All about sensitivity analysis in operations research

Sensitivity analysis in operations research allows us to understand the effects that occur in an optimal solution. This entry explains what it consists of and its keys.

A sensitivity analysis in operations research is an important tool in the search for an optimal solution to engineering problems in a project where it must be determined how different parameters will affect it. What exactly do these analyzes consist of? Next, its main characteristics and outstanding keys are offered.

Sensitivity analysis in operations research: what is it?

It is an analysis that seeks to determine the effects produced in the optimal solution by a change in any parameter of a linear programming model. It investigates how a modification in the coefficients of the basic and non-basic variables will affect the available resources or if a new restriction is introduced.

The objective is to determine to what extent the optimal solution is reliable according to the alterations that may occur. Keep in mind that the solution is based on the fact that the starting data will remain constant, which only occurs in short periods of time. Therefore, by using this analysis, you can anticipate how it will behave in the face of changes that may arise.

It also helps determine which parameters or variables can fluctuate without affecting the optimal solution. Some have larger intervals without causing changes, but others will be much more sensitive. By detecting them, it is possible to keep them under supervision to deal with the problems they may cause. Depending on its behavior, the appropriate adjustments will be made to prevent the solution from eventually failing.

How is the analysis carried out?

The analysis must address and verify each parameter individually. The coefficients of the objective function and the limits of the restrictions will also be expressed. Thus, useful information will be obtained that allows determining if the solution is still the optimal one. At the time of carrying it out, it is possible to use programs. In addition, this procedure will be followed to expedite activities:

Model revision: In this part, the changes in the parameters to be investigated are established. These will test the feasibility of the optimal solution and will allow the effects they cause to be identified.

Conversion to the appropriate form of Gaussian elimination: This methodology allows converting the data into an appropriate table to identify and evaluate the current solution.

Feasibility test: We examine whether the solution is feasible by checking all the basic variables that still have non-negative values.

Proof that the solution is optimal: The solution is verified to determine whether or not it is optimal, since it has previously been verified that it is feasible. The coefficients of nonbasic variables in the Z region that remain nonnegative are checked.

Optimization: If the solution does not pass any of the indicated tests, it will proceed to optimize it based on the results obtained. Thus, it will be refined until the appropriate values are found, those that offer satisfactory variables in key parameters.

ABC method of inventory classification, an example to take into account

The ABC method for inventory classification is an example of this analysis. It is used to find the optimal solution when it comes to segmenting and organizing products in a warehouse. The importance is the key parameter to order them. Thus, the relevance for the company, the economic value, the benefits provided or the turnover generated, among other factors, are taken into account.

When making the classification, three types of categories are established:

Category A

A includes those products of greatest importance to the company. These usually account for 20% of the inventory and are also the ones that generate a high movement or turnover. By prioritizing them, they are managed effectively and superior performance is achieved for the company.

Category B

Category B encompasses products with moderate importance and turnover. They come to represent 30% of merchandise, although they do not generate more than 20% of income. It is an intermediate group that it should be reviewed frequently, since some of its components could fit into class A or C depending on the circumstances.

Category C

Finally, C is the most numerous category, although it is the one that would contribute the least income. The products that make it up are not in high demand, so it is not necessary to allocate many resources to them. They generate only 5% of the profits and their control can be carried out sporadically, but always taking into account their expiration or obsolescence. They are located in secondary areas of the warehouse with poorer accessibility, since their priority is low.

How is it classified following the ABC method?

warehouse-worker-with-clipboard-in-the-storage-2021-12-09-01-20-47-utcABC method classification. Source: Envato

There are four ways to classify goods following this method.

The first takes into account the rotation of the products, the fundamental parameter when analyzing the situation of a warehouse. The most demanded will make up category A and the least, category C.

Another way is to pay attention to the unit cost, which leads to organizing the stock based on the investment made in the stored materials.

A third way is based on having the total inventory value as a reference, which would be the unit cost multiplied by the number of units. It is a useful method, but it requires a strict and continuous control of the products to redefine the categories based on changes in value.

Finally, the factors of use and value can be taken into account to make the categories. It is the most used and complete of the four. Attention is paid to the demand and value of products. Those of class A will be those that are most valuable to the company and that are also highly demanded by customers. Equations of variables, such as the product profitability equation, can be included to gain precision.