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Facility location in the plane: Steiner-Weber model

An iterative solution technique is used to find the location of a single warehouse that services a number of demand centers (e.g. retail stores) and that receives its products from a single supplier (e.g. a plant). The objective is to minimize the sum of inbound and outbound transportation costs. Starting with the center of gravity (which minimizes the sum of the weighted squared distances), an iterative solution technique is used to find the cost-minimal location.

The transportation volumes (demand quantities) of the demand centers are given. The transportation quantity between the supplier (plant) and the warehouse is set equal to the total demand quantity. If the inbound transportation costs (per-mile and per-unit transportation costs between the plant and the warehouse) are set to zero, then the plant will have no effect on the optimal location of the warehouse.

During the computations a map is displayed showing the locations of the demand centers (circles), the plant (green square) and the current location of the warehouse (white square).


i index of demand centers
VZX(i) X-coordinate of demand center i
VZY(i) Y-coordinate of demand center i
W(i) transportation volume to demand center i


  • transportation costs costs are proportional to straight-line distance
  • locations of the single supplier and the demand centers are given as points in the euclidean space (bzw. ein Lieferant)


- Nahmias (1993), Chapter 9
- Heizer/Render (1993), Chapter 8


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