The present paper examines the task of minimum cost flow finding in a fuzzy dynamic network with lower flow bounds. The distinguishing feature of this problem statement lies in the fuzzy nature of the network parameters, such as flow bounds, transmission costs and transit times. The arcs of the considered network have lower bounds. Another feature of this task is that fuzzy flow bounds, costs a...

Maximum flow problem on hypergraphs (hyper-networks) is an extension of maximum flow problem on normal graphs. In this paper, we consider a generalized fuzzy version of maximum flow problem in hyper-networks setting. Our algorithm is a class of genetic algorithms and based on genetic tricks. The crisp equivalents of fuzzy chance constraints in hyper-networks setting are defined, and the executi...

In this network we have two special vertices: a source vertex s and a sink vertex t. Our goal is to send the maximum amount of flow from s to t; flow can only travel along arcs in the right direction, and is constrained by the arc capacities. This “flow” could be many things: imagine sending water along pipes, with the capacity representing the size of the pipe; or traffic, with the capacity be...

We present our solution to the crew-scheduling problem for North American railroads. (Crew scheduling in North America is very different from scheduling in Europe, where it has been well studied.) The crew-scheduling problem is to assign operators to scheduled trains over a time horizon at minimal cost while honoring operational and contractual requirements. Currently, decisions related to crew...

Power flow (PF) study, which is performed to determine the power system static states (voltage magnitudes and voltage angles) at each bus to find the steady state operating condition of a system, is very important and is the most frequently carried out study by power utilities for power system planning, operation and control. In this paper, a counterpropagation neural network (CPNN) is proposed...

In this paper, we study shelf space allocation optimization which is important to retail operations management. Our approach is to formulate a model that is applicable to operational realities and to seek solutions with realistic test data. This model is linked to the multi-dimensional knapsack problem. We first solve a simplified version of the problem to achieve maximum profit by transforming...

In this paper, we propose a method to solve the Nonlinear Multicommodity Network Flow (NMNF) Problem. We have combined this method with a projected-Jacobi (PJ) method and a duality based method possessing decomposition effects. With the decomposition, our method can be parallel processed and is computationally efficient. We have tested our method on several examples of NMNF problem and obtained...

We consider the generalized network flow problem. Each arc e in the network has a gain factor y (e ) . If f ( e ) units of flow enter arc e , then f ( e ) r ( e ) units arrive at the other end of e. The generalized network flow problem is to maximize the net flow into one specific node, the sink. -We give an algorithm which solves this problem in O(m2 (m + n log log B ) log B ) time, where B is...

6.1 The Maximum Flow Problem In this section we define a flow network and setup the problem we are trying to solve in this lecture: the maximum flow problem. Definition 1 A network is a directed graph G = (V,E) with a source vertex s ∈ V and a sink vertex t ∈ V . Each edge = (v, w) from v to w has a defined capacity, denoted by u(e) or u(v, w). It is useful to also define capacity for any pair ...

Hop constraint is associated with modern communication network flows. We consider the problem of designing an optimal undirected network with integer-valued edge-capacities that meets a given set of single-commodity, hop-constrained network flow value requirements. We present a strongly polynomial, combinatorial algorithm for the problem with value of hop-parameter equal to three when values of...