The Uncapacitated Fixed-charge Network Flow (UFNF) problem is an instance of the broader class of Network Design (ND) problems. Let G = (S,A) be a digraph where S is the set of nodes and A is the set of arcs. Each arc (i, j) is associated with two costs: a fixed cost ci,j for selecting (i, j) and a variable cost di,j for routing flow on (i, j). The problem is to find a set of arcs that allow a ...

Given a directed network, the uncapacitated fixed-charge network flow problem is to find a minimum-cost arc combination that provides flows from the supply nodes to the demand nodes. Associated with all arcs are two costs: the fixed charge of using the arc and the variable cost depending on the amount of flow the arc actually carries. This generic model has applications for problems of distribu...

This paper presents a branching method for the solution of the fixed charge transportation problem. Starting with a linear formulation of the problem, we develop the method which converges to the optimal solution. The method is based on the computation of a lower bound and an upper bound embedded within a branching process. We present a detailed numerical example to illustrate the proposed meth...

We formulate the fixed-charge multiple knapsack problem (FCMKP) as an extension of the multiple knapsack problem (MKP). The Lagrangian relaxation problem is easily solved, and together with a greedy heuristic we obtain a pair of upper and lower bounds quickly. We make use of these bounds in the pegging test to reduce the problem size. We also present a branch-and-bound (B&B) algorithm to solve ...

The wavelet transform-domain least-mean square (WTDLMS) algorithm uses the self-orthogonalizing technique to improve the convergence performance of LMS. In WTDLMS algorithm, the trade-off between the steady-state error and the convergence rate is obtained by the fixed step-size. In this paper, the WTDLMS adaptive algorithm with variable step-size (VSS) is established. The step-size in each subf...

The fixed-charge transportation problem is a fixed-charge network flow problem on a bipartite graph. This problem appears as a subproblem in many hard transportation problems, and is also both a special case and a strong relaxation of the challenging bigbucket multi-item lot-sizing problem. In this paper, we provide a polyhedral analysis of the polynomially solvable special case in which the as...

Electron capture dissociation (ECD) studies of two modified amyloid beta peptides (20-29 and 25-35) were performed to investigate the role of H* radicals in the ECD of peptide ions and the free-radical cascade (FRC) mechanism. 2,4,6-Trimethylpyridinium (TMP) was used as the fixed charge tag, which is postulated to both trap the originally formed radical upon electron capture and inhibit the H* ...

The Fixed Charge Transportation Problem (FCTP) is a generalization of the well-known Transportation Problem, where the cost for sending goods from origins to destinations is composed of a fixed cost and a continuous cost proportional to the amount of goods sent. In practical applications, the fixed costs may represent toll charges on highways, landing fees at airports, setup costs in production...

We investigate a variant of the Fixed Charge Shortest Paths problem which enumerates the sequence of optimal solutions that arise as the focus shifts from the fixed cost parameters, (generating a Minimum Spanning Tree problem instance), to the variable costs, (generating a Shortest Paths problem instance). Thus we provide insight into the behavior of the problem, which is NP-hard and requires s...

Recent studies on methods of detecting the early onset of arthritic cartilage degradation using NMR-based techniques have shown that such detection is possible. The use of sodium NMR observations, along with an ideal Donnan single compartment model of cartilage, has already been validated as a means of measuring cartilage fixed charge density a known indicator of cartilage condition. Similar ca...