# A New Model for Determining the EOQ under Changing Price Parameters and Reordering Time

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## Abstract

**:**

## 1. Introduction

## 2. The Proposed Model of Lot Management with Time-Variant Cost Parameters

**Model**

**1.**

**Model**

**2.**

**Model**

**3.**

**Model**

**4.**

- for ${\alpha}_{c}={\alpha}_{p}$ we obtain model 1;
- for ${\alpha}_{p}=0$ we obtain model 2; and
- for ${\alpha}_{c}=0$ we obtain model 3.

## 3. Empirical illustration

#### Model 1

#### Model 2

#### Model 3

#### Model 4

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Dependence of the optimal time between deliveries of consignments of goods ${t}_{so}$ on α.

**Figure 2.**Dependence of total costs $TC\left({t}_{s},\text{}\alpha \right)$ on the time between deliveries of consignments of goods ${t}_{s}$ for different α values; dependence of the minimum total costs $TC\left({t}_{so},\text{}\alpha \right)$ on the optimal time between deliveries of consignments of goods ${t}_{so}$ for different values α; and the value of the total costs $TC\left({t}_{w},\text{}\alpha \right)$ for the time between deliveries of the consignment ${t}_{w}$ for different α values.

**Figure 3.**The dependence of optimal time between deliveries of consignments of goods ${t}_{so}$ on ${\alpha}_{c}$.

**Figure 4.**The dependence of total costs $TC\left({t}_{s},\text{}{\alpha}_{c}\right)$ on the time between deliveries of consignments of goods ${t}_{s}$ for different ${\alpha}_{c}$ values and the dependence of the minimum total costs $TC\left({t}_{so},\text{}{\alpha}_{c}\right)$ on the optimal time between deliveries of consignments of goods ${t}_{so}$ for different ${\alpha}_{c}$ values (black line and black squares).

**Figure 5.**The dependence of the optimal time between deliveries of consignments of goods ${t}_{so}$ on ${\alpha}_{c}$.

**Figure 6.**The dependence of total costs $TC\left({t}_{s},\text{}{\alpha}_{p}\right)$ on the time between deliveries of consignments of goods ${t}_{s}$ for different ${\alpha}_{p}$ values and the dependence of the minimum total costs $TC\left({t}_{so},\text{}{\alpha}_{p}\right)$ on the optimal time between deliveries of consignments of goods ${t}_{so}$ for different ${\alpha}_{p}$ values (black line and black squares).

**Figure 7.**The dependence of the optimal time between deliveries of consignments of goods ${t}_{so}$ on ${\alpha}_{c}$ and ${\alpha}_{p}.$

**Figure 8.**The dependence of the total costs $TC\left({t}_{s},\text{}{\alpha}_{c}=-3,\text{}{\alpha}_{p}\right)$ with a decrease in the cost of delivery (${\alpha}_{c}=-3$) on the time between deliveries of consignments of goods ${t}_{s}$ at different ${\alpha}_{p}$ values and the dependence of the minimum total costs $TC\left({t}_{so},\text{}{\alpha}_{c}=-3,{\alpha}_{p}\right)$ on the optimal time between deliveries of consignments of goods ${t}_{so}$ for different ${\alpha}_{p}$ values (black line and black squares).

**Figure 9.**The dependence of total costs $TC\left({t}_{s},\text{}{\alpha}_{c}=3,\text{}{\alpha}_{p}\right)$ with an increase in the cost of delivery (${\alpha}_{c}=3$) on the time between deliveries of consignments of goods ${t}_{s}$ for different ${\alpha}_{p}$ values and the dependence of the minimum total costs $TC\left({t}_{so},\text{}{\alpha}_{c}=3,{\alpha}_{p}\right)$ on the optimal time between deliveries of consignments of goods ${t}_{so}$ for different ${\alpha}_{p}$ values (black line and black squares).

No. | Reference | Model |
---|---|---|

1. | Sebatjane & Adetunji [38]. | Costs per cycle are multiplied by the number of cycles. Discounting is not applied. |

2. | Khan, Jaber & Bonney, M. [39] | Optimal order quantity in the presence of defective items in the order and with various options for defect detection: no implications to changing price parameters of an order are provided. |

3. | Birbil, Ş. İ., Bülbül, K., Frenk, H., & Mulder, H. M. [40] | The demand and unit price are assumed to be constant. |

4. | Taleizadeh, A. A. [41] | Divided payments are considered assuming constant parameters of the model. |

5. | Molamohamadi, Z., Arshizadeh, R., Ismail, N., & Azizi, A. [42] | The delay of payment is allowed (it may be considered as a proxy for changing price parameters of the order). The objective is optimizing trade credit terms rather than the lot size. |

6. | El-Kassar, A. N., Salameh, M., & Bitar, M. [43] | The model allows for identifying faulty intermediate consumption items rather than determining the optimal lot size. |

7. | Tungalag, N., Erdenebat, M., & Enkhbat, R. [44] | EOQ extended with the Euler–Lagrange equation without varying price parameters. |

8. | Jaggi, C. K., & Mittal, M. [45] | EOQ model with a focus on the lot size with regards to defected items and deterioration time. |

9. | Elyasi, M., Khoshalhan, F., & Khanmirzaee, M. [46] | The EOQ model with constant price and lead time. |

10. | Widyadana, G. A., Cárdenas-Barrón, L. E., & Wee, H. M. [47] | The model for deteriorating items. |

11. | Shanshan, L. & Yong, H. [1] | Focus on mitigating effects of an already occurred stock out. |

12. | Inprasit, T. & Tanachutiwat, S. [48] | A combination of machine learning and neural networks for determining a reordering point but not an EOQ. |

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**MDPI and ACS Style**

Nestorenko, T.; Morkunas, M.; Peliova, J.; Volkov, A.; Balezentis, T.; Streimkiene, D.
A New Model for Determining the EOQ under Changing Price Parameters and Reordering Time. *Symmetry* **2020**, *12*, 1512.
https://doi.org/10.3390/sym12091512

**AMA Style**

Nestorenko T, Morkunas M, Peliova J, Volkov A, Balezentis T, Streimkiene D.
A New Model for Determining the EOQ under Changing Price Parameters and Reordering Time. *Symmetry*. 2020; 12(9):1512.
https://doi.org/10.3390/sym12091512

**Chicago/Turabian Style**

Nestorenko, Tetyana, Mangirdas Morkunas, Jana Peliova, Artiom Volkov, Tomas Balezentis, and Dalia Streimkiene.
2020. "A New Model for Determining the EOQ under Changing Price Parameters and Reordering Time" *Symmetry* 12, no. 9: 1512.
https://doi.org/10.3390/sym12091512