The assignment problem is a kind of linear programming problem, but the hungarian method is a quicker algorithm for solving it.

1. Lesson 31 The Assignment Problem Math 20 Algebra and Multivariable Mathematics for Social Sciences December 10, 2007

4. Na ïve Solution—Guess #1 Total Cost = 53 + 87+ 36 = 176 36 92 60 C 41 87 47 B 37 96 53 A Bldg3 Bldg2 Bldg1

5. Na ïve Solution—Guess #2 Total Cost = 53 + 92+ 41 = 186 36 92 60 C 41 87 47 B 37 96 53 A Bldg3 Bldg2 Bldg1

6. Na ïve Solution—Guess #3 Total Cost = 47 + 96 + 36 = 179 36 92 60 C 41 87 47 B 37 96 53 A Bldg3 Bldg2 Bldg1

7. Na ïve Solution—Guess #4 Total Cost = 47 + 92 + 37 = 176 36 92 60 C 41 87 47 B 37 96 53 A Bldg3 Bldg2 Bldg1

8. Na ïve Solution—Guess #5 Total Cost = 47 + 96 + 41 = 197 36 92 60 C 41 87 47 B 37 96 53 A Bldg3 Bldg2 Bldg1

9. Na ïve Solution—Guess #6 Total Cost = 60 + 87 + 37 = 184 36 92 60 C 41 87 47 B 37 96 53 A Bldg3 Bldg2 Bldg1

10. Na ïve Solution—Completion 36 92 60 C 41 87 47 B 37 96 53 A 3 2 1 36 92 60 C 41 87 47 B 37 96 53 A 3 2 1 36 92 60 C 41 87 47 B 37 96 53 A 3 2 1 36 92 60 C 41 87 47 B 37 96 53 A 3 2 1 36 92 60 C 41 87 47 B 37 96 53 A 3 2 1 36 92 60 C 41 87 47 B 37 96 53 A 3 2 1

12. Rates of Growth

18. On our given matrix

26. Solutions

27. Na ïve Solution—Completion 36 92 60 C 41 87 47 B 37 96 53 A 3 2 1 36 92 60 C 41 87 47 B 37 96 53 A 3 2 1 36 92 60 C 41 87 47 B 37 96 53 A 3 2 1 36 92 60 C 41 87 47 B 37 96 53 A 3 2 1 36 92 60 C 41 87 47 B 37 96 53 A 3 2 1 36 92 60 C 41 87 47 B 37 96 53 A 3 2 1

36. Solutions

38. Integerizing the Matrix

39. Non-negativizing the Matrix

40. Covering the Zeroes Can do it with three!

41. Find Smallest Uncovered Entry

42. Subtract and Add

43. Cover Again Still three!

44. Find Smallest Uncovered

45. Subtract and Add

46. Cover Again Done!

47. Solutions Done!

48. Solutions Total Cost = 27.5