First-Dispatch Routing Protocol with a Maximum Dispatch Radius

Overview

This white paper outlines the implementation of the First-Dispatch Routing Protocol with a Maximum Dispatch Radius (MDR). The protocol aims to efficiently match a single rider requesting a pick-up with the closest available driver, considering a maximum dispatch radius to enhance the efficiency of the ride-hailing service.

Problem Statement

The task is to implement the first-dispatch protocol as an optimization problem, where the goal is to dispatch a single driver from a collection of available drivers to a single rider. The implementation must consider the following:

• Each request is immediately assigned to the open driver predicted to have the shortest en route time (ETA).
• A maximum dispatch radius (MDR) constraint is imposed to prevent drivers from being dispatched to pick up very distant riders.

Data Description

The data required for this implementation includes:

1. Rider Data: The location of a single rider requesting a pick-up.
2. Driver Data: A data frame containing:
   • Physical distances from the rider to each driver.
   • En route times (ETA) representing the estimated time it will take for a driver to meet the rider once dispatched.
3. Maximum Dispatch Radius (MDR): A cutoff value for dispatching drivers based on their distance to the rider.

Optimization Model

Decision Variables

• ( x_i ): A binary variable indicating whether driver ( i ) is dispatched (1 if dispatched, 0 otherwise).

Objective Function

Minimize the en route time (ETA) for the dispatched driver: [ ext{Minimize} \sum_{i} ext{ETA}_i \cdot x_i ]

Constraints

1. Dispatch Constraint: Only one driver can be dispatched: [ \sum_{i} x_i = 1 ]
2. MDR Constraint: Drivers can only be dispatched if their distance to the rider is within the MDR: [ x_i \cdot ext{Distance}_i \leq ext{MDR}, \quad orall i ]
3. Binary Constraint: The decision variables are binary: [ x_i \in {0, 1}, \quad orall i ]

Implementation Steps

1. Data Preparation: Load the rider data, driver data (distances and ETAs), and MDR.
2. Optimization Model Formulation: Define the decision variables, objective function, and constraints.
3. Solve the Optimization Problem: Use an appropriate solver to find the optimal solution.
4. Result Interpretation: Determine which driver is dispatched to the rider based on the optimization result.

Example

Consider the following randomly generated data:

• Rider: Location coordinates (e.g., latitude and longitude).
• Drivers: A data frame with distances and ETAs to the rider.
• MDR: A threshold value (e.g., 5 kilometers).

Using this data, the optimization model can be implemented and solved to determine the best driver to dispatch according to the first-dispatch protocol with an MDR constraint.

Conclusion

This implementation of the First-Dispatch Routing Protocol with a Maximum Dispatch Radius enhances the efficiency of ride-hailing services by ensuring that drivers are not dispatched to distant riders, thereby optimizing the matching process and reducing overall en route times.