
[15 1] [16 1] [8 3] [12 4] [18 6] [9 6] [17 7] [1 8] [11 11] [3 7] [6 13]
[14 7] [19 9] [7 10] [13 10] [4 8] [5 14] [2 14] [20 15] [10 15]
Mch8 =
[18 2] [12 2] [9 4] [16 4] [6 8] [8 4] [11 6] [19 5] [15 8] [20 5] [1 10]
[2 10] [17 12] [10 11] [7 11] [3 13] [14 11] [13 12] [5 15] [4 15]
Mch9 =
[5 1] [9 2] [2 2] [8 2] [16 2] [3 3] [17 4] [15 5] [1 6] [4 1] [14 5] [10 6]
[12 9] [11 12] [20 9] [19 10] [7 12] [18 13] [13 13] [6 15]
Mch10 =
[12 1] [19 1] [11 2] [9 3] [6 4] [2 3] [14 3] [1 7] [13 5] [3 8] [17 10]
[18 10] [10 7] [5 11] [20 11] [7 13] [8 12] [15 14] [16 13] [4 12]
Mch11 =
[11 1] [10 5] [19 3] [7 4] [18 7] [6 11] [16 8] [4 2] [8 7] [9 9] [13 8]
[15 11] [5 9] [14 9] [17 14] [12 13] [2 13] [20 14] [1 15] [3 15]
Mch12 =
[6 1] [5 2] [1 2] [10 3] [18 4] [7 3] [19 4] [16 7] [20 3] [2 7] [9 7]
[17 9] [12 10] [13 9] [3 11] [4 6] [8 11] [11 15] [15 15] [14 15]
Mch13 =
[9 1] [11 4] [7 6] [17 6] [13 3] [20 4] [6 12] [15 9] [3 9] [1 11] [10 10]
[5 10] [2 12] [14 10] [12 12] [16 11] [19 13] [18 14] [4 13] [8 15]
Mch14 =
[17 1] [18 1] [6 3] [7 1] [1 4] [15 4] [20 1] [13 2] [2 6] [3 5] [14 4]
[5 6] [9 8] [10 9] [16 9] [11 13] [4 7] [8 13] [12 14] [19 15]
Mch15 =
[10 2] [6 5] [3 4] [15 6] [18 8] [12 6] [17 8] [19 7] [2 9] [5 8] [7 9]
[20 10] [16 10] [8 10] [1 13] [14 12] [11 14] [13 14] [4 14] [9 15]
FILE: TA45
Makespan = 2021
Machine Sequence
Mch1 =
[26 1] [12 3] [23 5] [18 3] [30 1] [27 5] [22 5] [14 4] [9 9] [2 6] [8 7]
[28 7] [29 13] [19 7] [16 10] [25 10] [20 5] [3 10] [11 12] [1 12] [24 16]
[13 17] [7 15] [10 16] [21 16] [5 17] [17 16] [15 17] [6 19] [4 20]
Mch2 =
[15 1] [20 1] [30 2] [29 6] [25 5] [22 7] [9 10] [28 5] [23 9] [1 5] [13 9]
[8 9] [27 10] [11 9] [12 15] [16 14] [26 12] [10 12] [6 9] [14 14] [19 13]
[17 13] [18 17] [21 17] [7 18] [5 18] [3 15] [24 19] [4 19] [2 20]
Mch3 =
[4 1] [3 3] [29 7] [9 8] [5 5] [2 7] [16 7] [11 6] [28 9] [15 6] [6 6] [7 9]
[18 12] [13 13] [8 14] [24 15] [12 16] [23 15] [19 14] [20 11] [27 15]
[26 18] [21 18] [22 18] [30 17] [17 19] [1 18] [25 20] [14 20] [10 20]
Mch4 =
[21 3] [12 4] [15 3] [17 5] [18 6] [27 7] [7 4] [22 8] [23 10] [24 10] [16 9]
[1 7] [8 10] [28 10] [29 17] [14 10] [4 11] [30 10] [13 15] [25 13] [19 12]
[5 13] [2 15] [10 17] [20 13] [11 18] [6 18] [26 20] [9 18] [3 20]
Mch5 =
[14 1] [5 1] [22 2] [3 4] [4 3] [6 1] [20 2] [21 5] [24 7] [27 9] [13 8]
[7 8] [29 14] [12 13] [18 10] [17 10] [23 14] [28 14] [9 11] [8 15] [10 13]
[25 14] [30 12] [19 15] [1 13] [11 16] [15 13] [26 19] [2 18] [16 20]
Mch6 =
[22 1] [29 2] [23 4] [9 4] [25 4] [14 3] [21 4] [26 6] [8 6] [17 6] [11 5]
[5 8] [15 7] [4 9] [30 7] [13 12] [1 10] [3 13] [28 17] [6 13] [10 15]
[27 14] [19 16] [24 17] [12 19] [7 19] [20 14] [16 18] [2 19] [18 19]
Mch7 =
[8 1] [18 2] [13 1] [25 3] [10 1] [27 4] [29 8] [6 2] [2 5] [7 5] [12 8]
[4 6] [17 7] [24 12] [30 8] [28 13] [5 10] [19 11] [26 14] [21 13] [14 16]
[22 16] [1 14] [23 19] [15 15] [9 16] [16 19] [3 18] [11 20] [20 20]
Mch8 =
[18 1] [16 3] [22 3] [23 6] [29 3] [24 5] [12 6] [28 3] [11 3] [19 5] [3 6]
[21 6] [10 7] [26 9] [6 7] [1 9] [5 9] [8 13] [2 10] [4 12] [30 11] [17 12]
[20 10] [25 15] [9 13] [7 17] [15 12] [27 16] [13 18] [14 19]
Mch9 =
[2 1] [25 1] [29 5] [22 4] [26 8] [18 8] [8 8] [12 10] [19 6] [4 8] [13 10]
[15 8] [28 11] [11 11] [10 11] [5 11] [21 12] [17 11] [20 8] [7 14] [27 13]
[6 14] [16 17] [23 18] [1 15] [14 18] [9 17] [24 20] [3 19] [30 20]
Mch10 =
[12 2] [8 2] [17 4] [19 2] [18 5] [5 4] [27 6] [13 5] [4 5] [1 4] [24 8]
[7 6] [25 9] [10 6] [29 16] [26 10] [16 13] [21 11] [6 8] [15 10] [14 13]
[2 13] [23 16] [11 15] [30 15] [9 15] [20 15] [22 19] [3 17] [28 20]
Mch11 =
[21 1] [9 1] [11 1] [29 4] [13 3] [4 4] [26 5] [16 6] [30 4] [24 9] [1 6]
[3 7] [12 12] [10 8] [28 12] [7 12] [14 12] [2 11] [22 15] [6 11] [5 16]
[17 14] [25 16] [19 17] [8 19] [27 17] [15 18] [23 20] [20 19] [18 20]
Mch12 =
[29 1] [1 1] [14 2] [5 2] [27 3] [7 3] [22 6] [11 2] [24 6] [10 2] [2 8]
[28 6] [12 9] [16 8] [18 9] [15 5] [21 7] [23 13] [20 4] [25 12] [19 10]
[26 13] [4 14] [8 18] [17 17] [3 16] [13 20] [30 19] [6 20] [9 20]
Mch13 =
[16 2] [27 1] [17 3] [15 2] [19 1] [26 3] [8 4] [29 10] [23 8] [5 6] [4 7]
[14 6] [3 8] [18 11] [12 14] [11 10] [25 11] [30 9] [7 10] [13 14] [28 15]
[20 7] [2 14] [6 12] [21 15] [9 14] [22 17] [24 18] [10 18] [1 20]
Mch14 =
[23 1] [28 2] [25 2] [16 5] [13 4] [12 7] [27 8] [29 12] [2 9] [17 9] [14 7]
[24 13] [19 8] [1 8] [3 9] [8 12] [18 13] [22 14] [7 13] [9 12] [20 9]
[5 14] [10 14] [11 14] [26 17] [6 16] [15 14] [4 18] [21 19] [30 18]
Mch15 =
[24 1] [23 2] [27 2] [7 2] [12 5] [3 5] [16 4] [9 7] [29 9] [19 4] [26 7]
[25 7] [13 7] [11 4] [22 10] [10 5] [28 8] [6 5] [30 6] [14 9] [8 11]
[21 10] [5 15] [17 15] [4 16] [2 17] [15 16] [18 18] [20 18] [1 19]
Mch16 =
[2 2] [24 4] [9 5] [14 5] [15 4] [28 4] [10 3] [7 7] [12 11] [11 8] [22 13]
[27 12] [21 9] [29 19] [1 11] [3 12] [5 12] [18 16] [6 10] [16 16] [8 16]
[26 16] [23 17] [25 17] [19 18] [4 17] [30 16] [13 19] [20 16] [17 18]
Mch17 =
[17 1] [24 2] [23 3] [21 2] [9 2] [13 2] [2 4] [26 4] [8 5] [18 7] [6 3]
[30 5] [22 11] [5 7] [29 15] [16 11] [10 9] [19 9] [14 11] [15 9] [20 6]
[4 13] [11 13] [7 16] [3 14] [25 19] [12 20] [1 17] [27 18] [28 19]
Mch18 =
[3 1] [4 2] [9 3] [8 3] [29 11] [25 8] [22 9] [10 4] [17 8] [23 12] [13 11]
[16 12] [24 14] [7 11] [18 14] [28 16] [15 11] [26 15] [12 18] [14 17]
[30 14] [2 16] [11 17] [6 17] [1 16] [19 20] [20 17] [27 19] [5 20] [21 20]
Mch19 =
[28 1] [3 2] [1 2] [2 3] [9 6] [5 3] [23 7] [20 3] [13 6] [6 4] [24 11]
[27 11] [4 10] [26 11] [16 15] [29 20] [18 15] [14 15] [21 14] [12 17]
[30 13] [8 17] [25 18] [19 19] [7 20] [11 19] [10 19] [22 20] [17 20] [15 20]
Mch20 =
[16 1] [12 1] [17 2] [24 3] [7 1] [26 2] [18 4] [19 3] [25 6] [30 3] [1 3]
[23 11] [11 7] [22 12] [14 8] [21 8] [29 18] [10 10] [3 11] [2 12] [13 16]
[4 15] [20 12] [6 15] [28 18] [5 19] [15 19] [8 20] [9 19] [27 20]
FILE: TA46
Makespan = 2047
Machine Sequence
Mch1 =
[30 4] [7 6] [15 6] [20 8] [14 7] [13 10] [23 9] [24 9] [28 9] [6 10]
[12 10] [9 7] [29 8] [17 12] [19 9] [22 7] [18 10] [2 9] [16 13] [21 9]
[25 12] [5 13] [26 15] [10 16] [1 12] [11 17] [8 18] [4 18] [3 20] [27 20]
Mch2 =
[11 1] [15 3] [28 2] [26 5] [23 4] [4 5] [5 5] [27 8] [16 7] [1 9] [13 12]
[24 12] [12 11] [14 13] [6 16] [19 11] [3 9] [7 17] [2 11] [20 16] [25 14]
[22 12] [29 16] [8 14] [10 18] [21 15] [18 17] [17 19] [30 19] [9 19]
Mch3 =
[27 1] [14 1] [12 3] [5 2] [22 1] [20 6] [18 3] [17 1] [28 6] [15 9] [11 6]
[4 8] [25 5] [30 10] [13 13] [23 14] [16 11] [29 11] [7 16] [24 15] [10 14]
[26 14] [9 15] [3 17] [21 12] [19 17] [1 14] [2 17] [6 19] [8 19]
Mch4 =
[5 1] [20 2] [30 6] [13 3] [27 6] [16 6] [18 6] [10 5] [4 9] [24 11]
[14 10] [28 12] [8 4] [6 14] [12 13] [3 7] [19 12] [17 16] [21 7] [15 19]
[23 17] [9 14] [2 13] [25 17] [1 15] [11 19] [29 19] [7 19] [26 20] [22 20]
Mch5 =
[19 1] [23 2] [18 2] [30 5] [14 3] [26 6] [16 5] [27 7] [5 6] [22 4] [12 8]
[7 12] [15 13] [24 10] [17 6] [4 10] [10 10] [8 5] [28 14] [9 9] [13 15]
[21 6] [25 10] [3 15] [29 15] [11 16] [2 16] [1 16] [6 20] [20 20]
Mch6 =
[18 1] [15 2] [7 3] [2 2] [16 3] [13 2] [9 2] [24 4] [20 7] [23 6] [10 4]
