|
In this paper, an efficient throughput evaluation method for large series-parallel production lines is developed. The parallel machines follow the exponential reliability model and are not necessarily identical. The proposed method considers different aggregation techniques to transform each group of parallel machines into an equivalent station. Then, the throughput of the obtained buffered serial production line is evaluated using an analytical approach. This evaluation method is based on the analysis of buffer states using a birth-death Markov process. The strength of the approach lies in the analysis of only full and empty buffer states rather than all buffer states. Consequently, through the comparative numerical study against simulation and recent literature, the proposed approach demonstrates its accuracy and efficiency in evaluating throughput of large complex series-parallel systems in only few seconds. In addition, aggregation techniques used are compared and some relevant theoretical properties are derived.
| Citation: |
Figure 3. Representation of the different overlapping birth-death Markov processes [24]
Figure 4. Birth-death Markov process related to the buffer $ B_{j} $ [25]
Figure 5. A view of the model during simulation: instance 1 from the balanced configurations (table 2)
Table Algorithm 1. Throughput evaluation of series-parallel production lines (using [27] aggregation technique)
|
Table 1. Parallel workstations parameters [9]
| $S_{1}$ | $S_{2}$ | $S_{3}$ | $S_{4}$ | $S_{5}$ | $S_{6}$ | $S_{7}$ | $S_{8}$ | $S_{9}$ | $S_{10}$ | |
| $\lambda_{1}$ | 0.02 | 0.005 | 0.04 | 0.01 | 0.0025 | 0.00125 | 0.002 | 0.04 | 0.002 | 0.006 |
| $\mu_{1}$ | 0.2 | 0.06666 | 0.2 | 0.2 | 0.014286 | 0.016667 | 0.0166 | 0.2 | 0.025 | 0.1 |
| $\lambda_{2}$ | 0.006 | 0.002 | 0.0008 | 0.002 | 0.01 | 0.002 | 0.006 | 0.01 | 0.0025 | 0.01 |
| $\mu_{2}$ | 0.1 | 0.025 | 0.01 | 0.016 | 0.2 | 0.025 | 0.1 | 0.2 | 0.0166 | 0.2 |
| $S_{11}$ | $S_{12}$ | $S_{13}$ | $S_{14}$ | $S_{15}$ | $S_{16}$ | $S_{17}$ | $S_{18}$ | $S_{19}$ | $S_{20}$ | |
| $\lambda_{1}$ | 0.0008 | 0.0025 | 0.002 | 0.006 | 0.0025 | 0.01 | 0.005 | 0.0025 | 0.04 | 0.0008 |
| $\mu_{1}$ | 0.01 | 0.014286 | 0.025 | 0.1 | 0.014 | 0.2 | 0.066 | 0.014 | 0.2 | 0.01 |
| $\lambda_{2}$ | 0.04 | 0.005 | 0.0025 | 0.002 | 0.002 | 0.00083 | 0.04 | 0.01 | 0.01 | 0.005 |
| $\mu_{2}$ | 0.2 | 0.066 | 0.014 | 0.016 | 0.025 | 0.01 | 0.2 | 0.2 | 0.2 | 0.066 |
| $S_{21}$ | $S_{22}$ | $S_{23}$ | $S_{24}$ | $S_{25}$ | $S_{50}$ | $S_{27}$ | $S_{28}$ | $S_{29}$ | $S_{30}$ | |
| $\lambda_{1}$ | 0.002 | 0.005 | 0.02 | 0.04 | 0.05 | 0.07 | 0.005 | 0.02 | 0.002 | 0.02 |
| $\mu_{1}$ | 0.025 | 0.0666 | 0.2 | 0.2 | 0.9 | 0.75 | 0.066 | 0.2 | 0.025 | 0.2 |
| $\lambda_{2}$ | 0.0025 | 0.002 | 0.00666 | 0.00083 | 0.0025 | 0.002 | 0.002 | 0.006667 | 0.002 | 0.006 |
| $\mu_{2}$ | 0.016 | 0.025 | 0.1 | 0.01 | 0.016667 | 0.025 | 0.025 | 0.1 | 0.016 | 0.1 |
| $S_{31}$ | $S_{32}$ | $S_{33}$ | $S_{34}$ | $S_{35}$ | $S_{36}$ | $S_{37}$ | $S_{38}$ | $S_{39}$ | $S_{40}$ | |
| $\lambda_{1}$ | 0.00083 | 0.04 | 0.0025 | 0.04 | 0.0025 | 0.0025 | 0.0008 | 0.002 | 0.04 | 0.0025 |
| $\mu_{1}$ | 0.01 | 0.2 | 0.016667 | 0.2 | 0.0142 | 0.014 | 0.01 | 0.025 | 0.2 | 0.01 |
| $\lambda_{2}$ | 0.005 | 0.02 | 0.006667 | 0.000833 | 0.01 | 0.005 | 0.04 | 0.0025 | 0.000833 | 0.0025 |
| $\mu_{2}$ | 0.066 | 0.2 | 0.1 | 0.01 | 0.2 | 0.066 | 0.2 | 0.014 | 0.01 | 0.01 |
| $S_{41}$ | $S_{42}$ | $S_{43}$ | $S_{44}$ | $S_{45}$ | $S_{46}$ | $S_{47}$ | $S_{48}$ | $S_{49}$ | $S_{50}$ | |
| $\lambda_{1}$ | 0.04 | 0.04 | 0.0008 | 0.002 | 0.01 | 0.005 | 0.002 | 0.005 | 0.002 | 0.07 |
| $\mu_{1}$ | 0.2 | 0.2 | 0.01 | 0.016 | 0.2 | 0.06666 | 0.014 | 0.066 | 0.025 | 0.75 |
| $\lambda_{2}$ | 0.04 | 0.0025 | 0.02 | 0.006 | 0.005 | 0.00083 | 0.01 | 0.002 | 0.002 | 0.002 |
| $\mu_{2}$ | 0.2 | 0.01 | 0.2 | 0.1 | 0.066 | 0.01 | 0.2 | 0.025 | 0.0142 | 0.025 |
Table 2. Balanced lines instances [9]
| Instance | Number of stations | Workstations | Buffer capacities |
| 1 | 3 | All stations $S_{1}$ | All buffer capacities = 40 |
| 2 | 4 | All stations $S_{4}$ | All buffer capacities = 40 |
| 3 | 5 | All stations $S_{5}$ | All buffer capacities = 40 |
| 4 | 6 | All stations $S_{3}$ | All buffer capacities = 40 |
| 5 | 7 | All stations $S_{10}$ | All buffer capacities = 40 |
| 6 | 8 | All stations $S_{9}$ | All buffer capacities = 40 |
| 7 | 9 | All stations $S_{2}$ | All buffer capacities = 40 |
