Use the Northwest Corner method to create the initial solution and table. Decide

Question

Use the Northwest Corner method to create the initial solution and table. Decide if the initial solution is optimal. If not, perform one iteration of the streamlined simplex method for the transportation problem. Four cargo ships will be used for shipping goods from one port to four other ports (labeled 1, 2, 3, 4). Any ship can be used for making any one of these four trips. However, because of differences in the ships and cargos, the total cost of loading, transporting, and unloading the goods for the different ship-port combinations varies considerably, as shown in the table. The objective is to assign the four ships to four different ports in such a way as to minimize the total cost for all four shipments. Solve this assignment problem to get the optimal solution with the ship-port assignment and total cost.

Explanation / Answer

Destination Source 1 2 3 4 Supply 1 41 27 28 24 75 2 40 29 M 23 75 3 37 30 27 21 45 Demand 75 30 30 40 175/195 This is a Unbalanced transporatation Problem, we have to convert it into a Balanced transporation Destination Source 1 2 3 4 5 Supply 1 41 27 28 24 0 75 2 40 29 M 23 0 75 3 37 30 27 21 0 45 Demand 75 30 30 40 20 195/195 Applying the maximum possible on North West Corner Destination Source 1 2 3 4 5 Supply 1 41(75) 27 28 24 0 75(0) 2 40 29 M 23 0 75 3 37 30 27 21 0 45 Demand 75(0) 30 30 40 20 195/195 Destination Source 2 3 4 5 Supply 2 29(30) M 23 0 75(45) 3 30 27 21 0 45 Demand 30(0) 30 40 20 195/195 Destination Source 3 4 5 Supply 2 M 23 0 75(45) 3 27(30) 21 0 45(15) Demand 30(0) 40 20 195/195 Destination Source 4 5 Supply 2 23(40) 0 75(45)(5) 3 21 0 45(15) Demand 40(0) 20 195/195 Destination Source 5 Supply 2 0(5) 75(45)(5) 3 0(15) 45(15) Demand 20(0) 195/195

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