Chapter 7: Transportation Models

Chapter 7: Transportation Models

Chapter 7: Transportation Models

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1. Chapter 7: Transportation Models Skip Ship Routing & Scheduling (pp. 212-214) • Service Selection • Shortest Path • Transportation Problem • Vehicle Routing & Scheduling • One route: TSP • Multiple routes: VRP • Consolidation

2. Service Selection (Mode Selection) • Most important factors: • Dependability (on-time delivery). • Cost. • Safety. • Tracking. • Different modes have different costs and characteristics. • Lowest transportation cost is not always best.

3. Service Selection Tradeoff • Transportation Cost vs. Inventory Cost. • Shorter transit time:  Higher transportation cost.  Fewer days held  Lower inventory cost. • Usually, Shorter transit time  Smaller vehicles.  More frequent trips  Higher transportation cost.  Fewer units held  Lower inventory cost .

4. Service Selection for Competing Suppliers One buyer purchases 1000 cwt from each of two competing suppliers: A and B. Both use rail transport, but could use truck transport. Supplier profit = \$20/cwt - transport cost. Transport CostDelivery Time Rail \$2/cwt 6 days Truck \$5/cwt 3 days Buyer offers to switch 100 cwt to supplier A from B for each day decrease in delivery time. For supplier A: SalesProfit Rail (current) 1000 cwt 1000 cwt (\$20/cwt - \$2/cwt) = \$18,000 Truck 1300 cwt 1300 cwt (\$20/cwt - \$5/cwt) = \$19,500

5. Service Selection for Competing Suppliers What if supplier B also switches to truck? Buyer should give each equal business: SalesProfit Supplier A 1000 cwt 1000 cwt (\$20/cwt - \$5/cwt) = \$15,000 Supplier B 1000 cwt 1000 cwt (\$20/cwt - \$5/cwt) = \$15,000 So both suppliers are worse off than before! (\$15,000 profit vs. \$18,000 using rail)

6. C B A F E D Shortest Path Model • Network includes: • Nodes: cities, customers, demand points • Arcs or Links: Transportation links • Number for each link to represent travel cost, time or distance. 6 6 4 9 5 2 4 3 7

7. Shortest Path Problem • Given: • A network with a specified origin and destination. • The distance (or travel time or cost) for each link. • Determine the shortest path from the origin to the destination. • Solution: Labeling algorithm (one of many) • Nodes are labeled as "solved" or "unsolved". • Solved = shortest path from the origin to that node is known.

8. Shortest Path Labeling Algorithm 1. The origin is a solved node. All others are unsolved. 2. For each solved node, find the one unsolved node that is nearest and calculate the minimum totaldistance (origin to solved node + solved node to nearest unsolved node). 3. Make the unsolved node with the smallest total distance a solved node. 4. Repeat steps 2 and 3 until the destination is a solved node. 5. Trace the shortest path.

9. C B A F E D Shortest Path Example 1 • Find the shortest path from A to F. 27 22 17 10 12 20 16 5 6 18 30

10. C B A F E D Shortest Path Example 1 27 22 * 17 10 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 12 20 16 5 6 18 30

11. C B A F E D Shortest Path Example 1 27 22 * 17 * 10 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C 12 20 16 5 6 18 30

12. C B A F E D Shortest Path Example 1 27 22 * 17 * 10 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A C 12 20 16 5 6 18 30

13. C B A F E D Shortest Path Example 1 27 22 * 17 * 10 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 C 12 20 16 5 6 18 30

14. C B A F E D Shortest Path Example 1 27 22 * 17 * 10 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 C D 26 12 20 16 5 6 18 30

15. C B A F E D Shortest Path Example 1 * 27 22 * 17 * 10 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 12 20 16 5 6 18 30

16. C B A F E D Shortest Path Example 1 * 27 22 * 17 * 10 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A B C 12 20 16 5 6 18 30

17. C B A F E D Shortest Path Example 1 * 27 22 * 17 * 10 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B C 12 20 16 5 6 18 30

18. C B A F E D Shortest Path Example 1 * 27 22 * 17 * 10 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 C 12 20 16 5 6 18 30

19. C B A F E D Shortest Path Example 1 * 27 22 * 17 * 10 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 C D 26 12 20 16 5 6 18 30

20. C B A F E D Shortest Path Example 1 * 27 22 * 17 * 10 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 C D 26 D 26 C-D 12 20 16 5 6 * 18 30

21. * 27 22 17 * 10 12 20 16 5 6 18 30 C B A F E D * * Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B C D

22. * 27 22 17 * 10 12 20 16 5 6 18 30 C B A F E D * * Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B E 32 C E 32 D E 31

23. * 27 22 17 * 10 12 20 16 5 6 18 30 C B A F E D * * * Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B E 32 C E 32 E 31 D-E D E 31

24. * 27 22 17 * 10 12 20 16 5 6 18 30 C B A F E D * * * Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B E 32 C E 32 E 31 D-E D E 31 B D E

25. * 27 22 17 * 10 12 20 16 5 6 18 30 C B A F E D * * * Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B E 32 C E 32 E 31 D-E D E 31 B F 49 D F 44 E F 47

