Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Stepping-stone method

Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_1000

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 xij that represents the amount to be shipped from origin i to destination j. The evaluation process for a nonbasic variable xij starts in cell (i, j) and finds a path (steps) to current basic variable cells so that if xijdoes 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...

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA