# Facility location planning – Center of Gravity method

let us look at facility location planning using the center of gravity method the Mumbai baking company currently has four retail locations within the metropolitan area of a major city currently each retail outlet makes all of its own breads and pastries from scratch in order to reduce cost and ensure consistency of the firm's products across all locations the management has decided to build a central commissary where the products will be prepared and subsequently distributed to the four retail stores the question now is where to locate the commissary so of course the criteria to choose the location of the commissary would be at a place where the total cost of transportation to all these four store locations is minimized now we have been given the x and y coordinates of each of these four store locations and we have also been given the quantity of product being sold at each of these stores so now we have to find out where does it make sense to locate this commissary so let us first understand what is meant by the center of gravity method the center of gravity method is a quantitative technique that can be used to determine the optimal location of a facility based upon minimizing the transportation cost between where the goods are produced and where they are sold or distributed so the first step in the center of gravity method is to locate each of the existing retail operations on an x and y coordinate grid map and this grid map will help us in establishing the relative distances between these locations so step one is to locate each of the existing facilities on an x and y coordinate grid map and step number two is to find out the X&Y coordinates of the new plant by taking the weighted average of the x and y coordinates of all the existing facilities so step number two is find out the x and y coordinates of the new plant by taking the weighted average of the x and y coordinates of all the existing facilities so now let's look at the formula for finding the x and y coordinates of this new plant or new location so X is the x coordinate of the new location which we are trying to find is equal to the sum of the multiplication of X I and L I divided by the sum of L I and the y-axis is y is equal to some of the multiplication of the y-coordinates and Li divided by the sum of L I now here X 0 and y 0 are the coordinate of the new facility X I and why I are the coordinates of the existing facilities and Li is the load to be transported between the existing facilities and the new plant load to be transported between the existing facilities and the new facility so let us look at this further by means of solving this given example so here we have completed step number one which is to locate each of the existing facilities on the x and y coordinate grid map so this is the x axis this is the y axis basically this exercise is being done to find out the x and y coordinates of the existing locations now let's move to step number two this step is to find out the weighted average of the x and y coordinates of the existing facilities now the formula is X 0 is equal to the sum of the multiplication of the x coordinates of the existing facilities and the load being transported between the existing facility and the new facility divided by the sum of all the load which is being transported so let's find this out so let's say first we consider I as a so the x coordinate for a is 125 multiplied by the load being transported between a and the new plant or the new facility which is 1 2 5 0 plus next is B so 250 multiplied by 3,000 plus C 450 multiplied by 2 7 5 0 plus 200 x one five zero zero and this whole divided by the sum of all the loads which is one two five zero plus three thousand plus two seven five zero plus one five zero zero and this is equal to so let me pull my calculator here so 125 x 1 2 5 0 plus 250 x 3000 plus 450 x 2 7 5 zero plus 200 x 1 5 0 0 so this is 2 4 4 3 7 5 0 divided by one two five zero plus three thousand plus two seven five zero plus one five zero zero 8,500 so two four four three seven five zero divided by eight five zero zero and this is equal to two eighty seven point five to eighty seven point five this is the x-coordinate of the new facility now let's move to find out the y coordinate so y-coordinate again will be the same sum of Y I multiplied by L I divided by the sum of L I so this is equal to 4ei the y coordinate is 100 so 100 multiplied by the load being transported between the facility a and the new facility plus four be 75 so 75 multiplied by the load which is three thousand plus 4c three hundred multiplied by the load which is two seven five zero plus Ford e350 multiplied by the load which is 1500 and this whole divided by the load which is one two five zero plus three thousand plus two seven five zero plus one five zero zero so let me again pull my calculator so hundred multiply it by 1 2 5 0 plus 75 multiplied by three thousand plus three hundred multiplied by two seven five zero plus 350 multiply by one five zero zero so the numerator is one seven zero zero zero zero zero divided by the denominator and denominator we had found out earlier which is 8500 so this is equal to so divided by eight five zero zero two hundred so the y-coordinate of the new facility is two hundred so let us look at this new coordinates or the new facility on this grid map so to eighty seven point five which is the x coordinate will be somewhere here and the y coordinate which is two hundred will be somewhere here so this will be somewhere around here this is the new facility with coordinates two eighty seven point five and two hundred you

## 9 Comments

## Muskan Narang · May 15, 2019 at 7:54 am

how did you calculate the li(load)

## shweta1023 · May 15, 2019 at 7:54 am

Good Video..to the point ..excellent..thanks

## Nicοlas Theo · May 15, 2019 at 7:54 am

thank you very much sir

## Shubham Chaubey · May 15, 2019 at 7:54 am

Thanks for the video, kindly provide video on Load Distance method also.

## ProfBoggs · May 15, 2019 at 7:54 am

Clear video. This seems to be a variation of Weber's model of industrial location, though without the cost surfaces. Thank you for taking the time to make this.

## kevinsapokguy · May 15, 2019 at 7:54 am

What is Li

## Saiful Islam · May 15, 2019 at 7:54 am

you make it so complicated and as well as too much talking

## Sakti Ray · May 15, 2019 at 7:54 am

sir can u please share the minimax problem of facility layout

## Waiphyo Tun · May 15, 2019 at 7:54 am

very helpful and clear explanations.. thanks a lot sir