[19 4] [29 4] [17 3] [12 9] [5 7] [30 9] [8 2] [14 11] [27 14] [3 4] [25 6]
[22 6] [21 5] [11 13] [26 13] [4 12] [1 10] [28 19] [6 17]
Mch7 =
[13 1] [24 2] [14 2] [26 3] [20 5] [28 4] [29 3] [6 3] [11 5] [27 9] [7 11]
[19 6] [15 12] [2 6] [23 12] [17 9] [3 5] [25 7] [9 10] [30 16] [12 18]
[8 9] [10 15] [4 15] [16 18] [5 17] [18 19] [22 18] [1 19] [21 20]
Mch8 =
[30 2] [15 4] [12 6] [26 8] [1 6] [6 5] [22 5] [18 8] [19 7] [11 9] [14 9]
[16 9] [17 8] [20 12] [7 15] [3 6] [28 16] [29 12] [10 13] [13 16] [5 12]
[27 18] [21 10] [8 11] [2 14] [24 17] [9 17] [25 18] [23 20] [4 20]
Mch9 =
[30 3] [27 4] [26 4] [7 7] [5 4] [15 7] [13 9] [23 8] [2 4] [19 5] [28 8]
[9 5] [6 12] [10 8] [12 12] [14 14] [20 13] [25 9] [29 14] [18 13] [1 11]
[16 16] [22 13] [3 18] [21 16] [24 18] [4 16] [11 20] [17 20] [8 20]
Mch10 =
[15 1] [10 1] [26 1] [7 4] [4 2] [25 2] [19 2] [22 2] [13 7] [6 4] [30 8]
[20 11] [28 10] [27 15] [24 13] [14 15] [29 10] [3 8] [9 12] [17 17]
[12 19] [23 19] [8 12] [16 17] [18 16] [5 16] [11 18] [1 17] [2 19] [21 19]
Mch11 =
[7 2] [2 1] [16 4] [20 4] [5 3] [11 4] [1 4] [18 5] [9 4] [24 8] [15 11]
[14 8] [23 10] [3 3] [26 10] [28 13] [6 15] [17 14] [12 14] [4 11] [29 13]
[30 18] [21 11] [19 16] [10 17] [27 19] [8 16] [22 17] [13 19] [25 20]
Mch12 =
[12 1] [16 2] [24 3] [15 5] [13 4] [2 3] [6 2] [4 6] [25 4] [1 7] [27 10]
[9 6] [28 11] [30 12] [17 10] [11 11] [5 10] [23 15] [18 11] [21 8] [3 12]
[22 11] [26 16] [14 18] [8 13] [19 18] [20 19] [10 20] [29 20] [7 20]
Mch13 =
[23 1] [9 1] [10 3] [14 4] [1 2] [7 9] [13 8] [15 8] [17 2] [28 7] [20 10]
[27 12] [26 9] [30 11] [6 13] [5 9] [8 6] [19 10] [12 17] [11 14] [25 11]
[3 14] [4 13] [18 14] [21 13] [29 17] [22 16] [24 20] [16 20] [2 20]
Mch14 =
[24 1] [4 1] [21 2] [25 3] [19 3] [13 5] [28 5] [7 10] [20 9] [16 8] [6 7]
[10 6] [27 13] [17 4] [15 15] [29 7] [30 13] [26 11] [11 12] [9 11] [12 15]
[5 11] [8 8] [2 10] [22 10] [23 18] [14 20] [3 19] [18 18] [1 18]
Mch15 =
[16 1] [20 1] [25 1] [29 2] [4 3] [27 5] [12 5] [1 3] [13 6] [23 7] [18 7]
[6 8] [11 8] [7 14] [17 7] [8 3] [15 17] [24 16] [3 13] [30 17] [9 16]
[14 19] [21 14] [28 20] [26 19] [10 19] [2 18] [19 20] [5 19] [22 19]
Mch16 =
[7 1] [3 1] [10 2] [27 3] [18 4] [21 4] [1 5] [12 7] [11 7] [6 9] [15 14]
[23 11] [5 8] [16 10] [2 8] [28 15] [30 15] [8 7] [17 15] [14 17] [25 13]
[19 14] [13 17] [20 18] [22 14] [26 18] [29 18] [24 19] [9 18] [4 19]
Mch17 =
[20 3] [21 3] [26 7] [14 6] [24 6] [2 5] [29 6] [6 11] [10 9] [27 16]
[17 13] [15 18] [28 17] [12 16] [3 10] [23 16] [19 13] [9 13] [11 15]
[18 15] [5 14] [8 15] [22 15] [7 18] [4 17] [16 19] [25 19] [30 20]
[13 20] [1 20]
Mch18 =
[29 1] [21 1] [12 4] [28 3] [14 5] [24 5] [22 3] [1 8] [27 11] [7 13]
[19 8] [17 5] [23 13] [11 10] [9 8] [30 14] [10 12] [25 8] [16 12] [26 12]
[3 11] [18 12] [2 12] [20 17] [4 14] [5 15] [13 18] [6 18] [8 17] [15 20]
Mch19 =
[23 3] [26 2] [4 4] [11 3] [7 8] [30 7] [6 6] [29 5] [15 16] [14 12]
[13 14] [10 11] [24 14] [27 17] [22 8] [20 15] [8 10] [28 18] [3 16] [16 15]
[25 15] [1 13] [2 15] [17 18] [19 19] [21 18] [12 20] [5 20] [9 20] [18 20]
Mch20 =
[30 1] [12 2] [28 1] [27 2] [1 1] [7 5] [11 2] [6 1] [23 5] [9 3] [24 7]
[8 1] [15 10] [3 2] [4 7] [13 11] [10 7] [2 7] [17 11] [29 9] [18 9]
[20 14] [14 16] [22 9] [16 14] [19 15] [25 16] [26 17] [21 17] [5 18]
Private communication, 16.11.2005
the 14 solutions found by ChaoYong Zhang
The solutions describe the sequence of jobs on each machine. The first row
shows the schedule on the first machine, the second row the second machine
etc. Please note that the machine and job indexing starts from zero.
