Answer to Question #145131 in Operations Research for Joy Apostol

Question

four companies viz. W,X,Y, and Z supply the requirements of three warehouse viz. A, B, and C respectively. the companies availability, warehouse requirements and the unit cost of transporatation are given in the following table. find an initial basic feasible solution using

Answer 1

Let's Supply is $S_A, S_B, S_C$ for all warehouse.

Let's Requirement is $R_W, R_Y, R_X,R_Z$ for all factories .

Since $R_Y +R_Z=S_C$ so the given problem is a degeneracy problem.

Now we will solve the transportation problem by Matrix Minimum Method.

To resolve degeneracy, we make use of an artificial quantity(d). The quantity d is so small that it does not affect the supply and demand constraints. Degeneracy can be avoided if we ensure that no partial sum of si(supply) and rj (requirement) are the same.

Substituting $d=0.$

Degeneracy has been removed

$Answer = k_{1}R_W+ k_{2}(S_A-R_W)+k_{3}S_B+k_{4}R_Y$

where $k_1$ is a coefficient for $R_W$ and $S_A$ (from table)

$k_2$ is a coefficient for $R_X$ and $S_A$ (from table)

$k_3$ is a coefficient for $R_X$ and $S_B$ (from table)

$k_4$ is a coefficient for $R_Y$ and $S_C$ (from table)