Tesi di Laurea Magistrale (sperimentale) - Supply Chain Risk Management: a case study on the most relevant disruptions during the Covid-19 pandemic

4.7. SENSITIVITY ANALYSIS AND TORNADO DIAGRAMS

Following the results of the level partition and based on how the model is structured, the choice

of the two target variables for the sensitivity analysis falls on the two top-level variables

"Quality" (D16) and "Continuity" (D15).

Figure 19: Sensitivity analysis (D13 High; D11 High)

Source: elaborated by the author of the work. 95

Figure 20: Sensitivity analysis (D13 High; D11 Low)

Source: elaborated by the author of the work.

Following the considerations made in section 4.5.5., four different sensitivity analyses were

carried out; one for each combination of the states of the variables "Digitalization" and

"Insurance". These were both initially set to "High". The results of this sensitivity analysis are

presented in Figure 19. Figure 20 shows the sensitivity analysis performed after setting

"Insurance" to the "Low" state and "Digitalization" to the "High" state. Finally, the case with

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"Insurance" set to "High" and "Digitalization" set to "Low" is presented in Figure 26, while the

case where both "Digitalization" and "Insurance" are set to "Low" is presented in Figure 27.

When a sensitivity analysis is performed, the color assumed by the different variables is

indicative of their importance in the calculation of the posterior probability (defined in Chapter

3) distributions for the target nodes. Red nodes are the crucial ones in this respect, and the

intensity of the color is proportional to the importance of the node in question: the more intense

the red, the more important that variable is for the calculation of the posterior probability

distributions for target nodes. Nodes colored white, on the other hand, have no impact on the

calculation of posterior probability distributions and therefore have a sensitivity of 0. The nodes

colored grey indicate that, in that particular simulation, they are set to a probability state with a

probability of 100%. Since they cannot vary, therefore, they do not impact the posterior

probability distributions of the target variables and therefore also have a sensitivity of 0. (GeNIe

Modeler User Manual, 2022)

A comparison between Figure 19 and Figure 20 shows that, with the probability values of all

the other variables being equal, the mere variation of the variable "Insurance" from the "High"

state to the "Low" state significantly changes the probability of the variable "Quality" being in

the "Yes" state: from 69% to 44%. The variable 'Continuity', on the other hand, undergoes a

smaller change and its probability of being in the state 'Yes', with the variable 'Insurance' set to

'Low', goes from 48% to 39%. These changes in the probability of D15 and D16 give an

estimate of the impact in this case of the variable "Insurance" (D11) on the two target variables.

Using Tornado Diagrams, it is possible to observe which parameters are the "most sensitive for

each state of the target variable". These parameters are then presented in descending order of

sensitivity.

Within the tornado diagram, you will find information on the precise position of the node within

the network, the range of changes in the target variables due to the changes of the input

parameter within its range (parameter spread), the magnitude (given by the length of the bar)

and the sign of this change (red indicates a negative change, green a positive change).

Within the "tornado diagram" window, it is possible to customize it by choosing, for example,

the number of variables to show ("Show top" command) and the percentage of variation of all

input variables ("Parameter spread" command). Finally, the x-axis highlights the "absolute

change in the posterior probability" of a specific target when the input parameters undergo a

certain percentage change.

The following explains in detail what the additional information refers to that can be read inside

the grey box if the cursor is placed over a bar. 97

Figure 21: Additional information for a specific bar in a tornado diagram

Source: elaborated by the author of the work.

In Figure 21 The first value that catches the eye in this section is the Target Value Range,

which shows, for each target outcome (corresponding to a single bar in the tornado diagram),

what its minimum and maximum values are in terms of posterior probability. These clearly

depend on the choice made in terms of Parameter Spread. (GeNIe Modeler User Manual, 2022)

Figures 22, 23, 24, 25 instead present the four tornado charts (one for each state of the two

target variables) that refer to the scenario in which both D13 and D11 are in the 'High' state.

Within the Tornado Diagrams, the most sensitive parameters for that particular state of the

target variable under consideration are listed. In the case of Figure 22, for example, the most

sensitive parameters for the state 'Yes' of the target variable D15 (Continuity) are presented.

Figure 22: Tornado Chart for Continuity_D15 = Yes (D13 High; D11 High)

Source: elaborated by the author of the work.