ta11.prb, Makespan: 1359
12 7 1 10 6 13 11 16 2 5 4 9 14 8 0 3 19 18 15 17
7 9 6 3 10 4 13 11 1 5 12 8 18 16 0 14 19 15 2 17
11 6 7 17 2 4 18 8 15 3 12 10 13 0 1 5 14 16 19 9
10 14 13 11 3 16 1 5 18 12 7 0 2 9 17 8 15 4 6 19
8 13 7 3 1 11 9 12 15 10 4 6 2 18 16 0 17 19 14 5
15 8 19 1 11 14 5 7 3 13 4 2 18 16 10 6 9 0 12 17
11 19 15 14 8 12 17 6 10 5 13 7 1 4 18 9 16 3 0 2
11 12 7 8 16 6 10 1 5 17 2 0 14 3 13 9 15 4 18 19
3 4 17 11 12 6 1 15 10 16 5 18 9 7 2 8 19 13 14 0
13 8 19 10 12 3 4 11 15 14 2 17 7 18 6 1 16 0 5 9
17 6 10 3 19 8 12 16 5 4 13 11 9 0 1 2 7 14 18 15
19 17 7 0 15 12 3 16 11 5 9 4 10 18 2 6 1 8 13 14
13 6 12 15 18 7 1 4 8 2 10 11 16 14 0 5 9 19 17 3
3 7 19 17 14 18 6 15 11 12 4 16 9 8 5 13 1 2 10 0
4 19 15 12 14 11 3 16 10 6 17 2 1 0 9 18 7 13 5 8
ta15.prb, Makespan: 1339
17 7 2 6 1 14 0 15 13 3 19 4 12 18 8 11 5 10 16 9
19 12 18 1 2 8 6 11 14 4 15 0 16 7 5 10 17 13 9 3
17 4 1 7 6 10 19 15 14 11 0 8 5 3 2 12 13 9 16 18
1 9 0 13 10 4 11 6 17 12 14 5 19 3 7 8 16 18 15 2
13 9 7 17 14 8 1 19 18 11 6 2 12 15 10 3 4 5 0 16
8 16 1 15 12 17 10 19 7 4 0 5 11 9 14 18 3 2 13 6
4 1 0 10 15 19 12 14 18 7 9 8 2 5 16 17 13 6 11 3
0 7 13 5 12 17 11 15 19 8 1 3 4 14 18 16 9 6 2 10
1 15 14 13 9 6 16 0 17 2 18 10 19 12 8 7 4 5 3 11
9 17 1 6 4 14 16 0 15 19 10 5 18 8 13 12 2 7 3 11
15 19 13 4 7 10 17 1 18 3 16 11 0 14 12 9 6 8 2 5
10 8 3 7 14 11 4 6 15 1 19 16 12 17 2 18 13 5 9 0
1 0 19 12 8 4 11 10 17 15 5 14 2 16 13 7 9 18 3 6
15 7 10 19 6 3 14 16 12 13 1 8 5 4 9 17 18 2 11 0
4 6 1 9 15 19 8 16 2 13 11 12 3 14 0 17 7 10 18 5
ta20.prb, Makespan: 1348
9 0 8 12 19 11 4 14 5 1 13 6 15 16 17 3 2 7 18 10
2 4 11 9 0 8 6 16 3 18 19 1 5 14 7 17 12 15 13 10
5 15 8 7 0 14 18 11 4 12 13 9 3 16 10 2 19 1 6 17
19 12 1 5 8 7 13 2 18 10 15 16 0 17 11 4 14 3 6 9
4 6 1 12 2 0 10 7 13 5 16 17 14 9 8 15 11 19 3 18
9 3 6 19 16 14 15 7 13 18 2 0 11 4 8 1 17 10 5 12
15 11 5 6 13 19 4 3 18 0 1 14 2 8 16 7 17 12 10 9
0 1 7 2 14 15 6 11 3 12 13 19 8 17 5 16 18 10 9 4
1 6 14 5 19 15 8 2 10 11 13 17 3 9 12 0 4 18 16 7
11 16 17 1 3 19 0 4 12 15 9 10 6 2 18 14 7 8 5 13
19 7 6 13 9 16 0 2 5 1 4 11 14 8 12 17 18 15 10 3
4 8 3 7 14 0 15 19 1 11 5 18 17 16 10 12 13 6 9 2
19 4 9 15 0 13 18 3 1 16 11 17 14 10 6 2 8 7 5 12
8 2 1 9 12 19 15 11 14 4 16 3 0 18 13 5 6 7 10 17
8 6 15 14 19 7 12 11 5 16 18 0 4 17 2 1 10 3 9 13
ta24.prb, Makespan: 1646
8 4 5 9 6 2 0 19 1 15 11 10 12 7 16 18 14 17 13 3
0 2 4 17 13 12 8 1 6 3 9 14 19 10 5 7 18 11 16 15
15 1 12 16 18 4 19 9 5 3 8 13 17 7 14 2 6 0 11 10
6 19 15 5 9 18 1 16 3 12 2 17 4 10 11 14 7 13 0 8
17 14 12 1 6 0 7 3 11 5 15 2 19 4 10 9 18 16 8 13
18 5 12 0 14 6 2 1 17 15 10 19 13 3 11 7 9 8 16 4
11 9 5 2 15 12 4 7 18 10 6 3 19 17 16 0 8 14 1 13
15 5 7 11 13 10 12 16 19 17 14 8 4 18 2 0 6 3 9 1
2 17 19 6 11 10 7 16 3 8 12 13 0 4 15 1 18 5 9 14
9 6 5 19 13 10 16 2 3 15 12 17 8 7 11 1 4 0 18 14
17 4 10 14 18 12 0 6 13 19 7 15 2 11 1 8 16 3 5 9
6 13 8 19 4 7 12 17 14 16 11 18 2 15 9 5 3 0 1 10
4 10 12 17 9 19 13 15 7 2 18 5 8 6 3 11 14 0 16 1
18 19 7 6 2 4 9 1 15 17 0 8 13 16 5 3 14 12 10 11
13 18 15 1 2 5 4 19 11 17 0 6 14 8 3 10 9 16 7 12
4 18 0 16 17 2 14 10 19 6 8 13 7 15 1 3 9 12 5 11
2 12 7 10 6 0 19 5 14 4 16 1 9 15 18 13 3 8 11 17
6 12 7 18 19 17 11 4 1 16 9 13 10 15 14 2 8 5 3 0
0 15 19 18 2 11 17 12 14 6 10 16 8 1 3 7 9 5 4 13
3 12 4 14 0 18 6 2 17 19 13 5 16 11 9 15 1 10 7 8
ta28.prb, Makespan: 1603
14 5 15 10 8 18 16 7 1 4 9 6 0 19 2 13 17 12 3 11
7 13 10 12 18 1 2 5 8 3 16 14 19 11 17 6 9 0 15 4
13 19 8 11 7 16 14 6 17 18 4 1 12 9 5 0 15 2 3 10
1 14 2 4 11 17 5 12 8 19 3 18 15 0 6 9 10 7 16 13
