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← 10ps-04 Many Vans Solution

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Showing Revision 1 created 10/24/2012 by Amara Bot.

  1. So if we look at this, it's actually the case that n vans splitting up the work.

  2. We'll take quite a bit less time from when they need to deliver the mail to when they get back to base.
  3. Now, there might be some cases where it doesn't actually help out too much.
  4. For example, if you have a graph where it's just a straight line
  5. well then all the n vans are going to go here and here and here and here,
  6. and then dot, dot, dot, dot,--well, you haven't really save any time.
  7. However, if you have instead a graph like this, well then, you can have four vans
  8. each go out on one of the arms and come back to base instead of having a single van
  9. that would have to go here and come back and here and back,
  10. and here and back, and here and back.
  11. That's quite a bit more time.
  12. You don't want to have to do that and that's why you used more vans and it turns out
  13. that the time delivered the mail and return is always going to be less than or equal to
  14. depending on the actual case.
  15. Now, how bout the sum of time taken by the vans.
  16. This is going to be at least as much as and maybe more.
  17. To see this, let's actually take a look at those same two problems.
  18. In this case, it takes an hour to leave base and go along the road
  19. to where you're delivering the mail and then an hour to come back.
  20. This is a very long delivery route.
  21. Then if you have four vans then the time taken is two hours for each van
  22. which would be eight hours which in this case is actually the same.
  23. Now, the other case where you have to go along here.
  24. Now let's say if you have four vans then, well, neither van come up here and then go back.
  25. Neither van to come up here and go back and then come up here and go back
  26. and then come up here and go back, that's actually the quickest you can do it
  27. while still utilizing all four vans.
  28. In that case, you're taking two hours there, four hours there, six hours there, and eight hours there.
  29. Instead if one man, he will just take one, two, three, four, five, six, seven, eight total.
  30. So the actual total time taken is quite a bit larger in this case.
  31. So, it really depends on what you all want to optimize.
  32. Generally, the time that it takes to deliver all the mail is probably more important
  33. to most people than the sum of the individual driver's time
  34. and it's really a trade off which is one is better here.