26. * 27 22 17 * 10 12 20 16 5 6 18 30 C B A F E D * * * * Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B E 32 C E 32 E 31 D-E D E 31 B F 49 D F 44 F 44 D-F E F 47

27. Trace Shortest Path Backwards Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 20 C 20 A-C A B 22 B 22 A-B C D 26 A D 30 B E 32 D 26 C-D C D 26 B E 32 C E 32 E 31 D-E D E 31 B F 49 D F 44 F 44 D-F E F 47 A-C-D-F

28. C B A F E D Check Answer 27 22 17 10 12 20 16 5 6 18 30 A-C-D-F Length = 20+6+18 = 44

29. 3 9 3 3 6 1 5 3 E B C D F H G J 2 4 6 11 4 A 1 K 4 6 5 I Shortest Path Example 2 • Find the shortest path from A to K.

30. 3 9 3 3 6 1 5 3 E D H G J F C B 2 4 6 11 4 A 1 K 4 6 5 I 0 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 4 C 4 A-C

31. 3 9 3 3 6 1 5 3 E H F C J G B D 2 4 6 11 4 A 1 K 4 6 5 I 0 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 4 C 4 A-C A C

32. 3 9 3 3 6 1 5 3 E H F C J G B D 2 4 6 11 4 A 1 K 4 6 5 I 6 0 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8

33. 3 9 3 3 6 1 5 3 E H F C J G B D 2 4 6 11 4 A 1 K 4 6 5 I 6 0 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B C

34. 3 9 3 3 6 1 5 3 E C G D B F H J 2 4 6 11 4 A 1 K 4 6 5 I 6 0 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E

35. 3 9 3 3 6 1 5 3 E C G D B F H J 2 4 6 11 4 A 1 K 4 6 5 I 6 0 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E B C E

36. 3 9 3 3 6 1 5 3 E C G D B F H J 2 4 6 11 4 A 1 K 4 6 5 I 6 9 0 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E B D 15 C F 10 E H 9 H 9 E-H

37. 3 9 3 3 6 1 5 3 E C G D B F H J 2 4 6 11 4 A 1 K 4 6 5 I 6 9 0 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path B C E H

38. 3 9 3 3 6 1 5 3 E D G C B F H J 2 4 6 11 4 A 1 K 4 6 5 I 6 9 0 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path B D 15 C F 10 F 10 C-F E I 14 H D 12 10

39. 3 9 3 3 6 1 5 3 E D G C B F H J 2 4 6 11 4 A 1 K 4 6 5 I 6 9 0 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path B D 15 C F 10 F 10 C-F E I 14 H D 12 B C E H F 10

40. 3 9 3 3 6 1 5 3 E D G C B F H J 2 4 6 11 4 A 1 K 4 6 5 I 12 6 9 0 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path B D 15 C F 10 F 10 C-F E I 14 H D 12 B D 15 C I 15 E I 14 H D 12 D 12 H-D F I 14 10

41. 3 9 3 3 6 1 5 3 E D G C B F H J 2 4 6 11 4 A 1 K 4 6 5 I 12 6 9 0 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path C E H F D 10

42. 3 9 3 3 6 1 5 3 E G D C B F H J 2 4 6 11 4 A 1 K 4 6 5 I 12 6 9 0 14 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path C I 15 E I 14 H K 14 K 14 H-K F I 14 D J 15 10 Shortest Length = 14

43. Trace Shortest Path Backwards Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path B D 15 C F 10 F 10 C-F E I 14 H D 12 B D 15 C I 15 E I 14 H D 12 D 12 H-D F I 14 C I 15 E I 14 H K 14 K 14 H-K F I 14 D J 15

44. Trace Shortest Path Backwards Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E B D 15 C F 10 E H 9 H 9 E-H A-C-E-H-K

45. 3 9 3 3 6 1 5 3 E C D G F J H B 2 4 6 11 4 A 1 K 4 6 5 I Check Answer A-C-E-H-K Length = 4+4+1+5 = 14

46. 16 7 8 3 6 5 12 3 E B C D F H G J 12 4 6 10 4 A 1 K 4 16 5 I Shortest Path Example 3 • Find the shortest path from A to K.

47. 16 7 8 3 6 5 12 3 E C G D B F H J 12 4 6 10 4 A 1 K 4 16 5 I 6 0 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E First 3 steps are same as Example 2!

48. 16 7 8 3 6 5 12 3 E C G D B F H J 12 4 6 10 4 A 1 K 4 16 5 I 6 0 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E B C E

49. 16 7 8 3 6 5 12 3 E C G D B F H J 12 4 6 10 4 A 1 K 4 16 5 I 6 0 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E B D 13 C I 14 E H 13 Tie for minimum distance Select both!

50. 16 7 8 3 6 5 12 3 E D G C B F H J 12 4 6 10 4 A 1 K 4 16 5 I 13 6 13 0 8 4 Nearest Total Minimum Solved UnsolvedDistanceNearestDistance Path A C 4 C 4 A-C A B 6 B 6 A-B C E 8 B E 9 C E 8 E 8 C-E B D 13 D 13 B-D C I 14 E H 13 H 13 E-H