Centre of Gravity Method

Centre of gravity is based primarily on cost considerations. This method can be used to assist managers in balancing cost and service objectives. The centre of gravity method takes into account the locations of plants and markets, the volume of goods moved, and transportation costs in arriving at the best location for a single intermediate warehouse.

The centre of gravity is defined to be the location that minimizes the weighted distance between the warehouse and its supply and distribution points, where the distance is weighted by the number of tones supplied or consumed. The first step in this procedure is to place the locations on a coordinate system. The origin of the coordinate system and scale used are arbitrary, just as long as the relative distances are correctly represented. This can be easily done by placing a grid over an ordinary map. The centre of gravity is determined by the formula.

C_X = ∑D_ix.W_i/∑W_i and C_Y = ∑D_iy.W_i/∑W_i

Where C_x = x-coordinate of the centre of gravity

C_y = y-coordinate of the centre of gravity

D_ix = x-coordinate of location i

D_iy = y-coordinate of location i

ILLUSTRATION :

The new Health-care facility is targeted to serve seven census tracts in Delhi. The table given below shows the coordinates for the centre of each census tract, along with the projected populations, measured in thousands. Customers will travel from the seven census tract centre s to the new facility when they need health- care. Two locations being considered for the new facility are at (5.5, 4.5) and (7, 2), which are the centers of census tracts C and F. Details of seven census tract centers, coordinate distances along with the population for each centre are given below. Find the target area’s centre of gravity for the Health-care medical facility.

SOLUTION:
To calculate the centre of gravity, start with the following information, where population is given in thousands.

Next we find Cx and Cy

C_x= 453.5/68 = 6.67

C_y= 205.5/68 = 3.02

The centre of gravity is (6.67, 3.02). Using the centre of gravity as starting point, managers can now search in its vicinity for the optimal location.