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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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Sean
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    The problem is not well-defined. Can you explain in greater detail the relationship between the items, vendors, and delivery days? – Richard Dec 12 '19 at 06:27
  • @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. – Sean Dec 12 '19 at 06:33
  • 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. – Richard Dec 12 '19 at 06:48
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    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? – Richard Dec 12 '19 at 06:49
  • Exactly. You got it correctly. – Sean Dec 12 '19 at 06:55
  • So how do the vendors fit into the problem? – Richard Dec 12 '19 at 07:21
  • Vendors have different delivery times for their items. – Sean Dec 12 '19 at 07:38
  • But each item is sold by only one vendor, so each item has only one delivery time associated with it, so the vendors can be dropped from the problem? – Richard Dec 12 '19 at 07:42
  • This items should be ordered everyday week. The process repeats – Sean Dec 12 '19 at 08:50
  • Not necessarily. Sone vendors sell more than one items. – Sean Dec 12 '19 at 12:05
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    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. – LarrySnyder610 Dec 12 '19 at 13:54
  • @Sean: Then I think you may need to explain the question better and provide a more detailed example. – Richard Dec 12 '19 at 18:27
  • @Richard, the problem is exactly as you said; i want to know when to order to balance number of items arriving :) – Sean Dec 12 '19 at 19:33
  • @Sean: So, in your example the number of Items (leftmost) column is fixed, as are the vendors and delivery days, and you wish only to choose the Order Day Of Week to minimize some objective? It still seems as though the vendors don't add any constraint to the problem. – Richard Dec 12 '19 at 21:05
  • Yes. Vendors don’t add any constraint here. True. Just want the delivery of items be balanced. – Sean Dec 12 '19 at 21:39
  • @Sean: So why not just order the items randomly and divide them into 7 groups having roughly $n/7$ items each, then choose the order days so that the items arrive on the day corresponding to their group? – Richard Dec 14 '19 at 08:15

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