A Supplier Selection Model Using Alternative Ranking Process by Alternatives’ Stability Scores and the Grey Equilibrium Product
Abstract
:1. Introduction
2. Materials and Methods
2.1. A Ranking Process by Alternatives’ Stability Scores (ARPASS) Method
Algorithm 1 |
for if (), (), and (), then (), (), and (). end if end for Thus for if then the corresponding value is ; else if then the corresponding value is ; else if then the corresponding value is 1. end if end if end for |
CN | W | D | L | ||
---|---|---|---|---|---|
2.2. Steps of ARPASS
2.2.1. The First Stage
2.2.2. The Second Stage
2.3. ARPASS-E
2.4. ARPASS*
2.5. Grey Numbers and the Grey Equilibrium Product (GEP)
3. Results
3.1. Example 1: The Evaluation of Chain Store’s Cheese Suppliers
3.1.1. Data Collection
3.1.2. Application and Results
3.2. Example 2: The Cream Cheese Supplier Selection for Outsourcing Production
Application and Results
G | F | F | VG | VG | F | G | G | F | VG | G | VG | G | VG | VG | VG | F | F | G | G | G | F | G | G | F | G | F | MP | F | G | |
F | G | G | VG | F | VG | G | F | F | VG | G | F | G | VG | VG | VG | VG | VG | VG | VG | VG | G | G | G | G | G | G | F | G | F | |
VG | G | G | F | F | F | G | VG | F | F | G | F | G | G | VG | F | F | G | G | VG | VG | VG | G | G | G | G | G | F | F | G | |
VG | VG | F | VG | VG | G | G | G | G | VG | F | G | G | VG | VG | VG | G | VG | G | VG | VG | G | G | G | G | VG | G | G | G | G | |
G | VG | F | VG | VG | G | G | G | G | G | F | G | G | G | G | F | G | G | F | G | VG | G | G | G | G | F | G | G | G | G | |
F | G | G | VG | F | G | G | F | G | F | G | G | F | MP | F | F | G | F | G | VG | VG | G | G | G | G | F | G | G | F | G | |
VG | G | G | VG | VG | F | G | G | G | VG | G | G | G | VG | VG | VG | G | VG | VG | VG | VG | G | G | G | G | G | G | F | F | G | |
VG | G | G | VG | G | F | G | G | G | VG | G | F | G | VG | VG | VG | F | G | G | F | G | G | G | G | G | G | G | G | G | G | |
G | G | G | VG | G | VG | G | G | F | G | F | VG | F | VG | VG | VG | VG | VG | G | VG | VG | G | F | G | G | F | VG | G | F | F | |
VG | F | F | VG | VG | G | G | VG | G | G | F | G | G | VG | VG | VG | F | F | F | VG | VG | G | G | G | G | G | G | G | G | G | |
F | G | G | G | F | VG | G | F | G | F | G | F | MP | F | F | G | G | G | G | VG | VG | F | G | G | G | G | G | G | G | G | |
VG | G | VG | F | VG | F | G | VG | G | G | G | G | G | VG | VG | VG | VG | VG | VG | VG | VG | G | G | G | G | G | F | VG | G | G | |
F | VG | G | VG | VG | VG | G | F | G | VG | G | VG | G | VG | VG | VG | VG | VG | VG | VG | VG | F | G | G | F | G | VG | MP | F | F | |
G | G | G | VG | G | F | G | G | G | VG | F | G | F | G | G | F | G | VG | F | G | VG | VG | G | G | G | G | G | F | G | G | |
