Extreme Value Theory in Application to Delivery Delays

Area of Science:

• Operations Research
• Transportation Science
• Statistical Modeling

Background:

• Road transport delivery delays are stochastic, posing significant economic risks.
• Accurate modeling of rare, extreme delay events is crucial for logistics management.

Purpose of the Study:

• To apply Extreme Value Theory (EVT) for modeling rare delivery delay events in road transport.
• To estimate the extremal index and return level to characterize event clustering.
• To assess the applicability of EVT for predicting and managing delivery delays.

Main Methods:

• Utilized Extreme Value Theory (EVT) for modeling rare delivery delay events.
• Estimated Generalized Extreme Value Distribution (GEV) parameters using maximum likelihood and penalized maximum likelihood methods.
• Calculated the extremal index and return level with confidence intervals.

Main Results:

• EVT provides a robust framework for modeling extreme delivery delays.
• Penalized maximum likelihood method improved small-sample parameter estimation.
• Estimates of the extremal index and return level offer insights into delay clustering.

Conclusions:

• EVT-based prediction is advantageous and ready for practical application in road transport logistics.
• The study highlights the importance of specialized statistical tools for managing rare, high-impact events.
• Findings support the integration of EVT into transport management systems for enhanced reliability.