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The center of gravity method is a method used to determine the location of a distribution center that will minimize transportation costs. The method treats shipping cost as linear function of the distance and the quantity shipped. However, that the quantity to be shipped to each destination is fixed. The coordinates of the center of gravity i.e. the location of the distribution center can be obtained by finding the weighted average of the x coordinate and the weighted average of the y coordinates with weight being the quantities to be shipped.

Here,

^{­             —}_{X Σ XiQi / ΣQi}

             ^—_{Y Σ Yi Qi/ ΣQi}

 Where Qi= Quantity to be shipped to location i.

             xi= x coordinate of destination i.

             yi= y coordinate of destination i.

If the quantities shipped are equal, simple averages can be done with Qi terms.

Here is an illustration to show to determine the center of gravity as follows:

  Destination               (x,y)              Quantity

        A                            3, 5                 800

        B                            5, 1                 900

        C                            6, 7                 200

        D                            6, 4                 100

The Center of gravity can be explained as follows:

^—_{X Σ XiQi / ΣQi = 3(800) +5(900) +6(200) +8(100)/800+900+200+100 = 8900/2000 = 4.45}

 ^—_{Y ΣYi Qi/ ΣQi = 5(800) +1(900) +7(200) +4(100)/800 +900+200+100 = 6700/2000=33.35}

This method is used to pick the site that is close to the center of gravity.

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