{"id":12,"date":"2025-09-10T09:05:33","date_gmt":"2025-09-10T14:05:33","guid":{"rendered":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/?p=12"},"modified":"2025-09-30T17:16:31","modified_gmt":"2025-09-30T22:16:31","slug":"robotics-matrix-structure-assembly-system-scheduling-problem","status":"publish","type":"post","link":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/robotics-matrix-structure-assembly-system-scheduling-problem\/","title":{"rendered":"Robotics Matrix-Structure Assembly System Scheduling Problem"},"content":{"rendered":"\n
\n

The increasing demand for customized products with short life cycles and rapid delivery requirements has driven industries to adopt Robotics Assembly Systems (RAS) as a solution to these challenges. An RAS is an integrated manufacturing environment composed of one or multiple workstations capable of assembling diverse product types, interconnected through a material handling system, and coordinated by a centralized control unit. An RAS can be designed in various configurations: Robotic Assembly Lines (RAL), Robotic Assembly Cell (RAC) with one or multiple robots, and, more recently, a configuration known as the Robotic Matrix-Structure Assembly System (RMSAS) has emerged.<\/p>\n<\/div>

\"\"<\/figure><\/div>\n\n\n\n

<\/p>\n\n\n\n

P<\/em>=[1, 2<\/em>,\u2026,|P<\/em>|] be the set of product types. Jp<\/sub><\/em>=[J1p<\/sub>, J2p<\/sub>,\u2026,Jnp<\/sub><\/em>] the ordered set of assembly tasks required to produce product p<\/em> \u2208 P<\/em>, where n<\/em> denotes the total number of tasks for product p<\/em>. M<\/em>=[1, 2<\/em>,\u2026,|M<\/em>|] the set of available assembly workstations. Each assembly task Jjp\u200b<\/sub><\/em>corresponds to a set of operations required for product p<\/em>. A workstation m<\/em> \u2208 M<\/em> can execute only a subset of tasks, depending on its technological capabilities. This relationship is defined by the feasibility set:<\/p>\n\n\n\n

\u03a6(Jjp<\/sub><\/em>\u200b) \u2286 M<\/em>, \u2200Jjp<\/sub><\/em> \u200b\u2208 Jp<\/sub><\/em>\u200b, p<\/em> \u2208 P<\/em><\/p>\n\n\n\n

Where \u03a6 (Jjp<\/sub><\/em>) denotes the set of workstations capable of processing task Jjp<\/sub><\/em>\u200b<\/sub>. Since the RMSAS is designed to handle multiple product types, every product must have at least one feasible workstation for each of its tasks:<\/p>\n\n\n\n

\u03a6(Jjp<\/sub><\/em>\u200b) \u2260 \u2205, \u2200Jjp<\/sub><\/em> \u200b\u2208 Jp<\/sub><\/em>\u200b, p<\/em> \u2208 P<\/em><\/p>\n\n\n\n

Conversely, a workstation mmm can process tasks from different products, represented as:<\/p>\n\n\n\n

\u03a8(m<\/em>) = {Jjp<\/sub><\/em>\u200b \u2208 Jp<\/sub><\/em> \u200b\u2223 m<\/em> \u2208 \u03a6(Jjp<\/sub><\/em>\u200b), p<\/em> \u2208 P<\/em>} <\/p>\n\n\n\n

Where \u03a8(m<\/em>) is the set of tasks executable at workstation m<\/em>. Thus, the assignment of tasks to workstations is determined by the intersection between product requirements and workstation capabilities, with each \u03a8(m<\/em>) representing only a fraction of the global task set across all products.<\/p>\n\n\n\n

<\/p>\n\n\n\n

Instances<\/strong>:<\/h5>\n\n\n\n
Group I<\/strong><\/summary>\n

The execution of assembly operations by industrial robots tends to exhibit consistent and low variability across multiple runs. In contrast, stochastic processing times are typically associated with scenarios involving human\u2013robot interaction within the same assembly system. Some studies suggest that processing times can be modeled using a uniform probability distribution; however, the range of this distribution may vary depending on the type of assembly task being analyzed. For example, processing times in the electronics industry are usually short\u2014often measured in seconds\u2014while in the automotive industry, assembly tasks tend to be longer, typically measured in minutes. Based on this distinction, the present study evaluates each instance under two different processing time scenarios. For Group_I<\/em> of products, task durations are modeled using a uniform distribution in the range [2-10] time units, representing short-cycle tasks.<\/p>\n\n\n\n

Matrix-Structure 2 x 2<\/strong><\/p>\n\n\n\n

Int_1<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
\n
\n
Input Data: <\/strong>Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong>
1 4 4 1000 4
2 1000 2 2 1000
3 5 1000 5 5
4 6 6 1000 6
5 1000 4 4 1000
6 5 1000 5 5
7 1000 10 10 1000
8 4 4 1000 4
9 1000 8 8 1000
10 6 1000 6 6
11 4 4 1000 4
12 3 1000 3 3
13 5 5 1000 5
14 1000 7 7 1000
15 4 4 1000 4
16 4 4 1000 4
17 1000 6 6 1000
18 2 1000 2 2
19 1000 8 8 1000
20 5 1000 5 5<\/td>		Predecessor Successor<\/strong>
1 3
2 3
3 5
4 5
6 7
8 9
7 11
9 11
10 11
12 13
13 14
14 15
16 17
18 19
17 20
19 20




<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P1 1 0 4
1 P1 3 4 2
1 P1 4 14 9
1 P3 13 9 20
1 P4 20 22 27
2 P1 2 0 5
2 P2 11 23 15
2 P3 14 16 13
2 P4 17 10 23
2 P4 19 2 23
3 P1 5 23 27
3 P2 7 5 5
3 P2 9 15 14
3 P3 12 2 23
3 P4 18 0 27
4 P2 6 0 9
4 P2 8 9 16
4 P2 10 17 2
4 P3 15 23 10
4 P4 16 5 27<\/td>		Makespan = 27

Ws1: Total_Time=25.0, Utilization=0.9259
Ws2: Total_Time=27.0, Utilization=1.0000
Ws3: Total_Time=27.0, Utilization=1.0000
Ws4: Total_Time=23.0, Utilization=0.8519

Average System Utilization: 0.9444













<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 27 Run-time = 6,4 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_2<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong>
1 8 1000 8 8
2 1000 10 10 10
3 5 5 1000 1000
4 4 1000 4 4
5 1000 6 6 6
6 7 1000 7 7
7 1000 5 5 5
8 3 1000 3 3
9 1000 7 7 7
10 6 6 1000 1000
11 1000 2 2 2
12 9 1000 9 9
13 8 8 1000 1000
14 1000 6 6 6
15 3 1000 3 3
16 7 7 1000 1000
17 1000 4 4 4
18 5 5 1000 1000
19 8 8 1000 1000
20 1000 6 6 6
21 7 1000 7 7
22 4 4 1000 1000
23 10 1000 10 10
24 1000 6 6 6
25 2 2 1000 1000<\/td>		Predecessor Successor<\/strong>
1 3
2 3
4 5
3 6
5 6
7 8
9 10
8 11
10 11
12 14
13 14
16 17
14 18
15 18
17 18
19 20
20 21
21 22
23 25
24 25





<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P2 10 26 8
1 P3 12 7 21
1 P3 15 16 27
1 P3 16 0 11
1 P3 18 32 30
1 P4 21 19 37
2 P1 3 22 26
2 P3 13 14 35
2 P3 17 27 7
2 P4 19 0 32
2 P4 22 31 37
2 P5 24 8 16
2 P5 25 35 22
3 P1 2 11 32
3 P1 4 7 19
3 P2 7 21 7
3 P2 8 32 31
3 P2 9 0 37
3 P2 11 35 8
3 P3 14 26 14
4 P1 1 0 26
4 P1 5 24 35
4 P1 6 30 24
4 P4 20 8 14
4 P5 23 14 37<\/td>		Makespan = 37

Ws1: Total_Time=37.0, Utilization=1.0000
Ws2: Total_Time=37.0, Utilization=1.0000
Ws3: Total_Time=37.0, Utilization=1.0000
Ws4: Total_Time=37.0, Utilization=1.0000

Average System Utilization: 1.0000


















<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 37 Run-time = 15,6 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_3<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong>
1 4 1000 4 1000
2 1000 8 8 8
3 2 2 1000 2
4 6 6 1000 6
5 1000 5 5 5
6 4 1000 4 1000
7 1000 7 7 7
8 8 1000 8 1000
9 9 1000 9 1000
10 8 8 1000 8
11 1000 4 4 4
12 3 3 1000 3
13 1000 10 10 10
14 4 1000 4 1000
15 1000 6 6 6
16 8 1000 8 1000
17 3 3 1000 3
18 5 5 1000 5
19 7 7 1000 7
20 3 1000 3 1000
21 1000 8 8 8
22 4 1000 4 1000
23 6 1000 6 1000
24 2 2 1000 2
25 1000 8 8 8
26 4 1000 4 1000
27 1000 3 3 3
28 1000 10 10 10
29 7 7 1000 7
30 2 1000 2 1000<\/td>		Predecessor Successor<\/strong>
1 2
2 3
4 5
3 6
5 6
7 8
9 11
10 11
8 12
11 12
14 16
15 16
13 18
16 18
17 18
19 20
20 21
21 22
23 24
25 26
24 27
26 27
28 29
29 30






<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P1 4 6 10
1 P1 6 35 29
1 P2 9 18 35
1 P2 12 39 12
1 P3 16 27 23
1 P3 17 12 39
1 P4 20 15 14
1 P5 23 0 34
2 P1 3 33 27
2 P1 5 18 18
2 P2 10 10 39
2 P2 11 35 42
2 P5 24 23 20
2 P5 25 25 24
2 P5 27 39 6
2 P6 28 0 35
3 P1 1 6 15
3 P2 8 26 42
3 P3 13 10 7
3 P3 14 20 18
3 P3 15 0 37
3 P4 22 38 42
3 P5 26 34 6
3 P6 30 24 25
4 P1 2 21 33
4 P2 7 7 38
4 P3 18 37 42
4 P4 19 0 10
4 P4 21 29 21
4 P6 29 14 26<\/td>		Makespan = 42

Ws1: Total_Time=42.0, Utilization=1.0000
Ws2: Total_Time=42.0, Utilization=1.0000
Ws3: Total_Time=42.0, Utilization=1.0000
Ws4: Total_Time=42.0, Utilization=1.0000

Average System Utilization: 1.0000























<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 42 Run-time = 76,1 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_4<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong>
1 6 1000 1000 6
2 1000 8 8 8
3 4 4 4 1000
4 2 1000 1000 2
5 5 5 5 1000
6 1000 7 7 7
7 10 1000 1000 10
8 3 3 3 1000
9 3 1000 1000 3
10 6 6 6 1000
11 1000 7 7 7
12 5 5 5 1000
13 8 1000 1000 8
14 1000 9 9 9
15 4 4 4 1000
16 2 1000 1000 2
17 1000 8 8 8
18 7 7 7 1000
19 9 1000 1000 9
20 1000 5 5 5
21 6 1000 1000 6
22 1000 2 2 2
23 8 8 8 1000
24 7 1000 1000 7
25 5 5 5 1000
26 1000 3 3 3
27 1000 6 6 6
28 8 8 8 1000
29 4 1000 1000 4
30 1000 7 7 7
31 2 2 2 1000
32 1000 5 5 5
33 10 1000 1000 10
34 1000 4 4 4
35 8 8 8 1000<\/td>		Predecessor Successor<\/strong>
1 3
2 3
4 5
5 6
3 8
6 8
7 8
9 10
10 11
12 13
13 15
14 15
11 16
15 16
17 18
19 20
18 21
20 21
22 23
23 24
24 25
25 26
27 29
28 29
30 31
29 32
31 32
33 34
34 35






<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P1 7 27 11
1 P2 16 50 16
1 P3 19 18 24
1 P4 23 10 2
1 P4 25 37 20
1 P6 33 0 38
1 P6 35 42 37
2 P1 3 20 41
2 P1 5 15 5
2 P2 12 2 22
2 P3 17 24 46
2 P3 18 39 7
2 P4 22 7 19
2 P4 26 49 31
2 P5 27 9 47
2 P5 30 32 52
3 P1 2 8 32
3 P1 6 31 46
3 P1 8 38 27
3 P2 10 16 35
3 P2 14 22 52
3 P2 15 43 9
3 P5 28 0 18
3 P5 31 41 26
3 P5 32 47 42
4 P1 1 5 52
4 P1 4 0 15
4 P2 9 2 8
4 P2 11 39 30
4 P2 13 11 39
4 P3 20 30 43
4 P3 21 46 52
4 P4 24 19 10
4 P5 29 26 39
4 P6 34 35 50<\/td>		Makespan = 52

Ws1: Total_Time=52.0, Utilization=1.0000
Ws2: Total_Time=47.0, Utilization=0.9038
Ws3: Total_Time=52.0, Utilization=1.0000
Ws4: Total_Time=52.0, Utilization=1.0000

Average System Utilization: 0.9760




























<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 52 Run-time = 136 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_5<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong>
1 6 6 6 1000
2 1000 4 4 4
3 3 1000 1000 3
4 8 1000 1000 8
5 1000 7 7 7
6 6 6 6 1000
7 1000 10 10 10
8 4 1000 1000 4
9 8 8 8 1000
10 6 6 6 1000
11 5 5 5 1000
12 1000 8 8 8
13 7 1000 1000 7
14 1000 4 4 4
15 1000 6 6 6
16 2 1000 1000 2
17 8 8 8 1000
18 5 1000 1000 5
19 4 1000 1000 4
20 1000 9 9 9
21 5 5 5 1000
22 1000 10 10 10
23 6 1000 1000 6
24 1000 8 8 8
25 3 3 3 1000
26 6 1000 1000 6
27 6 6 6 1000
28 4 1000 1000 4
29 1000 10 10 10
30 2 2 2 1000
31 5 1000 1000 5
32 3 1000 1000 3
33 1000 5 5 5
34 7 1000 1000 7
35 4 4 4 1000
36 4 1000 1000 4
37 1000 3 3 3
38 8 8 8 1000
39 6 1000 1000 6
40 7 7 7 1000<\/td>		Predecessor Successor<\/strong>
1 3
2 3
4 5
3 6
5 6
7 8
8 9
11 12
10 13
12 13
9 14
13 14
15 16
17 18
19 20
16 21
18 21
20 21
22 23
23 24
24 25
25 26
27 28
28 30
29 30
30 31
32 33
33 34
34 35
36 37
38 39
37 40
39 40







<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P7 38 0 30
1 P3 19 8 33
1 P2 8 12 38
1 P3 18 16 35
1 P2 10 21 42
1 P1 4 27 48
1 P1 3 35 12
1 P3 16 38 16
1 P7 39 40 24
1 P6 34 46 27
1 P4 26 53 5
2 P2 7 2 26
2 P5 27 12 52
2 P2 12 18 59
2 P3 20 26 10
2 P1 5 35 40
2 P1 6 42 16
2 P5 30 48 21
2 P3 21 50 12
2 P6 35 55 35
3 P2 11 0 55
3 P7 37 5 23
3 P3 17 8 29
3 P2 9 16 45
3 P1 1 24 48
3 P5 29 30 59
3 P6 33 40 18
3 P4 25 45 37
3 P7 40 48 40
3 P2 14 55 50
4 P7 36 0 57
4 P3 15 4 13
4 P6 32 10 45
4 P4 22 13 53
4 P4 23 23 59
4 P1 2 29 4
4 P5 28 33 8
4 P4 24 37 8
4 P2 13 45 46
4 P5 31 52 55<\/td>		Makespan = 59

Ws1: Total_Time=59.0, Utilization=1.0000
Ws2: Total_Time=57.0, Utilization=0.9661
Ws3: Total_Time=59.0, Utilization=1.0000
Ws4: Total_Time=57.0, Utilization=0.9661

Average System Utilization: 0.9831

































<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 59 Run-time = 2467 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n

Matrix-Structure 2 x 3<\/strong><\/p>\n\n\n\n

Int_6<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong>
1 1000 1000 6 1000 6 6
2 1000 7 1000 7 1000 7
3 8 1000 1000 8 8 1000
4 4 4 4 1000 1000 1000
5 1000 1000 10 1000 10 10
6 5 5 5 1000 1000 1000
7 1000 3 1000 3 1000 3
8 1000 1000 5 1000 5 5
9 4 4 4 1000 1000 1000
10 1000 10 1000 10 1000 10
11 7 1000 1000 7 7 1000
12 1000 1000 6 1000 6 6
13 7 1000 1000 7 7 1000
14 9 9 9 1000 1000 1000
15 1000 2 1000 2 1000 2
16 1000 1000 4 1000 4 4
17 1000 9 1000 9 1000 9
18 1000 1000 5 1000 5 5
19 6 6 6 1000 1000 1000
20 3 1000 1000 3 3 1000
21 1000 3 1000 3 1000 3
22 6 1000 1000 6 6 1000
23 8 1000 1000 8 8 1000
24 7 7 7 1000 1000 1000
25 1000 2 1000 2 1000 2<\/td>		Predecessor Successor<\/strong>
1 3
2 3
4 5
3 6
5 6
7 8
8 9
9 11
10 11
12 13
13 16
14 16
15 16
17 18
18 19
19 20
21 22
23 24
22 25
24 25