F | G | G | VG | G | G | G | F | F | VG | G | G | G | VG | VG | VG | F | VG | VG | G | G | F | G | G | G | G | F | F | G | G | |
G | G | G | F | G | F | G | G | G | F | G | VG | F | F | G | F | G | G | G | G | F | G | G | G | G | G | F | MP | F | G | |
VG | VG | G | VG | G | F | G | VG | G | G | G | G | G | VG | VG | VG | G | VG | VG | VG | VG | VG | G | G | G | G | G | VG | G | G | |
VG | F | VG | VG | F | VG | G | G | G | G | G | G | G | VG | VG | VG | VG | VG | G | G | G | F | G | G | F | G | G | G | F | G | |
VG | VG | G | VG | F | G | G | VG | F | G | F | G | G | VG | VG | VG | G | VG | VG | VG | VG | F | G | G | G | VG | G | G | F | F | |
G | VG | VG | VG | F | G | G | F | G | F | G | G | G | F | F | F | G | G | G | G | G | VG | G | G | G | G | F | G | F | G |
4.7 | 8.06 | 8.058 | 9.501 | 4.701 | 9.501 | 8.06 | 4.701 | 4.7 | 9.5 | 8.06 | 4.7 | 8.06 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 8.06 | 8.06 | 8.06 | 8.06 | 8.06 | 8.06 | 4.7 | 8.06 | 4.7 | 234.109 | |
9.5 | 9.5 | 4.701 | 9.501 | 9.501 | 8.058 | 8.06 | 8.058 | 8.06 | 9.5 | 4.7 | 8.06 | 8.06 | 9.5 | 9.5 | 9.5 | 8.06 | 9.5 | 8.06 | 9.5 | 9.5 | 8.06 | 8.06 | 8.06 | 8.06 | 9.5 | 8.06 | 8.06 | 8.06 | 8.06 | 252.336 | |
9.5 | 8.06 | 8.058 | 9.501 | 9.501 | 4.701 | 8.06 | 8.058 | 8.06 | 9.5 | 8.06 | 8.06 | 8.06 | 9.5 | 9.5 | 9.5 | 8.06 | 9.5 | 9.5 | 9.5 | 9.5 | 8.06 | 8.06 | 8.06 | 8.06 | 8.06 | 8.06 | 4.7 | 4.7 | 8.06 | 247.537 | |
8.06 | 8.06 | 8.058 | 9.501 | 8.058 | 9.501 | 8.06 | 8.058 | 4.7 | 8.06 | 4.7 | 9.5 | 4.7 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 8.06 | 9.5 | 9.5 | 8.06 | 4.7 | 8.06 | 8.06 | 4.7 | 9.5 | 8.06 | 4.7 | 4.7 | 234.109 | |
9.5 | 8.06 | 9.501 | 4.701 | 9.501 | 4.701 | 8.06 | 9.501 | 8.06 | 8.06 | 8.06 | 8.06 | 8.06 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 8.06 | 8.06 | 8.06 | 8.06 | 8.06 | 4.7 | 9.5 | 8.06 | 8.06 | 250.422 | |
4.7 | 9.5 | 8.058 | 9.501 | 9.501 | 9.501 | 8.06 | 4.701 | 8.06 | 9.5 | 8.06 | 9.5 | 8.06 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 4.7 | 8.06 | 8.06 | 4.7 | 8.06 | 9.5 | 3.74 | 4.7 | 4.7 | 238.92 | |
9.5 | 9.5 | 8.058 | 9.501 | 8.058 | 4.701 | 8.06 | 9.501 | 8.06 | 8.06 | 8.06 | 8.06 | 8.06 | 9.5 | 9.5 | 9.5 | 8.06 | 9.5 | 9.5 | 9.5 | 9.5 | 9.5 | 8.06 | 8.06 | 8.06 | 8.06 | 8.06 | 9.5 | 8.06 | 8.06 | 257.136 | |
9.5 | 9.5 | 8.058 | 9.501 | 4.701 | 8.058 | 8.06 | 9.501 | 4.7 | 8.06 | 4.7 | 8.06 | 8.06 | 9.5 | 9.5 | 9.5 | 8.06 | 9.5 | 9.5 | 9.5 | 9.5 | 4.7 | 8.06 | 8.06 | 8.06 | 9.5 | 8.06 | 8.06 | 4.7 | 4.7 | 238.909 |
3.3. Application of Shannon’s Entropy in ARPASS (ARPASS-E)
4. Discussion
Comparison
5. Conclusions and Future Works
Author Contributions
Funding
Informed Consent Statement
Conflicts of Interest
References
