Operations Research20805 marksNumerical: Vogel's approximation methodVogel's Approximation Method
Find the initial solution by using Vogel's Approximation Method (VAM).
Find the initial solution by using Vogel's Approximation Method (VAM).
$$\begin{array}{|c|c|c|c|c|c|}\hline \text{From} & P & Q & R & S & \text{Supply} \ \hline A & 19 & 30 & 50 & 10 & 7 \ B & 70 & 30 & 40 & 60 & 9 \ C & 40 & 8 & 70 & 20 & 18 \ \hline \text{Demand} & 5 & 8 & 7 & 14 & 34 \ \hline \end{array}$$
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Cost matrix: From P Q R S Supply ------------------ A 19 30 50 10 7 B 70 30 40 60 9 C 40 8 70 20 18 Demand 5 8 7 14 Total supply = 7 + 9 + 18 = 34; total demand = 5 + 8 + 7 + 14 = 34. Balanced. Penalty = difference between two smallest costs in each row/column. Row penalties: A: $10-19=9$, B: