x18 Objective - To determine the optimal location for the new facility by using the given set of existing facilities co-ordinates on X-Y plane and movement of materials from a new facility to all existing facilities. Generally we follow rectilinear distance for such decision. The rectilinear distance between any two points whose co-ordinates are (X1,Y1 )and(X2,Y2) is given by the following formula d12=|X1 - X2| + |Y1 - Y2 some properties of an optimum solution to the rectilinear distance location problems are as follows: 1. The X-coordinate of the new facility will be same as the X-co-ordinate of some existing facility. Similarly the Y co-ordinate of the new facility will coincide with the Y coordinate of some existing facility. It is not necessary that both coordinates of the new facility 2. The optimum X or Y-co-ordinate location for new facility is a median location. A median location is defined to be a location such that no more than one half the item movement is to the left/below of the new facility location and no more than one half the item movement is to the right /above of the new facility location. EXAMPLE Consider the location of a new plant which will supply raw materials to a set of existing plants in a group of companies, let there are 5 existing plants which have a materials movement relationship with the new plant. Let the existing plants have locations of (400,200).(800,500).(1100,800).(200,900)and( 1300,300). Furthermore suppose that the number of tons of materials transported per year from the new plant to various existing plants are 450,1200,300,800 and 1500, respectively the objective is to determine optimum location for the new plant such that the distance moved(cost)is minimized