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5 | 3500 | 26 | 523 | 9 | |
7 | 2300 | 21 | 638 | 5 | |
9 | 1950 | 21 | 992 | 7 |
3 | |||||
3 | |||||
3 | |||||
3 | |||||
3 |
Scales for Rating the Alternative against Criteria | Scales for Weighting the Criteria | ||
---|---|---|---|
Linguistic Variables | Numerical Value | Linguistic Variables | Numerical Value |
Very poor (VP) | 1 | Very low (VL) | 0.1 |
Poor (P) | 2 | Low (L) | 0.2 |
Medium poor (MP) | 3 | Medium low (ML) | 0.3 |
Fair (F) | 5 | Medium (M) | 0.5 |
Medium good (MG) | 7 | Medium high (MH) | 0.7 |
Good (G) | 9 | High (H) | 0.9 |
Very good (VG) | 10 | Very high (VH) | 1 |
+ | + | + | + | + | + | + | − | + | + | |
---|---|---|---|---|---|---|---|---|---|---|
Appropriateness of the Product Price to the Market Price | Numbers of Promotion Times | Ability to Adapt to Increase, Decrease, and Change in Order Timing | Make-to-Order Production | Delivery Reliability | Variety | Brand Equity | Defect RATE | Reliability of Quality | After Sales Services | |
Kalleh | 10 | 12 | 9 | 10 | 10 | 9 | 10 | 0.048 | 7 | 9 |
Mihan | 9 | 14 | 7 | 7 | 7 | 3 | 9 | 0.021 | 7 | 7 |
Pegah | 10 | 12 | 9 | 10 | 7 | 7 | 9 | 0.090 | 5 | 5 |
Haraz | 9 | 12 | 9 | 7 | 9 | 7 | 7 | 0.043 | 7 | 7 |
Damdaran | 7 | 9 | 5 | 7 | 7 | 5 | 7 | 0.054 | 7 | 7 |
Sabbah | 9 | 18 | 7 | 9 | 9 | 7 | 5 | 0.041 | 7 | 5 |
Alima | 5 | 6 | 10 | 10 | 10 | 9 | 5 | 0.063 | 9 | 5 |
Gela | 10 | 12 | 9 | 5 | 7 | 3 | 2 | 0.047 | 10 | 5 |
Domino | 7 | 10 | 5 | 5 | 5 | 2 | 7 | 0.029 | 5 | 7 |
Rank | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2.564 | Kalleh | 10 | 12 | 9 | 10 | 10 | 9 | 10 | 0.890 | 7 | 9 | 35.40 | 3549.83 | 1 |
2.557 | Mihan | 9 | 14 | 7 | 7 | 7 | 3 | 9 | 0.952 | 7 | 7 | 28.93 | 2502.371 | 3 |
2.552 | Pegah | 10 | 12 | 9 | 10 | 7 | 7 | 9 | 0.794 | 5 | 5 | 26.88 | 2448.747 | 4 |
2.611 | Haraz | 9 | 12 | 9 | 7 | 9 | 7 | 7 | 0.901 | 7 | 7 | 28.79 | 2647.808 | 2 |
2.656 | Damdaran | 7 | 9 | 5 | 7 | 7 | 5 | 7 | 0.876 | 7 | 7 | 21.43 | 1826.83 | 8 |
2.536 | Sabbah | 9 | 18 | 7 | 9 | 9 | 7 | 5 | 0.906 | 7 | 5 | 27.32 | 2413.701 | 6 |
2.552 | Alima | 5 | 6 | 10 | 10 | 10 | 9 | 5 | 0.856 | 9 | 5 | 27.55 | 2416.304 | 5 |
2.509 | Gela | 10 | 12 | 9 | 5 | 7 | 3 | 2 | 0.892 | 10 | 5 | 24.61 | 1871.527 | 7 |
2.643 | Domino | 7 | 10 | 5 | 5 | 5 | 2 | 7 | 0.933 | 5 | 7 | 18.20 | 1425.418 | 9 |
Scale | Very Poor (VP) | Poor (P) | Medium Poor (MP) | Fair (F) | Medium Good (MG) | Good (G) | Very Good (VG) |
---|---|---|---|---|---|---|---|
Grey | [0, 1] | [1, 3] | [3, 4] | [4, 5] | [5, 7] | [7, 9] | [9, 10] |
Scale | Very Poor (VP) | Poor (P) | Medium Poor (MP) | Fair (F) | Medium Good (MG) | Good (G) | Very Good (VG) |
---|---|---|---|---|---|---|---|
Grey | [0, 1] | [1, 3] | [3, 4] | [4, 5] | [5, 7] | [7, 9] | [9, 10] |
0.5 | 2.2921 | 3.7415 | 4.7011 | 6.1373 | 8.058 | 9.5005 |
Nutritional Content | Fat | pH | Salt | DM |
---|---|---|---|---|
Standard content | 24 | 5 | 0.9 | 33 |
Acceptable interval | ||||
0.5 | 0.2 | 0.2 | 0.7 | |
0.9 | 0.5 | 0.3 | 0.9 | |
GEP | 23.414 | 4.981 | 0.785 | 33.8 |
Minimum acceptable content | 23.414 | 4.981 | 0.785 | 33.8 |
Fat | pH | Salt | DM | |
---|---|---|---|---|
Conditions | 23.414 | 4.981 | 0.785 | 33.8 |
0.2 | 0.2 | 0.2 | 0.05 | |
0.9 | 0.5 | 0.3 | 0.95 | |
23.9 | 4.98 | 0.7 | 33.71 | |
22.86 | 4.66 | 0.56 | 33.94 | |
23.81 | 4.62 | 0.74 | 33.99 | |
23.62 | 4.66 | 0.52 | 33.94 | |
23.01 | 4.8 | 0.58 | 33.52 | |
23.9 | 4.52 | 0.64 | 33 | |
23.95 | 4.62 | 0.63 | 34.13 | |
23.81 | 4.4 | 0.63 | 33.76 |
Suppliers | Fat | pH | Salt | DM | Rank | ||
---|---|---|---|---|---|---|---|
9.05 | 23.81 | 4.62 | 0.74 | 33.99 | 1255.841 | 2 | |
9.08 | 23.62 | 4.66 | 0.52 | 33.94 | 178.435 | 3 | |
9.03 | 23.95 | 4.62 | 0.63 | 34.13 | 20,129.32 | 1 |
Kalleh | Mihan | Pegah | Haraz | Damdaran | Sabbah | Alima | Gela | Domino | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.108 | 0.114 | 0.117 | 0.111 | 0.107 | 0.109 | 0.082 | 0.126 | 0.115 | ||||||
0.119 | 0.139 | 0.127 | 0.127 | 0.122 | 0.148 | 0.092 | 0.136 | 0.136 | ||||||
0.102 | 0.099 | 0.111 | 0.111 | 0.088 | 0.095 | 0.121 | 0.120 | 0.096 | ||||||
0.108 | 0.099 | 0.117 | 0.096 | 0.107 | 0.109 | 0.121 | 0.087 | 0.096 | ||||||
0.108 | 0.099 | 0.096 | 0.111 | 0.107 | 0.109 | 0.121 | 0.105 | 0.096 | ||||||
0.102 | 0.058 | 0.096 | 0.096 | 0.088 | 0.095 | 0.115 | 0.062 | 0.053 | ||||||
0.108 | 0.114 | 0.111 | 0.096 | 0.107 | 0.077 | 0.082 | 0.047 | 0.115 | ||||||
0.020 | 0.025 | 0.021 | 0.023 | 0.026 | 0.023 | 0.023 | 0.026 | 0.030 | ||||||
0.088 | 0.099 | 0.079 | 0.096 | 0.107 | 0.095 | 0.115 | 0.126 | 0.096 | ||||||
0.102 | 0.099 | 0.079 | 0.096 | 0.107 | 0.077 | 0.082 | 0.087 | 0.115 | ||||||
Rank | ||||||||||||||
0.077 | Kalleh | 10 | 12 | 9 | 10 | 10 | 9 | 10 | 0.890 | 7 | 9 | 35.40 | 51.471 | 3 |
0.121 | Mihan | 9 | 14 | 7 | 7 | 7 | 3 | 9 | 0.952 | 7 | 7 | 28.93 | 50.831 | 4 |
0.105 | Pegah | 10 | 12 | 9 | 10 | 7 | 7 | 9 | 0.794 | 5 | 5 | 26.88 | 50.438 | 5 |
0.082 | Haraz | 9 | 12 | 9 | 7 | 9 | 7 | 7 | 0.901 | 7 | 7 | 28.79 | 46.392 | 7 |
0.074 | Damdaran | 7 | 9 | 5 | 7 | 7 | 5 | 7 | 0.876 | 7 | 7 | 21.43 | 40.272 | 9 |
0.143 | Sabbah | 9 | 18 | 7 | 9 | 9 | 7 | 5 | 0.906 | 7 | 5 | 27.32 | 55.911 | 1 |
0.106 | Alima | 5 | 6 | 10 | 10 | 10 | 9 | 5 | 0.856 | 9 | 5 | 27.55 | 48.846 | 6 |
0.174 | Gela | 10 | 12 | 9 | 5 | 7 | 3 | 2 | 0.892 | 10 | 5 | 24.61 | 52.922 | 2 |
0.117 | Domino | 7 | 10 | 5 | 5 | 5 | 2 | 7 | 0.933 | 5 | 7 | 18.20 | 41.606 | 8 |
