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Stability analysis for generalized semi-infinite optimization problems under functional perturbations
An integrated approach based on Fuzzy Inference System for scheduling and process planning through multiple objectives
Department of Management, University of Isfahan, Isfahan, Iran |
Integrated process planning and scheduling (IPPS) problems are one of the most important flexible planning functions for a job shop manufacturing. In a manufacturing order to produce n jobs (parts) on m machines in a flexible manufacturing environment, an IPPS system intends to generate the process plans for all n parts and the overall job-shop schedule concurrently, with the objective of optimizing a manufacturing objective such as make-span. The optimization of the process planning and scheduling will be applied through an integrated approach based on Fuzzy Inference System (FIS), to provide for flexibilities of the given components and consider the qualitative parameters. The FIS, Constraint Programming (CP) and Simulated Annealing (SA) algorithms are applied in this design. The objectives of the proposed model consist of maximization of processes utility, minimization of make-span and total production costs including costs of flexible tools, machines, process and TADs. The proposed approach indicates that The CP and SA algorithms are able to resolve the IPPS problem with multiple objective functions. The experiments and related results indicate that the CP method outperforms the SA algorithm.
References:
[1] |
A. Akgun, E. A. Sezer, H. A. Nefeslioglu, C. Gokceoglu and B. Pradhan,
An easy-to-use MATLAB program (MamLand) for the assessment of landslide susceptibility using a Mamdani fuzzy algorithm, Computers & Geosciences, 38 (2012), 23-34.
doi: 10.1016/j.cageo.2011.04.012. |
[2] |
IBM, IBM ILOG CPLEX Optimization Studio 12.5 User's Manual, 2012. Google Scholar |
[3] |
S. Kirkpatrick, C. Gelatt and M. Vecchi,
Optimization by simulated annealing, Science, New Series, 220 (1983), 671-680.
doi: 10.1126/science.220.4598.671. |
[4] |
X. Li, L. Gao, X Shao and C. Wang,
Mathematical modeling and evolutionary algorithm-based approach for integrated process planning and scheduling, Computers & Operations Research, 37 (2010), 656-667.
doi: 10.1016/j.cor.2009.06.008. |
[5] |
W. Li and C. A. McMahon,
A simulated annealing-based optimization approach for integrated process planning and scheduling, International Journal of Computer Integrated Manufacturing, 20 (2007), 80-95.
doi: 10.1080/09511920600667366. |
[6] |
K. Lian,
Optimization of process planning with various flexibilities using an imperialist competitive algorithm, The International Journal of Advanced Manufacturing Technology, 59 (2012), 815-828.
doi: 10.1007/s00170-011-3527-8. |
[7] |
J. Lin, M. Liu, J. Hao and S. Jiang,
A multi-objective optimization approach for integrated production planning under interval uncertainties in the steel industry, Computers & Operations Research, 72 (2016), 189-203.
doi: 10.1016/j.cor.2016.03.002. |
[8] |
T. Majozi and X. Zhu,
A combined fuzzy set theory and MILP approach in integration of planning and scheduling of batch plants-Personnel evaluation and allocation, Computers & Chemical Engineering, 29 (2005), 2029-2047.
doi: 10.1016/j.compchemeng.2004.07.038. |
[9] |
X. N. Shen and X. Yao,
Mathematical modeling and multi-objective evolutionary algorithms applied to dynamic flexible job shop scheduling problems, Information Science, 298 (2015), 198-224.
doi: 10.1016/j.ins.2014.11.036. |
[10] |
J. M. Usher and K. J. Fernandes, Dynamic process planning-The staticphase, Journal of Materials Processing Technology, 61 (1996), 53-58. Google Scholar |
[11] |
S.-y. Wan, Integrated Process Planning and Scheduling with Setup Time Consideration by Ant Colony Optimization, HKU Theses Online (HKUTO), 2012.
doi: 10.5353/th_b4961807. |
[12] |
Y. Wang, A PSO-based multi-objective optimization approach to the integration of process planning and scheduling, in Control and Automation (ICCA), 8th IEEE International Conference on IEEE, eds. Y. Zhang and J. Y. H. Fuh, 2010.
doi: 10.1109/ICCA.2010.5524365. |
[13] |
L. A. Zadeh,
Fuzzy sets, Information and Control, 8 (1965), 338-353.
doi: 10.1016/S0019-9958(65)90241-X. |
[14] |
L. Zhang and T. Wong,
Solving integrated process planning and scheduling problem with constructive meta-heuristics, Information Sciences, 340/341 (2016), 1-16.
doi: 10.1016/j.ins.2016.01.001. |
[15] |
L. Zhang and T. Wong,
An object-coding genetic algorithm for integrated process planning and scheduling, European Journal of Operational Research, 244 (2015), 434-444.
doi: 10.1016/j.ejor.2015.01.032. |
[16] |
W. Zhanjie, The research about integration of process planning and production scheduling based on genetic algorithm, in Computer Science and Software Engineering, International Conference on IEEE, eds.T. Ju, 2008.
doi: 10.1109/CSSE.2008.845. |
show all references
References:
[1] |
A. Akgun, E. A. Sezer, H. A. Nefeslioglu, C. Gokceoglu and B. Pradhan,
An easy-to-use MATLAB program (MamLand) for the assessment of landslide susceptibility using a Mamdani fuzzy algorithm, Computers & Geosciences, 38 (2012), 23-34.
