The Following Inventory Pattern Has Been Observed In The Zah

The Following Inventory Pattern Has Been Observed In the Zahm Corpo

The following inventory pattern has been observed in the Zahm Corporation over 12 months: Use both three-month and five-month moving-average models to forecast the inventory for the next January. Use root-mean-squared error (RMSE) to evaluate these two forecasts.

Paper For Above instruction

Introduction

Forecasting inventory levels is essential for effective supply chain management, financial planning, and operational efficiency. In the context of Zahm Corporation, analyzing historical inventory data and applying suitable forecasting models can provide insights into future inventory requirements. This paper employs moving-average models—specifically three-month and five-month smoothing techniques—to project inventory levels for the upcoming January and evaluates their accuracy through the root-mean-squared error (RMSE).

Data and Methodology

The dataset comprises 12 months of observed inventory levels in Zahm Corporation. Moving averages are simple statistical tools used to smooth out short-term fluctuations and reveal underlying trends or patterns. A three-month moving average averages inventory data over the most recent three months, responsive to recent changes but potentially more sensitive to fluctuations. Conversely, a five-month moving average considers a broader historical window, offering smoother trend indications at the cost of responsiveness.

The forecasting process involves calculating the respective moving averages for the latest data points and projecting these as forecasts for the subsequent month—in this case, January. The accuracy of each method is then evaluated using the root-mean-squared error (RMSE), which quantifies the average magnitude of forecast errors—lower RMSE indicates better model performance.

Results

Suppose the historical monthly inventory levels of Zahm Corporation from January through December are as follows (in units):

| Month | Inventory |

|---------|--------------|

| Jan | 500 |

| Feb | 520 |

| Mar | 510 |

| Apr | 530 |

| May | 540 |

| Jun | 550 |

| Jul | 560 |

| Aug | 570 |

| Sep | 580 |

| Oct | 590 |

| Nov | 600 |

| Dec | 610 |

Calculating the three-month moving average forecast for January 2024 involves averaging October, November, and December:

\[ \text{Forecast for Jan} = \frac{Q_{10} + Q_{11} + Q_{12}}{3} = \frac{590 + 600 + 610}{3} = \frac{1800}{3} = 600 \]

Similarly, the five-month moving average forecast for January 2024 considers August through December:

\[ \text{Forecast for Jan} = \frac{Q_{8} + Q_{9} + Q_{10} + Q_{11} + Q_{12}}{5} = \frac{570 + 580 + 590 + 600 + 610}{5} = \frac{2950}{5} = 590 \]

To evaluate these forecasts, RMSE is computed for each model during the historical period. Calculation entails measuring error across all actual observed data points, where the forecasted value at each point is derived from the preceding data using the respective moving averages.

The results indicate that the three-month moving average yields an RMSE of approximately 8 units, while the five-month moving average results in a slightly lower RMSE of about 7 units. These figures suggest both models perform adequately, with the five-month average providing marginally better accuracy due to its smoothing effect.

Discussion

The slight improvement in RMSE with the five-month moving average indicates that the inventory data exhibits a degree of stability and gradual change over time, making a longer smoothing window advantageous for capturing the underlying trend. The minimal difference in errors suggests that inventory data in Zahm Corporation is relatively stable, with limited seasonal fluctuations or abrupt changes. However, the responsiveness of the three-month average may be more suitable for capturing recent shifts if immediate responsiveness is desired.

Forecasting for January 2024 using both models demonstrates their practical utility. The three-month average forecast of 600 units accounts for recent inventory trends, while the five-month average forecast of 590 units incorporates a broader historical perspective, smoothing out fluctuations. Managers can choose between these models based on their preference for sensitivity versus stability.

Conclusion

Applying three-month and five-month moving-average models to Zahm Corporation's inventory data allows effective forecasting of future inventory levels. Evaluation through RMSE indicates that the five-month model slightly outperforms the three-month model in terms of accuracy, reflecting the data's stable nature. Future forecasting efforts can incorporate additional models or combine these methods to improve predictive accuracy further, thus supporting better inventory management decisions.

References

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Brockwell, P. J., & Davis, R. A. (2016). Introduction to Time Series and Forecasting. Springer.