# Determine Centers of Gravity

Centers of Gravity (CoG) can be determined using the following types of solve:

## Number of CoGs

The Number of CoGs calculates the specified number of centers of gravity, which are possible locations for your DCs. They are calculated such that the total travel distance to all specified demand/supply locations is minimal. This type can be executed by entering the number of CoGs into the Number of CoGs widget. This value should be an integer between 1 and the total number of locations which you take into account. After specifying this number, click on the Solve Number of CoGs button to determine the location of those CoGs.

### Algorithm to determine CoGs using ‘Number of CoGs’

Suppose that each of your demand/supply locations has a certain force proportional to its load. They each pull on the location of a single center of gravity. When each location uses its force to pull in its own direction, the CoG ends up in the center of those forces. At that moment, the algorithm has found the location which minimizes the total load travel distance.

To find multiple (say, N) centers of gravity, the algorithm starts with N locations being the CoGs. The app assigns the closest CoG as the serving DC for each demand/supply location. For each DC (CoG), the algorithm finds the optimal location based on the loads of the locations which it serves.

This process is repeated. The demand/supply locations are reassigned to the closest CoG location, based on new locations calculated for CoGs. Then, according to the loads of new supply/demand assignments, the CoGs are relocated. The process is repeated until a final balance is found with N centers of gravity and each supply/demand location is served by the closest center of gravity, resulting in a minimal total load travel distance.

## Max Drive Time

In this type of solve, the Center of Gravity generates a grid of cities/locations on top of the data area and selects the minimum number of cities which can serve as DC, such that all customer locations can be reached within the specified maximum drive time. This means that for each demand/supply location, the drive time to its serving DC (center of gravity) will be at most the maximum drive time you specify. In the Maximum Drive Time widget you can specify the maximum number of hours that the demand/supply is allowed to travel from a DC to the demand location/the supply location. After entering this number, click on the Solve Max Drive Time button.

## Constrained CoG

The Constrained CoG mode is an extension of the Max Drive Time CoG solve, which incorporates additional constraints and data from the SC Navigator input dataset. This model aims to minimize the number of CoG locations or to minimize overall costs, subject to various operational constraints. In this mode, if you include suppliers it will actually include the cost of sourcing and delivering the supply to the CoGs/DCs.

### Data Inputs

Selected attributes from the following sheets can be included in this solve. If the data is not available, it will be considered as not restricted or not applicable.

Sheet

Attribute

Supplier Data

‘Variable Cost’, ‘Fixed Cost’, ‘Minimum Capacity’, ‘Maximum Capacity’

Warehouse Data

‘Minimum Capacity’, ‘Maximum Capacity’

Customer Product Data

‘Variable Cost’, ‘Lead Time’, ‘Minimum Fulfillment Rate’

Note

The value Maximum Drive Time impacts the solution time. The smaller this value, the faster a solution will be found.

### Constraints

The Constrained CoG mode offers the possibility to incorporates the following constraints, via the table “Constraint CoG”:

• Maximum Drive Time

The drive time, between each CoG and all customer locations that are served by this CoG, should be within this value. This value is mandatory unless Use Customer Lead Time is used.

Each CoG should be located within the ‘Lead Time’ of the customer it serves. If a customer location has multiple Lead Time values for multiple customers/products/periods, the smallest value will be used.

• Include Minimum Fulfillment Rate

The percentage of served demand of a customer location should be at least ‘Minimum Fulfillment Rate’. If a customer location has multiple Minimum Fulfillment Rate values for multiple customers/products/periods, the largest value will be used.

• Minimum Number of New CoGs

The minimum number of CoGs to be generated. Default is 0.

• Maximum Number of New CoGs

The maximum number of CoGs to be generated. Default is the number of customer locations.

• CoG Min Throughput Capacity

The minimum capacity for all CoGs. Zero means no minimum capacity.

• CoG Max Throughput Capacity

The maximum capacity for all CoGs. Zero means unlimited capacity.

• Include Warehouse Capacity

For fixed warehouse locations, include warehouse minimum/maximum capacity. This value is calculated from ‘Minimum Capacity’ and ‘Maximum Capacity’ in Warehouse Data sheet. If there are multiple capacity values in multiple warehouses/periods, the total value for each location will be used.

• Include Supplier Capacity

For included suppliers, include supplier minimum/maximum capacity. This value is calculated from ‘Minimum Capacity’ and ‘Maximum Capacity’ in Supplier Data sheet. If there are multiple capacity values in multiple locations/periods, the total value for each supplier will be used.

### Objectives

There are two objectives to choose from, the choice can be made in the above mentioned “Constrained CoG” table:

• Minimize Number of CoGs The solution will generate the minimum number of CoGs that meet all included constraints.

• Minimize Total Cost There are four categories of cost and their calculation detail is described in the table below.

Category

Detail

Supplier Cost

• Fixed and Variable Costs based on the Supplier Data sheet.

Warehouse Cost

• Warehouse Fixed Cost is calculated with “CoG Running Cost” in CoG Settings page. This cost is applied to all CoGs, including fixed location and generated CoGs.

• Warehouse Variable Cost is calculated with “CoG Variable Cost” in CoG Settings page.

Customer Cost

• Variable Cost based on the Customer Product Data sheet, applied to fulfilled demand.

Transport Cost

• Primary Cost is calculated with “Primary Transport Cost” in CoG Settings page.

• Secondary Cost is calculated with “Secondary Transport Cost” in CoG Settings page.