Operations Research & Linear Programming

1. Operations Research & Linear Programming Agenda • Introduction and History of OR • OR and Methods • Linear Programming • Approaches and Problems solved with OR • Benefits of OR • Conclusion Group 3 • VaheKarapetyan • Dena Rad • EidinBalali • Patrick Njathi • ZhongZheng • DamilareAdeoye

2. Introduction and History of OR • Industrial Revolution • Growing businesses • Department divisions • Limited resources • Came about during WWII • Effectively manage resources • Efficiently deploy new tools • US and British military asked scientists to apply this scientific method to deal with strategic and tactical problems • Success in Air Battle of Britain • Battle of the North Atlantic • OR improvement and implementation after the war • Research for new methods • Solving problems outside of the military • Help of Computers • Development of electronic digital computers • Development of PCs in the 1980s Vahe Karapetyan

3. OR and Methods • Methods • Linear programming • Integer linear programming • Network flow models • Project scheduling • Decision trees • Dynamic programming • Markov chains • Queuing model • Nonlinear programming • Simulation models • Game theory • Inventory theory • Reliability • Discipline of applying advanced analytical methods to help make better decisions • Maximize the profit and minimize risk/cost • All industries • One department • Each division • OR analyst: • Higher manager • Show solution • Decision making, planning, forecasting • Work Around you • Better scheduling of airline crew • Waiting line at Disney Dena Rad

4. Linear Programming • Illustration • Air force • police “entire efficient/optimal solution” • Manufacturing -- product choice • Agriculture -- feed choice • The Transportation Problem • Scheduling • Finance Eidin Balali

5. Approaches and Problems Solved with OR • Approaches • 1. Define problem of interest and gather relevant data. • 2. Formulate a mathematical model to represent the problem. • 3. Develop a computer-based procedure for solutions to the problem. • 4. Test model and refine it as needed. • 5. Prepare for the ongoing application of the model as prescribed by management. • 6. Implement process. • Problems • Critical path analysis or project planning • Floor planning • Network optimization • Routing Process • Supply chain management Patrick Njathi

6. Benefits of OR • Generally speaking, OR improves the effectiveness and the efficiency of an institution, hence some of the benefits offered by OR include: • Decrease Cost or Investment • Increase Revenue or Return on Investment • Increase Market Share • Manage and Reduce Risk • Improve Quality • Increase Throughput while Decreasing Delays • Achieve Improved Utilization from Limited Resources • Demonstrate Feasibility and Workability Zhong Zheng

7. Conclusion • Operations research has had an impressive impact on improving the efficiency of numerous organizations around the world and has done this by increasing the productivity of the economies of various countries. • The goal of OR is to provide rational bases for decision making by seeking to understand and structure complex situations, and to utilize this understanding to predict system behavior and improve system performance. • To arrive at this goal certain approaches and methods could be performed and applied. • Linear Programming being an important method used in OR, it is very effective in finding optimal solutions to a problem. Whether it is used to maximize profits and production or reduce risks and costs, Linear Programming provides a simple method to solving these problems. Damilare Adeoye