#### Quantifying Decisions Under Uncertainty

There are modeling approaches for predicting outcomes under **low uncertainty settings** and a different modeling approach for predicting outcomes **under high uncertainty**. Linear programming, under low uncertainty settings, allows us to calculate an objective function and determine if the solution is feasible based on resource constraints. For high uncertainty settings we need to calculate the distribution for the key performance indicators and compare the distributions of outcomes.

Steps to calculate the distribution of the **sales performance** KPI for a product under high levels of uncertainty:

- Define the KPI: Total number of units sold.
- Collect data: Collect data on the total number of units sold over a month.
- Calculate the average: Calculate the average number of units sold per day.
- Calculate the standard deviation: Calculate the standard deviation of the number of units sold per day.
- Plot the distribution: Plot the distribution of the number of units sold per day using a histogram or a box plot.

Roadmap for making decisions in high uncertainty environments:

- Confirm risk and reward measures
- Use simulation for each competing decision to estimate reward and risk measures via a distribution:
- Normal distribution
- Bernoulli
- Binomial
- Poisson
- Patterned
- Discrete
- Optimize reward (Demand Volume) as an objective function with risk measures as constraints
- Results of the simulations can be fed into an optimizer forming an effective management decisioning tool set

#### Digital Twins

A digital twin is a virtual representation of a physical object or system that is updated in real-time using data from sensors and other sources. It uses simulation, machine learning, and reasoning to help decision making. Digital twins are used to simulate the behavior of physical objects, systems, or processes to better understand how they work in real life. They can be used to study performance issues, generate possible improvements, and create valuable insights, which can then be applied back to the original physical object. There are various types of digital twins depending on the level of product magnification, such as component twins, parts twins, asset twins, and system or unit twins. Digital twins are used in various industries and applications, such as manufacturing, healthcare, and transportation.

###### Simulation of Manufacturing Processes

SAP HANA is an in-memory database and application development platform that provides real-time data processing and analytics capabilities. R is a popular open-source programming language for statistical computing and graphics. SAP HANA provides integration with R through the RLANG procedure, which allows embedding R code in SAP HANA SQL code and execute it using the external R environment. We use R to perform statistical analysis, data mining, and machine learning on data stored in SAP HANA.

Additionally, R is software tool used to simulate manufacturing processes, that is to create a **Digital Twin**. We use a simulation package in R for discrete-event simulation that allows us to create statistical variables required for simulation, define process trajectory, define and assign resources, define arrivals, run simulation in R, store results in data frames, plot charts, and interpret the results.

To simulate a manufacturing process, working with your organization, TekMetrix will create process maps, gather data, build and test the simulation mathematical models, and work with your organization to analyze and interpret the results.

**Delivery Methods**

- Build a virtual representation of the supply chain using R or equivalent
- Select the simulation technique:
- Enterprise modeling and simulation - create a Digital Twin of the manufacturing system to optimize various aspects of production planning, inventory management and resource allocation
- Data-driven simulation - using data and analytics with machine learning create a predictive model of the manufacturing system to optimize production scheduling, quality control and maintenance
- Process simulation - simulate individual business processes within the manufacturing system to identify bottlenecks, optimize resource alloction and improve efficiency
- Agent-based simulation - simulate the behavior of individual agents within the manufacturing system such as unit operations, machines, workers and customers to optimize production scheduling, resource allocation and customer service
- Discrete event simulation - simulate the flow of discrete events within the manufacturing system such as the arrival of raw materials, processing of parts and shipment of finished goods. Businesses can optimize various aspects of production scheduling, inventory management and quality control
- Monte Carlo - model project timelines seeking to optimize resources and used for financial forecasting
- Dynamic simulations - time based simulation models coded as solutions to partial differential equations.

- Engage TekMetrix Supply Chain Diagnostics
- Optimize customer value by leveraging innovation, transparency, efficiency and resillence in the supply chain
- Find new sources of innovation and value creation using the simulations
- Create sustainable value for your organization