| 8 | 10 | All stations $S_{45}$ | All buffer capacities = 40 |
| 9 | 15 | All stations $S_{45}$ | All buffer capacities = 40 |
| 10 | 20 | All stations $S_{8}$ | All buffer capacities = 40 |
| 11 | 25 | All stations $S_{17}$ | All buffer capacities = 40 |
| 12 | 30 | All stations $S_{30}$ | All buffer capacities = 40 |
| 13 | 40 | All stations $S_{10}$ | All buffer capacities = 40 |
| 14 | 50 | All stations $S_{45}$ | All buffer capacities = 40 |
Table 3. Asynchronous lines instances [9]
| Instance | Number of stations | Workstations | Buffer capacities |
| 1 | 3 | $S_{1}$-$S_{2}$-$S_{3}$ | $B_{1}$ = 50-$B_{2}$ = 70 |
| 2 | 4 | $S_{1}$-$S_{2}$-$S_{3}$-$S_{4}$ | $B_{1}$ = 50-$B_{2}$ = 70-$B_{3}$ = 60 |
| 3 | 5 | $S_{1}$-$S_{2}$-$S_{3}$-$S_{4}$-$S_{5}$ | $B_{1}$ = 50-$B_{2}$ = 70-$B_{3}$ = 60-$B_{4}$ = 60 |
| 4 | 6 | $S_{1}$-$S_{2}$-$S_{3}$-$S_{4}$-$S_{5}$-$S_{6}$ | $B_{1}$ = 50-$B_{2}$ = 70-$B_{3}$ = 60-$B_{4}$ = 60-$B_{5}$ = 50 |
| 5 | 7 | $S_{1}$-$S_{2}$-$S_{3}$-$S_{4}$-$S_{5}$-SS-$S_{7}$ | $B_{1}$ = 50-$B_{2}$ = 70-$B_{3}$ = 60-$B_{4}$ = 60-$B_{5}$ = 50-$B_{6}$ = 60 |
| 6 | 8 | $S_{1}$-$S_{2}$-$S_{3}$-$S_{4}$-$S_{5}$-$S_{6}$-$S_{7}$-$S_{8}$ | $B_{1}$ = 50-$B_{2}$ = 70-$B_{3}$ = 60-$B_{4}$ = 60-$B_{5}$ = 50-$B_{6}$ = 60-$B_{7}$ = 60 |
| 7 | 9 | $S_{1}$-$S_{2}$-$S_{3}$-$S_{4}$-$S_{5}$-$S_{6}$-$S_{7}$-$S_{8}$-$S_{9}$ | $B_{1}$ = 50-$B_{2}$ = 70-$B_{3}$ = 60-$B_{4}$ = 60-$B_{5}$ = 50-$B_{6}$ = 60- $B_{7}$ = 60-$B_{8}$ = 60 |
| 8 | 10 | $S_{1}$-$S_{2}$-$S_{3}$-$S_{4}$-$S_{5}$-$S_{6}$-$S_{7}$-$S_{8}$-$S_{9}$-$S_{10}$ | $B_{1}$ = 25-$B_{2}$ = 45-$B_{3}$ = 35-$B_{4}$ = 35-$B_{5}$ = 25-$B_{6}$ = 35-$B_{7}$ = 35-$B_{8}$ = 35-$B_{9}$ = 25 |
| 9 | 15 | $S_{45}$-$S_{46}$-$S_{48}$-$S_{1}$-$S_{2}$-$S_{4}$ $S_{6}$-$S_{27}$-$S_{28}$ $S_{30}$-$S_{31}$-$S_{27}$-$S_{28}$-$S_{45}$-$S_{46}$ | $B_{1}$ = 25-$B_{2}$ = 45-$B_{3}$ = 35-$B_{4}$ = 35-$B_{5}$ = 25-$B_{6}$ = 35-$B_{7}$ = 35-$B_{8}$ = 35-$B_{9}$ = 25 $B_{10}$ = 35-$B_{11}$ = 35-$B_{12}$ = 35-$B_{13}$ = 35-$B_{14}$ = 35 |