doi: 10.1016/j.cageo.2011.04.012. |
[2] |
IBM, IBM ILOG CPLEX Optimization Studio 12.5 User's Manual, 2012. Google Scholar |
[3] |
S. Kirkpatrick, C. Gelatt and M. Vecchi,
Optimization by simulated annealing, Science, New Series, 220 (1983), 671-680.
doi: 10.1126/science.220.4598.671. |
[4] |
X. Li, L. Gao, X Shao and C. Wang,
Mathematical modeling and evolutionary algorithm-based approach for integrated process planning and scheduling, Computers & Operations Research, 37 (2010), 656-667.
doi: 10.1016/j.cor.2009.06.008. |
[5] |
W. Li and C. A. McMahon,
A simulated annealing-based optimization approach for integrated process planning and scheduling, International Journal of Computer Integrated Manufacturing, 20 (2007), 80-95.
doi: 10.1080/09511920600667366. |
[6] |
K. Lian,
Optimization of process planning with various flexibilities using an imperialist competitive algorithm, The International Journal of Advanced Manufacturing Technology, 59 (2012), 815-828.
doi: 10.1007/s00170-011-3527-8. |
[7] |
J. Lin, M. Liu, J. Hao and S. Jiang,
A multi-objective optimization approach for integrated production planning under interval uncertainties in the steel industry, Computers & Operations Research, 72 (2016), 189-203.
doi: 10.1016/j.cor.2016.03.002. |
[8] |
T. Majozi and X. Zhu,
A combined fuzzy set theory and MILP approach in integration of planning and scheduling of batch plants-Personnel evaluation and allocation, Computers & Chemical Engineering, 29 (2005), 2029-2047.
doi: 10.1016/j.compchemeng.2004.07.038. |
[9] |
X. N. Shen and X. Yao,
Mathematical modeling and multi-objective evolutionary algorithms applied to dynamic flexible job shop scheduling problems, Information Science, 298 (2015), 198-224.
doi: 10.1016/j.ins.2014.11.036. |
[10] |
J. M. Usher and K. J. Fernandes, Dynamic process planning-The staticphase, Journal of Materials Processing Technology, 61 (1996), 53-58. Google Scholar |
[11] |
S.-y. Wan, Integrated Process Planning and Scheduling with Setup Time Consideration by Ant Colony Optimization, HKU Theses Online (HKUTO), 2012.
doi: 10.5353/th_b4961807. |
[12] |
Y. Wang, A PSO-based multi-objective optimization approach to the integration of process planning and scheduling, in Control and Automation (ICCA), 8th IEEE International Conference on IEEE, eds. Y. Zhang and J. Y. H. Fuh, 2010.
doi: 10.1109/ICCA.2010.5524365. |
[13] |
L. A. Zadeh,
Fuzzy sets, Information and Control, 8 (1965), 338-353.
doi: 10.1016/S0019-9958(65)90241-X. |
[14] |
L. Zhang and T. Wong,
Solving integrated process planning and scheduling problem with constructive meta-heuristics, Information Sciences, 340/341 (2016), 1-16.
doi: 10.1016/j.ins.2016.01.001. |
[15] |
L. Zhang and T. Wong,
An object-coding genetic algorithm for integrated process planning and scheduling, European Journal of Operational Research, 244 (2015), 434-444.
doi: 10.1016/j.ejor.2015.01.032. |
[16] |
W. Zhanjie, The research about integration of process planning and production scheduling based on genetic algorithm, in Computer Science and Software Engineering, International Conference on IEEE, eds.T. Ju, 2008.
doi: 10.1109/CSSE.2008.845. |









Parameters |
|
d: TAD indicator |
t: Tool indicator |
m: machine indicator |
Decision Variables |
Proposed Goal Programming Model: |
Parameters |
|
d: TAD indicator |
t: Tool indicator |
m: machine indicator |
Decision Variables |
