# Risk assessment and definition of damage, Example of calculation and minimization of expected damage - Supply Chain Management

## Risk assessment and definition of damage

Risk assessment is the next difficult stage after identifying and identifying risks. As a rule, risk analysis and assessment are based on the calculation of the probability of occurrence of risk events with the corresponding values ​​of possible violations.

There are at least three possible ways to assess the likelihood of a risk event: an empirical, theoretical and subjective (expert) assessment. For example, risks in the supply chain can be estimated:

• based on logical reasoning, empirically - as an extrapolation of past, already studied situations and predicting them for the future;

• on the basis of mass facts and processes, statistically - based on the study of loss statistics with the establishment of the frequency of occurrence of certain loss levels;

• expert - based on assessments and information received from experts;

• Calculation-analytical - based on the construction, for example, of the probability loss distribution curve.

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The choice of risk assessment methods is most often related to the circumstances and the need to obtain accurate or approximate estimates of damage (profits) from contracts, transactions and other transactions. Therefore, the variety of methods for assessing risk is great - from the simplest, allowing you to navigate in the current situation, to modern mathematical methods used to obtain accurate quantitative estimates with predicted dynamics.

Let's consider an example of calculation and minimization of expected damage because of possible losses of cargo in a way, i.e. consider the situation where the logistics risk in the supply chain is defined as the expected damage.

## Example of calculating and minimizing the expected damage

Let there be three possible acceptable routes for the vehicle when delivering cargo: routes Ml, M2 and M3. The cargo is not exclusive. Therefore, the risk is defined as the average expected damage due to the possibility of losing part of the cargo. The time for delivery of cargo for these routes can be considered approximately the same, therefore within the framework of the decision-making model presented below under risk conditions, it will not be taken into account. The specificity of the routes in question makes it possible to identify the corresponding dangerous stages for them. For each of them, the laws of probability distribution for damage due to the lost part of the cargo are known. To simplify the considered decision-making model under risk conditions, casual losses on separate allocated route sections can be considered independent. The required initial data are presented in Table. 8.3.

Table 8.3. Initial data for the example

 Dedicated Stages of the M1 Route Random losses (in thousands of rubles) H (0; 10) K (10; 30) R (0; 20) Selected stages of the M2 route Random losses (in thousands of rubles) N (10; 3) N (8; 2) N (12; 4) Selected stages of the M3 route Random losses (in thousands of rubles) 8 (0; 20) N (6; 2) 8 (0; 25)

The expression R ( a ; b ) denotes the uniform probability distribution law on the interval ( a ; b ) ; in this case, the mathematical expectation is determined by the formula ( a ; b ) /2. The expression Ν ( a ; σ ) denotes the normal law of probability distribution with parameters a and y; in this case the mathematical expectation is determined precisely by the parameter a. The corresponding losses are presented in thousands of rubles.

Assuming that the accidental loss of part of the cargo at the specified stages of the journey is independent, it is required to choose the best route within this risk management model based on minimizing the average expected damage. We estimate the average expected damage for each alternative according to the rules of probability theory.

1) The average expected damage Um1 when delivering cargo along the route Ml is equal to

2) The average expected damage to UM2 when delivering cargo along route M2 is

3) The average expected damage to Us while delivering cargo along the M3 route is

The best solution that minimizes the risk (as the average expected damage) in this situation will be the choice of the M3 route.

For supply chains, risk assessment can be based on various mathematical methods. However, the necessary mathematical methods are too time-consuming for such complex and volatile systems as supply chains.

Consider another example of the use of statistical methods for assessing logistics risks in the supply chain.

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