Linear Programming Framework Research Articles

Optimal Integration of Phasor Measurement Units in Power Systems Considering Conventional Measurements

This paper presents an integer linear programming (ILP) framework for the optimal placement of phasor measurement units (PMUs), in the presence of conventional measurements. Furthermore, by the proposed method, the power system remains completely observable during all possible single contingencies for lines and measurement devices. In doing so, the potential of circuit equations associated with both PMUs and conventional measurements as well as the network topology are fully utilized by a system of equations to reach the minimum possible numbers of required PMUs. The limitation of communication channels is also taken into account in the proposed ILP-based framework. The method is implemented on several IEEE test systems which have already been equipped with conventional measurements. The comparison between obtained results of the proposed method and those of other methods reveals its superiority in the modeling of robust PMU placement problem (OPP) in the presence of conventional measurements. As such, a smooth transition from the SCADA-based monitoring system to the PMU-dominated WAMS is ensured. Moreover, this method is successfully applied on three large-scale test systems, which demonstrates it can effectively be employed for robust OPP in realistic power systems.

Designing and planning a multi-echelon multi-period multi-product closed-loop supply chain utilizing genetic algorithm

Designing and planning a closed-loop supply chain in a comprehensive structure is vital for its applicability. To cope with the design and planning issue of a comprehensive closed-loop supply chain network, this paper develops an extended model, which is multi-echelon, multi-product, and multi-period in a mixed integer linear programming framework. The word “comprehensive,” in our mathematical approach, in designing and planning a closed-loop supply chain problem, can be analyzed from two complementary angles: including all possible entities (facilities) of a real condition and considering minimum limitations on possible flows between entities. In our proposed model, customers can be supplied via manufacturers, warehouses, and distributors, as an example. The proposed model is solved by CPLEX optimization software and by a developed genetic algorithm. During this computational analysis, we compare results of proposed pretuned genetic algorithm with a global optimum of CPLEX solver. Then, a sufficient number of large-size instances are generated and solved by the proposed genetic algorithm. To the best of our knowledge, there has been no similar multi-period multi-product closed-loop supply chain design and planning problem utilizing any kind of meta-heuristics let alone genetic algorithms. Therefore, in this issue, it is an original research, and results prove the acceptable performances of the developed genetic algorithm.

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Energy and Environmental Systems Planning with Recourse: Inexact Stochastic Programming Model Containing Fuzzy Boundary Intervals in Objectives and Constraints

AbstractIn this study, a feasibility-analysis-based inexact fuzzy multistage model (FA-IFMSM) was developed for supporting the planning of energy and environmental systems under multiform uncertainties. In FA-IFMSM, methods of feasibility-analysis-based fuzzy linear programming (FA-FLP) and inexact multistage stochastic programming (IMSP) with recourse were integrated into a general mixed-integer linear programming framework, such that the developed model could tackle uncertainties described in terms of probability distributions, interval values, fuzzy sets, and their hybrid and mixture. Moreover, it could reflect dynamic features of facility-capacity expansions and energy supplies over a multistage context. It could also quantify constraint violation degrees through the adoption of various acceptable degree levels. Then the proposed model was applied to a regional energy and environmental system to illustrate its applicability, where conventional and renewable energy resources and their economic and envi...

Tactical resource allocation and elective patient admission planning in care processes

Tactical planning of resources in hospitals concerns elective patient admission planning and the intermediate term allocation of resource capacities. Its main objectives are to achieve equitable access for patients, to meet production targets/to serve the strategically agreed number of patients, and to use resources efficiently. This paper proposes a method to develop a tactical resource allocation and elective patient admission plan. These tactical plans allocate available resources to various care processes and determine the selection of patients to be served that are at a particular stage of their care process. Our method is developed in a Mixed Integer Linear Programming (MILP) framework and copes with multiple resources, multiple time periods and multiple patient groups with various uncertain treatment paths through the hospital, thereby integrating decision making for a chain of hospital resources. Computational results indicate that our method leads to a more equitable distribution of resources and provides control of patient access times, the number of patients served and the fraction of allocated resource capacity. Our approach is generic, as the base MILP and the solution approach allow for including various extensions to both the objective criteria and the constraints. Consequently, the proposed method is applicable in various settings of tactical hospital management.

Food Security: How Rural Ghanaian Households Respond to Food Shortages in Lean Season

A rural household, with little or no formal education and limited opportunities for non-farm income generating activities, will produce rather than purchase staples for household consumption. Many subsistence farmers are net-food buyers, often facing the challenge of ensuring household food security in lean seasons of production when their stock is exhausted (cyclical food insecurity). This paper determined the optimal farm plan, profit levels of crops, and farmer behaviour when given the option to purchase or produce food using a linear programming framework. Findings from the LP model show that capital is the most constraining resource for both male and female farmers. Making an additional capital of US$180 available to female farmers will increase their net income by US$823 but making one additional acre of land available to them will only increase income by US$200. As land reforms take time, addressing their credit needs is an appropriate short-term intervention.

A Delay based MILP for Network Planning in Optical Networks

This research investigates a mixed integer linear programming (MILP) framework that solves the virtual topology problem under the communication delay constraint. An arbitrary optical network has been considered with different distances between the nodes and different link capacities. A traffic matrix is assumed for the optical network at an instance and the corresponding virtual topology design is solved by using the mixed integer linear formulation that includes lightpath routing, wavelength assignment, wavelength continuity, flow routing, and traffic losses.The numerical optimization results illustrate the efficiency of the proposed MILP formulation and superior network performances, validating the proposed framework for optimal virtual topology designs. Moreover, the proposed framework may alleviate computational time issues related to the network learning process of some heuristic approaches.

Optimization of environmental management strategies through a dynamic stochastic possibilistic multiobjective program

Greenhouse gas (GHG) emissions from municipal solid waste (MSW) management facilities have become a serious environmental issue. In MSW management, not only economic objectives but also environmental objectives should be considered simultaneously. In this study, a dynamic stochastic possibilistic multiobjective programming (DSPMP) model is developed for supporting MSW management and associated GHG emission control. The DSPMP model improves upon the existing waste management optimization methods through incorporation of fuzzy possibilistic programming and chance-constrained programming into a general mixed-integer multiobjective linear programming (MOP) framework where various uncertainties expressed as fuzzy possibility distributions and probability distributions can be effectively reflected. Two conflicting objectives are integrally considered, including minimization of total system cost and minimization of total GHG emissions from waste management facilities. Three planning scenarios are analyzed and compared, representing different preferences of the decision makers for economic development and environmental-impact (i.e. GHG-emission) issues in integrated MSW management. Optimal decision schemes under three scenarios and different pi levels (representing the probability that the constraints would be violated) are generated for planning waste flow allocation and facility capacity expansions as well as GHG emission control. The results indicate that economic and environmental tradeoffs can be effectively reflected through the proposed DSPMP model. The generated decision variables can help the decision makers justify and/or adjust their waste management strategies based on their implicit knowledge and preferences.

EllipsoidFN: a tool for identifying a heterogeneous set of cancer biomarkers based on gene expressions

Computationally identifying effective biomarkers for cancers from gene expression profiles is an important and challenging task. The challenge lies in the complicated pathogenesis of cancers that often involve the dysfunction of many genes and regulatory interactions. Thus, sophisticated classification model is in pressing need. In this study, we proposed an efficient approach, called ellipsoidFN (ellipsoid Feature Net), to model the disease complexity by ellipsoids and seek a set of heterogeneous biomarkers. Our approach achieves a non-linear classification scheme for the mixed samples by the ellipsoid concept, and at the same time uses a linear programming framework to efficiently select biomarkers from high-dimensional space. ellipsoidFN reduces the redundancy and improves the complementariness between the identified biomarkers, thus significantly enhancing the distinctiveness between cancers and normal samples, and even between cancer types. Numerical evaluation on real prostate cancer, breast cancer and leukemia gene expression datasets suggested that ellipsoidFN outperforms the state-of-the-art biomarker identification methods, and it can serve as a useful tool for cancer biomarker identification in the future. The Matlab code of ellipsoidFN is freely available from http://doc.aporc.org/wiki/EllipsoidFN.