1 3 2 16 15 18 17 8 0 19 13 14 6 9 12 11 4 7 5 10
5 13 3 2 6 15 0 4 18 1 8 19 14 9 7 16 12 17 11 10
19 1 12 6 17 3 10 5 16 9 7 18 2 14 4 11 13 15 8 0
8 15 2 0 5 16 18 9 19 4 17 7 3 6 10 1 11 13 14 12
15 16 2 14 4 6 13 5 8 18 1 17 19 0 10 9 12 3 7 11
18 17 9 19 10 14 0 16 11 7 1 3 2 15 5 8 4 13 6 12
1 8 13 15 4 18 16 11 9 14 2 12 7 3 6 5 0 19 10 17
7 16 8 19 1 12 13 10 9 2 11 18 4 15 0 3 5 6 17 14
15 9 18 16 13 4 5 0 6 2 17 19 8 12 3 1 14 11 10 7
3 2 15 8 7 1 13 5 16 12 11 4 18 9 14 10 0 19 17 6
14 9 6 18 13 4 1 12 19 7 2 17 0 3 10 5 16 15 11 8
9 7 11 2 1 4 16 18 10 15 5 19 6 12 17 13 3 14 0 8
2 1 7 8 18 17 9 4 6 15 11 5 10 13 19 16 14 12 0 3
8 6 4 19 0 5 18 13 2 12 9 1 10 11 14 17 7 3 16 15
1 9 3 18 6 2 10 7 19 15 13 0 4 8 17 12 5 14 11 16
13 16 5 9 2 12 19 11 10 1 8 18 3 4 14 17 15 6 0 7
ta32.prb, Makespan: 1795
0 18 10 1 22 11 16 12 3 27 13 28 6 24 19 26 4 5 15 17 9 8 29 20 23 7 25 2 14 21
15 25 10 2 3 23 4 18 1 6 17 20 26 0 16 9 11 7 22 27 28 24 29 14 19 21 12 13 5 8
26 15 24 0 16 6 27 28 11 18 2 22 13 1 4 3 14 10 17 12 21 19 7 9 23 5 8 29 20 25
18 26 1 9 6 27 2 11 20 28 4 14 7 3 17 24 5 29 25 8 19 10 21 23 15 12 13 0 16 22
27 9 28 19 5 18 6 3 0 1 16 2 11 15 13 7 22 4 26 14 12 25 24 10 21 8 29 20 17 23
18 13 19 10 6 9 15 28 16 5 4 2 0 26 24 11 22 7 8 3 29 14 23 21 12 25 17 27 20 1
9 29 15 22 8 18 10 16 19 0 2 21 27 13 1 28 3 14 17 4 7 25 24 5 20 11 23 26 6 12
1 15 7 19 22 18 4 29 25 13 3 10 26 6 9 16 23 27 28 12 11 14 5 21 2 17 8 24 20 0
13 6 22 25 17 0 1 16 21 15 27 29 4 18 28 26 19 9 3 24 23 12 8 2 20 14 11 5 10 7
28 14 17 6 18 22 15 27 13 16 23 12 9 7 19 20 24 21 0 10 5 11 3 1 4 8 29 26 2 25
19 8 0 2 18 13 20 26 15 22 1 16 11 17 5 14 25 28 7 29 3 4 21 24 9 10 23 27 6 12
29 19 22 16 5 10 12 2 20 15 11 1 0 6 18 9 27 13 26 3 14 17 28 4 7 24 25 21 8 23
18 2 28 11 6 0 1 3 21 10 9 22 26 23 13 12 4 16 15 19 20 8 7 24 5 29 14 25 27 17
0 16 13 18 3 11 26 2 1 10 22 6 21 24 20 28 8 9 4 29 27 12 23 7 14 25 5 17 19 15
27 26 2 3 8 21 13 1 18 6 20 7 9 15 0 5 25 22 29 16 11 24 4 23 14 28 12 17 10 19
ta33.prb, Makespan: 1791
9 2 27 17 14 26 10 12 25 18 21 22 23 8 0 4 3 13 20 1 7 5 16 11 28 15 29 6 19 24
20 23 6 0 14 22 16 24 15 1 8 21 9 4 3 12 26 5 13 28 19 27 11 7 18 29 2 17 10 25
15 10 24 17 8 13 11 7 0 28 3 29 16 14 9 5 2 21 26 22 1 12 27 18 25 19 20 23 6 4
7 25 2 3 9 8 22 24 1 17 14 27 12 13 4 6 5 20 19 28 23 15 21 29 26 10 0 18 16 11
23 14 25 28 9 17 15 13 4 0 29 10 11 5 12 1 19 8 21 24 6 20 22 7 27 18 26 2 3 16
11 15 13 18 24 12 4 0 17 3 23 6 14 5 22 1 9 21 20 8 26 16 25 29 7 27 10 19 2 28
22 23 16 14 18 4 0 13 29 3 20 6 11 8 1 26 28 15 9 7 2 27 19 5 25 10 21 24 17 12
24 9 22 3 0 21 5 6 4 23 19 1 8 17 28 12 15 13 20 25 27 18 7 29 26 10 11 14 16 2
1 0 19 27 22 18 9 16 11 29 5 3 13 8 24 6 12 10 15 28 4 23 17 25 21 7 14 20 26 2
8 0 7 14 27 24 23 22 13 4 5 19 9 16 6 1 26 11 3 28 17 21 15 2 25 18 10 20 12 29
0 24 23 16 14 8 22 17 18 13 21 2 29 3 4 19 27 1 20 10 7 28 25 5 15 11 9 26 6 12
6 0 26 7 22 19 21 5 23 18 16 24 29 3 28 14 8 4 1 17 25 13 27 12 20 9 2 11 15 10
1 2 6 10 22 26 25 15 27 23 13 16 8 5 14 17 7 20 9 29 11 19 12 18 0 28 24 3 21 4
19 2 22 8 26 14 9 7 24 0 18 4 1 29 13 17 20 6 10 15 23 28 25 3 12 5 11 16 27 21
12 3 1 9 7 13 29 8 23 2 6 20 0 27 17 19 10 4 18 15 16 22 24 11 21 25 5 28 26 14
ta37.prb, Makespan: 1771
1 2 21 14 27 24 4 11 18 22 28 19 9 26 0 23 8 5 13 12 17 29 7 16 3 20 6 15 25 10
22 12 21 18 11 7 1 6 24 28 9 26 16 27 13 17 23 19 0 10 25 8 15 3 20 4 29 5 14 2
24 10 26 8 21 29 22 16 4 19 20 11 14 13 7 1 5 0 28 9 3 12 23 25 15 17 2 6 18 27