Proposed Goal Programming Model: |
The cost peroperation(MC) | Symbol | Source |
50 | M1 | CNC milling machine 1 |
60 | M2 | CNC milling machine 2 |
30 | M3 | Grinding CNC machine |
35 | M4 | Column drilling equipment |
20 | M5 | Hand drilling equipment |
20 | M6 | Grinding machine |
The cost per operation(TC) | Symbol | Resource |
6 | T1 | Drill 1 |
5 | T2 | Drill 2 |
10 | T3 | Drill 3 |
15 | T4 | Drill 4 |
13 | T5 | Drill 5 |
14 | T6 | Drill 6 |
8 | T7 | Drill 7 |
10 | T8 | Drill 8 |
5 | T9 | Drill 9 |
10 | T10 | Polishers |
15 | T11 | Reamer 1 |
20 | T12 | Reamer 2 |
18 | T13 | Reamer 3 |
15 | T14 | Diamond blades |
18 | T15 | Milling plate |
13 | T16 | Spark |
24 | T17 | Magnetic stone |
The cost peroperation(MC) | Symbol | Source |
50 | M1 | CNC milling machine 1 |
60 | M2 | CNC milling machine 2 |
30 | M3 | Grinding CNC machine |
35 | M4 | Column drilling equipment |
20 | M5 | Hand drilling equipment |
20 | M6 | Grinding machine |
The cost per operation(TC) | Symbol | Resource |
6 | T1 | Drill 1 |
5 | T2 | Drill 2 |
10 | T3 | Drill 3 |
15 | T4 | Drill 4 |
13 | T5 | Drill 5 |
14 | T6 | Drill 6 |
8 | T7 | Drill 7 |
10 | T8 | Drill 8 |
5 | T9 | Drill 9 |
10 | T10 | Polishers |
15 | T11 | Reamer 1 |
20 | T12 | Reamer 2 |
18 | T13 | Reamer 3 |
15 | T14 | Diamond blades |
18 | T15 | Milling plate |
13 | T16 | Spark |
24 | T17 | Magnetic stone |
Features | Index | Operation | TAD candidate | Machine candidate | Tool candidate | Machining time for each candidate machine (s) |
F1 | Oper1 | Milling | -Z | M1, M2 | T14, T15, T16, T17 | 40, 38 |
F2 | Oper2 | Milling | +Z | M1, M2 | T14, T15, T16, T17 | 37, 38 |
F3 | Oper3 | Milling | -Z, -Y | M1, M2 | T14, T15, T16, T17 | 41, 43 |
F4 | Oper4 | Milling | +Y, -Z | M1, M2 | T14, T15, T16, T17 | 31, 30 |
F5 | Oper5 | Boring | +Y, -Y | M6 | T10 | 40 |
F6 | Oper6 | Drilling | -Z | M3, M4, M5 | T1 | 40, 50, 30 |
Oper7 | Reaming | -Z | M3, M4, M5 | T11 | 40, 50, 30 | |
F7 | Oper8 | Ribbing | -Z, -Y | M1, M2 | T14, T15, T16, T17 | 54, 52 |
F8 | Oper9 | Drilling | +X, -X | M3, M4, M5 | t2 | 20, 30, 21 |
F9 | Oper10 | Drilling | +X, -X | M3, M4, M5 | t3 | 50, 60, 40 |
F10 | Oper11 | Drilling | +Y | M3, M4, M5 | t4 | 60, 50, 30 |
Oper12 | reaming | +Y | M3, M4, M5 | T12 | 60, 50, 30 | |
F11 | Oper13 | Boring | A | M6 | T10 | 50 |
Features | Index | Operation | TAD candidate | Machine candidate | Tool candidate | Machining time for each candidate machine (s) |
F1 | Oper1 | Milling | -Z | M1, M2 | T14, T15, T16, T17 | 40, 38 |
F2 | Oper2 | Milling | +Z | M1, M2 | T14, T15, T16, T17 | 37, 38 |
F3 | Oper3 | Milling | -Z, -Y | M1, M2 | T14, T15, T16, T17 | 41, 43 |
F4 | Oper4 | Milling | +Y, -Z | M1, M2 | T14, T15, T16, T17 | 31, 30 |
F5 | Oper5 | Boring | +Y, -Y | M6 | T10 | 40 |
F6 | Oper6 | Drilling | -Z | M3, M4, M5 | T1 | 40, 50, 30 |
Oper7 | Reaming | -Z | M3, M4, M5 | T11 | 40, 50, 30 | |
F7 | Oper8 | Ribbing | -Z, -Y | M1, M2 | T14, T15, T16, T17 | 54, 52 |
F8 | Oper9 | Drilling | +X, -X | M3, M4, M5 | t2 | 20, 30, 21 |
F9 | Oper10 | Drilling | +X, -X | M3, M4, M5 | t3 | 50, 60, 40 |
F10 | Oper11 | Drilling | +Y | M3, M4, M5 | t4 | 60, 50, 30 |
Oper12 | reaming | +Y | M3, M4, M5 | T12 | 60, 50, 30 | |
F11 | Oper13 | Boring | A | M6 | T10 | 50 |
Features | Index | operation | TAD candidate | Machine candidate | Tool candidate | Machining time for each candidate machine (s) |
