Question B3:
Wood Business ADARWA is a lumber company with three wood sources and five markets to be supplied.
The annual availability of wood at sources A, B, and C is 120, 60, and 80 million board feet, respectively.
The amount that can be sold annually at markets 1, 2, 3, 4, and 5 is 45, 35, 60, 50, and 70 million board feet,
respectively.
1
2
3
4
5
A
5
6
5
9
9
B
6
9
10
6
5
C
8
4
6
4
8
The objective is to determine the overall shipping plan that minimizes the total equivalent uniform annual
cost (including shipping cost).
An intern student from Applied Statistics managed to find the following table as one of the basic feasible
solutions obtained by using one of the following methods: North-West Corner method, Minimum Cost
method, Minimum Row Cost method or Vogel’s Method.
1
2
3
4
5
A
5
45
6
5
5
60
9
10
B
5
60
C
4
30
4
50
You, as the head of the OR team at ADARWA that has been assigned to supervise the intern during his
internship period:
A. Among the three proposed approaches, which one gave the basic initial solution in the above
transportation tableau? (2 Marks)
B. What is the transport cost from the table proposed by the intern? (1 Marks)
C. Check for him the optimality test to know if the above solution is the optimum; (2 Marks)
D. If the optimality test fails for the above transport cost, determine the leaving variable(s) by using the
simplex feasibility condition and improve it until you show the optimum solution. (3 Marks)
A. The table proposed by the intern likely used the Minimum Cost method to obtain the initial solution.
B. The transport cost from the table proposed by the intern can be calculated by multiplying the amount shipped from each source to each market by the respective shipping cost per unit. The total transport cost can be obtained by summing these values.
C. To perform the optimality test, calculate the opportunity cost for each non-basic cell in the table. The opportunity cost is the amount by which the cell's cost could be changed without affecting the optimal cost. If all opportunity costs are non-positive, then the table is optimal.
D. If the optimality test fails, determine the leaving variable by identifying the cell with the largest opportunity cost. Then, apply the simplex feasibility condition to find the entering variable and improve the solution iteratively until an optimal solution is reached.