# Stepping-stone method

**DOI:**https://doi.org/10.1007/1-4020-0611-X_1000

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A procedure for solving a transportation problem based on a simplification of the simplex method as applied to the constraint structure that defines a transportation problem. It starts with an initial basic feasible solution and then evaluates, for every nonbasic variable, whether an improved solution can be obtained by introducing one of the nonbasic variables into the basis. The problem is structured into an *m*-origin by *n*-destination rectangular array of cells in which the cell location (*i*, *j*) corresponds to the variable *x*_{ij} that represents the amount to be shipped from origin *i* to destination *j*. The evaluation process for a nonbasic variable *x*_{ij} starts in cell (*i*, *j*) and finds a path (steps) to current basic variable cells so that if *x*_{ij}does come into the basis, a new feasible solution is generated. Such a path always exists, although degeneracy procedures may be needed to define the path if the current basic solution is degenerate. Associated with the path is a cost that...