20 22 8 24 2 9 10 14 3 21 17 18 11 1 28 25 23 12 26 16 0 29 13 19 15 27 6 4 7 5
0 25 13 18 26 15 24 28 10 1 27 3 11 6 7 21 20 17 12 29 9 5 2 23 14 16 19 8 22 4
10 19 26 2 14 22 28 3 7 21 0 5 12 24 11 16 29 1 25 9 13 27 17 15 20 4 18 8 23 6
14 29 17 22 3 20 21 4 23 28 26 18 13 1 8 6 15 11 19 0 27 7 24 16 5 12 9 25 10 2
20 25 7 26 18 16 6 29 4 19 13 15 22 21 17 1 2 27 3 0 28 5 10 24 9 8 23 11 12 14
4 15 29 20 17 10 2 6 26 22 8 7 14 18 3 24 1 21 11 19 28 16 25 12 0 13 5 9 27 23
26 19 6 1 7 0 10 25 17 14 24 11 12 5 23 13 21 27 28 20 15 2 8 3 16 9 22 4 29 18
27 8 18 6 26 4 7 9 10 16 17 1 21 0 24 28 3 12 23 29 25 20 14 22 11 5 2 19 15 13
13 27 7 9 14 16 19 18 20 0 1 25 11 23 28 12 8 5 29 10 26 4 3 22 24 2 21 17 6 15
26 18 0 19 1 8 16 12 4 14 24 21 10 28 17 3 11 13 23 2 25 15 6 5 27 22 7 29 20 9
28 20 14 11 4 7 13 8 17 15 19 21 5 23 27 6 24 9 12 1 10 2 26 29 25 0 3 22 16 18
29 27 28 1 11 8 26 12 21 13 7 0 3 17 20 19 9 16 2 24 15 25 5 6 4 23 22 18 10 14
ta42.prb, Makespan: 1949
12 8 26 14 4 24 21 18 7 15 0 11 19 13 10 2 29 22 16 17 23 27 1 9 5 20 28 3 25 6
14 4 9 1 23 26 20 3 7 21 6 2 27 18 16 28 0 29 24 13 11 5 19 17 12 15 8 25 22 10
12 15 1 17 6 4 8 3 14 13 23 24 25 21 20 5 26 7 11 27 0 10 28 18 2 16 19 9 22 29
24 4 6 1 0 9 25 15 14 16 27 29 11 28 10 5 13 26 8 22 21 18 17 19 3 20 23 2 7 12
0 6 28 25 13 23 8 24 16 22 18 5 15 19 21 11 12 7 10 3 9 26 1 29 17 2 14 27 20 4
11 12 0 29 8 24 10 26 28 20 25 16 23 13 5 2 27 1 21 9 22 18 7 6 14 15 17 3 4 19
1 22 11 25 17 9 14 23 0 16 24 4 7 2 18 29 13 5 21 10 28 6 26 3 15 19 12 20 27 8
22 3 4 8 16 25 1 12 18 7 14 20 6 10 21 19 17 29 26 24 0 15 13 28 11 5 23 9 27 2
20 25 16 29 13 0 2 28 21 19 5 18 24 10 26 22 27 6 3 9 15 17 14 11 23 12 7 8 4 1
23 9 8 11 15 14 12 24 16 25 5 29 18 19 2 28 21 3 6 27 26 20 13 10 22 4 1 0 17 7
4 13 26 0 7 24 10 1 21 14 18 2 9 19 12 16 22 6 23 11 29 28 17 25 27 8 15 5 20 3
28 9 29 18 1 23 20 24 26 16 8 0 10 19 12 25 7 13 21 6 5 15 11 27 4 14 3 17 2 22
24 13 0 9 1 26 16 23 29 4 11 8 15 19 5 2 21 7 28 27 6 20 22 18 14 10 17 12 3 25
25 6 17 1 21 26 13 10 16 27 9 28 2 29 0 24 15 8 4 14 18 19 23 5 3 11 22 20 12 7
29 10 24 15 17 1 23 21 22 11 2 9 8 28 27 14 18 0 16 3 13 6 7 12 5 26 19 4 25 20
18 6 2 14 21 0 24 22 27 29 13 11 23 7 20 16 15 1 3 12 26 9 4 10 28 8 5 17 19 25
29 14 21 9 27 15 23 2 20 4 7 13 3 10 6 0 1 19 24 17 11 22 5 25 26 18 28 16 12 8
6 8 16 4 2 14 19 23 29 22 13 11 7 21 3 20 28 24 0 15 1 27 5 26 12 9 18 10 17 25
10 11 12 4 17 16 8 14 7 1 21 28 29 25 24 18 5 0 19 15 9 13 2 3 6 27 23 22 26 20
10 18 6 14 29 16 12 27 0 1 20 13 25 21 22 11 26 15 8 5 9 19 28 24 17 4 3 7 2 23
ta43.prb, Makespan: 1858
12 21 26 10 17 9 8 15 2 28 18 7 27 23 24 6 20 14 29 5 16 1 13 25 22 3 11 4 0 19
9 11 3 5 10 13 2 23 6 1 14 28 19 24 18 8 22 17 7 21 15 0 16 27 12 26 4 25 20 29
6 23 17 9 11 3 12 7 16 4 28 14 10 5 13 22 15 2 18 8 29 1 25 26 20 19 27 0 21 24
17 28 8 13 19 3 14 10 25 27 15 12 0 11 16 23 29 21 2 26 6 1 20 9 7 18 24 4 22 5
26 25 3 6 11 17 12 22 8 9 14 2 24 19 23 1 4 29 18 7 20 15 5 16 0 27 10 21 28 13
4 13 22 5 26 28 6 21 8 2 9 17 7 0 10 14 27 20 25 29 15 3 16 23 24 11 1 19 12 18
25 6 19 24 22 17 9 16 5 15 2 8 27 7 18 28 12 1 29 4 26 0 14 3 20 21 10 23 11 13
29 6 25 9 13 1 27 7 24 20 11 16 12 19 22 4 26 2 10 3 21 0 15 23 8 14 18 28 17 5
25 7 21 1 26 20 8 15 28 22 27 2 16 4 17 23 0 19 12 10 6 14 9 3 24 18 13 5 11 29
5 10 12 15 28 21 17 23 26 27 16 8 2 11 1 19 22 6 20 4 13 29 0 9 3 7 25 14 18 24
4 12 25 9 22 17 7 13 29 14 6 15 0 26 3 23 24 21 2 27 18 8 19 5 11 10 1 20 16 28
13 3 28 11 2 5 15 17 24 14 12 23 29 20 27 16 26 7 4 18 22 25 6 1 9 19 8 10 0 21
