# A Heuristic Simulation–Optimization Approach to Information Sharing in Supply Chains

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. The Proposed Model

## 4. Experiment and Results Analysis

- ①
- The lead time for the distributor, wholesaler, and retailer is one week;
- ②
- The lead time for the factory tier is three weeks, considering the lead time of the raw-material supplier;
- ③
- The capacity of each tier is infinite;
- ④
- The order requested is never canceled; and
- ⑤
- The inventory left is never returned.

^{2}). The range of $\mathsf{\theta}$ is between 0 and 1. The size of the population is 200, and the number of generations is 100. The information lead time and the material lead time are one week, and the total replication length and warm-up period are 600 weeks and 100 weeks, respectively. Since $\mathrm{Q}=17$, ${\mathsf{\alpha}}_{\mathrm{S}}=0.317$, and $\left(\frac{{\mathsf{\alpha}}_{\mathrm{SL}}}{{\mathsf{\alpha}}_{\mathrm{S}}}\right)=0.317$, as suggested by Strozzi et al. [28], are reasonable, we applied those values in the present work. The shortage and inventory holding costs were kept unchanged so that the simulation results could be compared objectively. The inventory holding cost was 0.5 per unit, and the shortage cost was 2 per unit per period.

#### 4.1. The Case of Using the Downstream Information

^{−39}, the p-value is lower than the α-level. Thus, it can be concluded that there is a difference between adjusting $\mathsf{\theta}$ from 0 to 1 and fixing $\mathsf{\theta}$ to 0.25. Consequently, the method of determining the relative weight of the expected demand information is a more effective solution for TIC under non-information sharing conditions.

#### 4.2. The Case of Using the Information from the End-Customer

^{−221}. Thus, it can be concluded that there is a difference between adjusting the relative weight without information sharing and fixing the relative importance to 0 when information is shared. When comparing the mean values of TIC as shown Table 11, the TIC for adjusting the relative weight without information sharing was 101.2% higher than that for fixing the relative importance with information sharing. The coefficient of variance for adjusting the relative weight without information sharing was 0.098, and the coefficient of variance for fixing the relative importance to 0 with information sharing was 0.072. Thus, fixing the relative weight of the expected demand information to 0 can be considered to be more stable.

## 5. Discussion

## 6. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Simulation result under non-information sharing conditions, $\mathsf{\theta}\le 1$, $\mathrm{Q}=17$, ${\alpha}_{S}=0.317$, and $\left(\frac{{\mathsf{\alpha}}_{\mathrm{SL}}}{{\mathsf{\alpha}}_{\mathrm{S}}}\right)=0.317$.

**Figure 4.**Simulation result under non-information sharing conditions, $\mathsf{\theta}=0.25$, $\mathrm{Q}=17$, ${\alpha}_{S}=0.317$, and $\left(\frac{{\mathsf{\alpha}}_{\mathrm{SL}}}{{\mathsf{\alpha}}_{\mathrm{S}}}\right)=0.317$.

**Figure 5.**Simulation result under information sharing conditions, $\mathsf{\theta}=0.0$, $\mathrm{Q}=17$, ${\alpha}_{S}=0.317$, and $\left(\frac{{\mathsf{\alpha}}_{\mathrm{SL}}}{{\mathsf{\alpha}}_{\mathrm{S}}}\right)=0.317$.

**Figure 6.**Simulation result under information sharing conditions, $\mathsf{\theta}\le 1$, $\mathrm{Q}=17$, ${\alpha}_{S}=0.317$, and $\left(\frac{{\mathsf{\alpha}}_{\mathrm{SL}}}{{\mathsf{\alpha}}_{\mathrm{S}}}\right)=0.317$.

**Table 1.**Total ranges of the inventory cost and order fill rate under non-information sharing conditions.

$\mathsf{\theta}$ | $\mathsf{\theta}\le 1$ | $\mathsf{\theta}=0.25$ | |
---|---|---|---|

Objectives | |||

Total inventory cost | Min | 1,424,416.167 | 1,630,458.682 |

Max | 1,866,388.589 | 2,170,367.994 | |

Order fill rate | Min | 0.478 | 0.475 |

Max | 0.537 | 0.540 |

Factor | N | Total | Mean | Variance |
---|---|---|---|---|

TIC(0 $\le $ θ $\le $ 1) | 200 | 324,948,399.5 | 1,624,741.998 | 25,534,935,240 |

TIC(θ = 0.25) | 200 | 378,125,334.5 | 1,890,626.672 | 39,302,200,428 |

Cause of Variance | Sum of Squares | df | Mean Square | F | Sig. | Pr > F |
---|---|---|---|---|---|---|

Treatment (factor) | 7.06947 × 10^{12} | 1 | 7.06947 × 10^{12} | 218.1 | 1.16374 × 10^{−39} | 3.9 |

Residual | 1.29026 × 10^{13} | 398 | 32,418,567,834 | |||

Total | 1.99721 × 10^{13} | 399 |

**Table 4.**Statistical analysis of the order fill rate (OFR) under non-information sharing conditions.

Factor | N | Total | Mean | Variance |
---|---|---|---|---|

OFR(0 $\le $ θ $\le $ 1) | 200 | 103.585 | 0.517925 | 0.000289 |

OFR(θ = 0.25) | 200 | 104.05833 | 0.5202917 | 0.0002969 |

Cause of Variance | Sum of Squares | df | Mean Square | F | Sig. | Pr > F |
---|---|---|---|---|---|---|

Treatment (factor) | 0.0005601 | 1 | 0.0005601 | 1.9121508 | 0.1674999 | 3.9 |

Residual | 0.116583 | 398 | 0.0002929 | |||

Total | 0.1171431 | 399 |

**Table 6.**Ranges of total inventory cost and order fill rate considering the level of information quality under information sharing conditions.

