# A Novel Hybrid Artificial Intelligence Based Methodology for the Inventory Routing Problem

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Proposed Method

^{2}) of demand are compared with cutoffs of 1.32 for ADI and 0.49 for CV

^{2}. Details about the categorization can be found in Syntetos et al. [36]. The data used in this paper is taken from Chen et al. [37], whose dataset is available for one year. Data is adapted considering three different uneven demand patterns. In erratic demand, ADI is less than 1.32 and CV

^{2}is greater than 0.49. The mean of customer order quantity in erratic demand is 12 units. In intermittent demand, the ADI is greater than 1.32 and the CV

^{2}is less than 0.49. The mean of the customer order quantity in intermittent demand is 368 units. In lumpy demand, the ADI is greater than 1.32, the CV² is greater than 0.49. The mean of customer order quantity in lumpy demand is 368 units.

#### 3.1. Inventory Control Policy

#### 3.2. Routing Strategies

#### 3.3. Performance Measurements

## 4. Results and Discussion

#### 4.1. Cost Based Analysis

#### 4.2. Quantity Based Analysis

#### 4.3. Routing Based Analysis

#### 4.4. Lead Time Based Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The general structure of Phase 2. Maximal Overlap Discrete Wavelet Transform (MODWT); Artificial Neural Network (ANN).

DCs Related Cost Parameters ($) | Vehicle Related Cost Parameters ($) |
---|---|

Average Holding Cost: Uniform (2, 5) (${h}_{i}$) | Capital Cost per Vehicle: 2000 ($\mathsf{\tau}$) |

Lost Sales Cost: Uniform (50, 100) (${k}_{i}$) | Fixed Cost of Initiating Delivery: 100 (${\mathsf{\gamma}}_{d}$) |

Processing Cost: Uniform (5, 10) (${p}_{i}$) | Fixed Cost of Customer Stop: 100 (${\vartheta}_{i}$) |

Order Cost per Use: Uniform (50, 100) ($\text{}{c}_{i}$) | Transportation Cost per Unit Distance: 0.05 (α) |

Order Processing Cost Rate: Uniform (2, 5) | |

Cost per Use: Uniform (5, 10) |

Number of Neuron in First Hidden Layer | Number of Neuron in Second Hidden Layer | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Strategy 1 | Strategy 2 | Strategy 3 | Strategy 1 | Strategy 2 | Strategy 3 | ||||||||

Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | ||

Erratic demand | DC1 | 11 | 20 | 3 | 17 | 3 | 15 | 4 | 20 | 13 | 19 | 15 | 20 |

DC2 | 3 | 19 | 8 | 15 | 5 | 17 | 18 | 20 | 18 | 20 | 19 | 20 | |

DC3 | 10 | 19 | 10 | 19 | 5 | 18 | 4 | 17 | 4 | 17 | 3 | 20 | |

DC4 | 5 | 17 | 6 | 19 | 4 | 14 | 7 | 20 | 5 | 18 | 17 | 19 | |

DC5 | 6 | 14 | 3 | 13 | 3 | 19 | 5 | 18 | 16 | 20 | 7 | 19 | |

Intermittent demand | DC1 | 5 | 17 | 12 | 20 | 11 | 19 | 12 | 19 | 5 | 15 | 3 | 17 |

DC2 | 8 | 19 | 3 | 18 | 13 | 20 | 5 | 20 | 6 | 20 | 6 | 19 | |

DC3 | 9 | 19 | 12 | 18 | 13 | 18 | 5 | 16 | 4 | 8 | 4 | 11 | |

DC4 | 12 | 20 | 12 | 18 | 11 | 20 | 4 | 15 | 5 | 10 | 4 | 11 | |

DC5 | 11 | 19 | 2 | 18 | 10 | 20 | 4 | 19 | 6 | 18 | 6 | 20 | |

Lumpy demand | DC1 | 6 | 20 | 9 | 17 | 13 | 17 | 7 | 20 | 4 | 20 | 6 | 17 |

DC2 | 13 | 19 | 13 | 19 | 13 | 19 | 5 | 18 | 5 | 18 | 5 | 18 | |

DC3 | 13 | 20 | 8 | 17 | 13 | 18 | 7 | 19 | 3 | 17 | 5 | 14 | |

DC4 | 9 | 19 | 15 | 20 | 14 | 20 | 5 | 17 | 3 | 10 | 3 | 11 | |

DC5 | 9 | 19 | 10 | 20 | 9 | 19 | 4 | 20 | 4 | 19 | 7 | 20 |

Reorder Point | Order-Up-to Level | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Strategy 1 | Strategy 2 | Strategy 3 | Strategy 1 | Strategy 2 | Strategy 3 | ||||||||

Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | ||

Erratic demand | DC1 | 16 | 40 | 13 | 21 | 14 | 27 | 30 | 54 | 27 | 34 | 28 | 42 |

DC2 | 33 | 56 | 34 | 45 | 35 | 45 | 50 | 72 | 51 | 62 | 52 | 61 | |

DC3 | 24 | 36 | 22 | 32 | 22 | 30 | 40 | 51 | 38 | 47 | 37 | 45 | |

DC4 | 36 | 82 | 33 | 66 | 37 | 65 | 58 | 101 | 52 | 85 | 56 | 83 | |

DC5 | 18 | 34 | 32 | 47 | 18 | 32 | 32 | 48 | 18 | 31 | 32 | 47 | |

Intermittent demand | DC1 | 711 | 1762 | 742 | 2594 | 714 | 1716 | 1177 | 2178 | 1208 | 3010 | 1180 | 2131 |

DC2 | 597 | 2167 | 572 | 2636 | 622 | 2643 | 1097 | 2642 | 1072 | 3105 | 1122 | 3114 | |

DC3 | 418 | 2328 | 534 | 2099 | 529 | 2905 | 863 | 2720 | 979 | 2496 | 974 | 3297 | |

DC4 | 358 | 1400 | 441 | 1825 | 348 | 1404 | 660 | 1706 | 743 | 2149 | 348 | 1404 | |

DC5 | 714 | 2291 | 825 | 2271 | 705 | 2284 | 1292 | 2726 | 1403 | 2761 | 1283 | 2719 | |

Lumpy demand | DC1 | 543 | 1092 | 490 | 1372 | 543 | 2265 | 681 | 1373 | 776 | 1656 | 841 | 2549 |