<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P1 4 0 6
1 P3 14 4 8
1 P3 13 13 16
1 P1 6 20 4
2 P4 17 0 19
2 P5 21 9 25
2 P2 9 12 3
2 P4 19 16 11
2 P5 25 23 16
3 P1 1 0 18
3 P2 8 6 25
3 P4 18 11 9
3 P5 24 16 20
4 P1 2 1 13
4 P2 10 8 21
4 P2 11 18 25
5 P5 23 0 9
5 P1 3 8 16
5 P5 22 16 22
5 P4 20 22 25
6 P2 7 0 12
6 P3 12 3 22
6 P1 5 9 8
6 P3 15 19 23
6 P3 16 21 25<\/td>		Makespan = 25

Ws1: Total_Time=25.0, Utilization=1.0000
Ws2: Total_Time=24.0, Utilization=0.9600
Ws3: Total_Time=23.0, Utilization=0.9200
Ws4: Total_Time=24.0, Utilization=0.9600
Ws5: Total_Time=25.0, Utilization=1.0000
Ws6: Total_Time=25.0, Utilization=1.0000

Average System Utilization: 0.9733
















<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 25 Run-time = 18,8 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_7<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong>
1 1000 1000 7 1000 7 7
2 5 5 5 1000 1000 1000
3 3 1000 1000 3 3 1000
4 1000 1000 8 1000 8 8
5 1000 4 1000 4 1000 4
6 6 6 6 1000 1000 1000
7 1000 2 1000 2 1000 2
8 10 1000 1000 10 10 1000
9 1000 5 1000 5 1000 5
10 1000 1000 6 1000 6 6
11 4 4 4 1000 1000 1000
12 1000 1000 9 1000 9 9
13 3 1000 1000 3 3 1000
14 1000 1000 7 1000 7 7
15 1000 2 1000 2 1000 2
16 8 8 8 1000 1000 1000
17 4 1000 1000 4 4 1000
18 1000 1000 5 1000 5 5
19 6 1000 1000 6 6 1000
20 5 5 5 1000 1000 1000
21 1000 8 1000 8 1000 8
22 1000 1000 9 1000 9 9
23 2 2 2 1000 1000 1000
24 9 9 9 1000 1000 1000
25 6 1000 1000 6 6 1000
26 1000 3 1000 3 1000 3
27 1000 1000 4 1000 4 4
28 1000 10 1000 10 1000 10
29 7 1000 1000 7 7 1000
30 6 6 6 1000 1000 1000<\/td>		Predecessor Successor<\/strong>
1 3
2 3
4 5
5 6
3 7
6 7
9 10
8 11
10 11
11 13
12 13
14 15
15 18
16 18
17 18
19 20
20 21
21 22
22 23
25 26
24 27
26 27
28 29
29 30






<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P5 25 0 19
1 P4 20 6 24
1 P5 24 11 27
1 P1 6 22 8
2 P2 9 0 12
2 P6 28 5 28
2 P2 11 15 30
2 P1 2 19 11
2 P6 30 24 5
3 P2 12 0 15
3 P2 10 9 19
3 P3 16 15 9
3 P5 27 24 30
3 P4 23 28 17
4 P2 8 1 24
4 P4 21 11 23
4 P5 26 19 10
4 P3 15 22 30
4 P1 3 24 6
4 P2 13 27 11
5 P4 19 0 19
5 P3 17 6 28
5 P3 14 10 30
5 P6 29 17 20
5 P3 18 25 6
6 P1 4 0 22
6 P1 5 8 28
6 P1 1 12 15
6 P4 22 19 24
6 P1 7 28 30<\/td>		Makespan = 30

Ws1: Total_Time=26.0, Utilization=0.8667
Ws2: Total_Time=30.0, Utilization=1.0000
Ws3: Total_Time=29.0, Utilization=0.9667
Ws4: Total_Time=29.0, Utilization=0.9667
Ws5: Total_Time=29.0, Utilization=0.9667
Ws6: Total_Time=30.0, Utilization=1.0000

Average System Utilization: 0.9611





















<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 30 Run-time = 82,3 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_8<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong>
1 5 1000 1000 5 5 1000
2 1000 1000 8 1000 8 8
3 1000 6 1000 6 1000 6
4 4 4 4 1000 1000 1000
5 1000 1000 9 1000 9 9
6 3 1000 1000 3 3 1000
7 4 4 4 1000 1000 1000
8 6 1000 1000 6 6 1000
9 1000 7 1000 7 1000 7
10 3 1000 1000 3 3 1000
11 1000 1000 8 1000 8 8
12 1000 10 1000 10 1000 10
13 6 6 6 1000 1000 1000
14 1000 1000 2 1000 2 2
15 1000 2 1000 2 1000 2
16 8 8 8 1000 1000 1000
17 4 1000 1000 4 4 1000
18 1000 7 1000 7 1000 7
19 1000 1000 5 1000 5 5
20 6 6 6 1000 1000 1000
21 1000 8 1000 8 1000 8
22 4 1000 1000 4 4 1000
23 2 2 2 1000 1000 1000
24 1000 1000 5 1000 5 5
25 3 3 3 1000 1000 1000
26 1000 9 1000 9 1000 9
27 8 1000 1000 8 8 1000
28 3 3 3 1000 1000 1000
29 1000 1000 4 1000 4 4
30 2 1000 1000 2 2 1000
31 1000 5 1000 5 1000 5
32 2 1000 1000 2 2 1000
33 3 3 3 1000 1000 1000
34 1000 4 1000 4 1000 4
35 1000 1000 6 1000 6 6<\/td>		Predecessor Successor<\/strong>
1 2
2 3
4 5
3 6
5 6
7 8
8 9
10 11
11 13
12 13
9 14
13 14
15 16
16 17
18 19
17 20
19 20
21 22
22 23
23 24
24 25
26 28
27 28
29 30
28 31
30 31
32 33
33 34
34 35






<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P1 4 0 5
1 P1 6 28 13
1 P2 13 22 20
1 P3 16 4 4
1 P4 23 20 22
1 P5 27 12 31
2 P2 9 21 5
2 P3 15 0 11
2 P3 18 11 28
2 P4 21 2 3
2 P4 25 28 11
2 P6 33 18 10
3 P1 2 5 28
3 P1 5 13 30
3 P2 7 1 2
3 P3 20 25 12
3 P5 28 22 21
4 P1 1 0 18
4 P2 8 5 25
4 P5 26 12 31
4 P5 31 26 10
4 P6 34 21 15
5 P2 10 0 22
5 P2 11 3 28
5 P2 14 28 31
5 P3 17 17 21
5 P4 22 11 20
5 P4 24 23 25
5 P5 30 21 14
5 P6 32 15 23
6 P1 3 14 31
6 P2 12 0 17
6 P3 19 20 21
6 P5 29 10 25
6 P6 35 25 31<\/td>		Makespan = 31

Ws1: Total_Time=31.0, Utilization=1.0000
Ws2: Total_Time=30.0, Utilization=0.9677
Ws3: Total_Time=30.0, Utilization=0.9677
Ws4: Total_Time=29.0, Utilization=0.9355
Ws5: Total_Time=30.0, Utilization=0.9677
Ws6: Total_Time=31.0, Utilization=1.0000

Average System Utilization: 0.9731


























<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 31 Run-time = 546 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_9<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong>
1 1000 1000 4 1000 4 4
2 8 1000 1000 8 8 1000
3 1000 3 1000 3 1000 3
4 1000 1000 6 1000 6 6
5 1000 9 1000 9 1000 9
6 7 7 7 1000 1000 1000
7 2 1000 1000 2 2 1000
8 4 4 4 1000 1000 1000
9 7 1000 1000 7 7 1000
10 1000 3 1000 3 1000 3
11 1000 1000 5 1000 5 5
12 2 1000 1000 2 2 1000
13 1000 4 1000 4 1000 4
14 9 9 9 1000 1000 1000
15 1000 1000 6 1000 6 6
16 1000 5 1000 5 1000 5
17 3 3 3 1000 1000 1000
18 8 1000 1000 8 8 1000
19 1000 2 1000 2 1000 2
20 1000 1000 6 1000 6 6
21 4 4 4 1000 1000 1000
22 1000 6 1000 6 1000 6
23 10 1000 1000 10 10 1000
24 8 8 8 1000 1000 1000
25 1000 1000 9 1000 9 9
26 7 7 7 1000 1000 1000
27 1000 8 1000 8 1000 8
28 2 1000 1000 2 2 1000
29 4 4 4 1000 1000 1000
30 6 1000 1000 6 6 1000
31 1000 1000 3 1000 3 3
32 1000 7 1000 7 1000 7
33 1000 1000 5 1000 5 5
34 4 1000 1000 4 4 1000
35 6 6 6 1000 1000 1000
36 1000 3 1000 3 1000 3
37 1000 1000 2 1000 2 2
38 10 10 10 1000 1000 1000
39 8 1000 1000 8 8 1000
40 1000 1000 6 1000 6 6<\/td>		Predecessor Successor<\/strong>
1 3
2 3
4 5
5 6
3 7
6 7
8 9
9 10
11 14
12 13
13 14
10 15
14 15
16 17
17 18
19 20
18 21
20 21
22 23
23 24
24 25
25 26
27 29
28 29
30 32
31 32
29 33
32 33
34 35
35 36
36 37
38 40
39 40







<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P7 38 0 18
1 P6 34 10 36
1 P4 24 17 39
1 P2 14 25 6
1 P1 7 39 17
2 P5 27 0 30
2 P1 5 8 41
2 P6 35 17 22
2 P1 6 23 29
2 P3 21 30 35
2 P4 26 34 17
3 P1 4 0 6
3 P3 17 6 10
3 P5 29 9 34
3 P1 1 14 41
3 P2 8 18 5
3 P4 25 25 9
3 P2 15 35 28
4 P3 16 0 12
4 P5 28 6 23
4 P7 39 8 34
4 P5 30 16 6
4 P2 9 22 17
4 P5 32 29 25
4 P1 3 36 34
5 P2 12 4 41
5 P4 23 7 8
5 P3 18 20 8
5 P1 2 28 13
5 P5 33 36 22
6 P4 22 0 26
6 P2 13 6 36
6 P3 19 10 41
6 P2 11 12 14
6 P3 20 17 23
6 P5 31 23 38
6 P7 40 26 41
6 P2 10 32 10
6 P6 36 35 16
6 P6 37 39 32<\/td>		Makespan = 41

Ws1: Total_Time=33.0, Utilization=0.8049
Ws2: Total_Time=41.0, Utilization=1.0000
Ws3: Total_Time=36.0, Utilization=0.8780
Ws4: Total_Time=38.0, Utilization=0.9268
Ws5: Total_Time=33.0, Utilization=0.8049
Ws6: Total_Time=40.0, Utilization=0.9756

Average System Utilization: 0.8984































<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 41 Run-time = 1001 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_10<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong>
1 1000 8 1000 8 1000 8
2 6 1000 1000 6 6 1000
3 1000 1000 3 1000 3 3
4 9 9 9 1000 1000 1000
5 5 1000 1000 5 5 1000
6 1000 4 1000 4 1000 4
7 1000 1000 9 1000 9 9
8 7 7 7 1000 1000 1000
9 5 1000 1000 5 5 1000
10 8 1000 1000 8 8 1000
11 1000 4 1000 4 1000 4
12 3 3 3 1000 1000 1000
13 1000 1000 6 1000 6 6
14 1000 1000 6 1000 6 6
15 1000 10 1000 10 1000 10
16 1000 1000 9 1000 9 9
17 5 5 5 1000 1000 1000
18 6 1000 1000 6 6 1000
19 1000 1000 8 1000 8 8
20 3 3 3 1000 1000 1000
21 4 1000 1000 4 4 1000
22 1000 9 1000 9 1000 9
23 1000 1000 7 1000 7 7
24 2 2 2 1000 1000 1000
25 6 6 6 1000 1000 1000
26 1000 4 1000 4 1000 4
27 10 1000 1000 10 10 1000
28 8 8 8 1000 1000 1000
29 1000 1000 7 1000 7 7
30 3 1000 1000 3 3 1000
31 1000 4 1000 4 1000 4
32 1000 1000 5 1000 5 5
33 6 6 6 1000 1000 1000
34 10 1000 1000 10 10 1000
35 1000 7 1000 7 1000 7
36 9 1000 1000 9 9 1000
37 1000 2 1000 2 1000 2
38 1000 1000 8 1000 8 8
39 10 10 10 1000 1000 1000
40 1000 1000 5 1000 5 5
41 8 8 8 1000 1000 1000
42 10 1000 1000 10 10 1000
43 1000 6 1000 6 1000 6
44 1000 1000 7 1000 7 7
45 1000 5 1000 5 1000 5<\/td>		Predecessor Successor<\/strong>
1 3
2 3
4 5
3 6
5 6
7 8
8 9
10 11
11 12
9 13
12 13
14 17
15 17
16 17
18 19
19 20
20 21
22 23
21 24
23 24
25 26
26 27
27 28
28 29
29 30
31 32
33 34
32 35
34 35
36 37
38 39
37 40
39 40
41 42
42 43
43 44
44 45








<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P5 25 0 30
1 P7 39 6 16
1 P7 36 16 38
1 P2 8 25 11
1 P2 9 32 37
1 P4 21 37 44
1 P4 24 42 8
2 P1 4 2 32
2 P3 15 11 37
2 P2 11 21 8
2 P7 37 25 25
2 P6 35 27 37
2 P2 12 34 44
2 P3 17 37 35
2 P8 45 42 21
3 P6 33 0 6
3 P2 7 6 42
3 P8 41 8 8
3 P6 32 16 28
3 P5 28 21 32
3 P4 20 29 41
3 P8 44 32 22
3 P4 23 35 42
4 P6 31 1 44
4 P4 18 5 6
4 P6 34 8 10
4 P1 2 10 20
4 P8 42 16 29
4 P8 43 26 37
4 P1 5 32 40
4 P5 30 37 5
4 P1 6 40 21
5 P2 10 0 6
5 P5 27 10 10
5 P4 19 20 34
5 P3 14 29 25
5 P1 3 35 27
5 P2 13 38 2
6 P7 38 0 16
6 P3 16 2 42
6 P5 26 6 16
6 P4 22 13 26
6 P1 1 22 32
6 P5 29 30 35
6 P7 40 37 44<\/td>		Makespan = 44

Ws1: Total_Time=43.0, Utilization=0.9773
Ws2: Total_Time=42.0, Utilization=0.9545
Ws3: Total_Time=42.0, Utilization=0.9545
Ws4: Total_Time=43.0, Utilization=0.9773
Ws5: Total_Time=41.0, Utilization=0.9318
Ws6: Total_Time=39.0, Utilization=0.8864

Average System Utilization: 0.9470




































<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 44 Run-time = 3144 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n

Matrix-Structure 3 x 3<\/strong><\/p>\n\n\n\n

Int_11<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong>
1 7 1000 1000 1000 7 1000 1000 1000 7
2 8 1000 1000 8 1000 1000 1000 8 1000
3 1000 6 1000 1000 1000 6 1000 1000 6
4 1000 1000 4 1000 4 1000 1000 4 1000
5 1000 1000 5 1000 1000 5 5 1000 1000
6 1000 3 1000 3 1000 1000 3 1000 1000
7 4 1000 1000 4 1000 1000 1000 4 1000
8 8 1000 1000 1000 8 1000 1000 1000 8
9 1000 1000 9 1000 1000 9 9 1000 1000
10 1000 1000 3 1000 3 1000 1000 3 1000
11 1000 6 1000 6 1000 1000 6 1000 1000
12 1000 5 1000 1000 1000 5 1000 1000 5
13 10 1000 1000 10 1000 1000 1000 10 1000
14 8 1000 1000 1000 8 1000 1000 1000 8
15 1000 1000 7 1000 7 1000 1000 7 1000
16 1000 6 1000 6 1000 1000 6 1000 1000
17 2 1000 1000 1000 2 1000 1000 1000 2
18 1000 1000 5 1000 5 1000 1000 5 1000
19 1000 1000 3 1000 1000 3 3 1000 1000
20 1000 6 1000 6 1000 1000 6 1000 1000
21 1000 4 1000 1000 1000 4 1000 1000 4
22 3 1000 1000 1000 3 1000 1000 1000 3
23 1000 1000 6 1000 1000 6 6 1000 1000
24 8 1000 1000 8 1000 1000 1000 8 1000
25 1000 5 1000 1000 1000 5 1000 1000 5
26 1000 4 1000 4 1000 1000 4 1000 1000
27 1000 1000 8 1000 1000 8 8 1000 1000
28 2 1000 1000 2 1000 1000 1000 2 1000
29 1000 1000 4 1000 4 1000 1000 4 1000
30 1000 3 1000 1000 1000 3 1000 1000 3<\/td>		Predecessor Successor<\/strong>
1 2
2 3
4 5
3 6
5 6
7 8
9 11
10 11
8 12
11 12
13 16
14 16
15 16
17 18
18 19
19 20
20 21
22 23
24 25
23 26
25 26
27 28
28 29
29 30






