In: Operations Management
Determine the best distribution (minimum transportation costs) from suppliers A, B, C, and D to the five outlets Dallas, Phoenix, Portland, Montreal, and Orlando.
Two-stage distribution problem: RIFIN Company has recently
developed a new
method of manufacturing a type of chemical. The method involves
refining a certain
raw material that can be obtained from four overseas suppliers, A,
B, C, and D, who
have access to the four ports at Vancouver, Boston, Miami, and San
Francisco,
respectively. RIFIN wants to determine the location for plants that
will refine the
material. Once refined, the chemical will be transported via trucks
to five outlets
located in Dallas, Phoenix, Portland, Montreal, and Orlando.
After an initial study, the choice of location for RIFIN's
refineries has been narrowed
down to Denver, Atlanta, and Pittsburgh. Assume that one unit of
the raw material is
required to make one unit of the chemical. The amount of raw
material that can be
obtained from suppliers A, B, C, and D and the amount of chemical
required at the
five outlets are given in the following table (a). The cost of
transporting the raw
material from each port to each potential refinery and the cost of
trucking the
chemical to outlets are provided in tables (b) and (c),
respectively. Determine the
locations of RIFIN's refining plants, the capacities at these
plants, and the distribution
pattern for the raw material and processed chemical.
(a) Supply and demand for four sources and five outlets
Raw Material Source | Supply | Outlet | Demand |
A | 1000 | Dallas | 900 |
B | 800 | Phoenix | 800 |
C | 800 | Portland | 600 |
D | 700 | Montreal | 500 |
Orlando | 500 |
(b) Inland raw material transportation cost
From/To | Denver | Atlanta | Pittsburgh |
Vancouver | 4 | 13 | 9 |
Boston | 8 | 8 | 5 |
Miami | 12 | 2 | 9 |
San Francisco | 11 | 11 | 12 |
(c) Chemical trucking cost
From/To | Dallas | Phoenix | Portland | Montreal | Orlando |
Denver | 28 | 26 | 12 | 30 | 30 |
Atlanta | 10 | 22 | 23 | 29 | 8 |
Pittsburgh | 18 | 21 | 23 | 18 | 21 |
We solve this trans-shipment problem as shown below. We tabulate the data as shown:
Total supply = Total Demand = 3300. hence, we will get all "=" constraints in Excel solver
We solve the given problem as shown below:
The above solution in the form of formulas along with Excel Solver extract is shown below for better understanding and reference:
As seen from the above solution,
The location of refining plants are:
Denver with capacity of 600 units
, Atlanta with capacity of 1500 units
, Pittsburgh with capacity of 1200 units
The distribution pattern is shown in the above solution excel.
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