We consider Newton methods for common types of single commodity and multi-commodity network flow problems. Despite the potentially very large dimension of the problem, they can be implemented using the conjugate gradient method and low-dimensional network operations, as shown nearly thirty years ago. We revisit these methods, compare them to more recent proposals, and describe how they can be i...

it is well known that in operations research‎, ‎degeneracy can cause a cycle in a network‎ ‎simplex algorithm which can be prevented by maintaining strong‎ ‎feasible bases in each pivot‎. ‎also‎, ‎in a network consists of n arcs‎ ‎and m nodes‎, ‎not considering any new conditions on the entering‎ ‎variable‎, ‎the upper bound of consecutive degenerate pivots is equal‎ $left( ‎begin{array}{c}‎ ‎n...

While multi-commodity flow is a classical combinatorial optimization problem, it also directly addresses a number of practically important issues of congestion and bandwidth management in connection-oriented network architectures. We consider solutions for distributed multi-commodity flow problems, which are solved by multiple agents operating in a cooperative but uncoordinated manner. We provi...

Constitutive laws for multi-component fluids (MCF) is one of the thorniest problems in science. Two questions explored here are: how to ensure that these relations reduce to accepted forms when all but one of the constituents vanishes; and what constraints does the Second Law impose on the dynamics of viscous fluids at different temperatures? The analysis suggests an alternative to the metaphys...

The network design problem we study in this paper is as follows. Given an undirected network, a set of origin-destination node pairs (commodities) and a demand for each commodity, the non-bifurcated network design problem is to install integer multiples of some capacity unit on the edges of the network and to route the commodities so that each commodity follows a single path. The objective is t...

P∈Pi P∋e fi,P ≤ ce ∀e fi,P ≥ 0 Dual 1 solves the max-sum multi-commodity flow problem: ce represents the capacity of an edge, and fi,P is the amount of flow directed from si to ti along the path P . The LP tries to maximize the total amount of commodity flow. Lemma 17.1.1 Multicut is always larger than the corresponding max-sum multi-commodity flow. Lemma 17.1.2 Multicut is at most O(logK) time...

We propose a static uncapacitated multi-commodity flow model along with a time-based scheduling tool for solving evacuation scheduling problems with capacity constraints. The paper addresses the problem of modeling evacuation scheduling out of an affected area, there are a pre-defined set of exit points out of the target affected area and a set of source points for the evacuees. The proposed ap...

Proceedings Paper: Kwan, RSK, Lin, Z, Copado-Mendez, PJ et al. (1 more author) (2017) Multi-commodity flow and station logistics resolution for train unit scheduling. In: Gunawan, A, Kendall, G, Soon, LL, McCollum, B and Seow, H-V, (eds.) Proceedings of the 8th Multidisciplinary International Conference on Scheduling: Theory and Applications. Multidisciplinary International Scheduling Conferenc...

With the constant changes of the market demand trends and modern information technology which greatly influence supply chain operation and management, postponement has been developed to be an important strategy in some of the supply chain processes. This paper studies the multi-period and multi-commodity flow supply chain network equilibrium problem with postponement strategy under a type of su...