DC2 | 644 | 1172 | 637 | 1157 | 715 | 1355 | 918 | 1448 | 911 | 1433 | 989 | 1631 | |

DC3 | 237 | 1201 | 227 | 818 | 196 | 1036 | 436 | 1429 | 426 | 1043 | 395 | 1295 | |

DC4 | 532 | 1610 | 401 | 831 | 424 | 1151 | 840 | 1926 | 709 | 1143 | 732 | 1442 | |

DC5 | 276 | 767 | 341 | 1284 | 296 | 742 | 413 | 963 | 478 | 1484 | 433 | 938 |

Strategy 1 | Strategy 2 | Strategy 3 | |
---|---|---|---|

Erratic demand | 1 | 1 | 1 |

Intermittent demand | 0.9907 | 0.9981 | 0.9854 |

Lumpy demand | 0.9969 | 0.9874 | 0.9955 |

Erratic Demand | Intermittent Demand | Lumpy Demand | |
---|---|---|---|

Strategy 1 | 242081 | 908945 | 640675 |

Strategy 2 | 240150 | 986694 | 632658 |

Strategy 3 | 235570 | 847906 | 639104 |

Erratic Demand | Intermittent Demand | Lumpy Demand | ||
---|---|---|---|---|

Partially Lost Order Quantity | Strategy 1 | 56 | 347 | 626 |

Strategy 2 | 30 | 677 | 377 | |

Strategy 3 | 18 | 142 | 829 | |

Totally Lost Order Quantity | Strategy 1 | 140 | 620 | 1114 |

Strategy 2 | 166 | 1278 | 822 | |

Strategy 3 | 92 | 314 | 878 | |

Totally Met Order Quantity | Strategy 1 | 1282 | 45353 | 20529 |

Strategy 2 | 1316 | 43811 | 20541 | |

Strategy 3 | 1418 | 45792 | 20137 |

Strategy 1 | Strategy 2 | Strategy 3 | ||
---|---|---|---|---|

Erratic demand | DC1 | 0.194 | 0.232 | 0.204 |

DC2 | 0.240 | 0.226 | 0.237 | |

DC3 | 0.182 | 0.298 | 0.261 | |

DC4 | 0.273 | 0.217 | 0.206 | |

DC5 | 0.111 | 0.028 | 0.092 | |

Intermittent demand | DC1 | 0.132 | 0.142 | 0.129 |

DC2 | 0.242 | 0.199 | 0.239 | |

DC3 | 0.204 | 0.161 | 0.204 | |

DC4 | 0.167 | 0.168 | 0.165 | |

DC5 | 0.254 | 0.330 | 0.262 | |

Lumpy demand | DC1 | 0.224 | 0.197 | 0.256 |

DC2 | 0.156 | 0.225 | 0.147 | |

DC3 | 0.206 | 0.226 | 0.220 | |

DC4 | 0.279 | 0.223 | 0.234 | |

DC5 | 0.136 | 0.129 | 0.142 |

Strategy 1 | Strategy 2 | Strategy 3 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

DN * | Min | Mean | Max | DN | Min | Mean | Max | DN | Min | Mean | Max | |

Erratic demand | 23 | 7 | 27 | 74 | 22 | 9 | 27 | 128 | 26 | 7 | 24 | 83 |

Intermittent demand | 34 | 152 | 647 | 1609 | 30 | 180 | 828 | 2986 | 29 | 170 | 865 | 1874 |

Lumpy demand | 22 | 105 | 486 | 1393 | 26 | 102 | 408 | 1130 | 27 | 91 | 431 | 1528 |

Strategy 1 | Strategy 2 | Strategy 3 | |||||
---|---|---|---|---|---|---|---|

Min | Max | Min | Max | Min | Max | ||

Erratic demand | DC1 | 0.103 | 0.188 | 0.109 | 0.197 | 0.098 | 0.176 |

DC2 | 0.150 | 0.188 | 0.153 | 0.194 | 0.141 | 0.191 | |

DC3 | 0.104 | 0.224 | 0.109 | 0.226 | 0.113 | 0.219 | |

DC4 | 0.110 | 0.249 | 0.105 | 0.188 | 0.110 | 0.254 | |

DC5 | 0.144 | 0.157 | 0.172 | 0.219 | 0.148 | 0.162 | |

Intermittent demand | DC1 | 0.243 | 0.537 | 0.283 | 0.654 | 0.301 | 0.565 |

DC2 | 0.265 | 0.525 | 0.294 | 0.580 | 0.339 | 0.696 | |

DC3 | 0.205 | 0.486 | 0.318 | 0.580 | 0.235 | 0.663 | |

DC4 | 0.243 | 0.400 | 0.212 | 0.783 | 0.207 | 0.519 | |

DC5 | 0.329 | 0.729 | 0.280 | 0.607 | 0.285 | 0.615 | |

Lumpy demand | DC1 | 0.260 | 0.449 | 0.198 | 0.368 | 0.225 | 0.603 |

DC2 | 0.218 | 0.340 | 0.234 | 0.419 | 0.228 | 0.531 | |

DC3 | 0.181 | 0.470 | 0.158 | 0.525 | 0.162 | 0.508 | |

DC4 | 0.274 | 0.539 | 0.195 | 0.524 | 0.192 | 0.450 | |

DC5 | 0.209 | 0.375 | 0.215 | 0.554 | 0.194 | 0.353 |

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**MDPI and ACS Style**

Boru, A.; Dosdoğru, A.T.; Göçken, M.; Erol, R.
A Novel Hybrid Artificial Intelligence Based Methodology for the Inventory Routing Problem. *Symmetry* **2019**, *11*, 717.
https://doi.org/10.3390/sym11050717

**AMA Style**

Boru A, Dosdoğru AT, Göçken M, Erol R.
A Novel Hybrid Artificial Intelligence Based Methodology for the Inventory Routing Problem. *Symmetry*. 2019; 11(5):717.
https://doi.org/10.3390/sym11050717

**Chicago/Turabian Style**

Boru, Aslı, Ayşe Tuğba Dosdoğru, Mustafa Göçken, and Rızvan Erol.
2019. "A Novel Hybrid Artificial Intelligence Based Methodology for the Inventory Routing Problem" *Symmetry* 11, no. 5: 717.
https://doi.org/10.3390/sym11050717