Forecasting daily parcel count in e-commerce last-mile delivery with Moving Average and Smoothing

Project info

• Field of studyLogistics and Supply Chain
• LevelUndergraduate thesis (S1)
• Method typeTime Series
• Estimated build time± 3 working days
• Toolspandas Series.rolling, Series.ewm, numpy; matplotlib
• PriceUS$16 - US$100

Research goal

Forecast daily parcel count in e-commerce last-mile delivery with moving average and smoothing and compare errors on test data.

Variables

Example result

• 3Window k
• 6.451RMSE vs smoothed
• 5.254MAE vs smoothed
• -0.401Residual lag-1 corr.
• 16.848Variance removed %
• 111Observations

A window-3 moving average smooths daily parcel count with an RMSE of 6.451 against the raw series and removes 16.8% of short-run variation.

Computed from illustrative synthetic data, not from a real study.

About Moving Average and Smoothing

A moving average averages values over a time window to damp random fluctuation and reveal the trend. It is used when exploring a time series or as a simple benchmark forecast.

Steps

1. 1Sort data by time and check for gaps
2. 2Compute the simple moving average with several window widths
3. 3Compute an exponential moving average for comparison
4. 4Compare smoothness and lag of each window
5. 5Compute the one-step forecast error (MAE)
6. 6Plot the raw data and the smoothed series

Assumptions to check

• Observations are equally spaced in time
• The trend does not change drastically within a window
• Window width matches the seasonal period or the analysis goal

Reading and reporting the results

Explain how window width affects smoothness and lag, then report the MAE of the simple forecast. Stress that the method does not model seasonality explicitly.

Example Python code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

rng = np.random.default_rng(10)
n = 120
number_of_drop_points = np.arange(n)
daily_parcel_count = pd.Series(50 + 0.3 * number_of_drop_points + 5 * np.sin(2 * np.pi * number_of_drop_points / 12) + rng.normal(0, 3, n))

ma3 = daily_parcel_count.rolling(3).mean()
ma12 = daily_parcel_count.rolling(12).mean()
ema = daily_parcel_count.ewm(span=12, adjust=False).mean()

# One-step forecast: the MA of the previous window predicts the next value
for w in (3, 6, 12):
    fc = daily_parcel_count.rolling(w).mean().shift(1)
    mae = (daily_parcel_count - fc).abs().mean()
    print("Window", w, "MAE:", round(mae, 3))

plt.figure(figsize=(9, 4))
plt.plot(number_of_drop_points, daily_parcel_count, alpha=0.4, label="Raw")
plt.plot(number_of_drop_points, ma3, label="SMA 3")
plt.plot(number_of_drop_points, ma12, label="SMA 12")
plt.plot(number_of_drop_points, ema, "--", label="EMA 12")
plt.xlabel("Time"); plt.legend()
plt.show()

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions