Abstract:
Generally, the well-known method, popular among researchers for solving linear constrained problems, is
the simplex method using tableaus with many unclear features consuming virtually higher percentage of
the body of the work. Usually, the above operation requires a large number of arithmetic computations
which may be cumbersome particularly when the coe cient matrix is large. Hence, the need to reduce
the volume and operations is of highest priority for optimal control for this class of problems.
In this work, vector-matrix approach is used to enhance compactness with the objective and aims of
obtaining approximate solutions comparable to the optimal solution of the original problem after a little
change in any of the parameters.
The methodology decomposes the coe cient matrix into the basis matrix XB and the non basis matrix
XN. The basis matrix gives the current solution which is examined for optimality in which the relative
pro t coe cients are either 0 (for max problem) or 0 (for min problem). On the contrary, the above
process aided by the invertibility of the basis matrix which enhances less computations eases access to
the next iteration. In this fashion, we continue until the optimal solution is obtained comparable to the
original solution in terms of conciseness and clarity of work for further studies in the area of this class of
problems.
Real-life problems are considered to demonstrate the applicability of the vector-matrix approach to problems
in this class. Results of examples obtained are favourable with compactness and preciseness exhibited
by the reduction in volume of work compared to the tabular approach.