F1 | oper1 | Milling | -Y | M1, M2 | T14, T15, T16, T17 | 30, 20 |
F2 | oper2 | milling | +Z | M1, M2 | T14, T15, T16, T17 | 35, 29 |
F3 | oper3 | milling | -Y, -Y | M1, M2 | T14, T15, T16, T17 | 29, 24 |
F4 | oper4 | drilling | +Z, -Z | M3, M4, M5 | T4 | 57, 66, 51 |
F5 | oper5 | reaming | +X | M3, M4, M5 | T5 | 41, 59, 38 |
oper6 | drilling | +X | M3, M4, M5 | T13 | 52, 71, 41 | |
F6 | oper7 | reaming | -Y, +Y | M3, M4, M5 | t6 | 30, 41, 28 |
F7 | oper8 | ribbing | -Z, +Z, -X | M1, M2 | T14, T15, T16, T17 | 47, 49 |
F8 | oper9 | milling | A | M1, M2 | T14, T15, T16, T17 | 40, 41 |
F9 | oper10 | boring | +X, -X, +Y, -Y | m6 | T10 | 40 |
Features | Index | operation | TAD candidate | Machine candidate | Tool candidate | Machining time for each candidate machine (s) |
F1 | oper1 | Milling | -Y | M1, M2 | T14, T15, T16, T17 | 30, 20 |
F2 | oper2 | milling | +Z | M1, M2 | T14, T15, T16, T17 | 35, 29 |
F3 | oper3 | milling | -Y, -Y | M1, M2 | T14, T15, T16, T17 | 29, 24 |
F4 | oper4 | drilling | +Z, -Z | M3, M4, M5 | T4 | 57, 66, 51 |
F5 | oper5 | reaming | +X | M3, M4, M5 | T5 | 41, 59, 38 |
oper6 | drilling | +X | M3, M4, M5 | T13 | 52, 71, 41 | |
F6 | oper7 | reaming | -Y, +Y | M3, M4, M5 | t6 | 30, 41, 28 |
F7 | oper8 | ribbing | -Z, +Z, -X | M1, M2 | T14, T15, T16, T17 | 47, 49 |
F8 | oper9 | milling | A | M1, M2 | T14, T15, T16, T17 | 40, 41 |
F9 | oper10 | boring | +X, -X, +Y, -Y | m6 | T10 | 40 |
Features | Index | operation | TAD candidate | Machine candidate | Tool candidate | Machining time for each candidate machine (s) |
F1 | oper1 | Milling | -Y, -X | M1, M2 | T14, T15, T16, T17 | 30, 35 |
F2 | oper2 | Milling | +Z, +Z | M1, M2 | T14, T15, T16, T17 | 28, 30 |
F3 | oper3 | Milling | +Z, +Y | M1, M2 | T14, T15, T16, T17 | 33, 30 |
F4 | oper4 | Milling | +X, -X | M1, M2 | T14, T15, T16, T17 | 29, 25 |
F5 | oper5 | Milling | +X, -X | M1, M2 | T14, T15, T16, T17 | 37, 31 |
F6 | oper6 | Drilling | -Z, +Z | M3, M4, M5 | T9 | 50, 60, 40 |
F7 | oper7 | Milling | -Z | M1, M2 | T14, T15, T16, T17 | 40, 39 |
F8 | ooper8 | Drilling | -Z | M3, M4, M5 | T8 | 39, 50, 38 |
Features | Index | operation | TAD candidate | Machine candidate | Tool candidate | Machining time for each candidate machine (s) |
F1 | oper1 | Milling | -Y, -X | M1, M2 | T14, T15, T16, T17 | 30, 35 |
F2 | oper2 | Milling | +Z, +Z | M1, M2 | T14, T15, T16, T17 | 28, 30 |
F3 | oper3 | Milling | +Z, +Y | M1, M2 | T14, T15, T16, T17 | 33, 30 |
F4 | oper4 | Milling | +X, -X | M1, M2 | T14, T15, T16, T17 | 29, 25 |
F5 | oper5 | Milling | +X, -X | M1, M2 | T14, T15, T16, T17 | 37, 31 |
F6 | oper6 | Drilling | -Z, +Z | M3, M4, M5 | T9 | 50, 60, 40 |
F7 | oper7 | Milling | -Z | M1, M2 | T14, T15, T16, T17 | 40, 39 |
F8 | ooper8 | Drilling | -Z | M3, M4, M5 | T8 | 39, 50, 38 |
Precedence relations |
Oper1 is first operation. Oper2 is prior to Oper4, Oper5, Oper11 and Oper12. Oper3 is prior to Oper4, Oper5 and Oper10. Oper6 is prior to Oper7, Oper11 and Oper12. Oper8 is prior to Oper13. Oper9 is prior to Oper13. Oper11 is prior to Oper12. |
Precedence relations |
Oper1 is first operation. Oper2 is prior to Oper4, Oper5, Oper11 and Oper12. Oper3 is prior to Oper4, Oper5 and Oper10. Oper6 is prior to Oper7, Oper11 and Oper12. Oper8 is prior to Oper13. Oper9 is prior to Oper13. Oper11 is prior to Oper12. |
Precedence relations |
Oper1 is first operation Oper2 is prior to Oper7, Oper9. Oper3 is prior to Oper5, Oper9. Oper4 is prior to Oper5, Oper6. Oper5 is prior to Oper6. Oper7 is prior to Oper8, Oper10. Oper8 is prior to Oper10. |
Precedence relations |
Oper1 is first operation Oper2 is prior to Oper7, Oper9. Oper3 is prior to Oper5, Oper9. Oper4 is prior to Oper5, Oper6. Oper5 is prior to Oper6. Oper7 is prior to Oper8, Oper10. Oper8 is prior to Oper10. |
Precedence relations |
Oper1 is first operation. Oper2 is prior to Oper4, Oper5. Oper3 is prior to Oper4, Oper5. Oper4 is prior to Oper5, Oper6. Oper5 is prior to Oper6. Oper7 is prior to Oper8. |
Precedence relations |
Oper1 is first operation. Oper2 is prior to Oper4, Oper5. Oper3 is prior to Oper4, Oper5. Oper4 is prior to Oper5, Oper6. Oper5 is prior to Oper6. Oper7 is prior to Oper8. |
Ease in material displacement in different machines | ||||||
VL | L | M | H | VH | ||
Distance between installed machines | VH | X | X | X | U | U |
H | X | U | U | O | O | |
M | U | U | O | I | I | |
L | U | O | I | E | A | |
VL | U | O | I | A | A |
Ease in material displacement in different machines | ||||||
VL | L | M | H | VH | ||
Distance between installed machines | VH | X | X | X | U | U |
H | X | U | U | O | O | |
M | U | U | O | I | I | |
L | U | O | I | E | A | |
VL | U | O | I | A | A |
Ease in material flow | M1 | M2 | M3 | M4 | M5 | M6 |
M1 | 5.69 | 2.74 | 5.69 | 2.00 | 1.50 | 1.50 |
M2 | 3.74 | 5.69 | 2.56 | 3.00 | 4.37 | 1.50 |
M3 | 4.50 | 4.37 | 5.69 | 1.20 | 0.37 | 1.50 |
M4 | 1.50 | 1.50 | 1.20 | 5.69 | 2.50 | 1.20 |
M5 | 1.20 | 2.56 | 1.50 | 1.50 | 5.69 | 2.56 |
M6 | 1.50 | 2.00 | 1.50 | 1.20 | 3.56 | 5.69 |
Ease in material flow | M1 | M2 | M3 | M4 | M5 | M6 |
M1 | 5.69 | 2.74 | 5.69 | 2.00 | 1.50 | 1.50 |
M2 | 3.74 | 5.69 | 2.56 | 3.00 | 4.37 | 1.50 |
M3 | 4.50 | 4.37 | 5.69 | 1.20 | 0.37 | 1.50 |
M4 | 1.50 | 1.50 | 1.20 | 5.69 | 2.50 | 1.20 |
M5 | 1.20 | 2.56 | 1.50 | 1.50 | 5.69 | 2.56 |
M6 | 1.50 | 2.00 | 1.50 | 1.20 | 3.56 | 5.69 |
Compatibility | ||||||
VL | L | M/ | H | VH | ||
Setup Ease | VL | X | X | X | U | U |
L | X | U | U | O | O | |
M | U | U | O | I | I | |
H | U | O | I | E | A | |
VH | U | O | I | A | A |
Compatibility | ||||||
VL | L | M/ | H | VH | ||
Setup Ease | VL | X | X | X | U | U |
L | X | U | U | O | O | |
M | U | U | O | I | I | |
H | U | O | I | E | A | |
VH | U | O | I | A | A |
Ease in production | M1 | M2 | M3 | M4 | M5 | M6 |
M1 | 5.69 | 1.50 | 2.50 | 4.00 | 3.00 | 1.50 |
M2 | 4.23 | 5.69 | 3.00 | 5.69 | 3.00 | 1.50 |
M3 | 3.00 | 3.00 | 5.69 | 3.00 | 5.63 | 2.50 |
M4 | 2.50 | 2.50 | 1.50 | 5.69 | 2.50 | 1.50 |
M5 | 2.50 | 4.00 | 1.50 | 1.50 | 5.69 | 3.00 |
M6 | 3.00 | 3.00 | 3.50 | 3.50 | 3.00 | 5.69 |
Ease in production | M1 | M2 | M3 | M4 | M5 | M6 |
M1 | 5.69 | 1.50 | 2.50 | 4.00 | 3.00 | 1.50 |
M2 | 4.23 | 5.69 | 3.00 | 5.69 | 3.00 | 1.50 |
M3 | 3.00 | 3.00 | 5.69 | 3.00 | 5.63 | 2.50 |
M4 | 2.50 | 2.50 | 1.50 | 5.69 | 2.50 | 1.50 |
M5 | 2.50 | 4.00 | 1.50 | 1.50 | 5.69 | 3.00 |
M6 | 3.00 | 3.00 | 3.50 | 3.50 | 3.00 | 5.69 |
Objective Function | Goal | Weight |
TWC | 1 | |
Make Span | 2 | |
Utility | 3 |
Objective Function | Goal | Weight |
TWC | 1 | |
Make Span | 2 | |
Utility | 3 |
Parameters | |
The number of initial population |
The iterations time |
The number of neighborhood |
Alpha |
Parameters | |
The number of initial population |
The iterations time |
The number of neighborhood |
Alpha |
