Objective- The objective of the gravity location problem, the total material handling cost based on the squared Euclidian distance is minimized Assumption:- If the same type of material handling equipment/vehicle is used for all the movements, then it is equivalent to minimize the total weighted squared Euclidian distance, since the cost per unit distance is minimized ai = x-co-ordinate of the existing facilities i bir y-co-ordinate of the existing facilities i X = X-co-ordinate of the new facilities y= y-co-ordinate of the new facilities Wir weight associated with the existing facilities i. This is the quantum of materials moved between the new facility and existing facilities I per unit period m= total no of existing facilities the formula for the sum of the weighted squared Euclidian distance is given as: x17 f(x,y) = wi[(x - ai? + (y bi)*1 The objective is to minimize f(x,y) This is quadratic in nature the optimal values for the x and y may be obtained by equating partial derivatives to zero 8(x) = 0 8(XY) = 0 8x wiai XWE 41 wi wibt J = 410 Wibe mwi Optimal location (x* y*)= m, wiat 27, wi " w .) w These are weighted averages of the x-coordinate and y-co ordinates of the existing facilities. Problem There are five Existing facilities which are to be served by single new facilities are shown below in the table 5 (5.10) Existing facility (i) 1 2 3 4 Co-ordinates (ai,bi) (20,5) (15,20) (30,25) (15,20) (30,35) (25,40) (28,30) No of trips of loads/years 100 300 200 300 (wi) 200 300 400 500 (25,5) (32,40) 100 600 Find the optimal location of the new facilities based on giving location concept