<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P5 24 0 7
1 P3 13 8 15
2 P5 25 8 21
2 P4 20 14 11
2 P4 21 20 21
3 P2 10 2 24
3 P3 15 5 7
3 P6 29 12 19
3 P1 5 16 11
4 P6 28 9 5
4 P2 11 11 17
4 P5 26 17 24
4 P1 6 21 18
5 P4 17 0 18
5 P4 18 2 12
5 P1 4 7 24
5 P2 8 11 2
6 P6 27 1 7
6 P4 19 11 14
6 P1 3 15 20
6 P6 30 21 24
7 P2 9 2 10
7 P5 23 11 17
7 P3 16 18 8
8 P2 7 3 13
8 P1 2 7 21
9 P1 1 0 9
9 P5 22 7 11
9 P3 14 10 16
9 P2 12 19 24<\/td>		Makespan = 24

Ws1: Total_Time=18.0, Utilization=0.7500
Ws2: Total_Time=15.0, Utilization=0.6250
Ws3: Total_Time=19.0, Utilization=0.7917
Ws4: Total_Time=15.0, Utilization=0.6250
Ws5: Total_Time=19.0, Utilization=0.7917
Ws6: Total_Time=20.0, Utilization=0.8333
Ws7: Total_Time=21.0, Utilization=0.8750
Ws8: Total_Time=12.0, Utilization=0.5000
Ws9: Total_Time=23.0, Utilization=0.9583

Average System Utilization: 0.7500


















<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 24 Run-time = 5,47 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_12<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong>
1 1000 1000 5 5 1000 1000 1000 5 5
2 1000 8 8 1000 8 8 1000 1000 1000
3 6 6 1000 6 1000 1000 6 1000 1000
4 4 1000 1000 1000 4 4 4 1000 1000
5 1000 1000 9 9 1000 1000 1000 9 1000
6 3 1000 1000 1000 1000 3 3 1000 3
7 4 1000 1000 1000 4 4 4 1000 1000
8 1000 1000 6 6 1000 1000 1000 6 6
9 7 1000 1000 1000 1000 7 7 1000 7
10 3 3 1000 3 1000 1000 3 1000 1000
11 1000 8 8 1000 8 8 1000 1000 1000
12 10 1000 1000 1000 1000 10 10 1000 10
13 1000 1000 6 6 1000 1000 1000 6 1000
14 2 2 1000 2 1000 1000 2 1000 1000
15 1000 2 2 1000 2 2 1000 1000 1000
16 8 1000 1000 1000 8 8 8 1000 1000
17 4 4 1000 4 1000 1000 4 1000 1000
18 1000 1000 7 7 1000 1000 1000 7 7
19 1000 1000 5 5 1000 1000 1000 5 1000
20 3 1000 1000 1000 1000 3 3 1000 3
21 8 1000 1000 1000 1000 8 8 1000 8
22 4 4 1000 4 1000 1000 4 1000 1000
23 1000 2 2 1000 2 2 1000 1000 1000
24 1000 1000 5 5 1000 1000 1000 5 1000
25 3 1000 1000 1000 3 3 3 1000 1000
26 9 1000 1000 1000 1000 9 9 1000 9
27 1000 8 8 1000 8 8 1000 1000 1000
28 3 1000 1000 1000 3 3 3 1000 1000
29 1000 1000 4 4 1000 1000 1000 4 1000
30 2 2 1000 2 1000 1000 2 1000 1000
31 1000 1000 5 5 1000 1000 1000 5 5
32 1000 2 2 1000 2 2 1000 1000 1000
33 3 1000 1000 1000 3 3 3 1000 1000
34 1000 1000 4 4 1000 1000 1000 4 4
35 1000 1000 2 2 1000 1000 1000 2 1000<\/td>		Predecessor Successor<\/strong>
1 2
2 3
4 5
3 6
5 6
7 8
8 9
10 11
11 13
12 13
9 14
13 14
15 16
16 17
18 19
17 20
19 20
21 22
22 23
23 24
24 25
26 28
27 28
29 30
28 31
30 31
32 33
33 34
34 35






<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P4 21 0 5
1 P4 22 8 13
1 P2 9 13 19
1 P2 14 20 4
2 P3 15 0 16
2 P1 2 5 22
2 P1 3 13 7
3 P5 27 1 13
3 P3 19 9 20
3 P2 13 14 3
4 P5 29 1 12
4 P5 30 5 10
4 P2 8 7 20
4 P4 24 14 22
4 P6 35 19 2
5 P1 4 0 15
5 P2 11 4 19
5 P4 23 12 7
5 P5 28 14 14
5 P4 25 19 22
6 P2 12 0 8
6 P6 32 10 12
6 P6 33 12 14
6 P1 6 19 19
7 P2 10 0 22
7 P2 7 3 14
7 P3 16 7 9
7 P3 17 15 17
8 P3 18 0 5
8 P1 5 7 7
8 P5 31 17 22
9 P1 1 0 12
9 P5 26 5 15
9 P6 34 15 19
9 P3 20 19 21<\/td>		Makespan = 22

Ws1: Total_Time=21.0, Utilization=0.9545
Ws2: Total_Time=16.0, Utilization=0.7273
Ws3: Total_Time=19.0, Utilization=0.8636
Ws4: Total_Time=19.0, Utilization=0.8636
Ws5: Total_Time=20.0, Utilization=0.9091
Ws6: Total_Time=18.0, Utilization=0.8182
Ws7: Total_Time=19.0, Utilization=0.8636
Ws8: Total_Time=21.0, Utilization=0.9545
Ws9: Total_Time=21.0, Utilization=0.9545

Average System Utilization: 0.8788























<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 22 Run-time = 57,7seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_13<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong>
1 6 6 1000 6 1000 1000 6 1000 1000
2 8 1000 1000 1000 1000 8 8 1000 8
3 4 1000 1000 1000 4 4 4 1000 1000
4 1000 1000 5 5 1000 1000 1000 5 1000
5 1000 1000 7 7 1000 1000 1000 7 7
6 1000 3 3 1000 3 3 1000 1000 1000
7 1000 1000 2 2 1000 1000 1000 2 1000
8 4 1000 1000 1000 4 4 4 1000 1000
9 1000 1000 9 9 1000 1000 1000 9 9
10 5 5 1000 5 1000 1000 5 1000 1000
11 1000 1000 8 8 1000 1000 1000 8 1000
12 1000 3 3 1000 3 3 1000 1000 1000
13 5 1000 1000 1000 1000 5 5 1000 5
14 6 1000 1000 1000 1000 6 6 1000 6
15 4 1000 1000 1000 4 4 4 1000 1000
16 8 8 1000 8 1000 1000 8 1000 1000
17 1000 5 5 1000 5 5 1000 1000 1000
18 1000 1000 3 3 1000 1000 1000 3 3
19 1000 1000 9 9 1000 1000 1000 9 1000
20 2 2 1000 2 1000 1000 2 1000 1000
21 8 1000 1000 1000 1000 8 8 1000 8
22 4 1000 1000 1000 4 4 4 1000 1000
23 1000 1000 6 6 1000 1000 1000 6 1000
24 7 7 1000 7 1000 1000 7 1000 1000
25 1000 1000 3 3 1000 1000 1000 3 3
26 1000 3 3 1000 3 3 1000 1000 1000
27 4 1000 1000 1000 4 4 4 1000 1000
28 10 1000 1000 1000 1000 10 10 1000 10
29 1000 1000 6 6 1000 1000 1000 6 1000
30 1000 1000 5 5 1000 1000 1000 5 5
31 7 1000 1000 1000 7 7 7 1000 1000
32 1000 5 5 1000 5 5 1000 1000 1000
33 1000 3 3 1000 3 3 1000 1000 1000
34 8 1000 1000 1000 1000 8 8 1000 8
35 4 4 1000 4 1000 1000 4 1000 1000
36 8 1000 1000 1000 8 8 8 1000 1000
37 1000 3 3 1000 3 3 1000 1000 1000
38 4 4 1000 4 1000 1000 4 1000 1000
39 1000 1000 2 2 1000 1000 1000 2 1000
40 1000 1000 5 5 1000 1000 1000 5 5<\/td>		Predecessor Successor<\/strong>
1 3
2 3
4 5
3 6
5 6
7 8
8 9
10 12
11 12
9 13
12 13
14 15
16 17
18 19
15 20
17 20
19 20
21 22
22 23
23 24
24 25
26 27
27 29
28 29
29 30
31 32
33 34
32 35
34 35
36 37
37 38
38 39
39 40







<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P3 14 2 19
1 P4 22 8 18
1 P3 15 12 24
1 P7 38 16 8
1 P1 3 20 17
1 P3 20 26 27
2 P3 16 2 10
2 P7 37 10 14
2 P1 1 13 23
2 P6 32 19 5
2 P6 35 24 8
3 P3 18 0 17
3 P1 4 3 28
3 P2 7 8 8
3 P1 5 10 16
3 P5 29 17 10
4 P2 10 0 22
4 P3 19 5 3
4 P2 9 14 14
4 P4 25 25 28
5 P7 36 0 8
5 P6 33 10 12
5 P5 27 13 18
5 P1 6 24 25
6 P6 31 0 28
6 P5 26 7 10
6 P2 8 10 17
6 P2 12 14 10
6 P3 17 17 23
6 P2 13 23 28
7 P4 21 0 7
7 P1 2 10 24
7 P4 24 18 13
8 P2 11 0 23
8 P4 23 12 28
8 P7 39 20 8
8 P5 30 23 13
9 P5 28 0 20
9 P6 34 15 22
9 P7 40 23 28<\/td>		Makespan = 28

Ws1: Total_Time=24.0, Utilization=0.8571
Ws2: Total_Time=26.0, Utilization=0.9286
Ws3: Total_Time=23.0, Utilization=0.8214
Ws4: Total_Time=26.0, Utilization=0.9286
Ws5: Total_Time=18.0, Utilization=0.6429
Ws6: Total_Time=27.0, Utilization=0.9643
Ws7: Total_Time=23.0, Utilization=0.8214
Ws8: Total_Time=21.0, Utilization=0.7500
Ws9: Total_Time=23.0, Utilization=0.8214

Average System Utilization: 0.8373




























<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 28 Run-time = 392 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_14<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong>
1 6 1000 1000 1000 6 6 6 1000 1000
2 4 1000 1000 1000 1000 4 4 1000 4
3 7 7 1000 7 1000 1000 7 1000 1000
4 1000 1000 5 5 1000 1000 1000 5 1000
5 1000 3 3 1000 3 3 1000 1000 1000
6 1000 1000 8 8 1000 1000 1000 8 8
7 2 2 1000 2 1000 1000 2 1000 1000
8 9 1000 1000 1000 1000 9 9 1000 9
9 1000 1000 4 4 1000 1000 1000 4 1000
10 5 1000 1000 1000 5 5 5 1000 1000
11 1000 1000 10 10 1000 1000 1000 10 10
12 1000 6 6 1000 6 6 1000 1000 1000
13 4 1000 1000 1000 1000 4 4 1000 4
14 3 3 1000 3 1000 1000 3 1000 1000
15 6 1000 1000 1000 6 6 6 1000 1000
16 1000 1000 2 2 1000 1000 1000 2 1000
17 1000 8 8 1000 8 8 1000 1000 1000
18 1000 1000 3 3 1000 1000 1000 3 3
19 1000 6 6 1000 6 6 1000 1000 1000
20 8 1000 1000 1000 8 8 8 1000 1000
21 1000 1000 9 9 1000 1000 1000 9 1000
22 3 1000 1000 1000 1000 3 3 1000 3
23 10 10 1000 10 1000 1000 10 1000 1000
24 1000 1000 4 4 1000 1000 1000 4 4
25 1000 1000 2 2 1000 1000 1000 2 1000
26 1000 4 4 1000 4 4 1000 1000 1000
27 8 8 1000 8 1000 1000 8 1000 1000
28 2 1000 1000 1000 2 2 2 1000 1000
29 1000 1000 6 6 1000 1000 1000 6 6
30 1000 1000 7 7 1000 1000 1000 7 1000
31 5 1000 1000 1000 1000 5 5 1000 5
32 1000 1000 3 3 1000 1000 1000 3 3
33 10 1000 1000 1000 1000 10 10 1000 10
34 1000 4 4 1000 4 4 1000 1000 1000
35 2 1000 1000 1000 2 2 2 1000 1000
36 5 1000 1000 1000 1000 5 5 1000 5
37 1000 1000 9 9 1000 1000 1000 9 1000
38 4 1000 1000 1000 4 4 4 1000 1000
39 1000 7 7 1000 7 7 1000 1000 1000
40 6 6 1000 6 1000 1000 6 1000 1000
41 1000 1000 8 8 1000 1000 1000 8 8
42 5 1000 1000 1000 1000 5 5 1000 5
43 1000 1000 10 10 1000 1000 1000 10 1000
44 3 1000 1000 1000 3 3 3 1000 1000
45 4 4 1000 4 1000 1000 4 1000 1000<\/td>		Predecessor Successor<\/strong>
1 2
3 4
2 5
4 5
6 7
7 8
5 9
8 9
10 12
11 12
13 14
15 16
14 17
16 17
12 18
17 18
19 20
21 22
23 24
20 25
22 25
24 25
26 27
27 28
28 29
29 30
30 31
32 33
33 34
34 35
36 38
37 38
38 40
39 40
41 42
43 44
42 45
44 45







<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P2 14 6 12
1 P1 7 9 25
1 P5 33 11 12
1 P1 2 21 25
1 P6 40 26 28
2 P4 27 4 8
2 P2 17 13 11
2 P5 34 21 21
2 P1 5 25 32
2 P7 45 28 19
3 P7 41 0 23
3 P2 16 10 29
3 P2 11 13 4
3 P3 24 24 9
3 P1 9 28 10
4 P7 43 0 12
4 P3 23 10 21
4 P4 30 20 32
4 P3 25 30 16
5 P4 26 0 30
5 P1 1 6 18
5 P4 28 12 28
5 P2 10 14 20
5 P7 44 19 28
5 P3 20 22 32
6 P2 13 0 4
6 P2 15 4 12
6 P3 19 10 14
6 P6 39 16 20
6 P2 12 23 27
7 P6 36 0 32
7 P1 3 5 11
7 P1 8 12 21
7 P6 38 21 25
7 P3 22 25 32
7 P5 35 30 5
8 P6 37 0 9
8 P3 21 9 25
8 P1 4 20 23
8 P2 18 29 32
9 P1 6 0 8
9 P5 32 8 25
9 P4 29 14 10
9 P7 42 20 22
9 P4 31 27 32<\/td>		Makespan = 32

Ws1: Total_Time=25.0, Utilization=0.7812
Ws2: Total_Time=27.0, Utilization=0.8438
Ws3: Total_Time=28.0, Utilization=0.8750
Ws4: Total_Time=29.0, Utilization=0.9062
Ws5: Total_Time=28.0, Utilization=0.8750
Ws6: Total_Time=29.0, Utilization=0.9062
Ws7: Total_Time=30.0, Utilization=0.9375
Ws8: Total_Time=26.0, Utilization=0.8125
Ws9: Total_Time=27.0, Utilization=0.8438

