Answered Essay: During the war with Iraq, in 1991, the Terraco Motor company produced a lightweight, all

​During the war with Iraq, in 1991, the Terraco Motor company produced a lightweight, all terrian vehicle code named “J99 Terra” for the military. The company is now planning to sell the Terra to the public. It has five plants that manucature the vehicle and four region distribution centers. The company is unsure or public demand for the Terra, so it is considering reducing its fixed operating cost by closing one or more plants, even though it would incur an increase in transportation cost. The relevant cost for the are provided in the following table. The transportation cost are per thousand vehicles shipped; for example, the cost of shipping 1,000 vehicles from plant 1 to warehouse C is $32,000.

Transportation costs ($1,000s) to Warehouse

From plant A    B C D    Annual production capacity Annual fixed operating costs

1    $56 $21    $32    $65    12,000    $2,100,000

2    18 46 7 35 18,000 850,000

3    12 71    41    52 14,000 1,800,000

4    30 24    61    28 10,000 1,100,000

5    45 50    26    31 16,000 900,000

Annual Demand 6,000    14,000    8,000    10,000

Formulate and solve an integer programming model for this problem to assist the company in determining which plants should remain open and which should be closed and the number of vehicles that should be shipped from each plant to each warehouse to minimize total cost.

Expert Answer

The decision variable in Green
The constrains are in Blue
And the objective function is in Orange

On solving :

Transportation cost
Plants A B C D
1 56 21 32 65
2 18 46 7 35
3 12 71 41 52
4 30 24 61 28
5 45 50 26 31
Transportation cost
Plants A B C D Capacity Fixed cost Fixed cost Formula
1 0 12000 0 0 12000 <= 12000 Capacity constrain 2100000 2100000 IF(F10>0,J10,0)
2 0 0 8000 0 8000 <= 18000 850000 850000
3 6000 0 0 0 6000 <= 14000 1800000 1800000
4 0 2000 0 8000 10000 <= 10000 1100000 1100000
5 0 0 0 2000 2000 <= 16000 900000 900000
Demand constrain 6000 14000 8000 10000
= = = =
6000 14000 8000 10000
Transport cost 714000
Fixed cost 6750000
Total cost 7464000 Minimization
Obj func

So, the original solution is: Every of these should remain open.

On new situation of closing one:

Transportation cost
Plants A B C D
1 56 21 32 65
2 18 46 7 35
3 12 71 41 52
4 30 24 61 28
5 45 50 26 31
Transportation cost
Plants A B C D Capacity Fixed cost Fixed actual Formula
1 0 0 0 0 0 <= 0 12000 Capacity constrain 0 2100000 0 (SUMPRODUCT(B10:E10,B3:E3)+K10)*J10
2 0 8000 9999 17999 <= 18000 18000 1 850000 850000
3 6000 0 0 0 6000 <= 14000 14000 1 1800000 1800000
4 0 9843 0 1 9844 <= 10000 10000 1 1100000 1100000
5 0 4157 0 0 4157 <= 16000 16000 1 900000 900000
Demand constrain 6000 14000 8000 10000 4
= = = = <
6000 14000 8000 10000 5
Total cost 5572075 Minimization
Obj func
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