Tall-Brother company has three building projects in progress in this year. Each

Question

Tall-Brother company has three building projects in progress in this year. Each project needs a supply of bricks. There are three sources of bricks: red brick, black brick and grey brick available in the market, but shipping costs differ from location to location. The following Table summarizes the transportation costs.

From

Projects 1, 2 and 3 require 2500, 3750 and 4850 tons of brick supply respectively

• The red, black and grey brick stations have 3,000, 4,000 and 6,000 tons of bricks supply available respectively.

The goal is to minimize the total transportation costs for the Tall-Brother company.

1) Formulate the corresponding LP problem and solve it using Excel to find the optimal transportation quantities so as to minimize the total transportation cost. a. Hint: use transportation model and view three brick stations as supply source as we did.

2) It is the case that Red brick station and Black brick station can send bricks by rail to Grey brick station for $1 per ton. Once the bricks are relocated. It can be trucked to the projects. Reformulate this problem and solve it via Excel to minimize the total transportation costs and corresponding optimal shipment quantities.

From

Project 1 Project 2 Project 3 Tonnage Allowance Red Brick Station $9 $8 $7 3000 Black Brick Station $7 $11 $6 4000 Grey Brick Station $4 $3 $12 6000 Project Requirements (Tons) 2500 3750 4850

Explanation / Answer

Suppose the quantities transported from Red Brick station to Project 1, Project 2 and Project 3 be a, b and c respectively.

Suppose the quantities transported from Black Brick station to Project 1, Project 2 and Project 3 be d, e and f respectively.

Suppose the quantities transported from Grey Brick station to Project 1, Project 2 and Project 3 be g, h and i respectively.

The objective equation = 9 a + 8b + 7c + 7d + 11e + 6f + 4g + 3h + 12i =minimum value

Constraints

a+ b + c <= 3000

d+ e+ f <= 4000

g+ h +i <= 6000

a + d + g = 2500

b + e+ h = 3750

c + f + i = 4850

Solving using excel solve we get the solution as

a= 0, b = 0, c =1100 , d = 250 , e = 0, f= 3750, g = 2250, h= 3750, i=0

Total minimum cost = $52200

Please find attached the excel sheet in the following link as I am unable to put the screenshots here-

https://drive.google.com/file/d/0B61hMD5wWc0jMXhBNHhpRzk2SXM/view?usp=sharing

2) Here, the total cost of sending bricks from Red Brick station to Projects will be = cost of sending by rail to Grey Brick station + cost of sending from Grey brick station to various projects

and

the total cost of sending bricks from Black Brick station to Projects will be = cost of sending by rail to Grey Brick station + cost of sending from Grey brick station to various projects

Therefore the revised cost structure will be as follows-

Objective function for minimum transportation costs = 5 a+ 4b + 13c + 5d + 4e + 13f + 4g + 3h + 12i

Constraints

a + b + c <= 3000

d + e + f <= 4000

g + h + i <= 6000

a + d + g = 2500

b + e + h = 3750

c + f + i = 4850

a = 400, b = 2600, c = 0, d = 2100, e = 0, f = 0, g = 0, h= 1150, i = 4850

Minimum transportation cost = $84550

Please find attached the solution for the problem in the excel sheet attached in the link below

https://drive.google.com/file/d/0B61hMD5wWc0jNXVxdFdVTWNGcXc/view?usp=sharing

From Project 1 Project 2 Project 3 Tonnnage allowance Red Brick Station 5 4 13 3000 Black Brick Station 5 4 13 4000 Grey Brick Station 4 3 12 6000 2500 3750 4850

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