İŞLETME KARAR MODELLERİ

Iteration is a repetition of a mathematical procedure applied to the result of a previous application. An iterative algorithm aims to obtain successively closer approximations to the solution.

A basic solution—whether it is feasible or not—is a corner point of the solution space. The corner points of system of equations are obtained by setting n – m number of variables equal to zero and solving the equations for the remaining m number of variables.

The corner points of system of equations are obtained by setting n – m number of variables equal to zero and solving the equations for the remaining m number of variables.

The selection between the adjacent BF solutions is based on the improvement, not deterioration in Z. If there are many adjacent BF solutions that improve the Z, the one providing the largest improvement is selected. If none of the adjacent BF solutions improve Z, the current BF solution is optimal.

Artificial variables are dummy variables, which intend to initiate the iterations and leave from the basic variables as the operation iterates. This is provided by modifying the objective function with the artificial variables that have a large negative coefficient –M. Artificial variables are required to satisfy the non-negativity constraints and have no physical meaning in the real problem. Once an artificial variable leaves the basic variables, it can be omitted in the next iterations, since it will not be chosen against any other non-basic variable as an entering variable.

If a system has three equations (m=3) and five variables (n=5) then the number of basic solutions is 5!/(3!*(5-3)!) = 120/(6*2) = 120/12 = 10.

The steps of determining the pivotal row are given below: 1. Take each positive coefficient in the pivotal column. 2. Divide each of these into the right-hand side constant for the corresponding row. 3. Identify the row that has the minimum ratio. 4. Pivotal row is the row that is identified in the previous step.

If two corner-point feasible solutions are connected by a line segment, these cornerpoint feasible solutions are adjacent. Two corner-point feasible solutions are adjacent if all but one of their respective variables have the same value.

A slack or surplus is utilized to reconstruct a constraint to obtain equation format. A slack variable represents the remainder of an expendable resource and applies to less than or equal constraints. On the other hand, a surplus represents the excess amount of a restricted resource and applies to greater than or equal constraints.

The objective of minimizing Z is identical to maximizing -Z, and vice versa. Therefore, the maximization of -Z can be solved in substitute of minimization of Z.