### Abstract

In this paper, we study the performance of an Automatic Pipeline, Variable Inventory, Order-Based Production Control System (APVIOBPCS) using linear control theory. In particular, we consider a system with independent adjustments for the inventory and pipeline feedback loops and the use of triple exponential smoothing (the Holt-Winters no-trend, additive seasonality model) as a forecasting strategy. To quantify the performance of the system, we derive the transfer functions of the system and plot the frequency response of the system under a number of different parametrizations. We find that the system using Holt-Winters forecasting (the HW-model) significantly outperforms the system using simple exponential smoothing (the SES model), commonly found in the literature, under certain demand assumptions. However, we find that the HW-model is very sensitive to the demand frequency, while the SES is very robust. Thus, the performance range is substantially narrower for the SES model. Finally, we show that previous insights related to behavioral biases are not affected by the choice of forecasting strategy.

Language | English |
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Title of host publication | International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017 |

Publisher | American Institute of Physics |

Number of pages | 4 |

ISBN (Electronic) | 9780735416901 |

DOIs | |

State | Published - 10 Jul 2018 |

Event | 15th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2017) - Thessaloniki, Greece Duration: 25 Sep 2017 → 30 Sep 2017 Conference number: 15 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 1978 |

### Conference

Conference | 15th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2017) |
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Abbreviated title | ICNAAM 2017 |

Country | Greece |

City | Thessaloniki |

Period | 25/09/17 → 30/09/17 |

### Fingerprint

### Cite this

*International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017*[190007] (AIP Conference Proceedings; Vol. 1978). American Institute of Physics. DOI: 10.1063/1.5043834

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*International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017.*, 190007, AIP Conference Proceedings, vol. 1978, American Institute of Physics, 15th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2017), Thessaloniki, Greece, 25/09/17. DOI: 10.1063/1.5043834

**A control theoretic analysis of the Bullwhip effect under triple exponential smoothing forecasts.** / Udenio, Maximiliano; Vatamidou, Eleni; Fransoo, Jan C.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - A control theoretic analysis of the Bullwhip effect under triple exponential smoothing forecasts

AU - Udenio,Maximiliano

AU - Vatamidou,Eleni

AU - Fransoo,Jan C.

PY - 2018/7/10

Y1 - 2018/7/10

N2 - In this paper, we study the performance of an Automatic Pipeline, Variable Inventory, Order-Based Production Control System (APVIOBPCS) using linear control theory. In particular, we consider a system with independent adjustments for the inventory and pipeline feedback loops and the use of triple exponential smoothing (the Holt-Winters no-trend, additive seasonality model) as a forecasting strategy. To quantify the performance of the system, we derive the transfer functions of the system and plot the frequency response of the system under a number of different parametrizations. We find that the system using Holt-Winters forecasting (the HW-model) significantly outperforms the system using simple exponential smoothing (the SES model), commonly found in the literature, under certain demand assumptions. However, we find that the HW-model is very sensitive to the demand frequency, while the SES is very robust. Thus, the performance range is substantially narrower for the SES model. Finally, we show that previous insights related to behavioral biases are not affected by the choice of forecasting strategy.

AB - In this paper, we study the performance of an Automatic Pipeline, Variable Inventory, Order-Based Production Control System (APVIOBPCS) using linear control theory. In particular, we consider a system with independent adjustments for the inventory and pipeline feedback loops and the use of triple exponential smoothing (the Holt-Winters no-trend, additive seasonality model) as a forecasting strategy. To quantify the performance of the system, we derive the transfer functions of the system and plot the frequency response of the system under a number of different parametrizations. We find that the system using Holt-Winters forecasting (the HW-model) significantly outperforms the system using simple exponential smoothing (the SES model), commonly found in the literature, under certain demand assumptions. However, we find that the HW-model is very sensitive to the demand frequency, while the SES is very robust. Thus, the performance range is substantially narrower for the SES model. Finally, we show that previous insights related to behavioral biases are not affected by the choice of forecasting strategy.

UR - http://www.scopus.com/inward/record.url?scp=85049928545&partnerID=8YFLogxK

U2 - 10.1063/1.5043834

DO - 10.1063/1.5043834

M3 - Conference contribution

T3 - AIP Conference Proceedings

BT - International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017

PB - American Institute of Physics

ER -