# Quantitative Modeling of Supply Chain Disruptions and risks

## Supply Chain Disruptions

The view, during and after a snowstorm when you are safely and warmly tucked inside your home, is beautiful…as shown in the pic of my backyard. But if you have to be on the road during or right after a snowstorm, you know it can be a big pain in the neck.  Events like these are not only disruptive for our day to day life but also to day to day operations of large corporations.

Disruptive events can occur at various scales and the disruption that operations and Supply Chains will face will also vary accordingly. However, organization, in an era where customer is not forgiving and extremely demanding, can’t choose to always be reactive about these disruptions. Detailed planning is a necessity and needs to incorporate both qualitative and Quantitative methods.

## Supply Chain Risk Quantification models

The Risk Quantification models discussed in this section take a broader view of Supply Chain risks and model it as a function of:

• Occurrence
• Impact
• Deductability
• Recovery

These models are modified descriptions of a couple of models that I have been toying with, based on the original models developed primarily for financial services industry. I have been able to translate tow types of models into Supply Chain context but here we will discuss just one of them.

## Value at Risk type Models

These models are for Supply Chain disruption occurences that are Rare, but severe in Impact. Classic examples would be Hurricane, strike, fire, terrorist attack etc. These models were originally developed for the financial industry in the early 1990s where they are now considered as standard measure for market risk and used extensively in portfolio risk management. There is significant mathematics involved in the actual method but I will explain the method using for executives using a Supply Chain example.

### Monte Carlo Simulation approach

In this approach, the number of extreme events during a given period, and their impacts are simulated and aggregated. Thus, each simulation run will consist of the following steps:

Step 1: Sample from the occurrence function to generate the number of risk events during a given period

Step 2: For each risk event, sample from a distribution function to generate its impact, in terms of financial loss

Step 3: Sum the impacts to determine the total loss due to all the events

### Applied in a Supply Chain context

You will probably not find this method applied in a Supply Chain context in any literature so I have created one here to help you understand it better.

A Manufacturer in US wants to evaluate its risks from its suppliers in China. These suppliers are primarily located in Eastern China and therefore flood is a major problem effecting suppliers in these areas. These floods not only impact production but also logistics. As a result of that, the manufacturer suffers looses since they are highly dependent on a major supplier located in this area.

Senior Managers at the manufacturing company want to quantify the risk so that they can either buy business insurance accordingly or renegotiate their contracts with this supplier.

Without going into the Mathematical details (which are intense and use Generalized Extreme Value Distribution (GEVD) function and PWM method), the steps to calculate risk will be as follows:

Get historical Loss data in the format shown below

Year    Number of floods           Loss

2007                3                                \$ 344,000

Impact Function: Using the historical data points, you essentially create a cumulative distribution function model leveraging statistics and then test its fitness (using Kolmogorov- Smirnov method, if you are a nerd and must know).

Occurrence function : Then you define a parameter function, based on the number of events each year. Generally, it has a Poisson distribution (lumpy).

And then, in order to get the final disruption distribution function, you aggregate the impact function and the occurrence function, as explained in the steps below:

Step 1: Generate Poisson random numbers with Lambada = Parameter function calculated for occurence

Step 2: Generate as many uniform random variables as demanded by the frequency (numbers in the second column) and use them as probabilities

Step 3: Based on generated probabilities, find out the corresponding x value from the distribution

Final Step: Sum up the results