# Vogel's approximation method (VAM)

**DOI:**https://doi.org/10.1007/1-4020-0611-X_1113

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A method for finding a first feasible solution to a transportation problem. The procedure begins by finding the two lowest cost cells for each row and column in the transportation problem array. Subtracting the smaller of these costs from the other produces a Vogel number for each row and column. Select the largest Vogel number and make the first assignment to the corresponding lowest cost cell, where the assignment is the maximum amount that can be sent from the corresponding origin to the corresponding destination. After each assignment, the Vogel numbers are recomputed based on the remaining rows and columns in the array. The procedure is repeated until all assignments (shipments) are made. Although VAM tends to find a good (low cost) first feasible solution, the extra computational work required has proven to be a detriment to its use in computer-based software for solving transportation problems. Northwest-corner rule; Transportaion simplex method.