Position | Parts | Operations | Position | Parts | Operations | |
1 | 1 | 1 | 17 | 2 | 4 | |
2 | 1 | 2 | 18 | 2 | 5 | |
3 | 1 | 3 | 19 | 2 | 6 | |
4 | 1 | 4 | 20 | 2 | 7 | |
5 | 1 | 5 | 21 | 2 | 8 | |
6 | 1 | 6 | 22 | 2 | 9 | |
7 | 1 | 7 | 23 | 2 | 10 | |
8 | 1 | 8 | 24 | 3 | 1 | |
9 | 1 | 9 | 25 | 3 | 2 | |
10 | 1 | 10 | 26 | 3 | 3 | |
11 | 1 | 11 | 27 | 3 | 4 | |
12 | 1 | 12 | 28 | 3 | 5 | |
13 | 1 | 13 | 29 | 3 | 6 | |
14 | 2 | 1 | 30 | 3 | 7 | |
15 | 2 | 2 | 31 | 3 | 8 | |
16 | 2 | 3 |
Position | Parts | Operations | Position | Parts | Operations | |
1 | 1 | 1 | 17 | 2 | 4 | |
2 | 1 | 2 | 18 | 2 | 5 | |
3 | 1 | 3 | 19 | 2 | 6 | |
4 | 1 | 4 | 20 | 2 | 7 | |
5 | 1 | 5 | 21 | 2 | 8 | |
6 | 1 | 6 | 22 | 2 | 9 | |
7 | 1 | 7 | 23 | 2 | 10 | |
8 | 1 | 8 | 24 | 3 | 1 | |
9 | 1 | 9 | 25 | 3 | 2 | |
10 | 1 | 10 | 26 | 3 | 3 | |
11 | 1 | 11 | 27 | 3 | 4 | |
12 | 1 | 12 | 28 | 3 | 5 | |
13 | 1 | 13 | 29 | 3 | 6 | |
14 | 2 | 1 | 30 | 3 | 7 | |
15 | 2 | 2 | 31 | 3 | 8 | |
16 | 2 | 3 |
Random Position | Considering the Precedence relations | Feasible Position | Parts | Operations | Machines | Tools | TAD |
17 | 14 | 2 | 1 | 2 | 14 | -Z | |
5 | 17 | 2 | 4 | 1 | 15 | Z | |
3 | 16 | 2 | 3 | 2 | 16 | -Y | |
10 | 18 | 2 | 5 | 1 | 16 | -Z | |
2 | 19 | 2 | 6 | 6 | 10 | Y | |
31 | 15 | 2 | 2 | 4 | 1 | -Z | |
12 | 20 | 2 | 7 | 4 | 11 | -Z | |
19 | 21 | 2 | 8 | 2 | 16 | -Z | |
9 | 23 | 2 | 10 | 4 | 2 | X | |
27 | 24 | 3 | 1 | 5 | 3 | -X | |
21 | 26 | 3 | 3 | 3 | 4 | Y | |
18 | 30 | 3 | 7 | 5 | 12 | Y | |
14 | 31 | 3 | 8 | 6 | 10 | A | |
6 | 25 | 3 | 2 | 2 | 15 | -Y | |
13 | 27 | 3 | 4 | 1 | 17 | Z | |
4 | 28 | 3 | 5 | 2 | 15 | -Y | |
26 | 29 | 3 | 6 | 3 | 4 | Z | |
30 | 22 | 2 | 9 | 4 | 5 | X | |
7 | 1 | 1 | 1 | 5 | 13 | X | |
20 | 3 | 1 | 3 | 4 | 6 | -Y | |
16 | 10 | 1 | 10 | 2 | 17 | -Z | |
28 | 2 | 1 | 2 | 1 | 16 | A | |
8 | 5 | 1 | 5 | 6 | 10 | -X | |
25 | 9 | 1 | 9 | 2 | 15 | -Y | |
23 | 6 | 1 | 6 | 2 | 14 | X | |
29 | 4 | 1 | 4 | 2 | 17 | z | |
15 | 7 | 1 | 7 | 2 | 17 | X | |
24 | 8 | 1 | 8 | 2 | 16 | X | |
22 | 13 | 1 | 13 | 3 | 9 | z | |
1 | 11 | 1 | 11 | 2 | 14 | -Z | |
11 | 12 | 1 | 12 | 5 | 8 | -Z |
Random Position | Considering the Precedence relations | Feasible Position | Parts | Operations | Machines | Tools | TAD |
17 | 14 | 2 | 1 | 2 | 14 | -Z | |
5 | 17 | 2 | 4 | 1 | 15 | Z | |
3 | 16 | 2 | 3 | 2 | 16 | -Y | |
10 | 18 | 2 | 5 | 1 | 16 | -Z | |
2 | 19 | 2 | 6 | 6 | 10 | Y | |
31 | 15 | 2 | 2 | 4 | 1 | -Z | |
12 | 20 | 2 | 7 | 4 | 11 | -Z | |
19 | 21 | 2 | 8 | 2 | 16 | -Z | |
9 | 23 | 2 | 10 | 4 | 2 | X | |
27 | 24 | 3 | 1 | 5 | 3 | -X | |
21 | 26 | 3 | 3 | 3 | 4 | Y | |
18 | 30 | 3 | 7 | 5 | 12 | Y | |
14 | 31 | 3 | 8 | 6 | 10 | A | |
6 | 25 | 3 | 2 | 2 | 15 | -Y | |
13 | 27 | 3 | 4 | 1 | 17 | Z | |
4 | 28 | 3 | 5 | 2 | 15 | -Y | |
26 | 29 | 3 | 6 | 3 | 4 | Z | |
30 | 22 | 2 | 9 | 4 | 5 | X | |
7 | 1 | 1 | 1 | 5 | 13 | X | |
20 | 3 | 1 | 3 | 4 | 6 | -Y | |
16 | 10 | 1 | 10 | 2 | 17 | -Z | |
28 | 2 | 1 | 2 | 1 | 16 | A | |
8 | 5 | 1 | 5 | 6 | 10 | -X | |
25 | 9 | 1 | 9 | 2 | 15 | -Y | |
23 | 6 | 1 | 6 | 2 | 14 | X | |
29 | 4 | 1 | 4 | 2 | 17 | z | |
15 | 7 | 1 | 7 | 2 | 17 | X | |
24 | 8 | 1 | 8 | 2 | 16 | X | |
22 | 13 | 1 | 13 | 3 | 9 | z | |
1 | 11 | 1 | 11 | 2 | 14 | -Z | |
11 | 12 | 1 | 12 | 5 | 8 | -Z |
| Exclusive number of each member of the tuples |
The number of the parts | |
The number of operations necessary for part processing | |
The set of TAD candidates | |