Fat | 0.3770 | 0.3765 | 0.3782 | ||||
pH | 0.0731 | 0.0743 | 0.0730 | ||||
Salt | 0.0117 | 0.0083 | 0.0099 | ||||
DM | 0.5382 | 0.5410 | 0.5389 | ||||
0.681 | 0.673 | 0.676 | |||||
0.329 | 0.337 | 0.334 | |||||
Suppliers | Fat | pH | Salt | DM | Rank | ||
0.329 | 23.81 | 4.62 | 0.74 | 33.99 | 8.596 | 2 | |
0.337 | 23.62 | 4.66 | 0.52 | 33.94 | 8.451 | 3 | |
0.334 | 23.95 | 4.62 | 0.63 | 34.13 | 9.860 | 1 |
ARPASS | TOPSIS | VIKOR | SAW | |
---|---|---|---|---|
Kalleh | 1 | 1 | 1 | 1 |
Mihan | 3 | 3 | 4 | 3 |
Pegah | 5 | 5 | 5 | 2 |
Haraz | 2 | 2 | 2 | 4 |
Damdaran | 7 | 7 | 7 | 8 |
Sabbah | 6 | 4 | 3 | 5 |
Alima | 4 | 6 | 6 | 6 |
Gela | 8 | 9 | 8 | 7 |
Domino | 9 | 8 | 9 | 9 |
ARPASS | TOPSIS | VIKOR | SAW | |
---|---|---|---|---|
Kalleh | 1 | 1 | 1 | 1 |
Mihan | 3 | 3 | 4 | 3 |
Pegah | 5 | 5 | 5 | 2 |
Haraz | 2 | 2 | 2 | 4 |
Sabbah | 6 | 4 | 3 | 5 |
Alima | 4 | 6 | 6 | 6 |
Haraz | Kalleh | Mihan | Pegah | Alima | Sabbah | |
---|---|---|---|---|---|---|
2.611 | 2.564 | 2.557 | 2.552 | 2.552 | 2.536 |
ARPASS | ARPASS* | TOPSIS | VIKOR | SAW | |
---|---|---|---|---|---|
Kalleh | 1 | 1 | 1 | 1 | 1 |
Mihan | 3 | 3 | 3 | 4 | 3 |
Pegah | 5 | 4 | 5 | 5 | 2 |
Haraz | 2 | 2 | 2 | 2 | 4 |
Damdaran | 7 | 8 | 7 | 7 | 8 |
Sabbah | 6 | 5 | 4 | 3 | 5 |
Alima | 4 | 6 | 6 | 6 | 6 |
Gela | 8 | 7 | 9 | 8 | 7 |
Domino | 9 | 9 | 8 | 9 | 9 |
ARPASS | ARPASS* | TOPSIS | VIKOR | SAW | |
---|---|---|---|---|---|
Kalleh | 1 | 1 | 1 | 1 | 1 |
Mihan | 3 | 3 | 3 | 4 | 3 |
Pegah | 5 | 4 | 5 | 5 | 2 |
Haraz | 2 | 2 | 2 | 2 | 4 |
Sabbah | 6 | 5 | 4 | 3 | 5 |
Alima | 4 | 6 | 6 | 6 | 6 |
ARPASS | ARPASS* | ARPASS -E | TOPSIS | VIKOR | SAW | |
---|---|---|---|---|---|---|
Kalleh | 1 | 1 | 3 | 1 | 1 | 1 |
Mihan | 3 | 3 | 4 | 3 | 4 | 3 |
Pegah | 5 | 4 | 5 | 5 | 5 | 2 |
Haraz | 2 | 2 | 7 | 2 | 2 | 4 |
Damdaran | 7 | 8 | 9 | 7 | 7 | 8 |
Sabbah | 6 | 5 | 1 | 4 | 3 | 5 |
Alima | 4 | 6 | 6 | 6 | 6 | 6 |
Gela | 8 | 7 | 2 | 9 | 8 | 7 |
Domino | 9 | 9 | 8 | 8 | 9 | 9 |
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Zakeri, S.; Yang, Y.; Konstantas, D. A Supplier Selection Model Using Alternative Ranking Process by Alternatives’ Stability Scores and the Grey Equilibrium Product. Processes 2022, 10, 917. https://doi.org/10.3390/pr10050917
Zakeri S, Yang Y, Konstantas D. A Supplier Selection Model Using Alternative Ranking Process by Alternatives’ Stability Scores and the Grey Equilibrium Product. Processes. 2022; 10(5):917. https://doi.org/10.3390/pr10050917
Chicago/Turabian StyleZakeri, Shervin, Yingjie Yang, and Dimitri Konstantas. 2022. "A Supplier Selection Model Using Alternative Ranking Process by Alternatives’ Stability Scores and the Grey Equilibrium Product" Processes 10, no. 5: 917. https://doi.org/10.3390/pr10050917