Average System Utilization: 0.8646

































<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 32 Run-time = 948 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_15<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong>
1 2 1000 1000 1000 2 2 2 1000 1000
2 5 5 1000 5 1000 1000 5 1000 1000
3 1000 1000 6 6 1000 1000 1000 6 1000
4 4 1000 1000 1000 1000 4 4 1000 4
5 1000 7 7 1000 7 7 1000 1000 1000
6 1000 1000 3 3 1000 1000 1000 3 3
7 9 1000 1000 1000 9 9 9 1000 1000
8 1000 4 4 1000 4 4 1000 1000 1000
9 1000 1000 5 5 1000 1000 1000 5 1000
10 6 6 1000 6 1000 1000 6 1000 1000
11 8 1000 1000 1000 1000 8 8 1000 8
12 1000 1000 4 4 1000 1000 1000 4 4
13 1000 7 7 1000 7 7 1000 1000 1000
14 5 5 1000 5 1000 1000 5 1000 1000
15 1000 1000 3 3 1000 1000 1000 3 1000
16 9 1000 1000 1000 9 9 9 1000 1000
17 2 1000 1000 1000 1000 2 2 1000 2
18 4 1000 1000 1000 4 4 4 1000 1000
19 1000 1000 5 5 1000 1000 1000 5 1000
20 3 3 1000 3 1000 1000 3 1000 1000
21 1000 9 9 1000 9 9 1000 1000 1000
22 6 1000 1000 1000 1000 6 6 1000 6
23 10 10 1000 10 1000 1000 10 1000 1000
24 2 1000 1000 1000 2 2 2 1000 1000
25 1000 1000 6 6 1000 1000 1000 6 6
26 6 1000 1000 1000 6 6 6 1000 1000
27 8 1000 1000 1000 1000 8 8 1000 8
28 1000 4 4 1000 4 4 1000 1000 1000
29 1000 1000 6 6 1000 1000 1000 6 1000
30 1000 1000 5 5 1000 1000 1000 5 5
31 7 7 1000 7 1000 1000 7 1000 1000
32 8 1000 1000 1000 1000 8 8 1000 8
33 1000 1000 10 10 1000 1000 1000 10 1000
34 1000 1000 6 6 1000 1000 1000 6 6
35 1000 3 3 1000 3 3 1000 1000 1000
36 4 1000 1000 1000 4 4 4 1000 1000
37 10 10 1000 10 1000 1000 10 1000 1000
38 1000 2 2 1000 2 2 1000 1000 1000
39 4 1000 1000 1000 4 4 4 1000 1000
40 1000 1000 8 8 1000 1000 1000 8 8
41 3 1000 1000 1000 1000 3 3 1000 3
42 1000 1000 6 6 1000 1000 1000 6 1000
43 9 1000 1000 1000 1000 9 9 1000 9
44 1000 1000 5 5 1000 1000 1000 5 5
45 10 1000 1000 1000 10 10 10 1000 1000
46 4 4 1000 4 1000 1000 4 1000 1000
47 1000 3 3 1000 3 3 1000 1000 1000
48 8 1000 1000 1000 1000 8 8 1000 8
49 4 1000 1000 1000 4 4 4 1000 1000
50 2 1000 1000 1000 1000 2 2 1000 2<\/td>		Predecessor Successor<\/strong>
1 2
3 4
2 5
4 5
6 8
7 8
5 9
8 9
10 12
11 12
13 16
14 16
15 16
12 17
16 17
18 19
19 20
21 22
23 24
20 25
22 25
24 25
26 27
27 28
28 29
29 30
30 31
32 33
33 34
34 35
35 36
37 39
38 39
40 41
39 42
41 42
43 44
45 46
44 47
46 47
48 50
49 50








<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P1 1 0 2
1 P8 49 2 11
1 P4 27 6 6
1 P6 37 14 21
1 P3 20 24 31
1 P3 24 28 3
1 P2 17 34 9
2 P2 13 1 16
2 P2 10 8 36
2 P4 28 14 14
2 P7 46 22 8
2 P7 47 26 34
2 P4 31 29 8
3 P1 6 0 14
3 P3 21 3 3
3 P1 8 12 31
3 P6 38 16 36
3 P4 29 18 12
3 P1 9 31 24
4 P2 15 0 27
4 P1 2 6 12
4 P3 23 11 30
4 P7 44 21 21
4 P3 25 30 30
5 P4 26 0 36
5 P3 18 8 6
5 P7 45 12 14
5 P6 39 24 18
5 P5 35 28 24
6 P2 11 0 29
6 P7 43 8 36
6 P1 4 17 8
6 P6 41 21 18
6 P1 5 24 24
6 P8 50 34 31
7 P1 7 0 36
7 P2 14 9 24
7 P8 48 14 18
7 P2 16 22 28
7 P5 36 32 18
8 P1 3 0 24
8 P5 33 8 36
8 P3 19 19 17
8 P4 30 24 26
8 P6 42 30 22
9 P5 32 0 26
9 P6 40 10 29
9 P5 34 18 22
9 P3 22 24 6
9 P2 12 30 36<\/td>		Makespan = 36

Ws1: Total_Time=31.0, Utilization=0.8611
Ws2: Total_Time=31.0, Utilization=0.8611
Ws3: Total_Time=29.0, Utilization=0.8056
Ws4: Total_Time=29.0, Utilization=0.8056
Ws5: Total_Time=27.0, Utilization=0.7500
Ws6: Total_Time=33.0, Utilization=0.9167
Ws7: Total_Time=35.0, Utilization=0.9722
Ws8: Total_Time=32.0, Utilization=0.8889
Ws9: Total_Time=32.0, Utilization=0.8889

Average System Utilization: 0.8611






































<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 36 Run-time = 507 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_16<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th>Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong>
1 1000 6 6 1000 6 6 1000 1000 1000
2 2 2 1000 2 1000 1000 2 1000 1000
3 8 1000 1000 1000 1000 8 8 1000 8
4 4 1000 1000 1000 4 4 4 1000 1000
5 1000 1000 9 9 1000 1000 1000 9 9
6 1000 1000 7 7 1000 1000 1000 7 1000
7 3 1000 1000 1000 1000 3 3 1000 3
8 5 5 1000 5 1000 1000 5 1000 1000
9 1000 4 4 1000 4 4 1000 1000 1000
10 1000 1000 2 2 1000 1000 1000 2 1000
11 1000 1000 3 3 1000 1000 1000 3 3
12 7 1000 1000 1000 7 7 7 1000 1000
13 1000 5 5 1000 5 5 1000 1000 1000
14 10 1000 1000 1000 1000 10 10 1000 10
15 8 8 1000 8 1000 1000 8 1000 1000
16 1000 1000 4 4 1000 1000 1000 4 1000
17 6 1000 1000 1000 1000 6 6 1000 6
18 1000 9 9 1000 9 9 1000 1000 1000
19 1000 1000 3 3 1000 1000 1000 3 1000
20 2 1000 1000 1000 1000 2 2 1000 2
21 5 5 1000 5 1000 1000 5 1000 1000
22 6 1000 1000 1000 6 6 6 1000 1000
23 1000 1000 8 8 1000 1000 1000 8 8
24 4 1000 1000 1000 4 4 4 1000 1000
25 1000 1000 10 10 1000 1000 1000 10 10
26 2 1000 1000 1000 1000 2 2 1000 2
27 1000 4 4 1000 4 4 1000 1000 1000
28 1000 1000 6 6 1000 1000 1000 6 1000
29 5 5 1000 5 1000 1000 5 1000 1000
30 8 1000 1000 1000 8 8 8 1000 1000
31 3 1000 1000 1000 1000 3 3 1000 3
32 1000 9 9 1000 9 9 1000 1000 1000
33 1000 1000 6 6 1000 1000 1000 6 1000
34 1000 1000 7 7 1000 1000 1000 7 7
35 9 1000 1000 1000 1000 9 9 1000 9
36 3 1000 1000 1000 3 3 3 1000 1000
37 1000 1000 8 8 1000 1000 1000 8 1000
38 1000 2 2 1000 2 2 1000 1000 1000
39 4 4 1000 4 1000 1000 4 1000 1000
40 1000 1000 5 5 1000 1000 1000 5 5
41 1000 1000 4 4 1000 1000 1000 4 1000
42 1000 6 6 1000 6 6 1000 1000 1000
43 7 7 1000 7 1000 1000 7 1000 1000
44 2 1000 1000 1000 1000 2 2 1000 2
45 3 1000 1000 1000 3 3 3 1000 1000
46 1000 1000 9 9 1000 1000 1000 9 9
47 1000 5 5 1000 5 5 1000 1000 1000
48 10 1000 1000 1000 10 10 10 1000 1000
49 1000 1000 5 5 1000 1000 1000 5 1000
50 6 6 1000 6 1000 1000 6 1000 1000
51 4 1000 1000 1000 1000 4 4 1000 4
52 1000 1000 2 2 1000 1000 1000 2 1000
53 5 1000 1000 1000 5 5 5 1000 1000
54 6 6 1000 6 1000 1000 6 1000 1000
55 1000 3 3 1000 3 3 1000 1000 1000<\/td>		Predecessor Successor<\/strong>
1 2
3 4
2 5
4 5
6 7
7 8
5 9
8 9
10 12
11 12
13 16
14 16
15 16
12 17
16 17
18 19
20 21
22 23
19 24
21 24
23 24
25 26
26 27
27 28
28 29
30 31
31 33
32 33
34 36
35 36
37 39
38 39
36 40
39 40
41 42
43 44
42 45
44 45
46 47
47 48
48 49
49 50
50 51
52 53
53 54
54 55









<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P3 20 0 15
1 P9 53 2 17
1 P4 26 11 25
1 P7 44 13 29
1 P1 2 15 38
1 P8 48 17 13
1 P1 7 28 31
2 P7 43 0 36
2 P2 13 7 42
2 P5 32 12 21
2 P6 38 21 19
2 P3 21 27 36
2 P8 50 32 12
3 P8 46 0 20
3 P6 37 9 8
3 P4 27 17 36
3 P4 28 21 42
3 P6 40 27 9
3 P5 33 33 12
3 P9 55 39 2
4 P2 15 0 32
4 P3 19 9 28
4 P7 41 12 36
4 P2 11 16 40
4 P2 10 19 11
4 P9 54 21 13
4 P8 49 27 21
4 P2 16 32 27
4 P4 29 37 42
5 P5 30 0 8
5 P1 1 9 17
5 P7 42 16 21
5 P1 4 25 39
5 P1 9 38 20
6 P3 18 0 10
6 P8 47 9 23
6 P3 22 22 17
6 P2 12 29 23
6 P2 17 36 27
7 P6 35 1 32
7 P2 14 10 16
7 P4 26 11 22
7 P4 29 37 7
7 P7 45 28 15
7 P1 8 31 31
7 P3 24 36 9
8 P9 52 0 14
8 P1 6 6 27
8 P6 34 13 32
8 P1 5 29 38
9 P4 25 1 42
9 P5 31 14 2
9 P1 3 17 7
9 P3 23 28 27
9 P8 51 38 42<\/td>		Makespan = 42

Ws1: Total_Time=26.0, Utilization=0.6190
Ws2: Total_Time=34.0, Utilization=0.8095
Ws3: Total_Time=41.0, Utilization=0.9762
Ws4: Total_Time=40.0, Utilization=0.9524
Ws5: Total_Time=28.0, Utilization=0.6667
Ws6: Total_Time=33.0, Utilization=0.7857
Ws7: Total_Time=38.0, Utilization=0.9048
Ws8: Total_Time=25.0, Utilization=0.5952
Ws9: Total_Time=33.0, Utilization=0.7857

Average System Utilization: 0.7884











































<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 42 Run-time = 2278 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n

Matrix-Structure 3 x <\/strong>4<\/p>\n\n\n\n

Int_17<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong> Ws<\/strong>10<\/strong><\/strong> Ws11<\/strong><\/strong><\/strong> Ws12<\/strong><\/strong><\/strong>
1 6 1000 1000 1000 1000 6 6 1000 1000 1000 6 1000
2 1000 4 1000 1000 4 1000 1000 1000 4 1000 4 1000
3 8 1000 1000 1000 1000 8 1000 1000 8 1000 1000 8
4 10 1000 1000 1000 10 1000 1000 10 1000 10 1000 1000
5 1000 7 1000 1000 7 1000 7 1000 1000 7 1000 1000
6 1000 1000 2 2 1000 1000 2 1000 1000 1000 1000 2
7 1000 1000 9 9 1000 1000 1000 1000 9 1000 9 1000
8 2 1000 1000 1000 1000 2 2 1000 1000 1000 2 1000
9 1000 8 1000 1000 8 1000 8 1000 1000 8 1000 1000
10 1000 7 1000 1000 7 1000 1000 1000 7 1000 7 1000
11 6 1000 1000 1000 6 1000 1000 6 1000 6 1000 1000
12 1000 1000 4 4 1000 1000 4 1000 1000 1000 1000 4
13 1000 1000 10 10 1000 1000 1000 10 1000 1000 1000 10
14 5 1000 1000 1000 1000 5 1000 1000 5 1000 1000 5
15 1000 1000 3 3 1000 1000 1000 1000 3 1000 3 1000
16 1000 9 1000 1000 9 1000 9 1000 1000 9 1000 1000
17 4 1000 1000 1000 1000 4 1000 1000 4 1000 1000 4
18 1000 1000 2 2 1000 1000 2 1000 1000 1000 1000 2
19 7 1000 1000 1000 1000 7 7 1000 1000 1000 7 1000
20 10 1000 1000 1000 10 1000 1000 10 1000 10 1000 1000
21 1000 1000 5 5 1000 1000 1000 5 1000 1000 1000 5
22 1000 8 1000 1000 8 1000 1000 1000 8 1000 8 1000
23 1000 1000 6 6 1000 1000 1000 1000 6 1000 6 1000
24 4 1000 1000 1000 1000 4 4 1000 1000 1000 4 1000
25 1000 2 1000 1000 2 1000 1000 1000 2 1000 2 1000
26 7 1000 1000 1000 7 1000 1000 7 1000 7 1000 1000
27 1000 1000 3 3 1000 1000 1000 3 1000 1000 1000 3
28 4 1000 1000 1000 1000 4 1000 1000 4 1000 1000 4
29 1000 3 1000 1000 3 1000 3 1000 1000 3 1000 1000
30 1000 1000 6 6 1000 1000 6 1000 1000 1000 1000 6
31 1000 5 1000 1000 5 1000 1000 1000 5 1000 5 1000
32 1000 1000 2 2 1000 1000 1000 1000 2 1000 2 1000
33 1000 1000 8 8 1000 1000 1000 8 1000 1000 1000 8
34 6 1000 1000 1000 1000 6 6 1000 1000 1000 6 1000
35 2 1000 1000 1000 2 1000 1000 2 1000 2 1000 1000
36 1000 1000 8 8 1000 1000 8 1000 1000 1000 1000 8
37 1000 1000 4 4 1000 1000 1000 1000 4 1000 4 1000
38 1000 1000 10 10 1000 1000 1000 10 1000 1000 1000 10
39 1000 7 1000 1000 7 1000 7 1000 1000 7 1000 1000
40 6 1000 1000 1000 1000 6 1000 1000 6 1000 1000 6<\/td>		Predecessor Successor<\/strong>
1 2
2 3
4 5
3 6
5 6
7 8
8 9
10 11
12 13
11 14
13 14
9 15
14 15
16 17
18 19
20 21
17 22
19 22
21 22
23 24
24 25
25 26
26 27
28 29
29 31
30 31
31 32
33 34
32 35
34 35
36 37
38 39
37 40
39 40






<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P1 4 0 6
1 P2 8 10 13
1 P1 3 13 21
2 P2 10 0 10
2 P5 29 7 21
2 P4 25 10 23
2 P2 9 12 9
3 P6 38 0 12
3 P3 21 10 20
3 P1 6 21 7
4 P2 12 0 15
4 P2 13 4 4
4 P2 15 20 14
5 P3 16 0 20
5 P2 11 9 23
5 P3 22 15 9
6 P5 28 2 14
6 P4 24 6 2
6 P5 34 10 13
6 P6 40 17 10
7 P1 1 0 15
7 P5 30 8 23
7 P1 5 14 6
8 P5 33 0 10
8 P4 26 12 12
8 P4 27 19 19
9 P2 7 0 22
9 P1 2 9 6
9 P6 37 13 10
9 P5 32 19 14
10 P3 20 0 19
10 P6 39 10 21
10 P5 35 21 8
11 P4 23 0 16
11 P3 19 6 23
11 P5 31 14 10
12 P3 18 0 17
12 P6 36 2 10
12 P3 17 10 17
12 P2 14 15 23<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Makespan = 23

Ws1: Total_Time=20.0, Utilization=0.8696
Ws2: Total_Time=20.0, Utilization=0.8696
Ws3: Total_Time=17.0, Utilization=0.7391
Ws4: Total_Time=17.0, Utilization=0.7391
Ws5: Total_Time=23.0, Utilization=1.0000
Ws6: Total_Time=20.0, Utilization=0.8696
Ws7: Total_Time=19.0, Utilization=0.8261
Ws8: Total_Time=18.0, Utilization=0.7826
Ws9: Total_Time=19.0, Utilization=0.8261
Ws10: Total_Time=19.0, Utilization=0.8261
Ws11: Total_Time=18.0, Utilization=0.7826
Ws12: Total_Time=19.0, Utilization=0.8261

