Mile – center solution: this determines the geographical point that minimizes the combined distance to all demand centers. The assumption underlying the solution is that delivery costs are solely a function of distance. Therefore, if distance is minimized a least cost location is determined. The basic deficiency of this omission of weight and time considerations.
The mile center solution cannot be determined by solving for the weighted average co-ordinate location along each dimension. It requires a iterative process to determine an increasingly improved warehouse location. This optimum location is determined by utilizing the general formula for the length of a straight line between two points.
The procedure:
The solution uses initial X and Y co-ordinates to initiate an iterative process that refines the previous mile – center warehouse X,Y location co-ordinates. The location problem is solved when the incremental charges in the co-ordinates are within the acceptable range of the initial or previous values.
Example: initial values of X and Y are 30 and 40 respectively. The location solution is obtained by using these values to determine the new warehouse co-ordinates.
New values X=36 and Y=43. The new values indicate a shift, therefore the procedure is not complete
For next iteration the most recent values are used X=36 and Y=43. If the iteration results in values X=36 and Y=43 then the difference is minimal or zero, the problem is optimized.
Tolerance range= +/- 1 mile on X and Y co-ordinates.
Therefore 4 square mile area.
Xk,Yk= co-ordinate values of the warehouse for iteration k.
Xi,Yi= demand point, designated by the appropriate subscript.
di= distance between each demand point (Xi,Yi) and warehouse location for iteration k.
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