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Given n items of different weights and bins each of capacity c, assign each item to a bin such that number of total used bins is minimized. It may be assumed that all items have weights smaller than bin capacity.
The BIN PACKING decision problem asks the question whether – given a set of objects of distinct sizes, and a set of bins with specific capacity – there is a distribution of items to bins such that no item is left unpacked nor the capacity of any bin is exceeded.
The best existing algorithm for optimal bin packing is due to Martello and Toth (Martello & Toth 1990a; 1990b). We present a new algorithm for optimal bin packing, which we call bin completion, that explores a different problem space, and appears to be asymptotically faster than the Martello and Toth algorithm.
The problem of material requirements planning can be formalized as a bin-packing problem, which can be solved using a mixed-integer linear program (MILP).
You have n1 items of size s1, n2 items of size s2, and n3 items of size s3. You'd like to pack all of these items into bins each of capacity C, such that the total number of bins used is minimized.
How can we achieve a solution using minimum number of bins? Greedy isn't surely working.
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