The set of tool candidates | |
The set of machine candidates | |
The set of Machining time for each candidate machine (s) | |
The set of successor operations |
| Exclusive number of each member of the tuples |
The number of the parts | |
The number of operations necessary for part processing | |
The set of TAD candidates | |
The set of tool candidates | |
The set of machine candidates | |
The set of Machining time for each candidate machine (s) | |
The set of successor operations |
| A tuple type data represent the Task which the Mode is derived from |
Indicates the number of the parts which equal to |
|
Indicates the number of the operations in one part which equals to |
|
Indicates the number of TADs which is a member of |
|
Indicates the number of tools which are the members of |
|
Indicates the number of machines which are a member of |
|
Indicates the machining time for |
| A tuple type data represent the Task which the Mode is derived from |
Indicates the number of the parts which equal to |
|
Indicates the number of the operations in one part which equals to |
|
Indicates the number of TADs which is a member of |
|
Indicates the number of tools which are the members of |
|
Indicates the number of machines which are a member of |
|
Indicates the machining time for |
Part | Operation | Machine | TAD | Tool | Start Time | Machining Time | Finish Time |
1 | 1 | 2 | -3 | 16 | 0 | 38 | 38 |
1 | 2 | 1 | 3 | 14 | 100 | 37 | 137 |
1 | 3 | 1 | -3 | 14 | 59 | 41 | 100 |
1 | 4 | 1 | 2 | 16 | 323 | 31 | 354 |
1 | 5 | 6 | -2 | 10 | 394 | 40 | 434 |
1 | 6 | 5 | -3 | 1 | 139 | 30 | 169 |
1 | 7 | 3 | -3 | 11 | 169 | 40 | 209 |
1 | 8 | 1 | -3 | 16 | 269 | 54 | 323 |
1 | 9 | 5 | 1 | 2 | 38 | 21 | 59 |
1 | 10 | 5 | 1 | 3 | 354 | 40 | 394 |
1 | 11 | 5 | 2 | 4 | 209 | 30 | 239 |
1 | 12 | 5 | 2 | 12 | 239 | 30 | 269 |
1 | 13 | 6 | 4 | 10 | 434 | 50 | 484 |
2 | 1 | 2 | -2 | 16 | 38 | 20 | 58 |
2 | 2 | 2 | 3 | 15 | 82 | 29 | 111 |
2 | 3 | 2 | -3 | 16 | 58 | 24 | 82 |
2 | 4 | 4 | -1 | 4 | 269 | 66 | 335 |
2 | 5 | 4 | 1 | 5 | 335 | 59 | 394 |
2 | 6 | 5 | 1 | 13 | 394 | 41 | 435 |
2 | 7 | 5 | -2 | 6 | 111 | 28 | 139 |
2 | 8 | 2 | 3 | 14 | 180 | 49 | 229 |
2 | 9 | 2 | 4 | 16 | 139 | 41 | 180 |
2 | 10 | 6 | 1 | 10 | 229 | 40 | 269 |
3 | 1 | 1 | -2 | 14 | 0 | 30 | 30 |
3 | 2 | 2 | 3 | 14 | 298 | 30 | 328 |
3 | 3 | 2 | 3 | 14 | 229 | 30 | 259 |
3 | 4 | 1 | -1 | 17 | 354 | 29 | 383 |
3 | 5 | 2 | 1 | 14 | 383 | 31 | 414 |
3 | 6 | 5 | -3 | 9 | 453 | 40 | 493 |
3 | 7 | 2 | -3 | 15 | 259 | 39 | 298 |
3 | 8 | 3 | -3 | 8 | 414 | 39 | 453 |
Part | Operation | Machine | TAD | Tool | Start Time | Machining Time | Finish Time |
1 | 1 | 2 | -3 | 16 | 0 | 38 | 38 |
1 | 2 | 1 | 3 | 14 | 100 | 37 | 137 |
1 | 3 | 1 | -3 | 14 | 59 | 41 | 100 |
1 | 4 | 1 | 2 | 16 | 323 | 31 | 354 |
1 | 5 | 6 | -2 | 10 | 394 | 40 | 434 |
1 | 6 | 5 | -3 | 1 | 139 | 30 | 169 |
1 | 7 | 3 | -3 | 11 | 169 | 40 | 209 |
1 | 8 | 1 | -3 | 16 | 269 | 54 | 323 |
1 | 9 | 5 | 1 | 2 | 38 | 21 | 59 |
1 | 10 | 5 | 1 | 3 | 354 | 40 | 394 |
1 | 11 | 5 | 2 | 4 | 209 | 30 | 239 |
1 | 12 | 5 | 2 | 12 | 239 | 30 | 269 |
1 | 13 | 6 | 4 | 10 | 434 | 50 | 484 |
2 | 1 | 2 | -2 | 16 | 38 | 20 | 58 |
2 | 2 | 2 | 3 | 15 | 82 | 29 | 111 |
2 | 3 | 2 | -3 | 16 | 58 | 24 | 82 |
2 | 4 | 4 | -1 | 4 | 269 | 66 | 335 |
2 | 5 | 4 | 1 | 5 | 335 | 59 | 394 |
2 | 6 | 5 | 1 | 13 | 394 | 41 | 435 |
2 | 7 | 5 | -2 | 6 | 111 | 28 | 139 |
