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).
Notation:
|
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 |
Assumptions:
- 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)
Literature:
- Nahmias (1993), Chapter 9
- Heizer/Render (1993), Chapter 8
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