SENSITIVITY ANALYSIS OF OBJECTIVE FUNCTION COEFFICIENTS OF THE ASSIGNMENT PROBLEM

Information of sensitivity analysis, in a linear programming problem, is usually more important than the optimal solution itself. However, traditional sensitivity analysis, which perturbs exactly one coefficient and then determines the range preserving the optimality of the current optimal base, is impractical for the assignment problem. An optimal basic solution of the assignment problem is inherently degenerate, so it may be that the optimal base has changed but the optimal assignment remains unchanged. Furthermore, elements of a column (or row) in a cost matrix of assignment problem are usually closely related and change simultaneously, not uniquely. This paper focuses on two kinds of sensitivity analyses for the assignment problem. One is to determine the sensitivity range, over which the current optimal assignment or all the optimal assignments remain optimal, while perturbing the elements of one column (or row) in a cost matrix of the assignment problem simultaneously but dependently. The other is to perturb elements of one column (or row) in a cost matrix of the assignment problem simultaneously but independently. Numerical illustrations are presented to demonstrate that the approaches are useful in practice.

On some aspects of the matrix data perturbation in linear program

Linear program under changes in the system matrix coefficients has proved to be more complex than changes of the coefficients in objective functions and right hand sides. The most of the previous studies deals with problems where only one coefficient, a row (column), or few rows (columns) are linear functions of a parameter. This work considers a more general case, where all the coefficients are polynomial (in the particular case linear) functions of the parameter tT??R. For such problems, assuming that some non-singularity conditions hold and an optimal base matrix is known for some particular value t of the parameter, corresponding explicit optimal basic solution in the neighborhood of t is determined by solving an augmented LP problem with real system matrix coefficients. Parametric LP can be utilized for example to model the production problem where, technology, resources, costs and similar categories vary with time. .