What is Operations Research (OR)? <ul><li>A scientific approach to decision making, which seeks  </li></ul><ul><li>to dete...
The Methodology of OR (Winston 1994) <ul><li>Formulate the problem </li></ul><ul><li>Observe the system </li></ul><ul><li>...
The Traveling Salesman Problem (TSP) <ul><li>The traveling salesman must visit every city in his area and return home. The...
The Traveling Salesman Problem (TSP) <ul><li>Consider 5 city symmetric TSP problem.The search space could be the set of pe...
<ul><li>A 20 city TSP has about 10,000,000,000,000,000 possible solutions </li></ul>The Traveling Salesman Problem (TSP) <...
Practical examples of TSP <ul><li>A factory produces cars in various colors where there are  n  color altogether. We want ...
OR Techniques <ul><li>Classical Method </li></ul><ul><li>- Linear Programming </li></ul><ul><li>- Integer Programming </li...
OR Techniques <ul><li>Evolutionary algorithms and other local search technique </li></ul><ul><li>- Genetic algorithm (GA) ...
OR Techniques <ul><li>Simulation </li></ul><ul><li>-Use when optimization is inappropriate </li></ul><ul><ul><li>-The prob...
Steps in simulation Data  collection Selecting  input  distributions Selecting  alternative  configurations Creating  simu...
The Difficulty of Problems in OR The Difficulty of Problems in OR <ul><li>The size of the search space is so large </li></...
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first part

  1. 1. What is Operations Research (OR)? <ul><li>A scientific approach to decision making, which seeks </li></ul><ul><li>to determine how best to design and operate a system under </li></ul><ul><li>condition requiring the allocation of scarce resources </li></ul>
  2. 2. The Methodology of OR (Winston 1994) <ul><li>Formulate the problem </li></ul><ul><li>Observe the system </li></ul><ul><li>Formulate the mathematical model of the problem </li></ul><ul><li>Verify the model and use the model for Prediction </li></ul><ul><li>Select a suitable alternative </li></ul><ul><li>Present the results and Conclusion of the study of the organization </li></ul><ul><li>Implement and evaluate recommendations </li></ul>
  3. 3. The Traveling Salesman Problem (TSP) <ul><li>The traveling salesman must visit every city in his area and return home. The objective is to find the routing with the shortest distance </li></ul><ul><li>Symmetric TSP (where distance from city j to k is the same as from k to j) </li></ul><ul><li>- Asymmetric TSP </li></ul>
  4. 4. The Traveling Salesman Problem (TSP) <ul><li>Consider 5 city symmetric TSP problem.The search space could be the set of permutation of 5 cities </li></ul><ul><li>1-2-3-4-5, 2-3-4-5-1, 3-4-5-1-2, 4-5-1-2-3, 5-1-2-3-4 are the identical route. </li></ul><ul><li>Since the problem is symmetric 1-2-3-4-5 and 5-4-3-2-1 are also identical, we can shrink the search space by one-half. </li></ul><ul><li>Since there are 5! Ways to permute 5 numbers, the size of the search space is = 5!/(2*5) = (5-1)!/2 = 12 possible solutions. </li></ul>
  5. 5. <ul><li>A 20 city TSP has about 10,000,000,000,000,000 possible solutions </li></ul>The Traveling Salesman Problem (TSP) <ul><li>A 6-city TSP has 60 possible solutions </li></ul><ul><li>A 10 city TSP has about 181,100 possible </li></ul><ul><li>solutions </li></ul><ul><li>If we consider n! city, the size of the search space is (n-1)!/2 </li></ul><ul><li>A 50 city TSP has about 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 possible solutions </li></ul>
  6. 6. Practical examples of TSP <ul><li>A factory produces cars in various colors where there are n color altogether. We want to find an production schedule that will minimize the total cost of painting the cars. However, switching from one color to another incur cost. Each job can be viewed as a city and the distance between cities is the cost of color switching cost </li></ul><ul><li>In 1994, Applegate, et. al. solved a traveling salesman problem which models the production of printed circuit boards having 7,397 holes (cities). </li></ul>
  7. 7. OR Techniques <ul><li>Classical Method </li></ul><ul><li>- Linear Programming </li></ul><ul><li>- Integer Programming </li></ul><ul><li>etc. </li></ul><ul><li>Heuristics </li></ul><ul><li>- Solution Method especially designed to solve or provide a good solution for a specific problem </li></ul>
  8. 8. OR Techniques <ul><li>Evolutionary algorithms and other local search technique </li></ul><ul><li>- Genetic algorithm (GA) </li></ul><ul><li>- Ant colony </li></ul><ul><li>etc. </li></ul>
  9. 9. OR Techniques <ul><li>Simulation </li></ul><ul><li>-Use when optimization is inappropriate </li></ul><ul><ul><li>-The problem is too complicated to formulate as an efficient optimization model. </li></ul></ul><ul><ul><li>- Input data is unreliable. </li></ul></ul><ul><li>-Useful when consider the “ What if?” scenario </li></ul><ul><li>-Assuming input data is precisive, the output are valid </li></ul><ul><li>-However, the major disadvantage of simulation is that it is time-consuming </li></ul>
  10. 10. Steps in simulation Data collection Selecting input distributions Selecting alternative configurations Creating simulation models Validating simulation models Running the models Analysis of outputs Design of experiment Comparing alternatives Selecting the best alternative Steps in simulation
  11. 11. The Difficulty of Problems in OR The Difficulty of Problems in OR <ul><li>The size of the search space is so large </li></ul><ul><li>Simplification of the problem </li></ul><ul><li>Change over time (uncertainty) </li></ul><ul><li>Constraints </li></ul>

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