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This sounds like a variation on one of Dr. R. E.D. Woolsey's scheduling problems -- given a list of tasks requiring a constrained resource, what is an optimal schedule to get the most bang for the buck.
The original is set in terms of a machine-shop with five heavy drill-presses: build the proper order of the incoming work so as to keep the presses always busy during the shift (down-tune is to be minimized). But, the presses can not be run for more than seven hours per shift with out maintenance. The approach (if memory serves) is:
If K is greater than N, the number of servers (machines), then you a) have more work than you can handle and b) a measure of the value of having another server available. For each bucket, the sum of the resource consumed by the M items gives you that amount of additional work you could perform before running out of gas (the 'head-room'). In addition to giving you an optimal schedule for your servers, this gives you ammunition when Management asks pointed questions. ("Do you really need so many servers?", "Do we have enough capacity?", "How many more servers will we need to add if we double the work load?", etc)
---- OGB In reply to Re: Bin packing problem variation repost (see[834245])
by Old_Gray_Bear
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