In-Depth Notes on Prescriptive Models

Introduction to Models

Models serve to represent real-world systems but are not the actual systems themselves.

A model is defined as a parsimonious representation that is typically vague to encompass a large subset of possible models.

Types of Models

Concrete Models

- Physical Models: Physical representations of systems.
- Schematic Models: Graphical or visual representations.
- Management Models: Models used for managerial decision-making.
- Discrete Event Simulations: These models simulate systems where changes occur at specific points in time.

Abstract Models

- Mathematical Models: These include models described through mathematical expressions, such as Linear Programming (LP).
- Heuristic Models: Utilize algorithms to solve problems and aid decision-making in a computational environment.

Basic Components of a Model

Each model offers a perspective on reality with the following components:

- Abstraction: Models omit or simplify certain details of the real-world system to make it manageable.
- Purpose: Every model has a specific aim it must serve.
- Critical Inputs and Outputs: Only include essential variables needed to achieve its objectives.
- Transformation Process: Once validated, models can be viewed as 'black boxes' where only inputs and outputs are of concern.

Characteristics of Models

- Static vs. Dynamic:
- Static models remain unchanged over time, such as ANOVA.
- Dynamic models incorporate elements changing over time, like Time Series regression.

- Deterministic vs. Stochastic:
- Deterministic models have fixed input-output relationships with no randomness.
- Stochastic models account for random variations in inputs or processes.

- Linear vs. Non-linear:
- Linear models follow a strict mathematical formulation.
- Non-linear models allow more flexibility but are more complex to implement.

- Discrete vs. Continuous:
- Discrete models change at distinct intervals.
- Continuous models change fluidly without fixed increments.

Characteristics of Specific Models

- Discrete Event Simulation (DES):
- Properties: Dynamic, Stochastic, Discrete.

- Linear and Integer Programming (LP/IP):
- Properties: Static, Deterministic, Continuous.

The Modelling Process

1. Define the Business Question: Understand the problem that needs addressing.
2. Identify Outputs: Determine the results that need to be calculated to answer the question.
3. Identify Inputs: Recognize the variables affecting the outputs and assess data availability.
4. Collect Data: Gather necessary data for model parameters.
5. Define Relationships: Establish connections between inputs and outputs.
6. Build the Model: Create the analytical or simulation model.
7. Interpret Results: Analyze output to derive conclusions.
8. Test Scenarios: Perform sensitivity analysis to evaluate different scenarios.
9. Document Findings: Clearly record and present conclusions.
10. Post-Mortem: Reflect on the modelling process to learn for future applications.

Detailed Steps of Modelling Process

1. Problem Definition:
Clearly define the problem, its objectives, and relevant organizational parts.

2. Data Collection:
Collect essential data for estimating parameter values affecting the organization.

3. Model Development:
Develop either an analytical model or a simulation.

4. Model Verification:
Check if the model accurately represents reality.

5. Decision Making:
Analyze the model's outputs and make decisions aligned with organizational goals.

6. Model Communication:
Present findings and recommendations to stakeholders.

7. Model Implementation:
Assist with the practical application of the model while ensuring continuous monitoring for effectiveness.