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By David Simchi-Levi
Fierce pageant in ultra-modern international marketplace presents a robust motivation for constructing ever extra refined logistics platforms. This booklet, written for the logistics supervisor and researcher, provides a survey of the trendy thought and alertness of logistics. The aim of the publication is to present the cutting-edge within the technological know-how of logistics management. As a outcome, the authors have written a well timed and authoritative survey of this box that many practitioners and researchers will locate makes a useful spouse to their paintings.
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Extra resources for The logic of logistics: Theory, algorithms, and applications for logistics and supply chain management
Example text
In addition, a bin is said to be opened when an item is placed in a bin that was previously empty. 2, is based on the following observation. Recall XF=FF or BF. 3 Consider the j th bin opened by XF (j ≥ 2). Any item that was assigned to it before it was more than half full does not fit in any bin opened by XF prior to bin j . Proof. The property is clearly true for FF, and in fact holds for any item assigned to the j th bin, j ≥ 2, not necessarily to items assigned to it before it was more than half full.
We consider three cases. First, suppose bXFD (L) 3p for some integer p ≥ 1. Consider the bin with index 2p + 1. If this bin contains a 2 XFD b (L). Otherwise, large item we are done, since in that case b∗ (L) > 2p 3 bins 2p + 1 through 3p must contain at least 2p − 1 small items, none of which can fit in the first 2p bins. Hence, the total sum of the item sizes exceeds 2p − 1, meaning that b∗ (L) ≥ 2p 23 bXFD (L). Suppose bXFD (L) 3p + 1. If bin 2p + 1 contains a large item we are done. Otherwise, bins 2p + 1 through 3p + 1 contain at least 2p + 1 small items, none of which can fit in the first 2p bins, implying that the total sum of the item sizes exceeds 2p and hence b∗ (L) ≥ 2p + 1 > 23 bXFD (L).
The SI P (r) heuristic generates pairs of items, one item from Nj and one from N j , for every j 1, 2, . . , r −1. The items in N0 ∪N r are put in individual bins; one bin is assigned to each of these items. For any j 1, 2, . . , r − 1, we arbitrarily match one item from Nj with exactly nj , then all the items in one item from N j ; one bin holds each such pair. If nj j j Nj ∪N are matched. If, however, nj n , then we can match exactly min{nj , nj } pairs of items. The remaining |nj − nj | items in Nj ∪ N j that have not yet been matched are put one per bin.