Introduction to Design and Manufacture Supply Chain Analysis (K. Khammuang & H. S. Gan) A scientific approach to decision making, which seeks to determine how best to design and operate a system under condition requiring the allocation of scarce resources What is Operations Research (OR)?

Introduction to Design and Manufacture Supply Chain Analysis (K. Khammuang & H. S. Gan) 1.Formulate the problem 2.Observe the system 3.Formulate the mathematical model of the problem 4.Verify the model and use the model for Prediction 5.Select a suitable alternative 6.Present the results and Conclusion of the study of the organization 7.Implement and evaluate recommendations The Methodology of OR (Winston 1994)

Introduction to Design and Manufacture Supply Chain Analysis (K. Khammuang & H. S. Gan) The traveling salesman must visit every city in his area and return home. The objective is to find the routing with the shortest distanceThe traveling salesman must visit every city in his area and return home. The objective is to find the routing with the shortest distance -Symmetric TSP (where distance from city j to k is the same as from k to j) - Asymmetric TSP The Traveling Salesman Problem (TSP)

Introduction to Design and Manufacture Supply Chain Analysis (K. Khammuang & H. S. Gan) Consider 5 city symmetric TSP problem.The search space could be the set of permutation of 5 cities Consider 5 city symmetric TSP problem.The search space could be the set of permutation of 5 cities , , , , are the identical route , , , , are the identical route. Since the problem is symmetric and are also identical, we can shrink the search space by one-half.Since the problem is symmetric and are also identical, we can shrink the search space by one-half. 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. The Traveling Salesman Problem (TSP)

Introduction to Design and Manufacture Supply Chain Analysis (K. Khammuang & H. S. Gan) A 20 city TSP has about 10,000,000,000,000,000 possible solutionsA 20 city TSP has about 10,000,000,000,000,000 possible solutions A 6-city TSP has 60 possible solutions A 6-city TSP has 60 possible solutions A 10 city TSP has about 181,100 possible A 10 city TSP has about 181,100 possiblesolutions If we consider n! city, the size of the search space is (n-1)!/2If we consider n! city, the size of the search space is (n-1)!/2 A 50 city TSP has about 10,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000 possible solutionsA 50 city TSP has about 10,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000 possible solutions The Traveling Salesman Problem (TSP)

Introduction to Design and Manufacture Supply Chain Analysis (K. Khammuang & H. S. Gan) 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 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 In 1994, Applegate, et. al. solved a traveling salesman problem which models the production of printed circuit boards having 7,397 holes (cities).In 1994, Applegate, et. al. solved a traveling salesman problem which models the production of printed circuit boards having 7,397 holes (cities). Practical examples of TSP

Introduction to Design and Manufacture Supply Chain Analysis (K. Khammuang & H. S. Gan) Classical Method Classical Method - Linear Programming - Linear Programming - Integer Programming etc. Heuristics Heuristics - Solution Method especially designed to solve or provide a good solution for a specific problem OR Techniques

Introduction to Design and Manufacture Supply Chain Analysis (K. Khammuang & H. S. Gan) Evolutionary algorithms and other local search technique Evolutionary algorithms and other local search technique - Genetic algorithm (GA) - Ant colony etc. OR Techniques

Introduction to Design and Manufacture Supply Chain Analysis (K. Khammuang & H. S. Gan) Simulation Simulation -Use when optimization is inappropriate -The problem is too complicated to formulate as an efficient optimization model. - Input data is unreliable. -Useful when consider the “What if?” scenario -Assuming input data is precisive, the output are valid -However, the major disadvantage of simulation is that it is time-consuming OR Techniques

Introduction to Design and Manufacture Supply Chain Analysis (K. Khammuang & H. S. Gan) Data collection Data collection Selecting input distributions Selecting input distributions Selecting alternative configurations Selecting alternative configurations Creating simulation models Creating simulation models Validating simulation models Validating simulation models Running the models Running the models Analysis of outputs Analysis of outputs Design of experiment Design of experiment Comparing alternatives Comparing alternatives Selecting the best alternative Selecting the best alternative Steps in simulation

Introduction to Design and Manufacture Supply Chain Analysis (K. Khammuang & H. S. Gan) The Difficulty of Problems in OR The size of the search space is so largeThe size of the search space is so large Simplification of the problemSimplification of the problem Change over time (uncertainty)Change over time (uncertainty) ConstraintsConstraints The Difficulty of Problems in OR