Minimizing separable convex objectives on arbitrarily directed trees of variable upperbound constraints

Minimizing separable convex objectives on arbitrarily directed trees of variable upperbound constraints

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Article ID: iaor1992321
Country: United States
Volume: 16
Issue: 3
Start Page Number: 504
End Page Number: 533
Publication Date: Aug 1991
Journal: Mathematics of Operations Research
Authors: ,
Keywords: inventory
Abstract:

An extension of the Economic Order Quantity (EOQ) model to multi-stage production-distribution systems and the isotonic regression problem are known to be equivalent and to be solvable in O(N4) time. The following specializations of the model are solvable in O(NlogN) time: joint replenishment systems, pure assembly systems, nested policies in pure distribution systems, nonnested policies in one-warehouse multi-retailer systems, nested policies in multi-item, one-warehouse, multi-retailer systems, and systems in which the underlying network is a series-parallel digraph. The authors show here that a generalization of this problem is solvable in O(NlogN) time whenever the undirected version of the underlying network is a tree. The algorithm they propose is used as a subroutine in an algorithm solving the EOQ problem on general circuitless directed graphs, the subject of a compansion paper.

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