Average System Utilization: 0.8297<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 23 Run-time = 32,8 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_18<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong> Ws<\/strong>10<\/strong><\/strong> Ws11<\/strong><\/strong><\/strong> Ws12<\/strong><\/strong><\/strong>
1 6 1000 1000 1000 1000 6 6 1000 1000 1000 6 1000
2 1000 4 1000 1000 4 1000 1000 1000 4 1000 4 1000
3 1000 1000 10 10 1000 1000 1000 10 1000 1000 1000 10
4 8 1000 1000 1000 1000 8 1000 1000 8 1000 1000 8
5 1000 1000 3 3 1000 1000 1000 1000 3 1000 3 1000
6 5 1000 1000 1000 1000 5 5 1000 1000 1000 5 1000
7 6 1000 1000 1000 6 1000 1000 6 1000 6 1000 1000
8 1000 7 1000 1000 7 1000 7 1000 1000 7 1000 1000
9 1000 1000 5 5 1000 1000 5 1000 1000 1000 1000 5
10 7 1000 1000 1000 1000 7 7 1000 1000 1000 7 1000
11 1000 1000 9 9 1000 1000 1000 1000 9 1000 9 1000
12 1000 8 1000 1000 8 1000 8 1000 1000 8 1000 1000
13 1000 4 1000 1000 4 1000 1000 1000 4 1000 4 1000
14 6 1000 1000 1000 6 1000 1000 6 1000 6 1000 1000
15 1000 1000 10 10 1000 1000 10 1000 1000 1000 1000 10
16 1000 1000 3 3 1000 1000 1000 3 1000 1000 1000 3
17 5 1000 1000 1000 1000 5 1000 1000 5 1000 1000 5
18 1000 1000 3 3 1000 1000 1000 1000 3 1000 3 1000
19 1000 1000 8 8 1000 1000 1000 1000 8 1000 8 1000
20 1000 5 1000 1000 5 1000 5 1000 1000 5 1000 1000
21 4 1000 1000 1000 1000 4 1000 1000 4 1000 1000 4
22 1000 1000 2 2 1000 1000 2 1000 1000 1000 1000 2
23 7 1000 1000 1000 1000 7 7 1000 1000 1000 7 1000
24 10 1000 1000 1000 10 1000 1000 10 1000 10 1000 1000
25 1000 1000 5 5 1000 1000 1000 5 1000 1000 1000 5
26 1000 6 1000 1000 6 1000 1000 1000 6 1000 6 1000
27 8 1000 1000 1000 8 1000 1000 8 1000 8 1000 1000
28 4 1000 1000 1000 1000 4 4 1000 1000 1000 4 1000
29 1000 5 1000 1000 5 1000 5 1000 1000 5 1000 1000
30 1000 1000 7 7 1000 1000 7 1000 1000 1000 1000 7
31 1000 3 1000 1000 3 1000 1000 1000 3 1000 3 1000
32 1000 1000 6 6 1000 1000 1000 1000 6 1000 6 1000
33 1000 3 1000 1000 3 1000 3 1000 1000 3 1000 1000
34 4 1000 1000 1000 1000 4 1000 1000 4 1000 1000 4
35 1000 1000 8 8 1000 1000 8 1000 1000 1000 1000 8
36 1000 5 1000 1000 5 1000 1000 1000 5 1000 5 1000
37 1000 1000 4 4 1000 1000 1000 1000 4 1000 4 1000
38 1000 1000 9 9 1000 1000 1000 9 1000 1000 1000 9
39 7 1000 1000 1000 1000 7 7 1000 1000 1000 7 1000
40 2 1000 1000 1000 2 1000 1000 2 1000 2 1000 1000
41 1000 1000 8 8 1000 1000 8 1000 1000 1000 1000 8
42 1000 6 1000 1000 6 1000 1000 1000 6 1000 6 1000
43 1000 1000 10 10 1000 1000 1000 10 1000 1000 1000 10
44 1000 3 1000 1000 3 1000 3 1000 1000 3 1000 1000
45 4 1000 1000 1000 1000 4 1000 1000 4 1000 1000 4<\/td>		Predecessor Successor<\/strong>
1 2
2 4
3 4
5 6
6 7
7 8
4 9
8 9
10 12
11 12
13 14
15 16
14 17
16 17
12 18
17 18
19 20
20 21
22 23
24 25
21 26
23 26
25 26
27 28
28 29
29 30
30 31
32 33
34 35
33 36
35 36
38 39
37 40
39 40
41 42
42 43
43 44
44 45







<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P5 34 4 6
1 P4 28 8 12
1 P1 4 12 12
1 P3 21 20 20
1 P6 40 29 5
2 P1 2 8 12
2 P2 12 15 18
2 P3 26 24 25
3 P1 5 2 31
3 P5 32 5 7
3 P2 16 11 15
3 P3 22 14 23
3 P4 30 17 12
4 P6 38 0 23
4 P7 43 14 10
4 P6 37 24 14
4 P2 18 28 28
5 P4 27 0 31
5 P2 13 8 8
5 P3 20 12 17
5 P2 14 17 24
5 P5 36 26 16
6 P2 10 0 23
6 P1 6 7 12
6 P3 23 16 24
6 P2 17 23 30
7 P2 15 0 8
7 P5 33 11 12
7 P6 39 14 17
7 P7 44 24 24
8 P1 3 2 27
8 P1 7 12 11
9 P3 19 0 14
9 P7 42 8 8
9 P7 45 27 16
10 P3 24 2 31
10 P4 29 12 28
10 P1 8 18 9
11 P1 1 0 21
11 P2 11 6 31
11 P4 31 24 8
12 P7 41 0 14
12 P5 35 8 24
12 P3 25 19 27
12 P1 9 26 31<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Makespan = 31

Ws1: Total_Time=22.0, Utilization=0.7097
Ws2: Total_Time=18.0, Utilization=0.5806
Ws3: Total_Time=21.0, Utilization=0.6774
Ws4: Total_Time=26.0, Utilization=0.8387
Ws5: Total_Time=28.0, Utilization=0.9032
Ws6: Total_Time=24.0, Utilization=0.7742
Ws7: Total_Time=23.0, Utilization=0.7419
Ws8: Total_Time=16.0, Utilization=0.5161
Ws9: Total_Time=18.0, Utilization=0.5806
Ws10: Total_Time=22.0, Utilization=0.7097
Ws11: Total_Time=18.0, Utilization=0.5806
Ws12: Total_Time=26.0, Utilization=0.8387

Average System Utilization: 0.7043<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 31 Run-time = 472 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_19<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong> Ws<\/strong>10<\/strong><\/strong> Ws11<\/strong><\/strong><\/strong> Ws12<\/strong><\/strong><\/strong>
1 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 1000
2 1000 1000 3 3 1000 1000 1000 3 1000 1000 1000 3
3 5 1000 1000 1000 1000 5 5 1000 1000 1000 5 1000
4 6 1000 1000 1000 1000 6 1000 1000 6 1000 1000 6
5 1000 8 1000 1000 8 1000 1000 1000 8 1000 8 1000
6 1000 7 1000 1000 7 1000 7 1000 1000 7 1000 1000
7 2 1000 1000 1000 2 1000 1000 2 1000 2 1000 1000
8 1000 1000 9 9 1000 1000 1000 1000 9 1000 9 1000
9 1000 1000 4 4 1000 1000 4 1000 1000 1000 1000 4
10 1000 1000 5 5 1000 1000 5 1000 1000 1000 1000 5
11 1000 10 1000 1000 10 1000 1000 1000 10 1000 10 1000
12 8 1000 1000 1000 8 1000 1000 8 1000 8 1000 1000
13 7 1000 1000 1000 7 1000 1000 7 1000 7 1000 1000
14 1000 3 1000 1000 3 1000 3 1000 1000 3 1000 1000
15 1000 1000 9 9 1000 1000 1000 1000 9 1000 9 1000
16 3 1000 1000 1000 1000 3 1000 1000 3 1000 1000 3
17 2 1000 1000 1000 1000 2 2 1000 1000 1000 2 1000
18 1000 1000 5 5 1000 1000 5 1000 1000 1000 1000 5
19 2 1000 1000 1000 2 1000 1000 2 1000 2 1000 1000
20 1000 1000 5 5 1000 1000 1000 5 1000 1000 1000 5
21 1000 4 1000 1000 4 1000 4 1000 1000 4 1000 1000
22 9 1000 1000 1000 1000 9 1000 1000 9 1000 1000 9
23 1000 1000 3 3 1000 1000 1000 1000 3 1000 3 1000
24 1000 6 1000 1000 6 1000 1000 1000 6 1000 6 1000
25 1000 9 1000 1000 9 1000 1000 1000 9 1000 9 1000
26 1000 1000 4 4 1000 1000 1000 4 1000 1000 1000 4
27 8 1000 1000 1000 1000 8 8 1000 1000 1000 8 1000
28 5 1000 1000 1000 1000 5 1000 1000 5 1000 1000 5
29 1000 1000 6 6 1000 1000 6 1000 1000 1000 1000 6
30 1000 1000 2 2 1000 1000 1000 1000 2 1000 2 1000
31 1000 6 1000 1000 6 1000 1000 1000 6 1000 6 1000
32 9 1000 1000 1000 9 1000 1000 9 1000 9 1000 1000
33 4 1000 1000 1000 1000 4 4 1000 1000 1000 4 1000
34 1000 2 1000 1000 2 1000 2 1000 1000 2 1000 1000
35 5 1000 1000 1000 1000 5 5 1000 1000 1000 5 1000
36 1000 1000 4 4 1000 1000 4 1000 1000 1000 1000 4
37 10 1000 1000 1000 1000 10 1000 1000 10 1000 1000 10
38 1000 1000 3 3 1000 1000 1000 3 1000 1000 1000 3
39 1000 1000 7 7 1000 1000 1000 1000 7 1000 7 1000
40 1000 3 1000 1000 3 1000 3 1000 1000 3 1000 1000
41 3 1000 1000 1000 1000 3 1000 1000 3 1000 1000 3
42 1000 8 1000 1000 8 1000 1000 1000 8 1000 8 1000
43 10 1000 1000 1000 10 1000 1000 10 1000 10 1000 1000
44 4 1000 1000 1000 1000 4 4 1000 1000 1000 4 1000
45 1000 6 1000 1000 6 1000 6 1000 1000 6 1000 1000
46 1000 1000 4 4 1000 1000 4 1000 1000 1000 1000 4
47 8 1000 1000 1000 1000 8 8 1000 1000 1000 8 1000
48 5 1000 1000 1000 1000 5 1000 1000 5 1000 1000 5
49 1000 1000 6 6 1000 1000 1000 6 1000 1000 1000 6
50 1000 3 1000 1000 3 1000 1000 1000 3 1000 3 1000<\/td>		Predecessor Successor<\/strong>
1 2
3 4
2 5
4 5
6 7
7 8
5 9
8 9
10 12
11 12
13 16
14 16
15 16
12 17
16 17
18 19
20 21
22 23
19 24
21 24
23 24
25 26
26 27
27 28
28 29
29 30
31 33
32 33
34 36
35 36
37 39
38 39
36 40
39 40
41 42
43 44
42 45
44 45
46 47
47 48
48 49
49 50








<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P1 1 0 4
1 P6 35 5 7
1 P1 3 10 15
1 P1 7 17 21
1 P3 19 19 29
1 P2 12 21 17
2 P2 11 0 19
2 P1 6 10 30
2 P7 42 17 34
2 P6 40 31 13
3 P8 46 0 10
3 P2 15 12 29
3 P1 8 21 16
3 P1 9 30 28
4 P3 18 4 21
4 P4 26 9 32
4 P3 23 13 34
4 P3 20 16 9
4 P4 30 32 21
5 P4 25 0 21
5 P5 31 19 25
5 P3 24 25 9
6 P8 47 4 16
6 P1 4 15 31
6 P4 28 21 9
7 P6 34 6 13
7 P2 10 8 21
7 P4 27 13 26
7 P7 44 21 32
7 P2 14 25 34
7 P5 33 28 25
7 P2 17 32 9
8 P5 32 0 32
8 P2 13 9 8
8 P8 49 17 10
9 P3 22 0 14
9 P8 48 12 24
9 P1 5 21 4
9 P2 16 29 31
10 P7 43 11 34
10 P3 21 21 10
10 P7 45 25 25
11 P6 39 24 21
11 P8 50 31 25
12 P6 38 1 31
12 P1 2 4 4
12 P7 41 7 12
12 P6 36 10 17
12 P6 37 14 23
12 P4 29 26 34<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Makespan = 34

Ws1: Total_Time=26.0, Utilization=0.7647
Ws2: Total_Time=28.0, Utilization=0.8235
Ws3: Total_Time=26.0, Utilization=0.7647
Ws4: Total_Time=19.0, Utilization=0.5588
Ws5: Total_Time=21.0, Utilization=0.6176
Ws6: Total_Time=19.0, Utilization=0.5588
Ws7: Total_Time=28.0, Utilization=0.8235
Ws8: Total_Time=22.0, Utilization=0.6471
Ws9: Total_Time=25.0, Utilization=0.7353
Ws10: Total_Time=20.0, Utilization=0.5882
Ws11: Total_Time=10.0, Utilization=0.2941
Ws12: Total_Time=29.0, Utilization=0.8529

Average System Utilization: 0.6691<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 34 Run-time = 528 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_20<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong> Ws<\/strong>10<\/strong><\/strong> Ws11<\/strong><\/strong><\/strong> Ws12<\/strong><\/strong><\/strong>
1 1000 8 1000 1000 8 1000 1000 1000 8 1000 8 1000
2 5 1000 1000 1000 1000 5 5 1000 1000 1000 5 1000
3 1000 1000 7 7 1000 1000 1000 7 1000 1000 1000 7
4 1000 1000 3 3 1000 1000 3 1000 1000 1000 1000 3
5 2 1000 1000 1000 1000 2 1000 1000 2 1000 1000 2
6 1000 1000 10 10 1000 1000 1000 1000 10 1000 10 1000
7 1000 9 1000 1000 9 1000 9 1000 1000 9 1000 1000
8 6 1000 1000 1000 1000 6 6 1000 1000 1000 6 1000
9 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 1000
10 8 1000 1000 1000 1000 8 8 1000 1000 1000 8 1000
11 1000 1000 3 3 1000 1000 3 1000 1000 1000 1000 3
12 1000 5 1000 1000 5 1000 5 1000 1000 5 1000 1000
13 1000 1000 4 4 1000 1000 1000 1000 4 1000 4 1000
14 10 1000 1000 1000 1000 10 1000 1000 10 1000 1000 10
15 7 1000 1000 1000 7 1000 1000 7 1000 7 1000 1000
16 1000 2 1000 1000 2 1000 1000 1000 2 1000 2 1000
17 1000 1000 6 6 1000 1000 1000 6 1000 1000 1000 6
18 1000 1000 9 9 1000 1000 9 1000 1000 1000 1000 9
19 1000 10 1000 1000 10 1000 1000 1000 10 1000 10 1000
20 1000 3 1000 1000 3 1000 3 1000 1000 3 1000 1000
21 1000 1000 5 5 1000 1000 1000 1000 5 1000 5 1000
22 8 1000 1000 1000 1000 8 8 1000 1000 1000 8 1000
23 1000 2 1000 1000 2 1000 1000 1000 2 1000 2 1000
24 1000 1000 10 10 1000 1000 10 1000 1000 1000 1000 10
25 8 1000 1000 1000 1000 8 1000 1000 8 1000 1000 8
26 1000 1000 3 3 1000 1000 1000 1000 3 1000 3 1000
27 1000 4 1000 1000 4 1000 4 1000 1000 4 1000 1000
28 6 1000 1000 1000 6 1000 1000 6 1000 6 1000 1000
29 5 1000 1000 1000 1000 5 5 1000 1000 1000 5 1000
30 1000 2 1000 1000 2 1000 1000 1000 2 1000 2 1000
31 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 1000
32 1000 1000 6 6 1000 1000 1000 6 1000 1000 1000 6
33 8 1000 1000 1000 1000 8 1000 1000 8 1000 1000 8
34 7 1000 1000 1000 7 1000 1000 7 1000 7 1000 1000
35 9 1000 1000 1000 1000 9 9 1000 1000 1000 9 1000
36 1000 1000 3 3 1000 1000 1000 3 1000 1000 1000 3
37 8 1000 1000 1000 1000 8 1000 1000 8 1000 1000 8
38 1000 1000 2 2 1000 1000 2 1000 1000 1000 1000 2
39 1000 4 1000 1000 4 1000 4 1000 1000 4 1000 1000
40 1000 1000 5 5 1000 1000 1000 1000 5 1000 5 1000
41 1000 1000 5 5 1000 1000 1000 1000 5 1000 5 1000
42 1000 2 1000 1000 2 1000 1000 1000 2 1000 2 1000
43 7 1000 1000 1000 1000 7 7 1000 1000 1000 7 1000
44 6 1000 1000 1000 1000 6 1000 1000 6 1000 1000 6
45 1000 1000 3 3 1000 1000 1000 3 1000 1000 1000 3
46 1000 8 1000 1000 8 1000 8 1000 1000 8 1000 1000
47 9 1000 1000 1000 1000 9 1000 1000 9 1000 1000 9
48 3 1000 1000 1000 1000 3 3 1000 1000 1000 3 1000
49 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 1000
50 6 1000 1000 1000 1000 6 1000 1000 6 1000 1000 6
51 1000 1000 5 5 1000 1000 1000 5 1000 1000 1000 5
52 1000 10 1000 1000 10 1000 1000 1000 10 1000 10 1000
53 1000 1000 4 4 1000 1000 1000 1000 4 1000 4 1000
54 1000 1000 5 5 1000 1000 5 1000 1000 1000 1000 5
55 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 1000<\/td>		Predecessor Successor<\/strong>
1 2
3 4
2 5
4 5
6 7
7 8
5 9
8 9
10 12
11 12
13 16
14 16
15 16
12 17
16 17
19 21
20 21
18 23
21 23
22 23
24 25
25 26
26 27
27 28
28 29
30 31
31 33
32 33
34 36
35 36
37 39
38 39
36 40
39 40
41 42
43 44
42 45
44 45
46 47
47 48
48 49
49 50
50 51
52 53
53 54
54 55









