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Edexcel D1 scheduling

Discussion in 'Mathematics' started by chocolate_monkey, Mar 13, 2012.

  1. I have Googled thoroughly and drawn a blank with scheduling when you have less than the required number of workers. Everything is telling me to use the smallest latest start time (apart from the Pearson textbook I'm using which says smallest latest finish time, which I've tried too!).
    However I just can't get my head around a question from the Pearson textbook (p168 qu. 19 e), also in a past paper (January 2002 qu. 7e). I'm happy with scheduling worker 1 to do A then C and worker 2 to start off on B but could someone please explain to me why I then need to schedule worker 2 to do activity G (instead of activity D as I think it should be)? I've worked it through with activity D there instead and get a solution of 25 hours minimum, so I can see the solution in the book/answer scheme is better by 1 hour. I just can't see how I should know to put G instead of D for worker 2! Any help would be very very much appreciated. It's my first time teaching D1 so I'm struggling to work out how to explain this to pupils.
    Thanks.
     
  2. I have Googled thoroughly and drawn a blank with scheduling when you have less than the required number of workers. Everything is telling me to use the smallest latest start time (apart from the Pearson textbook I'm using which says smallest latest finish time, which I've tried too!).
    However I just can't get my head around a question from the Pearson textbook (p168 qu. 19 e), also in a past paper (January 2002 qu. 7e). I'm happy with scheduling worker 1 to do A then C and worker 2 to start off on B but could someone please explain to me why I then need to schedule worker 2 to do activity G (instead of activity D as I think it should be)? I've worked it through with activity D there instead and get a solution of 25 hours minimum, so I can see the solution in the book/answer scheme is better by 1 hour. I just can't see how I should know to put G instead of D for worker 2! Any help would be very very much appreciated. It's my first time teaching D1 so I'm struggling to work out how to explain this to pupils.
    Thanks.
     
  3. There are several cases in D1 where there is no perfect algorithm that always provides the optimum solution, e.g. full bin packing. The problem of scheduling with limited workers is one of these, which is why different texts use slightly different methods to try to get to an optimum solution. In a question like this one, as there are only two workers and not many activities, it is easy to get the solution by inspection (or a bit of trial and error). I always tell my students to check their solution for questions of this type as they may be able to find a better one.

    Good luck with teaching D1. I've been teaching it for 3 years now and I enjoy it more each time.
     
  4. Thank you very much! This was roughly the conclusion I had come to, it was just that the book (and other places online) seemed to be suggesting you could apply rules like picking the smallest latest start time, etc. which made me think there must be an algorithm for the optimal solution. Will happily tell my pupils tomorrow to treat it as a problem solving exercise and be prepared to try out different solutions.
    Thanks also for the encouragement - I taught M1 last year and I must admit I think D1 is working out better for our pupils (most of whom don't do physics) and, consequently, I'm enjoying teaching it much more!
     

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