NDLI: Minimum concave cost flow over a grid network

Content Provider	Springer Nature Link
Author	Nemhauser, George L. He, Qie Ahmed, Shabbir
Copyright Year	2014
Abstract	The minimum concave cost network flow problem (MCCNFP) is NP-hard, but efficient polynomial-time algorithms exist for some special cases such as the uncapacitated lot-sizing problem and many of its variants. We study the MCCNFP over a grid network with a general nonnegative separable concave cost function. We show that this problem is polynomially solvable when all sources are in the first echelon and all sinks are in two echelons, and when there is a single source but many sinks in multiple echelons. The polynomiality argument relies on a combination of a particular dynamic programming formulation and an investigation of the extreme points of the underlying flow polyhedron. We derive an analytical formula for the inflow into any node in an extreme point solution, which generalizes a result of Zangwill (Manag Sci 14(7):429–450, 1968) for the multi-echelon lot-sizing problem.
Ending Page	98
Page Count	20
Starting Page	79
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1
Volume Number	150
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-02-16
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Inventory, storage, reservoirs Mixed integer programming Grid network Network models, deterministic Min concave cost flow Programming involving graphs or networks Mathematical Methods in Physics Production models Lot-sizing model Calculus of Variations and Optimal Control; Optimization Mathematics of Computing Numerical Analysis Combinatorics
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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