This paper shows that partial differential equations may be a possible area of application of mathematical programming. The solution of Laplace's equation with Neumann's condition is shown to be a minimum cost network flow problem with cost proportional to the arc flow. An algorithm of solving minimum quadratic cost network flow is given.

We explore here surprising links between the time-cost-tradeoff problem and the minimum cost flow problem that lead to faster, strongly polynomial, algorithms for both problems. One of the main results is a new algorithm for the unit capacity min cost flow that culminates decades of efforts to match the complexity of the fastest strongly polynomial algorithm known for the assignment problem. Th...

This paper presents an algorithm for solving Bi-criteria Minimum Cost Dynamic Flow (BiCMCDF) problem with continuous flow variables. The approach is to transform a bi-criteria problem into a parametric one by building a single parametric linear cost out of the two initial cost functions. The algorithm consecutively finds efficient extreme points in the decision space by solving a series of mini...

We present strongly polynomial time algorithms for the minimum cost flow problem and for the weighted bipartite matching problem, also known as the assignment problem. 1 The minimum cost flow problem A flow network with prices, demands and capacities N = (G, a, b, c) is composed of a directed graph G = (V, E), a cost function a : E → R, a demand function b : V → R, and a capacity function c : E...

Definition of Artificial Neural Networks (ANNs) is made by computer scientists, artificial intelligence experts and mathematicians in various dimensions. Many of the definitions explain ANN by referring to graphics instead of giving well explained mathematical definitions; therefore, misleading weighted graphs (as in minimum cost flow problem networks) fit the definition of ANN. This study aims...

Cross docking is one of the options to reduce lead times and inventories and to improve customer response time in supply chains. Cross-docking centres are dynamic environments where products arrive, are regrouped, and leave the same day. In this paper we focus on the process of short-term storage of unit-loads in a cross-docking environment. The goal is to determine temporary storage locations ...

We present strongly polynomial time algorithms for the minimum cost flow problem and for the weighted bipartite matching problem, also known as the assignment problem. 1 The minimum cost flow problem A flow network with costs, demands and capacities N = (G, a, b, c) is composed of a directed graph G = (V,E), a cost function a : E → R, a demand function b : V → R, and a capacity function c : E →...

Many recent caching systems aim to improve hit ratios, but there is no good sense among practitioners of how much further hit ratios can be improved. In other words, should the systems community continue working on this problem? Currently, there is no principled answer to this question. Most prior work assumes that objects have the same size, but in practice object sizes often vary by several o...

We present a specialized network simplex algorithm for the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total value in a feasible flow is constrained by a given budget B. We present a fully combinatorial description of the algorithm that is based on a novel incorporatio...

This paper presents a faster algorithm for the M-convex submodular flow problem, which is a generalization of the minimum-cost flow problem with an M-convex cost function for the flow-boundary, where an M-convex function is a nonlinear nonseparable discrete convex function on integer points. The algorithm extends the capacity scaling approach for the submodular flow problem by Fleischer, Iwata ...