MAEP Solver

The Maximal Accessibility Equality Problem (MAEP), originally introduced by Jin et al., addresses capacity adjustments for minimizing inequality in accessibility. It takes into account the match ratio between supply and demand, along with intricate spatial interactions.

The optimization objective of MAEP aims to minimize inequality in facility accessibility, with a focus on reducing variance across geographic areas. This problem can be formulated as either a Nonlinear Programming (NLP) or a Quadratic Programming (QP) task.

The top input table contains three types of columns: demand size (e.g., population), distance columns to the existing facilities (n) and new facilities (k). The bottom input table contains two columns: the ID and the capacity columns for existing facilities.

The result table comprises three columns: Facility IDs and their assigned capacities under two scenarios, denoted by the 'All' and 'Fixed' columns: Global Optimization: New capacity is allocated to both existing and new facilities by adding the specified new capacity to the total capacity of existing facilities. Local Optimization: New capacity is exclusively assigned to new facilities based on the specified new capacity, with no impact on the capacities of existing facilities.

To solve the MAEP problem, this node utilizes the cvxopt package.


Demand size column

The column for demand size (e.g., population).

Distance columns

Distance columns representing the distances to the existing facilities.

Distance columns for candidate facilities

The columns representing the distance matrix between demand lcoation to candidate facilities.

Facility ID column

The column for facility IDs.

Capacity column of existing facilities

The column representing the capacities of existing supply facilities.

Distance decay model

The model representing distance decay effect.

Available options:

  • Power: Apply the power function, power(distance, -n), to model distance decay effect.
  • Exponential: Apply the exponential function, exp(-distance * n), to model distance decay effect.
  • 2SFCA binary: Use a threshold to create a binary value for distance decay effect.
Distance decay parameters

It works for the parameters for the chosen corresponding models.

Input new capacity

Total capacity assigned to all new facilities.

Input Ports


Each row in this table represents a demand location (m). It consists of three types of columns: demand size (e.g., population), distance columns to the existing facilities (n) and new facilities (k).


This table provides information regarding the supply capacity of each existing facility. The values in the Facility ID column must exactly match the column names for facilities in the demand table.

Output Ports


Facilities with assigned capacities.

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