Network Flow Approach Research Articles

A minimum-cost network flow approach to preemptive parallel-machine scheduling

We model and solve the problems of preemptive scheduling of n independent jobs with release dates on m parallel machines with machine availability and eligibility constraints to minimize the makespan and maximum lateness as the minimum-cost network flow problem. We show that the approach can be extended to solve the corresponding scheduling problems on two uniform parallel machines.

Modeling and analysis of a decentralized electricity market: An integrated simulation/optimization approach

In this study, a model is developed to investigate the implications of an hourly day-ahead competitive power market on generator profits, electricity prices, availability and supply security. An integrated simulation/optimization approach is employed integrating a multi-agent simulation model with two alternative optimization models. The simulation model represents interactions between power generator, system operator, power user and power transmitter agents while the network flow optimization model oversees and optimizes the electricity flows, dispatches generators based on two alternative approaches used in the modeling of the underlying transmission network: a linear minimum cost network flow model and a non-linear alternating current optimal power flow model. Supply, demand, transmission, capacity and other technological constraints are thereby enforced.The transmission network, on which the scenario analyses are carried out, includes 30 bus, 41 lines, 9 generators, and 21 power users. The scenarios examined in the analysis cover various settings of transmission line capacities/fees, and hourly learning algorithms. Results provide insight into key behavioral and structural aspects of a decentralized electricity market under network constraints and reveal the importance of using an AC network instead of a simplified linear network flow approach.

A network flow approach to predict drug targets from microarray data, disease genes and interactome network - case study on prostate cancer.

BackgroundSystematic approach for drug discovery is an emerging discipline in systems biology research area. It aims at integrating interaction data and experimental data to elucidate diseases and also raises new issues in drug discovery for cancer treatment. However, drug target discovery is still at a trial-and-error experimental stage and it is a challenging task to develop a prediction model that can systematically detect possible drug targets to deal with complex diseases.MethodsWe integrate gene expression, disease genes and interaction networks to identify the effective drug targets which have a strong influence on disease genes using network flow approach. In the experiments, we adopt the microarray dataset containing 62 prostate cancer samples and 41 normal samples, 108 known prostate cancer genes and 322 approved drug targets treated in human extracted from DrugBank database to be candidate proteins as our test data. Using our method, we prioritize the candidate proteins and validate them to the known prostate cancer drug targets.ResultsWe successfully identify potential drug targets which are strongly related to the well known drugs for prostate cancer treatment and also discover more potential drug targets which raise the attention to biologists at present. We denote that it is hard to discover drug targets based only on differential expression changes due to the fact that those genes used to be drug targets may not always have significant expression changes. Comparing to previous methods that depend on the network topology attributes, they turn out that the genes having potential as drug targets are weakly correlated to critical points in a network. In comparison with previous methods, our results have highest mean average precision and also rank the position of the truly drug targets higher. It thereby verifies the effectiveness of our method.ConclusionsOur method does not know the real ideal routes in the disease network but it tries to find the feasible flow to give a strong influence to the disease genes through possible paths. We successfully formulate the identification of drug target prediction as a maximum flow problem on biological networks and discover potential drug targets in an accurate manner.

Generalized Reduced-Form Auctions: A Network-Flow Approach

We develop a network-flow approach for characterizing interim-allocation rules that can be implemented by ex post allocations. Our method can be used to characterize feasible interim allocations in general multi-unit auctions where agents face capacity constraints, both ceilings and floors. Applications include a variety of settings of practical interest, ranging from individual and group-specific capacity constraints, set-aside sale, partnership dissolution, and government license reallocation.

Contributors

Contributors

How to efficiently incorporate facts devices in optimal active power flow model

This paper presents for the first time how to easily incorporatefacts devices in an optimal active power flow model such that an efficientinterior-point method may be applied. The optimal active power flow model isbased on a network flow approach instead of the traditional nodal formulationthat allows the use of an efficiently predictor-corrector interior point methodspeed up by sparsity exploitation. The mathematical equivalence between thenetwork flow and the nodal models is addressed, as well as the computationaladvantages of the former considering the solution by interior point methods.The adequacy of the network flow model for representing facts devices is presentedand illustrated on a small 5-bus system. The model was implementedusing Matlab and its performance was evaluated with the 3,397-bus and 4,075-branch Brazilian power system which show the robustness and efficiency of theformulation proposed. The numerical results also indicate an efficient tool foroptimal active power flow that is suitable for incorporating facts devices.

Valid inequalities for the fleet size and mix vehicle routing problem with fixed costs

AbstractIn the well‐known vehicle routing problem (VRP), a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. An important variant of the VRP arises when a mixed fleet of vehicles, characterized by different capacities and costs, is available for distribution activities. The problem is known as fleet size and mix VRP with fixed costs FSMF and has several practical applications. In this article, we present a new mixed integer programming formulation for FSMF based on a two‐commodity network flow approach. New valid inequalities are proposed to strengthen the linear programming relaxation of the mathematical formulation. The effectiveness of the proposed cuts is extensively tested on benchmark instances. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009

A network flow-based method to solve performance cost and makespan open-shop scheduling problems with time-windows

This paper deals with several bicriteria open-shop scheduling problems where jobs are pre-emptable and their corresponding time-windows must be strictly respected. The criteria are a performance cost and the makespan. Network flow approaches are used in a lexmin procedure with a bounded makespan and the considered bicriteria problems are solved. Finally, the computational complexity of the algorithm and a numerical example are reported.

Modeling partial harvesting in intensive shrimp culture: A network-flow approach

Despite the promising laboratory results and theoretical arguments on the potential of partial harvesting in enhancing the productivity and profitability of intensive shrimp growout facilities, the implementation of partial harvesting in practical operation is rather difficult due to its complex nature. In this paper, we developed a practical model of partial harvesting using the network-flow approach so that it can be readily implemented and solved in MS EXCEL. We demonstrated the use of this spreadsheet model with data from a commercial shrimp farm in Hawaii. The results indicate that the model is capable of identifying the efficient harvest policy as well as assessing the viability of partial harvesting under a variety of managerial conditions and objectives.

BioRoute: A Network-Flow-Based Routing Algorithm for the Synthesis of Digital Microfluidic Biochips

Due to recent advances in microfluidics, digital microfluidic biochips are expected to revolutionize laboratory procedures. One critical problem for biochip synthesis is the droplet routing problem. Unlike traditional very large scale integration routing problems, in addition to routing path selection, the biochip routing problem needs to address the issue of scheduling droplets under practical constraints imposed by the fluidic property and timing restriction of synthesis results. In this paper, we present the first network-flow-based routing algorithm that can concurrently route a set of noninterfering nets for the droplet routing problem on biochips. We adopt a two-stage technique of global routing followed by detailed routing. In global routing, we first identify a set of noninterfering nets and then adopt the network-flow approach to generate optimal global-routing paths for nets. In detailed routing, we present the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> polynomial-time algorithm for simultaneous routing and scheduling using the global-routing paths with a negotiation-based routing scheme. Our algorithm targets at both the minimization of cells used for routing for better fault tolerance and minimization of droplet transportation time for better reliability and faster bioassay execution. Experimental results show the robustness and efficiency of our algorithm.

Radio resource allocation problems for OFDMA cellular systems

Orthogonal frequency division multiple-access (OFDMA) manages to efficiently exploit the inherent multi-user diversity of a cellular system by performing dynamic resource allocation. Radio resource allocation is the technique that assigns to each user in the system a subset of the available radio resources (mainly power and bandwidth) according to a certain optimality criterion on the basis of the experienced link quality. In this paper we address the problem of resource allocation in the downlink of a multi-cellular OFDMA system. The allocation problem is formulated with the goal of minimizing the transmitted power subject to individual rate constraint for each user. Exact and heuristic algorithms are proposed for the both the single-cell and the multi-cell scenario. In particular, we show that in the single-cell scenario the allocation problem can be efficiently solved following a network flow approach. In the multi-cell scenario we assume that all cells use the same frequencies and therefore the allocation problem is complicated by the presence of strong multiple access interference. We prove that the problem is strongly NP-hard, and we present an exact approach based on an MILP formulation. We also propose two heuristic algorithms designed to be simple and fast. All algorithms are tested and evaluated through an experimental campaign on simulated instances. Experimental results show that, although suboptimal, a Lagrangian-based heuristic consisting in solving a series of minimum network cost flow problems is attractive for practical implementation, both for the quality of the solutions and for the small computational times.

Parallel machine scheduling with machine availability and eligibility constraints

In this paper we consider the problem of scheduling n independent jobs on m identical machines incorporating machine availability and eligibility constraints while minimizing the makespan. Each machine is not continuously available at all times and each job can only be processed on specified machines. A network flow approach is used to formulate this scheduling problem into a series of maximum flow problems. We propose a polynomial time binary search algorithm to either verify the infeasibility of the problem or solve it optimally if a feasible schedule exists.

Transmission Expansion Planning Using Contingency Criteria

This paper proposes a methodology for choosing the best transmission expansion plan considering various types of security (operating reliability) criteria. The proposed method minimizes the total cost that includes the investment cost of transmission as well as the operating cost and standby cost of generators. The purpose of the study is development of new methodology for solving transmission system expansion planning problem subject to contingency criteria which are essentially extensions of the (N-1) contingency criterion. The transmission expansion problem uses an integer programming framework, and the optimal strategy is determined using a branch and bound method that utilizes a network flow approach and the maximum flow-minimum cut set theorem. The characteristics of the proposed method are illustrated by applying it to a five-bus system and a 21-bus system. The results of these case studies demonstrate that the proposed method provides a practical way to find an optimal plan for power system expansion planning.