| 10 | 20 | $S_{1}$-0.99$S_{1}$-0.98$S_{1}$-0.97$S_{1}$-0.96 $S_{1}$-0.95 $S_{1}$-0.94 $S_{1}$-0.93 $S_{1}$-0.92 $S_{1}$-0.91 $S_{1}$-0.9$S_{1}$-0.91 $S_{1}$-0.92 $S_{1}$-0.93 $S_{1}$-0.94 $S_{1}$-0.95 $S_{1}$-0.96 $S_{1}$-0.97 $S_{1}$-0.98$S_{1}$-0.99 $S_{1}$ | $B_{1}$ = 25-$B_{2}$ = 45-$B_{3}$ = 35-$B_{4}$ = 35-$B_{5}$ = 25-$B_{6}$ = 35-$B_{7}$ = 35-$B_{8}$ = 35-$B_{9}$ = 25 $B_{10}$ = 35-$B_{11}$ = 35-$B_{12}$ = 35-$B_{13}$ = 35-$B_{14}$ = 35 $B_{15}$ = 25-$B_{16}$ = 45-$B_{17}$ = 35-$B_{18}$ = 45-$B_{19}$ = 25 |
| 11 | 25 | $S_{48}$-$S_{16}$-$S_{20}$-$S_{22}$ $S_{48}$-$S_{1}$-$S_{2}$-$S_{4}$-$S_{6}$-$S_{27}$-$S_{28}$ $S_{30}$-$S_{2}$-$S_{4}$-$S_{45}$-$S_{46}$-$S_{45}$-$S_{46}$-$S_{48}$-$S_{1}$-$S_{2}$-$S_{4}$-$S_{48}$-$S_{1}$-$S_{2}$ | $B_{1}$ = 25-$B_{2}$ = 45-$B_{3}$ = 35-$B_{4}$ = 35-$B_{5}$ = 25-$B_{6}$ = 35-$B_{7}$ = 35-$B_{8}$ = 35-$B_{9}$ = 25 $B_{10}$ = 35-$B_{11}$ = 35-$B_{12}$ = 35-$B_{13}$ = 35-$B_{14}$ = 35 $B_{15}$ = 25-$B_{16}$ = 45-$B_{17}$ = 35-$B_{18}$ = 45-$B_{19}$ = 25 $B_{20}$ = 35-$B_{21}$ = 25-$B_{22}$ = 25-$B_{23}$ = 45-$B_{24}$ = 35 |
| 12 | 30 | 2.0 $S_{10}$-1.99 $S_{10}$-1.98 $S_{10}$-1.97 $S_{10}$-1.96 $S_{10}$-1.95 $S_{10}$-1.94$S_{10}$-1.93 $S_{10}$-1.92 $S_{10}$-1.91 $S_{10}$-1.9 $S_{10}$-1.899 $S_{10}$-1.898$S_{10}$-1.897 $S_{10}$-1.895 $S_{10}$-1.896 $S_{10}$-1.897 $S_{10}$-1.898 $S_{10}$-1.899 $S_{10}$-1.9 $S_{10}$-1.91 $S_{10}$-1.92 $S_{10}$-1.93 $S_{10}$-1.94 $S_{10}$-1.95S10-1.96 $S_{10}$-1.97 $S_{10}$-1.98 $S_{10}$-1.99 $S_{10}$-2.0 $S_{10}$ | $B_{1}$ = 25-$B_{2}$ = 45-$B_{3}$ = 35-$B_{4}$ = 35-$B_{5}$ = 25-$B_{6}$ = 35-$B_{7}$ = 35-$B_{8}$ = 35-$B_{9}$ = 25 $B_{10}$ = 35-$B_{11}$ = 35-$B_{12}$ = 35-$B_{13}$ = 35-$B_{14}$ = 35 $B_{15}$ = 25-$B_{16}$ = 45-$B_{17}$ = 35-$B_{18}$ = 45-$B_{19}$ = 25 $B_{20}$ = 35-$B_{21}$ = 25-$B_{22}$ = 25-$B_{23}$ = 45-$B_{24}$ = 35 $B_{25}$ = 25-$B_{26}$ = 25-$B_{27}$ = 25-$B_{28}$ = 35 $B_{29}$ = 25 |
| 13 | 40 | $S_{4}$-$S_{6}$-$S_{27}$-$S_{28}$-$S_{1}$-$S_{2}$-$S_{4}$-$S_{30}$-$S_{2}$-$S_{4}$-$S_{45}$-$S_{28}$-$S_{45}$-$S_{4}$-$S_{45}$-$S_{48}$-$S_{1}$-$S_{2}$-$S_{45}$-$S_{46}$-$S_{6}$-$S_{27}$-$S_{28}$ $S_{30}$-$S_{31}$-$S_{1}$-$S_{2}$-$S_{4}$-$S_{45}$-$S_{46}$-$S_{48}$-$S_{16}$-$S_{20}$-$S_{22}$-$S_{23}$-$S_{48}$-$S_{1}$-$S_{2}$-$S_{4}$-$S_{45}$ | $B_{1}$ = 25-$B_{2}$ = 45-$B_{3}$ = 35-$B_{4}$ = 35-$B_{5}$ = 25-$B_{6}$ = 35-$B_{7}$ = 35-$B_{8}$ = 35-$B_{9}$ = 25 $B_{10}$ = 35-$B_{11}$ = 35-$B_{12}$ = 35-$B_{13}$ = 35-$B_{14}$ = 35 $B_{15}$ = 25-$B_{16}$ = 45-$B_{17}$ = 35-$B_{18}$ = 45-$B_{19}$ = 25 $B_{20}$ = 35-$B_{21}$ = 25-$B_{22}$ = 25-$B_{23}$ = 45-$B_{24}$ = 35 $B_{25}$ = 25-$B_{26}$ = 25-$B_{27}$ = 25-$B_{28}$ = 35 $B_{29}$ = 25 $B_{30}$ = 25-$B_{31}$ = 45-$B_{32}$ = 35-$B_{33}$ = 45-$B_{34}$ = 25-$B_{35}$ = 45-$B_{36}$ = 45-$B_{37}$ = 45-$B_{38}$ = 45-$B_{39}$ = 45 |
| 14 | 50 | $S_{1}$-$S_{2}$-$S_{3}$-$S_{4}$-$S_{5}$-$S_{6}$-$S_{7}$-$S_{8}$-$S_{9}$-$S_{10}$-$S_{11}$-$S_{12}$-$S_{13}$-$S_{14}$-$S_{15}$-$S_{16}$-$S_{17}$-$S_{18}$-$S_{19}$-$S_{20}$-$S_{21}$-$S_{22}$-$S_{23}$-$S_{24}$-$S_{25}$-$S_{26}$-$S_{27}$-$S_{28}$-$S_{29}$-$S_{30}$-$S_{31}$-$S_{32}$-$S_{33}$-$S_{34}$-$S_{35}$-$S_{36}$-$S_{37}$-$S_{38}$-$S_{39}$-$S_{40}$-$S_{41}$-$S_{42}$-$S_{43}$-$S_{44}$-$S_{45}$-$S_{46}$-$S_{47}$-$S_{48}$-$S_{49}$-$S_{50}$ | $B_{1}$ = 25-$B_{2}$ = 45-$B_{3}$ = 35-$B_{4}$ = 35-$B_{5}$ = 25-$B_{6}$ = 35-$B_{7}$ = 35-$B_{8}$ = 35-$B_{9}$ = 25 $B_{10}$ = 35-$B_{11}$ = 35-$B_{12}$ = 35-$B_{13}$ = 35-$B_{14}$ = 35 $B_{15}$ = 25-$B_{16}$ = 45-$B_{17}$ = 35-$B_{18}$ = 45-$B_{19}$ = 25 $B_{20}$ = 35-$B_{21}$ = 25-$B_{22}$ = 25-$B_{23}$ = 45-$B_{24}$ = 35 $B_{25}$ = 25-$B_{26}$ = 25-$B_{27}$ = 25-$B_{28}$ = 35 $B_{29}$ = 25 $B_{30}$ = 25-$B_{31}$ = 45-$B_{32}$ = 35-$B_{33}$ = 45-$B_{34}$ = 25-$B_{35}$ = 45-$B_{36}$ = 45-$B_{37}$ = 45-$B_{38}$ = 45-$B_{39}$ = 45 $B_{40}$ = 45-$B_{41}$ = 45-$B_{42}$ = 25-$B_{43}$ = 25-$B_{44}$ = 25-$B_{45}$ = 25-$B_{46}$ = 25-$B_{47}$ = 25-$B_{48}$ = 45-$B_{49}$ = 25 |
Table 4. Numerical results for balanced lines
| Instance | Number of stations | $\psi_{EMM(AS)}$ | $\psi_{EMM(PW)}$ | $\psi_{EMM(LM)}$ | CPU(s) | $\psi_{D-Deco}$ | $\psi_{Simulation}$ | Gap % ($\psi_{EMM}$/$\psi_{Simulation}$) | Gap % ($\psi_{D-Deco}$/$\psi_{Simulation}$) |
| 1 | 3 | 1.7845 | 1.7845 | 1.7845 | 4.50 | 1.7455 | 1.8324 | 2.61% | 4.74% |
| 2 | 4 | 1.7682 | 1.7682 | 1.7682 | 4.70 | 1.6197 | 1.7386 | 1.70% | 6.84% |
| 3 | 5 | 1.7284 | 1.7284 | 1.7284 | 4.89 | 1.5612 | 1.6329 | 5.84% | 4.39% |
| 4 | 6 | 1.6864 | 1.6864 | 1.6864 | 5.06 | 1.3849 | 1.5411 | 9.43% | 10.13% |
| 5 | 7 | 1.8102 | 1.8102 | 1.8102 | 5.24 | 1.7657 | 1.8813 | 3.78% | 6.14% |
| 6 | 8 | 1.7177 | 1.7177 | 1.7177 | 5.56 | 1.5131 | 1.5887 | 8.12% | 4.76% |