$\mathsf{\theta}$ | $\mathsf{\theta}\le 0$ | $\mathsf{\theta}=1$ | |
---|---|---|---|

Objective Function | |||

Total inventory cost | Min | 707,502.4 | 747,763.7 |

Max | 1,072,705.1 | 909,893.5 | |

Order fill rate | Min | 0.503 | 0.502 |

Max | 0.543 | 0.548 |

Factor | N | Total | Mean | Variance |
---|---|---|---|---|

TIC($\mathsf{\theta}\le 1$) | 200 | 168517700 | 842,588.4999 | 15,474,607,605 |

TIC($\mathsf{\theta}=0$) | 200 | 161474921 | 807,374.6062 | 3,400,844,185 |

Cause of Variance | Sum of Squares | df | Mean Square | F | Sig. | Pr > F |
---|---|---|---|---|---|---|

Treatment (factor) | 1.24002 × 10^{11} | 1 | 1.24002 × 10^{11} | 13.13895233 | 0.0003267 | 3.8649292 |

Residual | 3.75621 × 10^{12} | 398 | 9437725895 | |||

3.88022 × 10^{11} | 399 |

Factor | N | Total | Mean | Variance |
---|---|---|---|---|

OFR($\mathsf{\theta}\le 1$) | 200 | 106.3083 | 0.531542 | 0.000163 |

OFR($\mathsf{\theta}=0$) | 200 | 105.3917 | 0.526958 | 0.000205 |

Cause of Variance | Sum of Squares | df | Mean Square | F | Sig. | Pr > F |
---|---|---|---|---|---|---|

Treatment (factor) | 0.002101 | 1 | 0.002101 | 11.42235 | 0.000797 | 3.864929 |

Residual | 0.073197 | 398 | 0.000184 | |||

Total | 0.075297 | 399 |

**Table 11.**Statistical information on total inventory cost and order fill rate under both information non-sharing and sharing conditions.

Sharing Condition | Objective Function | $\mathsf{\theta}\le 1$ | $\mathsf{\theta}=0.25$ | |
---|---|---|---|---|

Non-Information Sharing | Total inventory cost | Min | 1,424,416.167 | 1,630,458.682 |

Max | 1,866,388.589 | 2,170,367.994 | ||

Mean | 1,624,741.998 | 1,890,626.672 | ||

Variance | 2,553,493,5240 | 39,302,200,428 | ||

Order fill rate | Min | 0.478 | 0.475 | |

Max | 0.537 | 0.540 | ||

Mean | 0.517925 | 0.5202917 | ||

Variance | 0.000289 | 0002969 | ||

$\mathsf{\theta}\le 1$ | $\mathsf{\theta}=0$ | |||

Information Sharing | Total inventory cost | Min | 707,502.400 | 747,763.700 |

Max | 1,072,705.100 | 909,893.500 | ||

Mean | 842,588.4999 | 807,374.6062 | ||

Variance | 15,474,607,605 | 3,400,844,185 | ||

Order fill rate | Min | 0.503 | 0.502 | |

Max | 0.543 | 0.548 | ||

Mean | 0.531542 | 0.526958 | ||

Variance | 0.000163 | 0.000205 |

Cause of Variance | Sum of Squares | df | Mean Square | F | Sig. | Pr > F |
---|---|---|---|---|---|---|

Treatment(factor) | 6.68 × 10^{13} | 1 | 6.68 × 10^{13} | 4617.739 | 4.3 × 10^{−221} | 3.864929 |

Residual | 5.76 × 10^{12} | 398 | 1.45 × 10^{10} | |||

Total | 7.26 × 10^{13} | 399 |

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**MDPI and ACS Style**

Park, K.
A Heuristic Simulation–Optimization Approach to Information Sharing in Supply Chains. *Symmetry* **2020**, *12*, 1319.
https://doi.org/10.3390/sym12081319

**AMA Style**

Park K.
A Heuristic Simulation–Optimization Approach to Information Sharing in Supply Chains. *Symmetry*. 2020; 12(8):1319.
https://doi.org/10.3390/sym12081319

**Chicago/Turabian Style**

Park, KyoungJong.
2020. "A Heuristic Simulation–Optimization Approach to Information Sharing in Supply Chains" *Symmetry* 12, no. 8: 1319.
https://doi.org/10.3390/sym12081319