Mathematical Models in Decision Making

Advantages of Experimenting with Models

• Experimenting with models has the main advantage of avoiding the risks and costs associated with experimenting with the real situation.

Mathematical Modeling

• Decision variables are typically related to controllable inputs.
• Models where uncontrollable inputs are subject to variation are described as stochastic models.
• The goal of transforming model inputs into output in mathematical modeling is to obtain a desired output or solution.
• The values of decision variables that provide the mathematically-best output in a model are described as optimal solutions.

Solving Mathematical Models

• The approach commonly used to solve mathematical models and identify the best output is optimization.
• The main goal of constructing a Model Problem is to represent a real-world problem in a mathematical framework.

Types of Models

• A logical model is a conceptual representation of a real-world problem, used as a starting point for constructing a mathematical model.
• A physical model, also known as a scale model, involves physical replicas of real objects.

Representation of Real-World Problems

• Mathematical models represent real-world problems by using mathematical equations and algorithms to describe the relationships between variables.

Constructing a Model Problem

• A mathematical model primarily consists of decision variables, objective functions, and constraints.

Iconic and Analog Models

• An iconic model is a physical replica of a real object, whereas an analog model is a representation of a real object or system using a different medium or platform.

Challenges and Limitations

• A common challenge of using mathematical models for practical applications is inaccuracies or simplifications in the model.
• If inaccuracies are identified in a mathematical model, a recommended action is to revise and refine the model.

Implementation of Mathematical Models

• It is important to have a user-friendly system during the implementation of a mathematical model to ensure ease of use and understanding.
• A key consideration for successful implementation and follow-up of a model's results is proper documentation and maintenance of the model.
• A managerial report based on the model's results should be prepared when the results are finalized and validated.
• Special solution procedures are developed for specific mathematical models because different models require customized approaches to solve them efficiently.