7
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Assuming that I should buy 50 items from 25 different vendors with pre-known delivery duration between 2-7 day for each, which day of a week should I place each order so that the delivery days be even and balanced and even as much as possible?

What is the best way to model the simple problem below?

So a simple example is like this:

Items Vendors Delivery     order day of week 
1      v1       2 days       ?
2      v2       3 days       ?
3      v3       4 days       ?
4      v4       7 days       ?
.      .        .            . 
.      .        .            . 
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    $\begingroup$ The problem is not well-defined. Can you explain in greater detail the relationship between the items, vendors, and delivery days? $\endgroup$ – Richard Dec 12 '19 at 6:27
  • $\begingroup$ @Richard, I have added a simple example, So I want to know which day of week ( Monday, Tuesday, ...Sunday) should I place each order so that they deliver in a distributed way( for example if I want to order 16 items deliveries be like: 4 on Monday, 4 Tuesday, 4 Wednesday, 5 Thursday). The delivery duration for items are fixed. $\endgroup$ – Sean Dec 12 '19 at 6:33
  • $\begingroup$ The formatting in your question is confusing. I think you've tried to make a table, but it's come out all on one line. $\endgroup$ – Richard Dec 12 '19 at 6:48
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    $\begingroup$ Do I understand right then that you have 50 items you must order; each item is uniquely associated with a single delay in delivery time; and you must choose when you order the item to somehow balance the number of deliveries arriving on each day? $\endgroup$ – Richard Dec 12 '19 at 6:49
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    $\begingroup$ It seems to me that the most straightforward way to address this problem would be to formulate it as a MIP. It's possible that your problem reduces to something simpler, like the Wagner-Whitin model, but I don't think so. $\endgroup$ – LarrySnyder610 Dec 12 '19 at 13:54

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