BUS606: Operations and Supply Chain Management

This method is one of the most multiple attribute decision-making techniques. In the linear assignment method of a problem given options based on their scores for each indicator and then ranking the final ranking Options linear compensation will be determined through a process. In the linear assignment method based on simplex properties of the solution space, keeping in mind all the arrangements implicitly extracted the optimal solution under a convex simplex. In addition to the compensatory nature of the exchange between the ranking criteria and options are obtained, although the weight vector of indices based on expert opinion is obtained. In comparison with other methods of multiple attribute decision making, including the strengths and linear assignment method, it is important that this method Such as hybrid technology (hard and soft) is considered. The techniques are known techniques of hard decisions that define the model based on mathematical equations. Soft decision techniques are techniques where the model is expressed on a contingency table. Therefore decision making techniques are combination of hard skills and soft skills. This means that these techniques seems to follow the logic of the application techniques is defined on the basis of contingency table, but in practice and in the process of solving the mathematical system of equations are therefore soft and hard skills are strengths. The steps application of this technique is as follows: 

First step: to determine the level of risk for each of the indicators in the form of a matrix (m × m), which represents rank and row of columns that represent the index.

Step two: allocation matrix or gamma matrix $(\gamma)$, which is a square matrix $(\mathrm{m} \times \mathrm{m})$ of the row is risk i and the column of rank is $\mathrm{k}$. Component matrix $\gamma\left(\gamma_{i k}\right)$ is the total weight of the risk indices $i$ in which grade is $\mathrm{k}$. Gamma matrix is a matrix that can be allocated to each of the allocation methods (transport, by Hungarian network and linear programming approach zero and one) to achieve the optimal solution. The most common solution is to allocate linear linear programming methods.

Step Three: calculate the optimum (final ranking) using linear programming through the following models:

$\operatorname{Max} Z=\sum\limits_{i=1}^{m} \sum\limits_{k=1}^{m} \gamma_{i k} h_{i k}$     (1)

$\sum\limits_{k=1}^{m} h_{i k}=1 \quad, i=1,2, \ldots \ldots, 17$                                              (2)

$\sum\limits_{i=1}^{m} h_{i k}=1 \quad, k=1,2, \ldots \ldots, 17 \quad \mathrm{~h}_{\mathrm{ik}}=0 \, or \, 1$               (3)

Such as main feature of this technique can be follows:

1) Above method using a simple ranking of options will be exchanged between the variables and calculations are complex.

2) This method does not require same values measure and the parameters can be of any scale.