Operation Research PDF

**Operation Research** **Introduction of Operation Research** **Operation Research** is a scientific approach to decision-making, using mathematical models and analysis to optimize complex systems. 》》It is popular because it helps businesses optimize processes, improve efficiency, minimize cost...

**Operation Research** **Introduction of Operation Research** **Operation Research** is a scientific approach to decision-making, using mathematical models and analysis to optimize complex systems. 》》It is popular because it helps businesses optimize processes, improve efficiency, minimize costs, and make data-driven decisions, ultimately leading to increased productivity and competitive advantage. ! ! Goal ! ! - **Origin and Development** 》It\'s main origin was during the World War \|\|. The military leaders needed to optimize the use of limited resources. 》 Post-War Growth - **Key Pioneers🔑** - - - - - - **Introduction to Linear Programming** **Linear Programming** is a mathematical method for determining a way to achieve the best outcome in a given mathematical model. 》APPLICATION AREAS: - - - - - **Problem Formulation of Linear Programming** Components of LP 1. 2. 3. **Objective Function** 》It represents the goal of the linear programming problem. Example: - P=𝑐\_1x+𝑐\_2y **Identifying Decision Variables** 》 A variables that decision-makers will control. Example: - - **Establishing Constraints** 》 It is a conditions that limit the decision variables. Example: - **Characteristics of Linear Programming Problems** 1. - 2. - 3. - 4. - 5. - - 6. - **Application of Linear Programming** - - - Summary: **Linear programming** is a powerful tool for optimization, characterized by its linearity, additivity, and certainty. Problem Solving Examples: Problem \# 1: PROBLEM \# 2: PROBLEM \# 3 & 4: