Determine the best distribution (minimum transportation costs) from suppliers A, B, C, and D to the...

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

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

Solutions

Expert Solution

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.

_______________________________________________________________________________________

In case of any doubt, please ask through the comment section before Upvote/downvote.

keosha answered 2 days ago

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