<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P2 10 0 10
1 P8 47 8 15
1 P6 35 17 17
1 P1 9 32 30
2 P1 1 2 32
2 P1 7 10 10
2 P4 27 21 19
2 P3 23 34 26
3 P6 38 0 36
3 P1 3 10 8
3 P3 18 17 10
3 P6 36 26 19
3 P6 40 31 4
4 P1 6 0 23
4 P7 41 15 20
4 P9 53 20 25
4 P7 45 24 35
4 P1 4 27 26
4 P8 51 31 24
5 P8 46 0 29
5 P6 39 13 34
5 P5 31 17 15
5 P7 42 21 36
5 P2 16 23 10
6 P6 37 0 18
6 P2 14 13 21
6 P5 33 23 25
6 P4 29 31 31
7 P4 24 0 36
7 P1 2 10 17
7 P8 48 17 21
7 P1 8 20 7
8 P2 15 13 31
8 P8 49 20 26
8 P4 28 25 26
9 P2 13 0 29
9 P9 52 4 8
9 P3 19 14 2
9 P8 50 24 17
9 P1 5 30 36
10 P2 12 14 20
10 P6 34 19 23
10 P3 20 26 7
10 P9 55 29 24
11 P7 43 0 27
11 P3 22 7 8
11 P5 30 15 17
11 P4 26 18 20
11 P3 21 29 24
12 P5 32 1 30
12 P2 11 7 36
12 P4 25 10 14
12 P7 44 18 24
12 P9 54 24 29
12 P2 17 29 33<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Makespan = 36

Ws1: Total_Time=20.0, Utilization=0.8696
Ws2: Total_Time=20.0, Utilization=0.8696
WWs1: Total_Time=30.0, Utilization=0.8333
Ws2: Total_Time=23.0, Utilization=0.6389
Ws3: Total_Time=26.0, Utilization=0.7222
Ws4: Total_Time=30.0, Utilization=0.8333
Ws5: Total_Time=20.0, Utilization=0.5556
Ws6: Total_Time=31.0, Utilization=0.8611
Ws7: Total_Time=24.0, Utilization=0.6667
Ws8: Total_Time=17.0, Utilization=0.4722
Ws9: Total_Time=32.0, Utilization=0.8889
Ws10: Total_Time=19.0, Utilization=0.5278
Ws11: Total_Time=25.0, Utilization=0.6944
Ws12: Total_Time=34.0, Utilization=0.9444

Average System Utilization: 0.7199<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 36 Run-time = 348 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_21<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong> Ws<\/strong>10<\/strong><\/strong> Ws11<\/strong><\/strong><\/strong> Ws12<\/strong><\/strong><\/strong>
1 1000 1000 8 8 1000 1000 8 1000 1000 1000 1000 8
2 10 1000 1000 1000 1000 10 10 1000 1000 1000 10 1000
3 1000 6 1000 1000 6 1000 1000 1000 6 1000 6 1000
4 7 1000 1000 1000 7 1000 1000 7 1000 7 1000 1000
5 3 1000 1000 1000 1000 3 1000 1000 3 1000 1000 3
6 1000 1000 5 5 1000 1000 1000 5 1000 1000 1000 5
7 1000 4 1000 1000 4 1000 4 1000 1000 4 1000 1000
8 1000 4 1000 1000 4 1000 1000 1000 4 1000 4 1000
9 1000 1000 2 2 1000 1000 1000 1000 2 1000 2 1000
10 8 1000 1000 1000 8 1000 1000 8 1000 8 1000 1000
11 6 1000 1000 1000 1000 6 6 1000 1000 1000 6 1000
12 1000 1000 3 3 1000 1000 1000 3 1000 1000 1000 3
13 9 1000 1000 1000 1000 9 1000 1000 9 1000 1000 9
14 1000 1000 5 5 1000 1000 5 1000 1000 1000 1000 5
15 1000 1000 7 7 1000 1000 1000 7 1000 1000 1000 7
16 10 1000 1000 1000 10 1000 1000 10 1000 10 1000 1000
17 1000 1000 4 4 1000 1000 1000 4 1000 1000 1000 4
18 1000 8 1000 1000 8 1000 8 1000 1000 8 1000 1000
19 6 1000 1000 1000 1000 6 1000 1000 6 1000 1000 6
20 1000 2 1000 1000 2 1000 1000 1000 2 1000 2 1000
21 1000 1000 3 3 1000 1000 3 1000 1000 1000 1000 3
22 1000 1000 9 9 1000 1000 1000 1000 9 1000 9 1000
23 5 1000 1000 1000 1000 5 5 1000 1000 1000 5 1000
24 8 1000 1000 1000 1000 8 8 1000 1000 1000 8 1000
25 1000 9 1000 1000 9 1000 1000 1000 9 1000 9 1000
26 10 1000 1000 1000 10 1000 1000 10 1000 10 1000 1000
27 5 1000 1000 1000 1000 5 1000 1000 5 1000 1000 5
28 1000 1000 6 6 1000 1000 1000 6 1000 1000 1000 6
29 1000 1000 4 4 1000 1000 1000 1000 4 1000 4 1000
30 1000 4 1000 1000 4 1000 4 1000 1000 4 1000 1000
31 3 1000 1000 1000 1000 3 3 1000 1000 1000 3 1000
32 1000 1000 6 6 1000 1000 6 1000 1000 1000 1000 6
33 1000 1000 8 8 1000 1000 1000 8 1000 1000 1000 8
34 5 1000 1000 1000 1000 5 1000 1000 5 1000 1000 5
35 1000 1000 4 4 1000 1000 1000 1000 4 1000 4 1000
36 7 1000 1000 1000 7 1000 1000 7 1000 7 1000 1000
37 1000 2 1000 1000 2 1000 1000 1000 2 1000 2 1000
38 8 1000 1000 1000 1000 8 1000 1000 8 1000 1000 8
39 1000 10 1000 1000 10 1000 1000 1000 10 1000 10 1000
40 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 1000
41 6 1000 1000 1000 1000 6 6 1000 1000 1000 6 1000
42 1000 1000 7 7 1000 1000 1000 1000 7 1000 7 1000
43 9 1000 1000 1000 9 1000 1000 9 1000 9 1000 1000
44 1000 1000 4 4 1000 1000 4 1000 1000 1000 1000 4
45 3 1000 1000 1000 1000 3 1000 1000 3 1000 1000 3
46 6 1000 1000 1000 1000 6 6 1000 1000 1000 6 1000
47 8 1000 1000 1000 8 1000 1000 8 1000 8 1000 1000
48 1000 1000 3 3 1000 1000 1000 1000 3 1000 3 1000
49 1000 1000 5 5 1000 1000 5 1000 1000 1000 1000 5
50 1000 1000 9 9 1000 1000 1000 9 1000 1000 1000 9
51 1000 2 1000 1000 2 1000 2 1000 1000 2 1000 1000
52 1000 1000 10 10 1000 1000 1000 10 1000 1000 1000 10
53 7 1000 1000 1000 1000 7 1000 1000 7 1000 1000 7
54 9 1000 1000 1000 9 1000 1000 9 1000 9 1000 1000
55 6 1000 1000 1000 1000 6 6 1000 1000 1000 6 1000
56 10 1000 1000 1000 1000 10 1000 1000 10 1000 1000 10
57 1000 1000 3 3 1000 1000 1000 3 1000 1000 1000 3
58 1000 1000 4 4 1000 1000 4 1000 1000 1000 1000 4
59 1000 6 1000 1000 6 1000 6 1000 1000 6 1000 1000
60 1000 2 1000 1000 2 1000 1000 1000 2 1000 2 1000<\/td>		Predecessor Successor<\/strong>
1 3
2 3
4 5
5 6
3 7
6 7
8 10
9 10
11 14
12 14
13 14
10 15
14 15
17 18
19 20
18 21
20 21
16 23
21 23
22 23
24 25
25 26
26 27
27 28
28 29
30 32
31 32
34 35
33 36
35 36
32 37
36 37
38 40
39 40
41 42
43 44
42 45
44 45
46 47
47 48
48 49
49 50
50 51
52 53
53 54
54 55
56 58
57 58
58 60
59 60










<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P10 56 0 8
1 P7 41 13 10
1 P2 10 19 24
1 P4 27 27 7
1 P7 45 35 10
1 P6 40 38 25
2 P4 25 8 42
2 P5 37 34 14
2 P1 7 38 15
3 P9 52 0 27
3 P5 32 11 29
3 P8 50 23 20
3 P4 28 32 27
3 P4 29 38 34
4 P1 1 0 42
4 P3 22 8 17
4 P2 12 17 10
4 P1 6 20 22
4 P7 44 25 6
4 P10 57 29 24
4 P3 21 32 35
4 P2 15 35 17
5 P6 39 0 40
5 P2 8 10 8
5 P3 18 14 17
5 P3 20 22 27
5 P9 54 24 32
6 P8 46 0 38
6 P1 5 7 42
6 P5 34 10 4
6 P9 53 15 11
6 P6 38 22 17
6 P9 55 33 18
7 P4 24 0 15
7 P5 31 8 19
7 P10 59 12 34
7 P8 49 18 36
7 P2 11 23 30
7 P2 14 29 10
7 P10 58 34 42
7 P8 51 40 19
8 P1 4 0 35
8 P8 47 7 25
8 P7 43 16 29
9 P2 9 13 38
9 P8 48 15 6
9 P1 3 18 15
9 P7 42 28 18
10 P5 30 0 23
10 P3 16 7 32
10 P4 26 17 42
10 P5 36 27 10
11 P1 2 0 22
11 P5 35 15 33
11 P3 23 35 39
11 P10 60 40 10
12 P3 19 0 32
12 P3 17 6 38
12 P5 33 10 18
12 P3 20 22 42<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Makespan = 42

Ws1: Total_Time=36.0, Utilization=0.8571
Ws2: Total_Time=15.0, Utilization=0.3571
Ws3: Total_Time=35.0, Utilization=0.8333
Ws4: Total_Time=42.0, Utilization=1.0000
Ws5: Total_Time=33.0, Utilization=0.7857
Ws6: Total_Time=35.0, Utilization=0.8333
Ws7: Total_Time=39.0, Utilization=0.9286
Ws8: Total_Time=24.0, Utilization=0.5714
Ws9: Total_Time=18.0, Utilization=0.4286
Ws10: Total_Time=31.0, Utilization=0.7381
Ws11: Total_Time=21.0, Utilization=0.5000
Ws12: Total_Time=20.0, Utilization=0.4762

Average System Utilization: 0.6925<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 42 Run-time = 3932 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n

Matrix-Structure 4 x 4<\/strong><\/p>\n\n\n\n

Int_22<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong> Ws<\/strong>10<\/strong><\/strong> Ws11<\/strong><\/strong><\/strong> Ws12<\/strong><\/strong><\/strong> Ws13<\/strong><\/strong><\/strong> Ws<\/strong>14<\/strong><\/strong> Ws15<\/strong><\/strong><\/strong> Ws16<\/strong><\/strong><\/strong>
1 1000 8 1000 8 1000 8 1000 1000 8 1000 8 1000 1000 8 1000 1000
2 1000 1000 4 4 1000 4 1000 4 4 1000 1000 1000 1000 1000 4 1000
3 1000 10 1000 1000 10 1000 1000 1000 10 1000 1000 10 1000 10 1000 10
4 1000 1000 6 1000 6 1000 6 1000 1000 6 1000 6 1000 1000 1000 6
5 7 1000 1000 7 1000 7 1000 1000 1000 1000 7 1000 7 1000 1000 7
6 1000 2 1000 1000 1000 1000 2 2 1000 1000 2 1000 1000 2 1000 2
7 3 1000 1000 3 3 1000 1000 3 1000 3 1000 1000 1000 1000 3 1000
8 1000 1000 5 1000 5 1000 1000 5 1000 5 1000 5 5 1000 1000 1000
9 2 1000 1000 1000 1000 1000 2 1000 2 1000 2 1000 1000 2 2 1000
10 1000 2 2 1000 1000 2 1000 1000 1000 1000 1000 2 2 1000 2 1000
11 8 1000 1000 8 1000 8 1000 1000 1000 1000 8 1000 8 1000 1000 8
12 5 1000 1000 5 5 1000 1000 5 1000 5 1000 1000 1000 1000 5 1000
13 1000 6 1000 6 1000 6 1000 1000 6 1000 6 1000 1000 6 1000 1000
14 1000 1000 9 9 1000 9 1000 9 9 1000 1000 1000 1000 1000 9 1000
15 4 1000 100011000 1000 1000 4 1000 4 1000 4 1000 1000 4 4 1000
16 1000 1000 7 1000 7 1000 7 1000 1000 7 1000 7 1000 1000 1000 7
17 1000 3 1000 1000 3 1000 1000 1000 3 1000 1000 3 1000 3 1000 3
18 1000 10 1000 1000 1000 1000 10 10 1000 1000 10 1000 1000 10 1000 10
19 1000 1000 6 1000 6 1000 1000 6 1000 6 1000 6 6 1000 1000 1000
20 1000 2 2 1000 1000 2 1000 1000 1000 1000 1000 2 2 1000 2 1000
21 8 1000 1000 1000 1000 1000 8 1000 8 1000 8 1000 1000 8 8 1000
22 3 1000 1000 3 3 1000 1000 3 1000 3 1000 1000 1000 1000 3 1000
23 1000 4 1000 4 1000 4 1000 1000 4 1000 4 1000 1000 4 1000 1000
24 5 1000 1000 5 1000 5 1000 1000 1000 1000 5 1000 5 1000 1000 5
25 1000 1000 4 1000 4 1000 4 1000 1000 4 1000 4 1000 1000 1000 4
26 1000 2 1000 1000 2 1000 1000 1000 2 1000 1000 2 1000 2 1000 2
27 4 1000 1000 4 1000 4 1000 1000 1000 1000 4 1000 4 1000 1000 4
28 1000 3 3 1000 1000 3 1000 1000 1000 1000 1000 3 3 1000 3 1000
29 1000 5 1000 5 1000 5 1000 1000 5 1000 5 1000 1000 5 1000 1000
30 1000 1000 2 2 1000 2 1000 2 2 1000 1000 1000 1000 1000 2 1000
31 10 1000 1000 10 10 1000 1000 10 1000 10 1000 1000 1000 1000 10 1000
32 4 1000 1000 4 1000 4 1000 1000 1000 1000 4 1000 4 1000 1000 4
33 6 1000 1000 1000 1000 1000 6 1000 6 1000 6 1000 1000 6 6 1000
34 1000 1000 7 1000 7 1000 7 1000 1000 7 1000 7 1000 1000 1000 7
35 1000 1000 5 1000 5 1000 1000 5 1000 5 1000 5 5 1000 1000 1000
36 1000 8 8 1000 1000 8 1000 1000 1000 1000 1000 8 8 1000 8 1000
37 6 1000 1000 1000 1000 1000 6 1000 6 1000 6 1000 1000 6 6 1000
38 9 1000 1000 9 1000 9 1000 1000 1000 1000 9 1000 9 1000 1000 9
39 4 1000 1000 4 4 1000 1000 4 1000 4 1000 1000 1000 1000 4 1000
40 1000 1000 3 1000 3 1000 3 1000 1000 3 1000 3 1000 1000 1000 3
41 1000 10 1000 10 1000 10 1000 1000 10 1000 10 1000 1000 10 1000 1000
42 1000 3 1000 1000 3 1000 1000 1000 3 1000 1000 3 1000 3 1000 3
43 5 1000 1000 5 1000 5 1000 1000 1000 1000 5 1000 5 1000 1000 5
44 1000 9 1000 1000 1000 1000 9 9 1000 1000 9 1000 1000 9 1000 9
45 1000 1000 6 6 1000 6 1000 6 6 1000 1000 1000 1000 1000 6 1000
46 1000 2 1000 2 1000 2 1000 1000 2 1000 2 1000 1000 2 1000 1000
47 1000 1000 6 6 1000 6 1000 6 6 1000 1000 1000 1000 1000 6 1000
48 3 1000 1000 3 1000 3 1000 1000 1000 1000 3 1000 3 1000 1000 3
49 5 1000 1000 5 5 1000 1000 5 1000 5 1000 1000 1000 1000 5 1000
50 1000 4 4 1000 1000 4 1000 1000 1000 1000 1000 4 4 1000 4 1000<\/td>		Predecessor Successor<\/strong>
1 2
2 4
3 4
5 6
6 7
7 8
4 9
8 9
10 12
11 12
13 16
14 16
15 16
12 17
16 17
18 20
19 20
21 22
20 23
22 23
23 24
25 26
26 27
27 28
28 29
29 30
31 33
32 33
34 36
35 36
37 39
38 39
36 40
39 40
41 42
43 44
42 45
44 45
46 47
47 48
48 49
49 50