6 16 28 1 2 13 22 9 11 12 7 26 0 10 27 18 8 15 20 23 3 17 24 14 25 4 19 29 21 5
23 7 19 6 10 4 21 16 5 28 25 13 2 22 9 8 17 15 26 12 3 27 20 11 24 14 18 29 0 1
22 6 11 7 13 24 8 2 16 17 15 1 27 10 5 0 26 9 20 12 3 29 25 23 14 4 28 21 19 18
21 3 17 28 25 6 4 24 13 8 22 2 27 26 14 9 12 15 1 0 18 5 23 20 19 11 29 16 7 10
5 29 22 6 28 7 16 4 10 17 24 13 11 2 8 19 21 9 3 18 23 26 20 25 27 1 0 15 12 14
13 22 16 23 3 9 28 8 0 1 2 17 18 12 6 29 4 24 21 5 15 19 20 11 14 7 25 27 26 10
29 2 27 16 25 19 26 20 4 22 13 17 9 0 18 23 6 15 3 12 11 24 7 8 28 10 5 21 14 1
23 9 22 19 14 28 4 7 16 25 1 27 17 2 15 13 24 6 12 10 5 29 8 20 18 26 21 3 0 11
ta44.prb, Makespan: 1983
29 6 0 19 12 11 4 10 27 20 13 18 23 2 5 26 22 16 14 21 3 17 24 25 1 7 28 8 15 9
22 9 3 4 20 2 17 18 1 13 26 14 5 23 29 0 8 19 16 28 21 10 7 6 24 11 27 15 12 25
25 4 11 22 27 0 3 19 13 9 8 12 17 1 21 29 2 20 23 10 24 18 26 5 14 6 28 15 16 7
12 4 15 18 23 13 5 9 22 19 21 0 7 1 29 25 3 26 6 14 24 10 28 2 17 16 27 11 20 8
8 18 20 21 23 29 1 0 14 10 28 12 25 16 13 5 26 9 19 22 17 4 11 24 27 3 6 7 15 2
0 12 13 17 11 21 9 16 8 23 22 5 10 29 18 4 27 6 26 25 1 19 14 15 7 3 28 2 24 20
5 18 24 0 13 8 29 27 22 14 19 10 4 9 26 15 3 16 25 6 1 28 11 7 20 12 21 17 2 23
23 5 20 10 1 9 27 24 18 8 15 19 12 2 22 16 0 13 21 26 11 29 4 14 25 7 17 6 28 3
18 7 22 23 21 24 9 2 1 19 5 12 13 14 8 20 3 16 15 6 29 28 0 26 10 17 4 27 11 25
7 24 2 23 15 13 8 10 9 12 11 21 0 27 4 19 14 6 17 29 5 3 25 26 1 18 20 16 22 28
19 7 27 6 14 3 0 21 1 24 23 22 18 10 13 16 5 9 29 4 20 17 28 26 15 12 8 11 25 2
28 23 18 26 10 1 29 11 12 24 6 5 22 19 15 13 25 4 20 14 17 9 0 7 27 2 3 16 21 8
9 13 18 5 12 22 0 21 27 19 10 29 17 14 26 1 8 15 16 28 6 4 11 2 24 25 3 20 7 23
11 4 3 12 13 26 16 22 1 7 0 20 28 29 23 2 17 19 21 5 14 10 8 18 6 27 25 9 15 24
11 18 21 22 5 20 19 12 26 27 24 1 23 13 4 2 6 15 9 10 17 25 28 0 7 3 29 14 8 16
28 13 2 17 10 0 18 6 4 14 11 26 7 20 12 9 5 19 21 23 8 25 22 16 27 1 3 15 29 24
25 21 0 13 24 19 26 1 20 2 11 12 15 7 8 27 4 17 5 29 10 6 3 14 28 16 18 22 9 23
9 5 20 13 10 21 1 24 19 28 2 25 11 22 18 14 6 26 29 4 0 12 17 23 15 8 3 7 27 16
29 13 2 16 23 5 20 28 22 4 7 27 8 17 21 14 24 0 15 11 25 18 9 19 10 12 6 26 1 3
28 24 29 4 3 5 2 19 0 8 27 14 20 12 21 17 9 1 18 13 22 10 11 25 15 6 16 23 26 7
ta46.prb, Makespan: 2015
6 29 14 5 19 8 13 22 11 28 16 12 17 21 27 15 18 20 1 0 23 4 24 25 9 10 26 3 7 2
10 14 22 25 15 26 27 3 11 4 5 12 2 13 0 18 6 21 1 17 28 20 16 23 24 19 7 29 9 8
26 13 16 11 21 19 17 4 24 14 10 15 27 3 29 22 28 12 6 8 20 9 2 0 25 18 1 23 5 7
19 4 15 26 29 12 17 9 5 3 13 7 2 11 16 20 27 8 18 22 14 1 23 0 6 28 24 10 25 21
18 22 17 13 15 29 16 26 25 11 21 6 8 14 3 7 4 20 9 12 27 2 28 24 23 10 1 0 5 19
17 14 6 8 15 16 12 19 28 22 1 9 11 2 18 7 21 29 26 20 13 4 23 24 0 10 3 25 27 5
12 5 13 25 19 28 23 16 26 10 6 27 14 8 2 22 18 1 7 24 11 29 9 17 3 15 4 21 0 20
5 14 29 11 16 15 25 0 17 21 10 13 2 18 6 28 19 26 20 9 27 7 4 1 8 12 23 24 22 3
26 29 25 6 8 14 22 5 1 12 4 18 11 27 17 9 13 28 0 19 24 21 15 20 2 16 3 23 10 7
14 25 3 5 6 9 24 18 21 29 12 19 8 26 28 2 27 13 16 17 11 7 22 15 23 4 10 1 0 20
6 1 19 15 8 10 17 0 4 2 13 14 22 25 5 16 3 11 28 27 20 23 29 18 26 9 7 21 12 24
11 5 15 14 24 8 12 26 1 16 3 23 10 17 29 0 22 27 20 2 21 4 13 7 25 18 19 28 6 9
22 8 16 0 13 9 6 14 19 25 5 12 26 27 29 7 17 18 11 2 4 20 10 3 24 28 21 1 15 23
3 23 20 5 16 24 18 15 6 19 12 28 27 8 26 14 9 29 25 11 7 21 10 1 22 4 17 2 13 0
19 15 24 28 3 26 0 5 11 16 22 17 12 10 7 6 14 2 8 29 20 27 13 25 1 23 9 18 4 21
6 2 26 9 5 17 11 0 20 15 10 22 14 16 7 4 1 29 27 13 18 21 24 28 25 8 12 19 3 23
