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If you are given 30 trucks with 30 different delivery schedules (Monday - Sunday). Each truck has total of 82 deliveries in a given week:

For Example:

    List 1 (7   14  8   13  10  13  17)
    List 2 (12  13  10  15  8   14  10)
...
    List 30 (8  13  10  14  7   17  13)

Each truck delivers Monday - Sunday (Mon Tues Wed Thurs Fri Sat Sun). You are only allowed to choose a max combination of 13 different truck schedules of the 30 total. How do you choose the best combination of trucks to maximize your distribution (most amount of deliveries per day while having the smallest amount of variance between each day) throughout the week?

I want to have the most evenly distributed deliveries in a given week. So I would think that I would want to choose the deliveries with the least amount of variance from each other?

Euxitheos
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  • What do you mean by "maximize your distribution"? And how does "quarter" relate? Did you mean "week"? – quasi Oct 29 '17 at 00:39
  • Updated the description – Euxitheos Oct 29 '17 at 05:50
  • A possible alternative goal: How about maximizing the least daily delivery amount? – quasi Oct 29 '17 at 05:59
  • Wouldn’t that lead to the opposite solution? – Euxitheos Oct 29 '17 at 06:01
  • By maximizing the least daily delivery amount, I mean find a schedule such that the daily distribution totals $(d_1,...,d_7)$ has the largest possible value of $d_{\text{min}}$, where $d_\text{min} = \min(d_1,...,d_7)$. – quasi Oct 29 '17 at 06:05
  • In any case, whatever you choose as an objective function, my sense is that the easiest and most practical approach is to write a program that checks all choices of $13$ trucks from $30$. If implemented in C, the program would run in less than a minute, probably far less. – quasi Oct 29 '17 at 06:08
  • What about Python? – Euxitheos Oct 29 '17 at 06:09
  • Slower by a factor of maybe $100$, but still OK. – quasi Oct 29 '17 at 06:09
  • So if I implement this in C, is the program generating all the possible combinations of the numbers then sorting the solution based on which combination of 13 trucks gives me the largest value of dmin? What type of problem does this fall under/categorized as? – Euxitheos Oct 29 '17 at 17:07

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