| 7 | 9 | 1.7732 | 1.7732 | 1.7732 | 7.66 | 1.6559 | 1.7862 | 0.73% | 7.30% |
| 8 | 10 | 1.7966 | 1.7966 | 1.7966 | 5.41 | 1.7389 | 1.8682 | 3.83% | 6.92% |
| 9 | 15 | 1.7478 | 1.7478 | 1.7478 | 6.18 | 1.6806 | 1.8640 | 6.24% | 9.84% |
| 10 | 20 | 1.6644 | 1.6644 | 1.6644 | 5.36 | 1.5795 | 1.7519 | 4.99% | 9.84% |
| 11 | 25 | 1.6635 | 1.6635 | 1.6635 | 6.21 | 1.5530 | 1.7301 | 3.85% | 10.24% |
| 12 | 30 | 1.7223 | 1.7223 | 1.7223 | 7.06 | 1.6435 | 1.8245 | 5.60% | 9.92% |
| 13 | 40 | 1.7597 | 1.7597 | 1.7597 | 15.30 | 1.6987 | 1.8738 | 6.09% | 9.34% |
| 14 | 50 | 1.7478 | 1.7478 | 1.7478 | 8.27 | 1.6764 | 1.8575 | 5.91% | 9.75% |
Table 5. Numerical results for asynchronous lines
| Instance | Number of stations | $\psi_{EMM(AS)}$ | $\psi_{EMM(PW)}$ | $\psi_{EMM(LM)}$ | CPU(s) | $\psi_{D-Deco}$ | $\psi_{Simulation}$ | Gap % ($\psi_{EMM}$/$\psi_{Simulation}$) | Gap % ($\psi_{D-Deco}$/$\psi_{Simulation}$) |
| 1 | 3 | 1.7504 | 1.7504 | 1.7504 | 3.51 | 1.7053 | 1.7377 | 0.73% | 1.87% |
| 2 | 4 | 1.7412 | 1.7412 | 1.7412 | 4.23 | 1.6607 | 1.7376 | 0.21% | 4.43% |
| 3 | 5 | 1.7367 | 1.7367 | 1.7367 | 6.60 | 1.6330 | 1.7292 | 0.44% | 5.56% |
| 4 | 6 | 1.7347 | 1.7347 | 1.7347 | 6.71 | 1.6199 | 1.7292 | 0.32% | 6.32% |
| 5 | 7 | 1.7344 | 1.7344 | 1.7344 | 6.80 | 1.6162 | 1.7291 | 0.30% | 6.53% |
| 6 | 8 | 1.7328 | 1.7328 | 1.7328 | 7.86 | 1.6148 | 1.7285 | 0.25% | 6.58% |
| 7 | 9 | 1.7311 | 1.7311 | 1.7311 | 7.25 | 1.6133 | 1.7270 | 0.24% | 6.58% |
| 8 | 10 | 1.6986 | 1.6986 | 1.6986 | 7.57 | 1.5582 | 1.6395 | 3.60% | 4.96% |
| 9 | 15 | 1.7361 | 1.7361 | 1.7361 | 8.20 | 1.6182 | 1.7025 | 1.98% | 4.95% |
| 10 | 20 | 1.5895 | 1.5895 | 1.5895 | 8.91 | 1.5430 | 1.6500 | 3.66% | 6.48% |
| 11 | 25 | 1.7289 | 1.7289 | 1.7289 | 7.11 | 1.6180 | 1.7019 | 1.58% | 4.93% |
| 12 | 30 | 3.3816 | 3.3816 | 3.3816 | 7.08 | 3.2493 | 3.5307 | 4.22% | 7.97% |
| 13 | 40 | 1.7247 | 1.7247 | 1.7247 | 6.69 | 1.6111 | 1.6644 | 3.62% | 3.21% |
| 14 | 50 | 1.5685 | 1.5685 | 1.5685 | 6.04 | 1.3107 | 1.3852 | 13.23% | 5.38% |
| [1] |
D. C. Alexandros and P. T. Chrissoleon, Exact analysis of a two-workstation one-buffer flow line with parallel unreliable machines, European Journal of Operational Research, 197 (2009), 572-580.
