ij x ≥ for all i , j . ( non-negative restrictions) Some Definitions Feasible Solution : A feasible solution to a transportation problem is a set of non-negative values x ij ( i = , ,.., m , j = , ,… n ) that satisfies the constraints. Basic Feasible Solution : A feasible solution is called a basic feasible solution if it contains not more than m + n – allocations, where m is the number of rows and n is the number of columns in a transportation problem. Optimal Solution : Optimal Solution is a feasible solution (not necessarily basic) which optimizes(minimize) the total transportation cost.
Non degenerate basic feasible Solution : If a basic feasible solution to a transportation problem contains exactly m + n – allocations in independent positions, it is called a Non degenerate basic feasible solution. Here m is the number of rows and n is the number of columns in a transportation problem. Degeneracy : If a basic feasible solution to a transportation problem contains less than m + n – allocations, it is called a degenerate XII Std - Business Maths & Stat EM Chapter - - basic feasible solution. Here m is the number of rows and n is the number of columns in a transportation problem.
. . Methods of finding initial Basic Feasible Solutions There are several methods available to obtain an initial basic feasible solution of a transportation problem. We discuss here only the following three.
For finding the initial basic feasible solution total supply must be equal to total demand. (i.e) i j j i m Method:1North-West Corner Rule (NWC) It is a simple method to obtain an initial basic feasible solution. Various steps involved in this method are summarized below. Step : Choose the cell in the north-west corner of the transportation Table10.
and allocate as much as possible in this cell so that either the capacity of first row (supply)is exhausted or the destination requirement of the first column(demand) is exhausted.(i.e) x = min( a , b ) Step : If the