Facility Location Calculator

Determine optimal facility locations using multiple methods including Center of Gravity and Load-Distance

Facility Location Methods

This calculator helps determine the optimal location for a new facility based on different methodologies. Choose the method that best fits your scenario.

Center of Gravity: (X,Y) = (∑(wᵢxᵢ)/∑wᵢ, ∑(wᵢyᵢ)/∑wᵢ)
Load-Distance Score: LD = ∑(wᵢ × dᵢ)

Where:

  • Center of Gravity: Finds the location that minimizes transportation costs based on weights (shipment volumes, demand, etc.)
  • Load-Distance: Evaluates potential locations based on distance to demand points weighted by importance
  • Single Facility Location: Determines the best location for one new facility
  • Multi-Facility Location: Helps allocate demand points to multiple facilities

Calculation Method

Select the facility location method you want to use:

Center of Gravity
Load-Distance
Single Facility
Multi-Facility

Center of Gravity Method

This method finds the location that minimizes transportation costs based on weights (shipment volumes, demand, etc.). Add your demand points with their coordinates and weights below.

Result

Optimal Location (Center of Gravity):

Input Points

Location X Coordinate Y Coordinate Weight

Load-Distance Method

This method evaluates potential locations based on distance to demand points weighted by importance. Add your demand points and potential facility locations below.

Demand Points

Potential Facility Locations

Result

Best Facility Location:

Lowest Load-Distance Score:

Load-Distance Scores

Facility Location Coordinates Load-Distance Score Rank

Single Facility Location

This method determines the best location for one new facility based on demand points and transportation costs.

Demand Points

Result

Optimal Facility Location:

Method Used:

Demand Points

Location Coordinates Demand Distance to Facility

Multi-Facility Location

This method helps allocate demand points to multiple facilities to minimize total transportation costs.

Demand Points

Result

Optimal Facility Locations:

    Demand Allocation

    Facility Coordinates Assigned Demand Points Total Assigned Demand

    Practical Examples

    Example 1: Warehouse Location

    Using Center of Gravity to locate a new warehouse serving 5 retail stores with coordinates and weekly shipment volumes:

    • Store A: (10, 20) - 200 units
    • Store B: (30, 40) - 150 units
    • Store C: (50, 10) - 300 units
    • Store D: (20, 30) - 250 units
    • Store E: (40, 50) - 100 units

    Optimal Warehouse Location: (29.0, 26.5)

    Example 2: Emergency Facility

    Using Load-Distance method to choose between 3 potential locations for a fire station serving 4 neighborhoods with different population sizes:

    Neighborhoods: (5,5)-2000, (10,15)-3000, (15,5)-1500, (20,10)-2500

    Potential locations: (8,8), (12,10), (15,12)

    Best location: (12,10) with lowest load-distance score

    Example 3: Distribution Centers

    Using Multi-Facility method to locate 2 distribution centers for 8 retail stores in a region.

    Optimal solution assigns 4 stores to each DC based on proximity and demand.

    Facility Location Methods Comparison

    Method Best For Advantages Limitations
    Center of Gravity Single facility with weighted demand points Minimizes transportation costs, simple calculation Assumes straight-line distances, may not be on road network
    Load-Distance Choosing between predefined locations Flexible, can use different distance metrics Requires predefined alternatives
    Median Urban locations with grid layouts Works well with rectilinear distances Less accurate for non-grid areas
    Multi-Facility Network of facilities Optimizes entire system, good for large territories More complex, may require iterative solutions