doi: 10.1016/j.ejor.2008.07.004.
|
| [2] |
B. Ancelin and A. Semery, Calcul de la productivité d'une ligne intégrée de fabrication: Calif, un logiciel industriel basé sur une nouvelle heuristique, Automatique-Productique Informatique Industrielle, 21 (1987), 209-238.
|
| [3] |
Y. Bai, J. Tu, M. Yang, L. Zhang and P. Denno, A new aggregation algorithm for performance metric calculation in serial production lines with exponential machines: Design, accuracy and robustness, International Journal of Production Research, 59 (2021), 4072-4089.
doi: 10.1080/00207543.2020.1757777.
|
| [4] |
D. Bergeron, M. Anouar Jamali and H. Yamamoto, Modelling and analysis of manufacturing systems: A review of existing models, International Journal of Product Development, 10 (2010), 46-61.
doi: 10.1504/IJPD.2010.029986.
|
| [5] |
M. H. Burman, New Results in Flow Line Analysis, PhD thesis, Massachusetts Institute of Technology, 1995.
|
| [6] |
Y. Dallery and S. B. Gershwin, Manufacturing flow line systems: A review of models and analytical results, Queueing Systems, 12 (1992), 3-94.
doi: 10.1007/BF01158636.
|
| [7] |
Y. Dallery, R. David and X.-L. Xie, An efficient algorithm for analysis of transfer lines with unreliable machines and finite buffers, IIE Transactions, 20 (1988), 280-283.
doi: 10.1080/07408178808966181.
|
| [8] |
Y. Dallery, R. David and X.-L. Xie, Approximate analysis of transfer lines with unreliable machines and finite buffers, IEEE Transactions on Automatic Control, 34 (1989), 943-953.
doi: 10.1109/9.35807.
|
| [9] |
A. Diamantidis, J.-H. Lee, C. T. Papadopoulos, J. Li and C. Heavey, Performance evaluation of flow lines with non-identical and unreliable parallel machines and finite buffers, International Journal of Production Research, 58 (2020), 3881-3904.
doi: 10.1080/00207543.2019.1636322.
|
| [10] |
A. C. Diamantidis, C. T. Papadopoulos and C. Heavey, Approximate analysis of serial flow lines with multiple parallel-machine stations, IIE Transactions, 39 (2007), 361-375.
doi: 10.1080/07408170600838423.
|
| [11] |
S. B. Gershwin, An efficient decomposition method for the approximate evaluation of tandem queues with finite storage space and blocking, Operations Research, 35 (1987), 291-305.
doi: 10.1287/opre.35.2.291.
|
| [12] |
E. Ignall and A. Silver, The output of a two-stage system with unreliable machines and limited storage, AIIE Transactions, 9 (1977), 183-188.
doi: 10.1080/05695557708975141.
|
| [13] |
D. Jacobs and S. M. Meerkov, Mathematical theory of improvability for production systems, Mathematical Problems in Engineering, 1 (1995), 95-137.
doi: 10.1155/S1024123X9500010X.
|
| [14] |
K.-C. Jeong and Y.-D. Kim, An approximation method for performance analysis of assembly/disassembly systems with parallel-machine stations, IIE Transactions, 31 (1999), 391-394.
doi: 10.1080/07408179908969842.
|
| [15] |
H. Le Bihan and Y. Dallery, A robust decomposition method for the analysis of production lines with unreliable machines and finite buffers, Annals of Operations Research, 93 (2000), 265-297.
doi: 10.1023/A:1018996428429.
|
| [16] |
J. Li, Modeling and analysis of manufacturing systems with parallel lines, IEEE Transactions on Automatic Control, 49 (2004), 1824-1832.
doi: 10.1109/TAC.2004.835584.
|
| [17] |
J. Li, Overlapping decomposition: A system-theoretic method for modeling and analysis of complex manufacturing systems, IEEE Transactions on Automation Science and Engineering, 2 (2005), 40-53.
doi: 10.1109/TASE.2004.835576.
|
| [18] |
J. Li, D. E. Blumenfeld and J. M. Alden, Comparisons of two-machine line models in throughput analysis, International Journal of Production Research, 44 (2006), 1375-1398.
doi: 10.1080/00207540500371980.
|
| [19] |
J. Li and S. M. Meerkov, Due-time performance of production systems with markovian machines, In Analysis and Modeling of Manufacturing Systems, Springer, 2003,221-253.
doi: 10.1007/978-1-4615-1019-2_10.
|
| [20] |
J. Li and S. M. Meerkov, Production Systems Engineering, Springer Science & Business Media, 2008.
doi: 10.1007/978-0-387-75579-3.
|
| [21] |
J. Liu and A. Wu, Analytical analysis of production lines with parallel machines, In Proceedings of the 30th Chinese Control Conference, IEEE, 2011, 5480-5483.
|
| [22] |
J. Liu, S. Yang, A. Wu and S. Jack Hu, Multi-state throughput analysis of a two-stage manufacturing system with parallel unreliable machines and a finite buffer, European Journal of Operational Research, 219 (2012), 296-304.
doi: 10.1016/j.ejor.2011.12.025.
|
| [23] |
D. Mitra, Stochastic theory of a fluid model of producers and consumers coupled by a buffer, Advances in Applied Probability, 20 (1988), 646-676.
doi: 10.2307/1427040.
|
| [24] |
Y. Ouazene, Maîtrise des Systèmes Industriels: Optimisation de la Conception des Lignes de Production, PhD thesis, Université de Technologie de Troyes, 2013.
|
| [25] |
Y. Ouazene, H. Chehade, A. Yalaoui and F. Yalaoui, Equivalent machine method for approximate evaluation of buffered unreliable production lines, In 2013 IEEE Symposium on Computational Intelligence in Production and Logistics Systems (CIPLS), IEEE, 2013, 33-39.
doi: 10.1109/CIPLS.2013.6595197.
|
| [26] |
Y. Ouazene, F. Yalaoui, H. Chehade and A. Yalaoui, Analysis of an unreliable series-parallel production system with limited storage capacity, Math. Methods Syst. Sci. Eng, 2015.
|
| [27] |
A. Patchong and D. Willaeys, Modeling and analysis of an unreliable flow line composed of parallel-machine stages, Iie Transactions, 33 (2001), 559-568.
doi: 10.1080/07408170108936854.
|
| [28] |
Y. W. Shin and D. H. Moon, Approximation of throughput in tandem queues with multiple servers and blocking, Applied Mathematical Modelling, 38 (2014), 6122-6132.
doi: 10.1016/j.apm.2014.05.015.
|
| [29] |
Y. W. Shin and D. H. Moon, Throughput of flow lines with unreliable parallel-machine workstations and blocking, Journal of Industrial & Management Optimization, 13 (2017), 901-916.
doi: 10.3934/jimo.2016052.
|
| [30] |
Z. Wang, H. Mu and J. You, Analysis of a serial production line with single part-type and multiple parallel-machine workstations, IFAC Proceedings Volumes, 47 (2014), 306-313.
doi: 10.3182/20140514-3-FR-4046.00033.
|
| [31] |
C.-B. Yan and Q. Zhao, A unified effective method for aggregating multi-machine stages in production systems, IEEE Transactions on Automatic Control, 58 (2013), 1674-1687.
doi: 10.1109/TAC.2013.2240111.
|
Series-parallel production line
Parallel machines aggregation
Representation of the different overlapping birth-death Markov processes [24]
Birth-death Markov process related to the buffer
A view of the model during simulation: instance 1 from the balanced configurations (table 2)