19 20 5 25 13 28 1 16 8 26 14 2 9 11 17 23 22 18 27 10 4 6 21 7 3 15 29 24 12 0
28 20 11 16 13 21 27 8 26 6 10 15 22 17 18 0 2 23 29 25 9 24 1 3 4 19 5 7 12 14
22 25 5 3 10 6 29 28 14 21 13 26 12 9 7 16 2 0 15 27 19 1 24 23 18 11 20 17 8 4
5 11 26 0 29 6 8 10 27 22 2 14 7 16 3 17 28 12 9 1 21 13 23 15 19 18 20 25 24 4
ta48.prb, Makespan: 1949
24 13 22 18 2 16 15 11 4 5 9 8 21 12 29 25 14 0 20 27 28 7 17 23 19 6 3 10 26 1
28 26 16 24 4 8 22 2 14 5 23 12 20 7 10 27 13 19 9 21 29 0 1 3 17 18 11 15 25 6
13 1 10 12 7 5 27 29 23 24 19 6 21 22 3 0 15 8 26 28 2 25 14 20 11 16 4 17 18 9
17 9 4 27 16 13 8 5 20 2 15 25 14 28 21 7 6 3 24 19 1 23 10 0 26 18 12 29 11 22
8 1 24 16 28 10 27 4 25 15 19 7 5 12 23 13 20 18 21 29 3 0 9 2 22 14 11 26 17 6
27 26 7 17 11 29 4 24 14 0 12 20 3 28 15 23 19 16 6 18 21 2 22 1 10 5 25 9 13 8
29 24 27 5 21 11 28 0 23 20 25 22 13 8 9 6 10 17 2 4 26 3 18 15 19 1 16 12 7 14
22 12 4 19 6 11 2 28 26 10 24 21 29 13 23 27 17 14 16 20 7 18 1 3 0 25 5 9 8 15
4 28 27 13 24 5 20 29 7 8 9 21 10 25 0 14 17 23 3 6 16 18 11 19 2 22 15 26 1 12
7 3 11 4 5 22 25 26 14 8 24 20 9 29 23 19 27 6 0 28 21 2 16 1 18 12 13 15 17 10
16 21 26 23 13 12 3 28 20 7 4 9 29 22 27 25 5 0 8 14 15 10 18 24 17 19 11 2 6 1
1 11 18 17 26 8 25 22 19 4 28 12 7 24 14 13 3 0 29 23 27 20 6 21 5 9 16 15 10 2
24 12 1 23 6 4 17 13 2 15 5 28 18 3 8 26 25 16 14 19 27 21 22 0 20 9 7 29 10 11
11 1 29 12 17 2 5 4 13 28 7 27 6 23 26 0 24 25 20 19 14 18 8 16 3 9 10 22 15 21
18 9 22 28 2 26 12 4 5 14 27 13 29 3 19 15 1 7 21 10 24 20 23 6 16 17 8 0 11 25
23 17 9 10 27 8 28 4 12 24 20 5 15 19 0 29 2 22 26 25 6 11 16 13 7 21 14 1 18 3
8 12 17 23 2 6 15 1 10 11 27 26 4 13 28 19 20 24 7 21 9 25 5 18 0 14 16 3 29 22
15 21 9 11 13 16 4 1 24 12 29 28 23 8 20 22 7 26 0 17 5 6 25 10 14 2 19 18 27 3
23 28 2 1 13 25 29 26 20 5 9 3 8 10 17 27 18 6 15 24 21 22 11 12 7 4 0 14 19 16
13 12 27 17 1 2 29 5 25 21 9 4 19 20 7 10 23 22 0 16 3 8 14 24 11 15 6 28 26 18
ta49.prb, Makespan: 1967
19 6 27 25 14 8 24 20 28 21 3 15 23 0 16 29 4 26 18 10 11 9 17 7 2 1 5 12 22 13
15 5 6 29 28 1 11 3 18 26 7 20 8 14 0 2 19 17 21 23 16 10 25 24 9 12 4 13 22 27
11 5 8 10 1 16 23 3 14 2 21 22 13 0 12 28 18 7 9 20 26 6 17 19 4 29 25 24 27 15
10 3 13 29 8 20 18 0 11 28 16 22 19 26 14 23 25 1 27 24 17 2 7 15 21 4 12 9 6 5
20 10 24 5 22 11 26 16 18 13 8 19 2 17 3 0 23 4 27 7 21 14 28 9 12 1 25 15 29 6
4 25 0 20 19 16 27 2 28 10 3 26 23 7 22 8 24 21 13 17 12 6 5 29 18 1 14 15 9 11
20 21 24 2 5 27 10 23 17 8 6 3 1 22 11 19 9 18 16 14 0 12 29 4 25 13 15 7 28 26
27 5 17 14 29 15 23 8 10 9 24 16 3 0 1 11 7 28 19 2 12 18 21 25 13 6 20 26 4 22
0 21 20 22 8 23 25 9 3 16 13 18 2 6 26 11 1 17 10 7 29 5 19 14 27 24 28 15 12 4
9 2 5 17 28 16 8 22 26 4 21 1 0 12 20 19 14 13 10 7 23 3 27 29 15 25 6 24 11 18
8 16 23 0 9 19 3 18 2 12 21 4 26 7 25 22 14 17 24 5 6 29 1 13 15 28 10 27 11 20
19 17 26 0 4 16 28 7 3 8 23 11 13 15 27 20 9 2 14 25 21 22 18 12 1 6 29 10 5 24
17 22 6 13 20 21 24 19 9 8 12 10 28 0 16 11 23 3 25 7 15 2 27 14 18 26 1 29 4 5
20 25 2 0 27 8 1 29 22 15 17 26 28 13 21 23 11 16 24 9 14 4 3 19 18 7 6 5 10 12
1 3 21 9 15 6 25 7 18 12 27 20 28 23 0 16 22 26 11 19 24 8 17 2 4 10 29 5 13 14
18 8 26 24 10 23 19 28 11 16 0 14 2 17 4 3 25 12 7 20 9 29 22 21 1 13 27 5 15 6
26 28 22 24 27 17 29 16 4 7 12 3 10 1 11 0 18 15 8 20 25 2 19 9 6 23 14 13 21 5
28 19 18 16 26 17 29 0 15 27 3 13 4 11 1 23 25 12 10 6 21 24 7 5 8 9 2 22 14 20
26 27 8 20 10 23 1 6 16 14 3 0 7 18 28 4 21 12 9 11 2 25 5 13 24 29 15 19 22 17
8 25 15 17 22 9 0 12 14 3 1 2 21 29 16 4 27 28 26 6 11 7 23 24 5 18 20 10 19 13