2 | 8 | 2 | 3 | 14 | 180 | 49 | 229 |
2 | 9 | 2 | 4 | 16 | 139 | 41 | 180 |
2 | 10 | 6 | 1 | 10 | 229 | 40 | 269 |
3 | 1 | 1 | -2 | 14 | 0 | 30 | 30 |
3 | 2 | 2 | 3 | 14 | 298 | 30 | 328 |
3 | 3 | 2 | 3 | 14 | 229 | 30 | 259 |
3 | 4 | 1 | -1 | 17 | 354 | 29 | 383 |
3 | 5 | 2 | 1 | 14 | 383 | 31 | 414 |
3 | 6 | 5 | -3 | 9 | 453 | 40 | 493 |
3 | 7 | 2 | -3 | 15 | 259 | 39 | 298 |
3 | 8 | 3 | -3 | 8 | 414 | 39 | 453 |
Part | Operation | Machine | TAD | Tool | Start Time | Machining Time | Finish Time |
1 | 1 | 2 | -3 | 16 | 0 | 38 | 38 |
1 | 2 | 2 | 3 | 16 | 38 | 37 | 75 |
1 | 3 | 1 | -3 | 16 | 75 | 41 | 116 |
1 | 8 | 1 | -3 | 16 | 116 | 52 | 168 |
1 | 10 | 3 | 1 | 3 | 168 | 40 | 208 |
1 | 6 | 5 | -3 | 1 | 208 | 30 | 238 |
1 | 9 | 5 | -1 | 2 | 238 | 20 | 258 |
1 | 11 | 5 | 2 | 4 | 258 | 30 | 288 |
1 | 7 | 5 | -3 | 11 | 288 | 30 | 318 |
1 | 13 | 6 | 4 | 10 | 318 | 50 | 368 |
1 | 5 | 6 | 2 | 10 | 368 | 40 | 408 |
1 | 12 | 5 | 2 | 12 | 408 | 30 | 438 |
1 | 4 | 1 | -3 | 16 | 438 | 30 | 468 |
2 | 1 | 1 | -2 | 16 | 0 | 20 | 20 |
2 | 3 | 1 | -3 | 16 | 20 | 24 | 44 |
2 | 2 | 1 | 3 | 16 | 44 | 29 | 73 |
2 | 4 | 5 | 3 | 4 | 73 | 51 | 124 |
2 | 5 | 5 | 1 | 5 | 124 | 38 | 162 |
2 | 6 | 5 | 1 | 13 | 162 | 41 | 203 |
2 | 7 | 5 | 2 | 6 | 318 | 28 | 346 |
2 | 8 | 1 | -3 | 16 | 351 | 47 | 398 |
2 | 9 | 1 | 4 | 16 | 398 | 40 | 438 |
2 | 10 | 6 | 1 | 10 | 438 | 40 | 478 |
3 | 1 | 1 | -2 | 16 | 168 | 30 | 198 |
3 | 7 | 1 | -3 | 16 | 198 | 39 | 237 |
3 | 2 | 1 | 1 | 16 | 237 | 28 | 265 |
3 | 3 | 1 | 3 | 16 | 265 | 30 | 295 |
3 | 4 | 1 | 1 | 16 | 295 | 25 | 320 |
3 | 5 | 1 | -1 | 16 | 320 | 31 | 351 |
3 | 6 | 5 | -3 | 9 | 351 | 40 | 391 |
3 | 8 | 5 | -3 | 8 | 438 | 38 | 476 |
Part | Operation | Machine | TAD | Tool | Start Time | Machining Time | Finish Time |
1 | 1 | 2 | -3 | 16 | 0 | 38 | 38 |
1 | 2 | 2 | 3 | 16 | 38 | 37 | 75 |
1 | 3 | 1 | -3 | 16 | 75 | 41 | 116 |
1 | 8 | 1 | -3 | 16 | 116 | 52 | 168 |
1 | 10 | 3 | 1 | 3 | 168 | 40 | 208 |
1 | 6 | 5 | -3 | 1 | 208 | 30 | 238 |
1 | 9 | 5 | -1 | 2 | 238 | 20 | 258 |
1 | 11 | 5 | 2 | 4 | 258 | 30 | 288 |
1 | 7 | 5 | -3 | 11 | 288 | 30 | 318 |
1 | 13 | 6 | 4 | 10 | 318 | 50 | 368 |
1 | 5 | 6 | 2 | 10 | 368 | 40 | 408 |
1 | 12 | 5 | 2 | 12 | 408 | 30 | 438 |
1 | 4 | 1 | -3 | 16 | 438 | 30 | 468 |
2 | 1 | 1 | -2 | 16 | 0 | 20 | 20 |
2 | 3 | 1 | -3 | 16 | 20 | 24 | 44 |
2 | 2 | 1 | 3 | 16 | 44 | 29 | 73 |
2 | 4 | 5 | 3 | 4 | 73 | 51 | 124 |
2 | 5 | 5 | 1 | 5 | 124 | 38 | 162 |
2 | 6 | 5 | 1 | 13 | 162 | 41 | 203 |
2 | 7 | 5 | 2 | 6 | 318 | 28 | 346 |
2 | 8 | 1 | -3 | 16 | 351 | 47 | 398 |
2 | 9 | 1 | 4 | 16 | 398 | 40 | 438 |
2 | 10 | 6 | 1 | 10 | 438 | 40 | 478 |
3 | 1 | 1 | -2 | 16 | 168 | 30 | 198 |
3 | 7 | 1 | -3 | 16 | 198 | 39 | 237 |
3 | 2 | 1 | 1 | 16 | 237 | 28 | 265 |
3 | 3 | 1 | 3 | 16 | 265 | 30 | 295 |
3 | 4 | 1 | 1 | 16 | 295 | 25 | 320 |
3 | 5 | 1 | -1 | 16 | 320 | 31 | 351 |
3 | 6 | 5 | -3 | 9 | 351 | 40 | 391 |
3 | 8 | 5 | -3 | 8 | 438 | 38 | 476 |
Objective | TWC | Make Span | Utility | Time (Sec) |
Max(Min) Function | Min | Min | Max | |
Goal | 1484 | 468 | 288 | |
CP | 1514 | 478 | 258.3761 | 300 |
SA | 1669 | 493 | 87.30202 | 300 |
Objective | TWC | Make Span | Utility | Time (Sec) |
Max(Min) Function | Min | Min | Max | |
Goal | 1484 | 468 | 288 | |
CP | 1514 | 478 | 258.3761 | 300 |
SA | 1669 | 493 | 87.30202 | 300 |
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