<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P2 11 0 8
1 P3 22 8 12
1 P8 49 11 10
1 P3 24 16 18
2 P7 41 0 7
2 P3 20 10 11
2 P3 23 12 14
3 P6 34 0 19
3 P1 2 8 21
3 P1 8 14 2
4 P1 5 0 8
4 P4 27 7 15
4 P5 32 11 9
5 P4 25 0 9
5 P3 19 4 11
5 P1 7 11 18
5 P6 39 14 21
5 P2 17 18 10
6 P1 1 0 10
6 P8 48 8 12
6 P4 28 11 8
6 P8 50 17 11
7 P3 21 0 16
7 P6 37 8 21
8 P6 35 0 4
8 P7 44 5 6
8 P7 45 14 11
9 P2 14 0 14
9 P7 42 11 19
9 P4 30 19 21
10 P5 31 0 10
10 P2 12 10 15
11 P8 46 0 21
11 P2 13 3 7
11 P1 6 9 5
11 P4 29 14 18
11 P1 9 19 14
12 P1 3 0 14
12 P2 16 11 18
12 P6 40 18 21
13 P7 43 0 10
13 P6 38 5 14
14 P4 26 4 5
14 P2 15 7 14
14 P5 33 15 20
15 P2 10 0 2
15 P8 47 2 8
15 P6 36 10 11
16 P3 18 0 16
16 P1 4 12 21<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Makespan = 21

Ws1: Total_Time=21.0, Utilization=1.0000
Ws2: Total_Time=16.0, Utilization=0.7619
Ws3: Total_Time=16.0, Utilization=0.7619
Ws4: Total_Time=15.0, Utilization=0.7143
Ws5: Total_Time=20.0, Utilization=0.9524
Ws6: Total_Time=18.0, Utilization=0.8571
Ws7: Total_Time=14.0, Utilization=0.6667
Ws8: Total_Time=20.0, Utilization=0.9524
Ws9: Total_Time=14.0, Utilization=0.6667
Ws10: Total_Time=15.0, Utilization=0.7143
Ws11: Total_Time=17.0, Utilization=0.8095
Ws12: Total_Time=20.0, Utilization=0.9524
Ws13: Total_Time=14.0, Utilization=0.6667
Ws14: Total_Time=12.0, Utilization=0.5714
Ws15: Total_Time=16.0, Utilization=0.7619
Ws16: Total_Time=16.0, Utilization=0.7619

Average System Utilization: 0.7857<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 21 Run-time = 344 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_23<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong> Ws<\/strong>10<\/strong><\/strong> Ws11<\/strong><\/strong><\/strong> Ws12<\/strong><\/strong><\/strong> Ws13<\/strong><\/strong><\/strong> Ws<\/strong>14<\/strong><\/strong> Ws15<\/strong><\/strong><\/strong> Ws16<\/strong><\/strong><\/strong>
1 1000 5 1000 1000 5 1000 1000 1000 5 1000 1000 5 1000 5 1000 5
2 1000 6 1000 6 1000 6 1000 1000 6 1000 6 1000 1000 6 1000 1000
3 10 1000 1000 10 1000 10 1000 1000 1000 1000 10 1000 10 1000 1000 10
4 4 1000 1000 1000 1000 1000 4 1000 4 1000 4 1000 1000 4 4 1000
5 8 1000 1000 8 8 1000 1000 8 1000 8 1000 1000 1000 1000 8 1000
6 1000 1000 7 1000 7 1000 1000 7 1000 7 1000 7 7 1000 1000 1000
7 1000 1000 3 3 1000 3 1000 3 3 1000 1000 1000 1000 1000 3 1000
8 1000 9 9 1000 1000 9 1000 1000 1000 1000 1000 9 9 1000 9 1000
9 1000 2 1000 1000 1000 1000 2 2 1000 1000 2 1000 1000 2 1000 2
10 1000 1000 5 1000 5 1000 5 1000 1000 5 1000 5 1000 1000 1000 5
11 6 1000 1000 1000 1000 1000 6 1000 6 1000 6 1000 1000 6 6 1000
12 8 1000 1000 8 1000 8 1000 1000 1000 1000 8 1000 8 1000 1000 8
13 1000 4 1000 1000 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 4
14 1000 7 7 1000 1000 7 1000 1000 1000 1000 1000 7 7 1000 7 1000
15 3 1000 1000 3 3 1000 1000 3 1000 3 1000 1000 1000 1000 3 1000
16 1000 5 1000 5 1000 5 1000 1000 5 1000 5 1000 1000 5 1000 1000
17 1000 1000 10 1000 10 1000 10 1000 1000 10 1000 10 1000 1000 1000 10
18 3 1000 1000 3 1000 3 1000 1000 1000 1000 3 1000 3 1000 1000 3
19 1000 1000 4 4 1000 4 1000 4 4 1000 1000 1000 1000 1000 4 1000
20 8 1000 1000 8 8 1000 1000 8 1000 8 1000 1000 1000 1000 8 1000
21 1000 1000 6 1000 6 1000 1000 6 1000 6 1000 6 6 1000 1000 1000
22 1000 7 1000 1000 1000 1000 7 7 1000 1000 7 1000 1000 7 1000 7
23 2 1000 1000 1000 1000 1000 2 1000 2 1000 2 1000 1000 2 2 1000
24 1000 2 2 1000 1000 2 1000 1000 1000 1000 1000 2 2 1000 2 1000
25 1000 5 1000 1000 5 1000 1000 1000 5 1000 1000 5 1000 5 1000 5
26 1000 3 1000 3 1000 3 1000 1000 3 1000 3 1000 1000 3 1000 1000
27 4 1000 1000 4 4 1000 1000 4 1000 4 1000 1000 1000 1000 4 1000
28 6 1000 1000 1000 1000 1000 6 1000 6 1000 6 1000 1000 6 6 1000
29 3 1000 1000 3 1000 3 1000 1000 1000 1000 3 1000 3 1000 1000 3
30 1000 10 1000 1000 1000 1000 10 10 1000 1000 10 1000 1000 10 1000 10
31 3 1000 1000 1000 1000 1000 3 1000 3 1000 3 1000 1000 3 3 1000
32 1000 1000 5 1000 5 1000 1000 5 1000 5 1000 5 5 1000 1000 1000
33 1000 1000 7 7 1000 7 1000 7 7 1000 1000 1000 1000 1000 7 1000
34 1000 8 1000 1000 8 1000 1000 1000 8 1000 1000 8 1000 8 1000 8
35 1000 1000 6 1000 6 1000 6 1000 1000 6 1000 6 1000 1000 1000 6
36 4 1000 1000 4 4 1000 1000 4 1000 4 1000 1000 1000 1000 4 1000
37 1000 6 1000 6 1000 6 1000 1000 6 1000 6 1000 1000 6 1000 1000
38 1000 3 3 1000 1000 3 1000 1000 1000 1000 1000 3 3 1000 3 1000
39 9 1000 1000 1000 1000 1000 9 1000 9 1000 9 1000 1000 9 9 1000
40 1000 4 1000 1000 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 4
41 1000 1000 3 3 1000 3 1000 3 3 1000 1000 1000 1000 1000 3 1000
42 10 1000 1000 10 1000 10 1000 1000 1000 1000 10 1000 10 1000 1000 10
43 1000 9 1000 1000 1000 1000 9 9 1000 1000 9 1000 1000 9 1000 9
44 1000 4 1000 1000 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 4
45 1000 1000 6 1000 6 1000 6 1000 1000 6 1000 6 1000 1000 1000 6
46 1000 8 8 1000 1000 8 1000 1000 1000 1000 1000 8 8 1000 8 1000
47 3 1000 1000 3 3 1000 1000 3 1000 3 1000 1000 1000 1000 3 1000
48 1000 1000 7 7 1000 7 1000 7 7 1000 1000 1000 1000 1000 7 1000
49 1000 2 1000 2 1000 2 1000 1000 2 1000 2 1000 1000 2 1000 1000
50 1000 1000 3 1000 3 1000 1000 3 1000 3 1000 3 3 1000 1000 1000
51 1000 5 1000 5 1000 5 1000 1000 5 1000 5 1000 1000 5 1000 1000
52 1000 1000 7 1000 7 1000 7 1000 1000 7 1000 7 1000 1000 1000 7
53 1000 2 1000 1000 1000 1000 2 2 1000 1000 2 1000 1000 2 1000 2
54 1000 1000 3 3 1000 3 1000 3 3 1000 1000 1000 1000 1000 3 1000
55 1000 6 6 1000 1000 6 1000 1000 1000 1000 1000 6 6 1000 6 1000<\/td>		Predecessor Successor<\/strong>
1 2
2 4
3 4
5 6
5 7
6 7
8 9
9 11
10 11
12 15
13 15
14 15
11 16
15 16
18 19
19 21
20 21
17 23
21 23
22 23
24 25
25 26
26 27
27 28
28 29
30 32
31 32
33 35
34 35
32 36
35 36
37 38
38 40
39 40
41 42
43 44
42 45
44 45
46 47
47 48
48 49
49 50
51 52
52 53
53 54
54 55









<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P2 12 3 5
1 P2 11 12 11
2 P2 13 0 19
2 P5 34 4 23
3 P2 8 0 8
3 P3 19 9 19
3 P5 35 13 23
4 P6 37 0 9
4 P3 18 6 12
4 P1 3 9 5
5 P1 5 0 18
5 P4 27 10 11
5 P5 32 14 4
5 P6 40 19 10
6 P8 46 0 14
6 P8 48 11 23
7 P5 31 0 20
7 P7 43 3 9
7 P9 53 12 13
7 P3 22 14 8
7 P3 23 21 20
8 P7 41 0 21
8 P1 6 12 23
8 P5 36 19 2
9 P1 1 0 7
9 P5 33 5 10
9 P9 54 14 14
9 P8 49 18 20
9 P1 7 20 23
10 P3 20 0 10
10 P8 47 8 3
10 P2 15 11 19
10 P3 21 14 12
10 P8 50 20 12
11 P9 51 0 19
11 P1 2 5 23
11 P4 28 14 6
12 P2 10 0 17
12 P9 52 5 19
12 P7 45 17 23
13 P4 24 0 3
13 P7 42 3 13
13 P6 38 14 12
13 P9 55 17 17
14 P4 25 2 23
14 P4 26 7 8
14 P2 9 10 11
14 P7 44 13 18
14 P2 16 18 20
15 P2 14 3 23
15 P6 39 10 5
15 P1 4 19 12
16 P5 30 0 14
16 P3 17 10 17
16 P4 29 20 23<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Makespan = 23

Ws1: Total_Time=14.0, Utilization=0.6087
Ws2: Total_Time=12.0, Utilization=0.5217
Ws3: Total_Time=19.0, Utilization=0.8261
Ws4: Total_Time=19.0, Utilization=0.8261
Ws5: Total_Time=21.0, Utilization=0.9130
Ws6: Total_Time=15.0, Utilization=0.6522
Ws7: Total_Time=23.0, Utilization=1.0000
Ws8: Total_Time=14.0, Utilization=0.6087
Ws9: Total_Time=20.0, Utilization=0.8696
Ws10: Total_Time=23.0, Utilization=1.0000
Ws11: Total_Time=17.0, Utilization=0.7391
Ws12: Total_Time=18.0, Utilization=0.7826
Ws13: Total_Time=21.0, Utilization=0.9130
Ws14: Total_Time=19.0, Utilization=0.8261
Ws15: Total_Time=20.0, Utilization=0.8696
Ws16: Total_Time=23.0, Utilization=1.0000

Average System Utilization: 0.8098<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 23 Run-time = 482 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_24<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong> Ws<\/strong>10<\/strong><\/strong> Ws11<\/strong><\/strong><\/strong> Ws12<\/strong><\/strong><\/strong> Ws13<\/strong><\/strong><\/strong> Ws<\/strong>14<\/strong><\/strong> Ws15<\/strong><\/strong><\/strong> Ws16<\/strong><\/strong><\/strong>
1 6 1000 1000 6 6 1000 1000 6 1000 6 1000 1000 1000 1000 6 1000
2 7 1000 1000 1000 1000 1000 7 1000 7 1000 7 1000 1000 7 7 1000
3 1000 9 1000 9 1000 9 1000 1000 9 1000 9 1000 1000 9 1000 1000
4 1000 3 1000 1000 3 1000 1000 1000 3 1000 1000 3 1000 3 1000 3
5 1000 1000 5 5 1000 5 1000 5 5 1000 1000 1000 1000 1000 5 1000
6 1000 1000 4 1000 4 1000 4 1000 1000 4 1000 4 1000 1000 1000 4
7 1000 2 2 1000 1000 2 1000 1000 1000 1000 1000 2 2 1000 2 1000
8 8 1000 1000 8 1000 8 1000 1000 1000 1000 8 1000 8 1000 1000 8
9 1000 4 1000 1000 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 4
10 1000 5 1000 1000 1000 1000 5 5 1000 1000 5 1000 1000 5 1000 5
11 1000 1000 9 1000 9 1000 1000 9 1000 9 1000 9 9 1000 1000 1000
12 10 1000 1000 10 10 1000 1000 10 1000 10 1000 1000 1000 1000 10 1000
13 7 1000 1000 1000 1000 1000 7 1000 7 1000 7 1000 1000 7 7 1000
14 1000 6 1000 6 1000 6 1000 1000 6 1000 6 1000 1000 6 1000 1000
15 1000 1000 3 3 1000 3 1000 3 3 1000 1000 1000 1000 1000 3 1000
16 1000 4 4 1000 1000 4 1000 1000 1000 1000 1000 4 4 1000 4 1000
17 1000 1000 2 1000 2 1000 2 1000 1000 2 1000 2 1000 1000 1000 2
18 1000 1000 5 1000 5 1000 1000 5 1000 5 1000 5 5 1000 1000 1000
19 3 1000 1000 3 1000 3 1000 1000 1000 1000 3 1000 3 1000 1000 3
20 10 1000 1000 1000 1000 1000 10 1000 10 1000 10 1000 1000 10 10 1000
21 1000 8 1000 1000 8 1000 1000 1000 8 1000 1000 8 1000 8 1000 8
22 1000 1000 7 7 1000 7 1000 7 7 1000 1000 1000 1000 1000 7 1000
23 6 1000 1000 6 6 1000 1000 6 1000 6 1000 1000 1000 1000 6 1000
24 1000 4 1000 1000 1000 1000 4 4 1000 1000 4 1000 1000 4 1000 4
25 1000 3 1000 3 1000 3 1000 1000 3 1000 3 1000 1000 3 1000 1000
26 7 1000 1000 7 1000 7 1000 1000 1000 1000 7 1000 7 1000 1000 7
27 2 1000 1000 1000 1000 1000 2 1000 2 1000 2 1000 1000 2 2 1000
28 1000 6 6 1000 1000 6 1000 1000 1000 1000 1000 6 6 1000 6 1000
29 1000 1000 3 1000 3 1000 1000 3 1000 3 1000 3 3 1000 1000 1000
30 1000 1000 5 5 1000 5 1000 5 5 1000 1000 1000 1000 1000 5 1000
31 1000 1000 8 1000 8 1000 8 1000 1000 8 1000 8 1000 1000 1000 8
32 6 1000 1000 6 1000 6 1000 1000 1000 1000 6 1000 6 1000 1000 6
33 9 1000 1000 9 9 1000 1000 9 1000 9 1000 1000 1000 1000 9 1000
34 1000 3 3 1000 1000 3 1000 1000 1000 1000 1000 3 3 1000 3 1000
35 1000 2 1000 2 1000 2 1000 1000 2 1000 2 1000 1000 2 1000 1000
36 1000 4 1000 1000 1000 1000 4 4 1000 1000 4 1000 1000 4 1000 4
37 1000 1000 5 1000 5 1000 1000 5 1000 5 1000 5 5 1000 1000 1000
38 1000 4 1000 1000 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 4
39 10 1000 1000 10 10 1000 1000 10 1000 10 1000 1000 1000 1000 10 1000
40 1000 1000 6 1000 6 1000 6 1000 1000 6 1000 6 1000 1000 1000 6
41 1000 8 1000 8 1000 8 1000 1000 8 1000 8 1000 1000 8 1000 1000
42 1000 2 1000 1000 1000 1000 2 2 1000 1000 2 1000 1000 2 1000 2
43 1000 3 1000 1000 3 1000 1000 1000 3 1000 1000 3 1000 3 1000 3
44 1000 9 9 1000 1000 9 1000 1000 1000 1000 1000 9 9 1000 9 1000
45 7 1000 1000 7 1000 7 1000 1000 1000 1000 7 1000 7 1000 1000 7
46 3 1000 1000 3 3 1000 1000 3 1000 3 1000 1000 1000 1000 3 1000
47 2 1000 1000 1000 1000 1000 2 1000 2 1000 2 1000 1000 2 2 1000
48 1000 4 4 1000 1000 4 1000 1000 1000 1000 1000 4 4 1000 4 1000
49 1000 8 1000 1000 1000 1000 8 8 1000 1000 8 1000 1000 8 1000 8
50 1000 1000 6 6 1000 6 1000 6 6 1000 1000 1000 1000 1000 6 1000
51 1000 2 1000 2 1000 2 1000 1000 2 1000 2 1000 1000 2 1000 1000
52 1000 1000 9 1000 9 1000 1000 9 1000 9 1000 9 9 1000 1000 1000
53 4 1000 1000 4 1000 4 1000 1000 1000 1000 4 1000 4 1000 1000 4
54 1000 5 1000 1000 5 1000 1000 1000 5 1000 1000 5 1000 5 1000 5
55 6 1000 1000 1000 1000 1000 6 1000 6 1000 6 1000 1000 6 6 1000
56 1000 1000 6 1000 6 1000 6 1000 1000 6 1000 6 1000 1000 1000 6
57 1000 7 1000 7 1000 7 1000 1000 7 1000 7 1000 1000 7 1000 1000
58 1000 2 1000 1000 1000 1000 2 2 1000 1000 2 1000 1000 2 1000 2
59 10 1000 1000 1000 1000 1000 10 1000 10 1000 10 1000 1000 10 10 1000
60 1000 5 1000 1000 5 1000 1000 1000 5 1000 1000 5 1000 5 1000 5<\/td>		Predecessor Successor<\/strong>
1 2
2 4
3 4
5 6
4 7
6 7
8 10
9 10
11 14
12 14
13 14
10 15
14 15
17 18
18 19
19 21
20 21
16 23
21 23
22 23
24 25
25 26
26 27
27 28
28 29
30 32
31 32
33 35
34 35
32 36
35 36
37 38
38 40
39 40
41 42
43 44
42 45
44 45
46 47
47 48
48 49
49 50
50 51
52 53
53 54
54 55
56 58
57 58
58 60
59 60