Multicommodity network flow approach to the railroad crew-scheduling problem

We present our solution to the crew-scheduling problem Jor 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 are made manually. We present our work developing a network-flow-based crew-optimization model that can be applied at the tactical, planning, and strategic levels of crew scheduling. Our network flow model maps the assignment of crews to trains as the flow of crews on an underlying network, where different crew types are modeled as different commodities in this network. We formulate the problem as an integer programming problem on this network, which allows it to be solved to optimality. We also develop several highly efficient algorithms using problem decomposition and relaxation techniques, in which we use the special structure of the underlying network model to obtain significant increases in speed. We present very promising computational results of our algorithms on the data provided by a major North American railroad. Our network flow model is likely to form a backbone for a decision-support system for crew scheduling.

Production planning with limited inventory capacity and allowed stockout

In production planning, there is a situation where the production quantity is limited by inventory capacity rather than production capacity. This situation often happens in petrochemical manufacturing, food processing, glass manufacturing, etc. Only a few studies can be found in literature for this situation, among which the stockout strategy is not well studied. In this paper, we consider the production-planning problem with inventory capacity as a limiting factor. We further consider the problem with the following features: (1) the stockout is allowed, (2) production and lost sale cost functions are time varying and non-increasing, and (3) inventory capacity is constant. These features have their roots in practice. In this paper, first we present a stockout model, and then we prove some properties at an optimal solution to our model. Based on these properties, we further develop an algorithm with polynomial time complexity using the network flow approach. The paper also provides a case study to further justify practicability of the stockout strategy with limited inventory and to show the effectiveness of our model and algorithm.

A network flow approach to optimizing hospital bed capacity decisions

The delivery of cost-effective and quality hospital-based health care remains an important and ongoing challenge for the American health care industry. Despite numerous advances in medical procedures and technologies, a growing array of outpatient health care options, limits on inpatient reimbursements, and almost two decades of hospital contraction and consolidation, annual inpatient admissions in the United States are currently at levels not seen since the early 1980s. This combination of increased demand and diminished resources makes planning for hospital bed capacity a difficult problem for health care decision makers. We examine this problem by developing a network flow model that incorporates facility performance and budget constraints to determine optimal hospital bed capacity over a finite planning horizon. Under modest assumptions, we demonstrate that for realistic sized capacity planning problems, our network formulation is not computationally intensive, and allows us to obtain optimal bed capacity plans quickly.

Network flow approaches to pre-emptive open-shop scheduling problems with time-windows

This paper deals with pre-emptive open-shop scheduling problems with time-windows. Network flow procedures to check feasibility and a max-flow parametrical algorithm to minimize the makespan are introduced. Also, computational complexities are evaluated for these feasibility and optimization algorithms. The proposed method is a strongly polynomial algorithm to minimize the makespan of the pre-emptive open-shop scheduling problems with time-windows strictly respected. Finally, the applications of the proposed algorithms are illustrated with numerical examples.

A network flow approach to the Minimum Common Integer Partition Problem

In the k-Minimum Common Integer Partition Problem, abbreviated as k-MCIP, we are given k multisets X 1 , … , X k of positive integers, the goal is to find an integer multiset T of the minimum size such that for every i, we can partition each of the integers in X i so that the disjoint (multiset) union of their partitions equals T. This problem has applications in computational molecular biology, in particular, ortholog assignment and DNA hybridization fingerprint assembly. The problem is known to be NP-hard for any k ⩾ 2 . In this article, we improve the approximation ratio for k-MCIP by viewing this problem as a flow decomposition problem in some flow network. We show an efficient 0.5625 k -approximation algorithm, improving upon the previously best known 0.6139 k -approximation algorithm for this problem.

A network flow approach for static and dynamic traffic grooming in WDM networks

In WDM networks , traffic grooming is a fundamental and important operation for aggregating multiple low-rate channels from the end users into a high-rate wavelength channel . In the literature, several traffic grooming problems were formulated where the common objective is to minimize the number of add-drop multiplexers required, and each of these problems was solved by specific algorithms. In this paper, we propose a network flow approach for solving a class of static and dynamic traffic grooming problems. In this approach, we transform a traffic grooming problem onto the minimum edge-cost flow problem through proper graph transformation and assignment of edge weights, and then solve this resulting network flow problem by an efficient heuristic algorithm . The network flow approach has two main advantages: (1) It is generally applicable to many static and dynamic traffic grooming problems. It can solve some existing traffic grooming problems as well as new problems that cannot be solved by the existing algorithms. (2) It performs at least as good as the best existing algorithm for static traffic grooming and significantly outperforms the existing algorithms for dynamic traffic grooming.

05/02215 Short term hydroelectric scheduling combining network flow and interior point approaches

05/02215 Short term hydroelectric scheduling combining network flow and interior point approaches