1. Koenigsberg Bridge Problem 1 Can you take a walking tour of the town that crosses every bridge once and only once returning to your starting point? (Euler tour or Euler circuit)

2. Trash Pickup, Snow Plow Routing, Mail Delivery, FedEx and UPS Routing 2 Is it possible to plow every street without repeating?

3. Another Type of Routing Problem What is the shortest route passing through Indianapolis, Fort Wayne, Gary, Evansville, and Louisville, returning to the starting point and not passing through any city twice? What type of problem is this? 3

4. 4 10 1 2 2 3 3 4 56 7 8 - 1 7 6 5 4 12 11 10 9 8 Indianapolis Gary Fort Wayne Evansville Louisville Here is a possible route.

5. 5 10 1 2 2 3 3 4 56 7 8 - 1 7 6 5 4 12 11 10 9 8 Indianapolis Gary Fort Wayne Evansville Louisville Here is a shorter one. This is called the travelling salesman problem and is used a lot in truck routing and communication networks. GPS and computer dispatch makes it necessary to resolve these problems while the trucks may be in route.

6. Maximum Flow Systems of Pipes Capacity related to diameter  Oil and gas pipelines  Traffic flow  Communication networks  Water pipes  Sewers  Storm sewers  Drainage ditches/ waterways  Computer networks  Sorting systems (FedEx) 6

7. Location Problems such as the 8 Queens Problem 7 Can you arrange 8 queens on a chessboard so that none are in the same row or column or on the same diagonal? none This can be solved as a maximum flow problem for any size of chess board.

8. Project Planning  Build a facility such as: Distribution center Intermodal facility Factory Retail center  Install an information system  Change technologies  Manufacture a product and design the manufacturing process 8

9. How do you make an apple pie? This is a manufacturing process. Crust  2 cups flour  1 teaspoon salt  ½ cup cooking oil  ¼ cup + 1 tablespoon water Filling  3 cups diced apples  2/3 cup sugar  1 tablespoon flour  ½ teaspoon cinnamon  2 tablespoons butter 9

10. 10 Sift together flour and salt Mix oil and water, beat until creamy Mix oil/water with flour/salt, form into ball Divide ball of dough in half Roll out top crust Roll out bottom crust Peel apples Core apples Dice apples Mix apples with sugar, cinnamon, and flour Put bottom crust in pan Put apple mix in pan Cover apple mix with top crust Dot with butter Bake

11. Project Planning – Like building a distribution center  Arrows represent precedence, dots are tasks  Add times to dots – figure out how long project will take critical path how to divide up tasks between people  how many people needed 11

12. Design of Assembly Lines And Sorting Systems (FedEx)  Assign people to tasks so that everyone has the same amount of work.  Rebalance as workflow changes 12

13. 13 Consumer Retailer Manufacturing Material Flow VISA ® Credit Flow Supplier Wholesaler Retailer Cash Flow Order Flow Schedules What is a Supply Chain?

14. Supply Chain Management Leslie Gardner, Ph.D. Professor Mathematics University of Indianapolis