heeeeelp

solve the by IBM ILOG CPLEX OPL program.and show the results on the network(write down the amount sent from each supply point to each demand point)

Unbalanced transportation problem example A company produces tables in three plants (A, B, C) and distributes its products to three customers (1, 2, 3). The number of demands of each customer and the capacity of the supply for each plant is given in the below table. The unit penalty cost of unmet demand for customer 1 is $100, customer 2 is $120 and customer 3 is $80. Formulate an LP for a balanced transportation problem that minimizes the total cost. 1 2 3 $ 40 $ 10 $ 20 15 20 10 20 25 30 950 400 550 Supply 700 400 A B Demand 500 Unbalanced transportation problem example A B Demand 1 2 3 $ 40 $ 10 $ 20 15 20 10 20 25 30 950 400 550 Supply 700 400 500 Total Supply - 1600 Total Demand-1900 Total Demand> Total Supply A dummy plant D should be defined with a supply of 300 units. Associated costs of this dummy plant should be $100 for customer 1, $120 for customer 2 and $80 for customer 3. (penalty costs of unmet demand) Unbalanced transportation problem example Updated Transportation Table 2 A B 10 - 20 Supply 20 700 10400 30 500 80 300 40 15 20 100 950 D Demand 25 120 400 550 A dummy plant D is defined with a supply of 300 units. Associated costs of this dummy plant are $100 for customer 1, $120 for customer 2 and $80 for customer 3. Total Demand (1900) = Total Supply (1900) Problem becomes a balanced transportation problem Unbalanced transportation problem example Decision Variables: Xij- # of tables distributed from plant i to customer A,B,C,D/-1,2,3 Min Z-40XAI + 10XA2 + 20XA3 + 15XBI +20XB2 + 10XB3+ 20XC1 +25%C2 + 30XC3+ 100XDI + 120XD2 + 80XD3 S.. XA1 + XA2 + XA3 - 700 (supply constraint for Plant A) XB1 + XB2+ XB3 - 400 (supply constraint for Plant B) XCI+ XC2 + XC3 - 500 (supply constraint for Plant C) XDI + XD2 + XD3 - 300 (supply constraint for Plant D) XAI + XB1 + XCI+XDI - 950 (demand constraint for customer ) XA2 + XB2+ XC2 + XD2400 (demand constraint for customer 2) XA3 + XB3 + XC3 + XD3 - 550 (demand constraint for customer 3) Xijov A,B,C,D/-1,2,3 Unbalanced transportation problem example A company produces tables in three plants (A, B, C) and distributes its products to three customers (1, 2, 3). The number of demands of each customer and the capacity of the supply for each plant is given in the below table. The unit penalty cost of unmet demand for customer 1 is $100, customer 2 is $120 and customer 3 is $80. Formulate an LP for a balanced transportation problem that minimizes the total cost. 1 2 3 $ 40 $ 10 $ 20 15 20 10 20 25 30 950 400 550 Supply 700 400 A B Demand 500 Unbalanced transportation problem example A B Demand 1 2 3 $ 40 $ 10 $ 20 15 20 10 20 25 30 950 400 550 Supply 700 400 500 Total Supply - 1600 Total Demand-1900 Total Demand> Total Supply A dummy plant D should be defined with a supply of 300 units. Associated costs of this dummy plant should be $100 for customer 1, $120 for customer 2 and $80 for customer 3. (penalty costs of unmet demand) Unbalanced transportation problem example Updated Transportation Table 2 A B 10 - 20 Supply 20 700 10400 30 500 80 300 40 15 20 100 950 D Demand 25 120 400 550 A dummy plant D is defined with a supply of 300 units. Associated costs of this dummy plant are $100 for customer 1, $120 for customer 2 and $80 for customer 3. Total Demand (1900) = Total Supply (1900) Problem becomes a balanced transportation problem Unbalanced transportation problem example Decision Variables: Xij- # of tables distributed from plant i to customer A,B,C,D/-1,2,3 Min Z-40XAI + 10XA2 + 20XA3 + 15XBI +20XB2 + 10XB3+ 20XC1 +25%C2 + 30XC3+ 100XDI + 120XD2 + 80XD3 S.. XA1 + XA2 + XA3 - 700 (supply constraint for Plant A) XB1 + XB2+ XB3 - 400 (supply constraint for Plant B) XCI+ XC2 + XC3 - 500 (supply constraint for Plant C) XDI + XD2 + XD3 - 300 (supply constraint for Plant D) XAI + XB1 + XCI+XDI - 950 (demand constraint for customer ) XA2 + XB2+ XC2 + XD2400 (demand constraint for customer 2) XA3 + XB3 + XC3 + XD3 - 550 (demand constraint for customer 3) Xijov A,B,C,D/-1,2,3