Operations Research Overview and Models

Operations Research Definition and Scope

• Operations Research (OR) is a discipline that uses advanced analytical methods to help make better decisions.
• Scope encompasses optimization techniques, statistical analysis, simulation, and decision analysis.
• Aim is to improve efficiency and productivity in various sectors, including manufacturing, services, logistics, and healthcare.

Advantages and Functions of OR

• Provides quantitative data for decision-making.
• Facilitates complex problem-solving through modeling techniques.
• Enhances performance by optimizing resources and processes.
• Functions include resource allocation, scheduling, and risk management.

Applications of OR

• Used in supply chain management for optimizing logistics.
• Applied in finance for portfolio optimization and risk assessment.
• Employed in transportation for route optimization and scheduling.

Limitations of OR

• Predicted outcomes may rely heavily on assumptions and models.
• Complex models can be difficult to communicate and understand.
• Requires high-quality data for accurate results, which may not always be available.

Waiting Line Models

• Finite Population Model: Limits the number of potential customers, relevant in scenarios like bank queues.
• Infinite Population Model: Assumes an infinite number of incoming customers, applicable to service systems like call centers.

Applications of Simulation

• Utilized in system design to test performance under varying conditions.
• Helps in forecasting demand and assessing risks in business.
• Enables training and operational planning by mimicking real-world processes.

Applications of Markov-Chain Model

• Used in predicting future states of a system based on current states.
• Applicable in inventory management and queueing systems.
• Effective in modeling customer behavior patterns.

Transportation Model

• Optimizes shipping routes and costs while meeting supply and demand constraints.
• Example: Minimizing transportation costs from multiple plants to various sales centers.

Assignment Model

• Focuses on assigning resources efficiently to tasks to minimize costs.
• Example: Assigning workers to tasks while optimizing team performance.

Replacement Model

• Determines the optimal timing for replacing existing assets to minimize costs.
• Example: Assessing the lifecycle of machinery to decide replacement timing.

Game Theory

• Analyzes competitive situations to determine optimal strategies for players.
• Example: Price wars between competing firms or negotiation scenarios.

LPP Model

• Linear Programming Problem (LPP) focuses on maximizing or minimizing a linear objective subject to constraints.
• Example: Resource allocation decisions in production systems.

LPP Problem – Simplex Table Method

• Objective Function: Maximize ( z = 21x_1 + 15x_2 ).
• Constraints:
  • ( -x_1 - 2x_2 \geq -6 ) (can be converted to ( x_1 + 2x_2 \leq 6 ))
  • ( 4x_1 + 3x_2 \leq 12 )
• Non-negativity constraints: ( x_1 \geq 0 ), ( x_2 \geq 0 ).

Transportation Problem – VAM and MODI Method

• Setup involves optimizing transportation cost from plants to sales centers based on supply and demand.
• Apply VAM (Vogel’s Approximation Method) for initial feasible solution.
• Test optimality using the MODI (Modified Distribution) method.

Hungarian Method for Project Assignment

• Objective is to assign projects to contractors at minimum total cost.
• Matrix setup compares costs for each contractor-project assignment.
• Example matrix displays costs, facilitating the selection of optimal assignments.

This quiz covers key concepts in Operations Research, including its definition, scope, advantages, and various applications. It also discusses different Waiting Line Models, Simulation applications, and the Markov-Chain Model. Additionally, students will explore important models such as Transportation, Assignment, Replacement, Game Theory, and Linear Programming.