<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P2 12 0 6
1 P9 53 10 15
1 P4 27 14 9
1 P7 45 18 23
2 P5 34 0 5
2 P4 25 4 23
2 P7 44 9 25
2 P5 36 21 15
3 P1 5 0 7
3 P8 48 5 22
3 P3 22 9 9
3 P8 50 17 10
4 P1 1 0 16
4 P4 26 7 22
4 P2 14 16 25
4 P2 15 22 19
5 P2 11 0 2
5 P4 29 22 8
6 P10 57 0 11
6 P2 8 7 10
6 P5 32 15 19
6 P1 7 23 16
7 P10 59 0 25
7 P10 56 10 4
7 P10 58 17 7
7 P6 40 19 14
8 P4 24 0 16
8 P5 30 4 22
8 P8 49 9 25
8 P2 10 17 9
9 P7 41 0 10
9 P1 2 8 21
9 P1 4 20 15
10 P8 46 0 3
10 P3 18 3 20
10 P6 39 8 25
10 P3 23 19 14
11 P1 3 0 18
11 P2 13 9 18
11 P7 42 16 25
11 P5 35 18 8
12 P3 17 0 18
12 P5 31 2 3
12 P3 21 11 18
12 P10 60 20 25
13 P9 52 0 3
13 P6 37 9 5
13 P4 28 16 9
14 P3 20 0 17
14 P6 38 14 23
14 P8 51 23 25
15 P8 47 3 9
15 P5 33 6 14
15 P3 16 15 19
15 P9 55 19 25
16 P7 43 0 16
16 P2 9 3 7
16 P3 19 8 19
16 P9 54 14 10
16 P1 6 19 25<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Makespan = 25

Ws1: Total_Time=23.0, Utilization=0.9200
Ws2: Total_Time=19.0, Utilization=0.7600
Ws3: Total_Time=22.0, Utilization=0.8800
Ws4: Total_Time=22.0, Utilization=0.8800
Ws5: Total_Time=12.0, Utilization=0.4800
Ws6: Total_Time=23.0, Utilization=0.9200
Ws7: Total_Time=24.0, Utilization=0.9600
Ws8: Total_Time=22.0, Utilization=0.8800
Ws9: Total_Time=18.0, Utilization=0.7200
Ws10: Total_Time=24.0, Utilization=0.9600
Ws11: Total_Time=20.0, Utilization=0.8000
Ws12: Total_Time=23.0, Utilization=0.9200
Ws13: Total_Time=20.0, Utilization=0.8000
Ws14: Total_Time=16.0, Utilization=0.6400
Ws15: Total_Time=21.0, Utilization=0.8400
Ws16: Total_Time=19.0, Utilization=0.7600

Average System Utilization: 0.8200<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 25 Run-time = 579 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n\n\n\n
Int_25<\/summary>\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n
\n
Input Data:<\/strong> Processing Time<\/th>List of Precedents:<\/strong><\/th>Output Data:<\/strong><\/th><\/tr><\/thead>
Tasks Ws1 Ws<\/strong>2 Ws<\/strong>3 Ws<\/strong>4<\/strong><\/strong> Ws<\/strong><\/strong>5<\/strong> Ws<\/strong>6<\/strong><\/strong> Ws<\/strong>7<\/strong><\/strong> Ws<\/strong><\/strong>8<\/strong> Ws9<\/strong><\/strong><\/strong> Ws<\/strong>10<\/strong><\/strong> Ws11<\/strong><\/strong><\/strong> Ws12<\/strong><\/strong><\/strong> Ws13<\/strong><\/strong><\/strong> Ws<\/strong>14<\/strong><\/strong> Ws15<\/strong><\/strong><\/strong> Ws16<\/strong><\/strong><\/strong>
1 6 1000 1000 1000 1000 1000 6 1000 6 1000 6 1000 1000 6 6 1000
2 1000 8 8 1000 1000 8 1000 1000 1000 1000 1000 8 8 1000 8 1000
3 1000 10 1000 1000 10 1000 1000 1000 10 1000 1000 10 1000 10 1000 10
4 9 1000 1000 9 1000 9 1000 1000 1000 1000 9 1000 9 1000 1000 9
5 1000 1000 3 1000 3 1000 3 1000 1000 3 1000 3 1000 1000 1000 3
6 1000 7 1000 7 1000 7 1000 1000 7 1000 7 1000 1000 7 1000 1000
7 1000 1000 5 5 1000 5 1000 5 5 1000 1000 1000 1000 1000 5 1000
8 1000 4 1000 1000 1000 1000 4 4 1000 1000 4 1000 1000 4 1000 4
9 1000 1000 2 1000 2 1000 1000 2 1000 2 1000 2 2 1000 1000 1000
10 1000 1000 8 1000 8 1000 8 1000 1000 8 1000 8 1000 1000 1000 8
11 4 1000 1000 4 4 1000 1000 4 1000 4 1000 1000 1000 1000 4 1000
12 1000 5 5 1000 1000 5 1000 1000 1000 1000 1000 5 5 1000 5 1000
13 9 1000 1000 1000 1000 1000 9 1000 9 1000 9 1000 1000 9 9 1000
14 1000 1000 10 10 1000 10 1000 10 10 1000 1000 1000 1000 1000 10 1000
15 1000 7 1000 1000 7 1000 1000 1000 7 1000 1000 7 1000 7 1000 7
16 1000 1000 6 1000 6 1000 1000 6 1000 6 1000 6 6 1000 1000 1000
17 1000 3 1000 3 1000 3 1000 1000 3 1000 3 1000 1000 3 1000 1000
18 1000 5 1000 1000 5 1000 1000 1000 5 1000 1000 5 1000 5 1000 5
19 3 1000 1000 3 3 1000 1000 3 1000 3 1000 1000 1000 1000 3 1000
20 4 1000 1000 1000 1000 1000 4 1000 4 1000 4 1000 1000 4 4 1000
21 1000 1000 2 1000 2 1000 1000 2 1000 2 1000 2 2 1000 1000 1000
22 1000 10 1000 1000 1000 1000 10 10 1000 1000 10 1000 1000 10 1000 10
23 1000 8 8 1000 1000 8 1000 1000 1000 1000 1000 8 8 1000 8 1000
24 9 1000 1000 9 1000 9 1000 1000 1000 1000 9 1000 9 1000 1000 9
25 1000 7 1000 7 1000 7 1000 1000 7 1000 7 1000 1000 7 1000 1000
26 1000 1000 6 6 1000 6 1000 6 6 1000 1000 1000 1000 1000 6 1000
27 1000 1000 8 8 1000 8 1000 8 8 1000 1000 1000 1000 1000 8 1000
28 3 1000 1000 3 3 1000 1000 3 1000 3 1000 1000 1000 1000 3 1000
29 1000 7 7 1000 1000 7 1000 1000 1000 1000 1000 7 7 1000 7 1000
30 1000 4 1000 1000 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 4
31 6 1000 1000 1000 1000 1000 6 1000 6 1000 6 1000 1000 6 6 1000
32 2 1000 1000 2 1000 2 1000 1000 1000 1000 2 1000 2 1000 1000 2
33 1000 10 10 1000 1000 10 1000 1000 1000 1000 1000 10 10 1000 10 1000
34 1000 4 1000 1000 1000 1000 4 4 1000 1000 4 1000 1000 4 1000 4
35 1000 6 1000 6 1000 6 1000 1000 6 1000 6 1000 1000 6 1000 1000
36 5 1000 1000 1000 1000 1000 5 1000 5 1000 5 1000 1000 5 5 1000
37 1000 8 1000 1000 8 1000 1000 1000 8 1000 1000 8 1000 8 1000 8
38 1000 2 2 1000 1000 2 1000 1000 1000 1000 1000 2 2 1000 2 1000
39 1000 1000 4 1000 4 1000 4 1000 1000 4 1000 4 1000 1000 1000 4
40 6 1000 1000 6 1000 6 1000 1000 1000 1000 6 1000 6 1000 1000 6
41 8 1000 1000 8 8 1000 1000 8 1000 8 1000 1000 1000 1000 8 1000
42 1000 7 1000 1000 1000 1000 7 7 1000 1000 7 1000 1000 7 1000 7
43 1000 1000 3 1000 3 1000 1000 3 1000 3 1000 3 3 1000 1000 1000
44 1000 10 1000 10 1000 10 1000 1000 10 1000 10 1000 1000 10 1000 1000
45 2 1000 1000 1000 1000 1000 2 1000 2 1000 2 1000 1000 2 2 1000
46 1000 10 10 1000 1000 10 1000 1000 1000 1000 1000 10 10 1000 10 1000
47 3 1000 1000 1000 1000 1000 3 1000 3 1000 3 1000 1000 3 3 1000
48 8 1000 1000 8 1000 8 1000 1000 1000 1000 8 1000 8 1000 1000 8
49 1000 4 1000 1000 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 4
50 5 1000 1000 5 5 1000 1000 5 1000 5 1000 1000 1000 1000 5 1000
51 1000 3 1000 1000 3 1000 1000 1000 3 1000 1000 3 1000 3 1000 3
52 6 1000 1000 6 1000 6 1000 1000 1000 1000 6 1000 6 1000 1000 6
53 1000 1000 4 4 1000 4 1000 4 4 1000 1000 1000 1000 1000 4 1000
54 1000 8 1000 1000 1000 1000 8 8 1000 1000 8 1000 1000 8 1000 8
55 1000 1000 5 1000 5 1000 5 1000 1000 5 1000 5 1000 1000 1000 5
56 1000 2 2 1000 1000 2 1000 1000 1000 1000 1000 2 2 1000 2 1000
57 1000 10 1000 10 1000 10 1000 1000 10 1000 10 1000 1000 10 1000 1000
58 6 1000 1000 6 6 1000 1000 6 1000 6 1000 1000 1000 1000 6 1000
59 5 1000 1000 1000 1000 1000 5 1000 5 1000 5 1000 1000 5 5 1000
60 1000 4 1000 1000 4 1000 1000 1000 4 1000 1000 4 1000 4 1000 4
61 1000 1000 8 8 1000 8 1000 8 8 1000 1000 1000 1000 1000 8 1000
62 5 1000 1000 5 1000 5 1000 1000 1000 1000 5 1000 5 1000 1000 5
63 2 1000 1000 2 2 1000 1000 2 1000 2 1000 1000 1000 1000 2 1000
64 10 1000 1000 1000 1000 1000 10 1000 10 1000 10 1000 1000 10 10 1000
65 1000 3 1000 1000 1000 1000 3 3 1000 1000 3 1000 1000 3 1000 3<\/td>		Predecessor Successor<\/strong>
1 3
2 3
3 5
4 5
6 7
7 8
5 9
8 9
10 12
11 12
13 16
14 16
15 16
12 17
16 17
18 19
19 20
21 22
22 23
24 25
20 26
23 26
25 26
27 28
28 29
29 30
30 31
31 32
33 35
34 35
36 38
37 38
35 39
38 39
40 41
42 43
41 44
43 44
44 45
46 47
48 49
47 50
49 50
51 52
52 53
53 54
54 55
55 56
57 58
58 59
59 60
61 63
62 63
63 65
64 65










<\/td>		WorkStation Product Task Start_Time Completion_Time<\/strong>
1 P7 48 0 12
2 P9 57 0 11
2 P7 49 10 25
2 P5 34 14 25
2 P6 44 18 28
3 P7 46 1 7
3 P8 53 11 24
3 P2 16 21 28
3 P1 9 28 30
4 P3 24 1 8
4 P9 58 10 6
1 P1 4 16 13
4 P4 32 28 17
5 P3 21 0 18
5 P2 11 2 21
5 P4 28 8 27
5 P6 43 11 30
5 P10 63 14 5
5 P5 37 16 16
10 P1 5 25 21
6 P10 61 0 2
6 P2 14 8 12
6 P1 7 19 24
6 P3 26 24 10
7 P6 42 0 19
7 P2 13 8 30
7 P10 64 17 8
8 P4 27 0 11
8 P8 54 15 18
8 P1 8 24 22
9 P1 6 0 28
9 P5 36 7 30
9 P3 25 12 16
9 P5 35 19 18
9 P9 60 26 25
10 P2 10 0 12
10 P6 41 8 24
11 P6 40 0 26
11 P1 1 6 30
11 P3 20 17 6
11 P9 59 21 16
11 P2 17 27 7
12 P8 51 0 14
12 P1 2 3 28
12 P4 29 11 30
12 P4 30 18 11
12 P8 55 23 15
12 P8 56 28 8
13 P10 62 0 14
13 P5 33 6 21
13 P3 23 16 3
13 P5 38 24 11
14 P3 22 2 15
14 P7 47 12 23
14 P1 3 15 28
14 P10 65 27 30
15 P2 12 8 10
1 P3 19 13 16
15 P7 50 16 26
15 P4 31 22 30
15 P6 45 28 8
16 P3 18 0 5
16 P8 52 5 16
16 P2 15 14 27
16 P5 39 26 30<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Utilization Rate:<\/strong><\/th><\/tr><\/thead>
Makespan = 30

Ws1: Total_Time=20.0, Utilization=0.6667
Ws2: Total_Time=28.0, Utilization=0.9333
Ws3: Total_Time=22.0, Utilization=0.7333
Ws4: Total_Time=17.0, Utilization=0.5667
Ws5: Total_Time=22.0, Utilization=0.7333
Ws6: Total_Time=29.0, Utilization=0.9667
Ws7: Total_Time=26.0, Utilization=0.8667
Ws8: Total_Time=20.0, Utilization=0.6667
Ws9: Total_Time=29.0, Utilization=0.9667
Ws10: Total_Time=19.0, Utilization=0.6333
Ws11: Total_Time=24.0, Utilization=0.8000
Ws12: Total_Time=29.0, Utilization=0.9667
Ws13: Total_Time=25.0, Utilization=0.8333
Ws14: Total_Time=26.0, Utilization=0.8667
Ws15: Total_Time=18.0, Utilization=0.6000
Ws16: Total_Time=22.0, Utilization=0.7333

Average System Utilization: 0.7833<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n

Makespan = 30 Run-time = 4456 seconds<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
Gantt Chart<\/strong><\/h5>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/div>\n<\/details>\n<\/details>\n\n\n\n

<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

The increasing demand for customized products with short life cycles and rapid delivery requirements has driven industries to adopt Robotics Assembly Systems (RAS) as a solution to these challenges. An RAS is an integrated manufacturing environment composed of one or multiple workstations capable of assembling diverse product types, interconnected through a material handling system, and […]<\/p>\n","protected":false},"author":6504,"featured_media":31,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[11],"tags":[],"class_list":["post-12","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-instanceas"],"_links":{"self":[{"href":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/wp-json\/wp\/v2\/posts\/12","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/wp-json\/wp\/v2\/users\/6504"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/wp-json\/wp\/v2\/comments?post=12"}],"version-history":[{"count":75,"href":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/wp-json\/wp\/v2\/posts\/12\/revisions"}],"predecessor-version":[{"id":252,"href":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/wp-json\/wp\/v2\/posts\/12\/revisions\/252"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/wp-json\/wp\/v2\/media\/31"}],"wp:attachment":[{"href":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/wp-json\/wp\/v2\/media?parent=12"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/wp-json\/wp\/v2\/categories?post=12"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.utp.edu.co\/johnandresmunoz\/wp-json\/wp\/v2\/tags?post=12"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}