Question

Fork Motor Company is an automobile manufacturer operating in the US.

It has divided its market into three regions and has built three regional distribution centers (RDC) to serve these markets. The RDCs are located in California, Florida and Texas.

The annual demand at each regional distribution center is estimated as follows and the company wants to meet all the demand.

- RDC – California: 1.5M automobiles (i.e., 1.5 million)

- RDC – Florida: 0.5M automobiles

- RDC – Texas: 1M automobiles

Fork Motor has two plants in Michigan and Nevada and wants to distribute the automobiles to the RDCs at the lowest cost. So they need to decide how many cars to ship from each of the plants to each of the RDCs to achieve minimum cost. You are asked to model and solve this allocation problem.

Below, you are given the shipping distance between Fork Motor’s facilities in miles.

	Plant – Michigan	Plant – Nevada
RDC – California	2000	300
RDC – Florida	1000	1300
RDC – Texas	1200	800

The head of supply chain informs you that you need to consider the capacity limits of the plants. The Michigan plant is much larger than the one in Nevada. He adds that the capacity limits are as follows:

- Plant – Michigan: 2.5M

- Plant – Nevada: 0.7M

The company estimates that transportation of each car will cost 8.53 dollars per mile.

What is the minimum cost of shipping cars to RDCs in million dollars?

Answer 1

calculation of minimum transportation cost by using NORTH WEST CORNER METHOD

STEP1; allocate the maximum amount to the selected cell and adjust the associated supply demand quantities by subtracting the allocated quantity.

STEP2: exit the row or the column when the supply or demand reaches zero and cross it out, to show that you cannot make any more allocations to that row or column. if a row or a column simultaneous reaches to the zero, only cross out that row or column and leaves a zero supply in the row or column that is not crossed out.

STEP3: if exactly one row or column is left that is not crossed out, stop. otherwisee, advance to the cell to the right if a column has just been crossed out, or to the cell below if a row was crossed out. continue with step 1.

solution:

	MICHIGAN	NEVADA	DEMAND
CALIFORNIA	2000(1.5	300	1.5
FLORIDA	1000(0.5	1300	0.5
TEXAS	1200(0.5	800(0.5	1
DUMMY	0	0(0.2	0.2
SUPPLY	2.5	0.7	3.2

MINIMUM COST-

CALIFORNIA	1.5*2000*8.53	25590
FLORIDA	0.5*1000*8.53	4265
TEXAS	0.5*1200*8.53	5118
TEXAS	0.5*800*8.53	3412
TOTAL		38385