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These are presented in descending order of sensitivity and are characterized by an unambiguous

position in the model: the node or nodes with their own states (which are influenced and

conditioned by the parent nodes and the states assumed by them) are indicated. The color of the

bar relating to a specific parameter indicates the direction of deviation in the probability of the

target state: green indicates a positive variation while red symbolizes a negative variation. The

length of the bar, on the other hand, is an indication of the range of changes and thus indicates

how much the target state varies as the parameter varies. The parameter, however, can vary

within a certain range, which can be set using the "Parameter Spread" command. In the tornado

diagrams proposed here, this value has been set to 10%, which means that the parameter can

vary within this range, increasing or decreasing its current value by 10%.

Figure 23: Tornado Chart for Continuity_D15 = No (D13 High; D11 High)

Source: elaborated by the author of the work.

Observation of Figure 22 shows that the most sensitive parameter for the state

"Continuity=Yes" is the bar containing the following combination: "Quality=Yes | Financial

related disruption=No". In contrast, the strings "Continuity=Yes | Financial performance=Yes |

Quality=Yes", "Financial performance=Yes | Logistics related disruption=No |

Insurance=High" and "Financial performance=Yes | Logistics related disruption=Yes |

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Insurance=High" rank immediately after and represent the second, third and fourth strength in

terms of sensitivity, respectively.

In Figure 24, for example, it is possible to observe on the horizontal axis the absolute variation

in terms of posterior probability for the "Yes" status of the variable "Quality" (D16) associated

with the percentage variation (of 10%). Further information regarding a given bar can be

obtained by positioning the cursor over the bar in question, as shown in Figure 24. In fact, by

positioning the cursor over one of the bars in the tornado diagrams, a grey box appears

summarizing certain information regarding that particular combination of variable states.

Specifically, if we position the cursor over the first bar in Figure 24, we can observe the Target

value range, which gives information about the minimum and maximum values of the posterior

probability for the target state under consideration (in this case Quality=Yes). The Target value

range inevitably depends on the choice of Parameter Spread. The same applies to Parameter

range, which gives information about the minimum and maximum value assumed by the

parameter.

The Current parameter value finally estimates the probability value in the Conditional

probability table of the parameter under consideration (GeNIe Modeler User Manual, 2022).

Figure 24: Tornado Chart for Quality_D16 = Yes (D13 High; D11 High)

Source: elaborated by the author of the work.

100

From Figures 24 and 25 it emerges how, unlike the states "Continuity=Yes" and

"Continuity=No", here the two target states ("Quality=Yes" and "Quality=No") are only

particularly sensitive to the combination "Quality=Yes | Financial related disruption=No". In

particular, the possible variation of the state "Quality=No" is substantial and falls within a range

of 24.69% to 37.81% (with the current value being 31.25%.

Figure 25: Tornado Chart for Quality_D16 = No (D13 High; D11 High)

Source: elaborated by the author of the work.

Figure 26 and Figure 27 show some inconsistencies with regard to the probability values of

the two target variables. These in fact, in the D13 "Low" and D11 "High" scenario presented in

Figure 26, return to be the same as those in the D13 "High" and D11 "High" scenario, meaning

that within the model thus constructed, the variation of "Digitalization" from the "High" state

to the "Low" state has no impact on the probability of "Quality" and "Continuity" being in the

"Yes" state. This result is incongruent with that obtained from the MICMAC analysis, which

assigns a driver power of 14 to "Digitalization", the highest of all the variables in the model.

This inconsistency is confirmed by comparing Figure 20 and Figure 27: in both, "Quality" has

a 39% probability of being in the "Yes" state, while "Continuity" is in the "Yes" state with a

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44% probability. This confirms the irrelevance of one of the crucial variables of the model, such

as "Digitalization".

Figure 26: Sensitivity analysis (D13 Low; D11 High) – ISM Map

Source: elaborated by the author of the work.

102 Figure 27: Sensitivity analysis (D13 Low; D11 Low) – ISM Map

Source: elaborated by the author of the work.

The reason for this inconsistency, however, is due to the construction of the model itself. This,

in fact, makes all the effects of the variables at the bottom of the model (of which

"Digitalization" is also a part) converge on the variable "Logistics-related disruption", which,

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however, has no significant impact on "Financial performance", thus nullifying all the effects

of the variables before it in the model.

Figure 28: CPT for Financial Performance (D14)

Source: elaborated by the author of the work.

Figure 29: Tornado Chart for Continuity_D15 = Yes (D13 High; D11 Low)

Source: elaborated by the author of the work.

104 Figure 30: Tornado Chart for Continuity_D15 = No (D13 High; D11 Low)

Source: elaborated by the author of the work.

With regard to Figures 29, 30, 31 and 32, which depict the Tornado Diagrams referring to the

D13=High | D11=Low scenario, plea