Optimal multi-stage PMU placement in electric power systems using Boolean algebra

SUMMARY Placement of phasor measurement units (PMUs) in power systems has often been formulated for achieving total network observability. In practice, however, the installation process is not implemented at once, but at several stages, because the number of available PMUs at each time period is restricted due to financial problems. This paper presents a novel integer linear programming framework for optimal multi-stage PMU placement (OMPP) over a preset schedule, in order to improve the network observability during intermediate stages, in addition to its complete observability by the end of the PMU placement process. To precisely evaluate the network observability and fully exploit the potential of circuit rules, the observability function is formulated by Boolean algebra. Next, it will be utilized to formulate the optimal PMU placement problem and then construct a unified optimization model for OMPP. As such, among various strategies for installing PMUs over the scheduled horizon, the one achieving the maximum total observability of the system during intermediate stages is found. Moreover, the unified optimization model allows for considering the network expansion scenarios as well as the diverse importance of critical buses during the installation process so that these buses may be equipped with PMUs at primary stages. Finally, to illustrate the applicability and efficiency of the proposed method, it is applied to several IEEE test systems and two practical large-scale power systems, and the results are studied. Copyright © 2012 John Wiley & Sons, Ltd.

Neighbor sensor networks: Increasing lifetime and eliminating partitioning through cooperation

In this paper we consider neighbor sensor networks which are defined as multiple wireless sensor networks under the administration of different authorities but located physically on the same area or close to each other. We construct a Linear Programming framework to characterize the cooperation of neighbor sensor networks in comparison to non-cooperating networks. We show that if neighbor sensor networks cooperate with each other for relaying data packets then this cooperation brings two advantages as compared to no cooperation case. First, lifetime of both networks is prolonged — the results of our analysis show that cooperation between neighbor sensor networks can significantly extend the overall network lifetime. Second, cooperation reduces the probability of disjoint partitions arising due to the limited transmission ranges of sensor nodes. When neighbor sensor networks cooperate, eliminating disjoint partitions is possible with sensors having shorter transmission ranges as demonstrated and quantified by our analysis.

A coupled factorial-analysis-based interval programming approach and its application to air quality management

In this study, a coupled factorial-analysis-based interval programming (CFA-IP) approach is developed through incorporating factorial analysis within an interval-parameter linear programming framework. CFA-IP can tackle uncertainties presented as intervals that exist in the objective function and the left- and right-hand sides of constraints, as well as robustly reflect interval information in the solutions for the objective-function value and decision variables. Moreover, CFA-IP has the advantage of investigating the potential interactions among input parameters and their influences on lower- and upper-bound solutions, which is meaningful for supporting an in-depth analysis of uncertainty. A regional air quality management problem is studied to demonstrate applicability of the proposed CFA-IP approach. The results indicate that useful solutions have been generated for planning the air quality management practices. They can help decision makers identify desired pollution mitigation strategies with minimized total cost and maximized environmental efficiency, as well as screen out dominant parameters and explore the valuable information that may be veiled beneath their interrelationships. Implications: The CFA-IP approach can not only tackle uncertainties presented as intervals that exist in the objective function and the left- and right-hand sides of constraints, but also investigate their interactive effects on model outputs, which is meaningful for supporting an in-depth analysis of uncertainty. Thus CFA-IP would be applicable to air quality management problems under uncertainty. The results obtained from CFA-IP can help decision makers identify desired pollution mitigation strategies, as well as investigate the potential interactions among factors and analyze their consequent effects on modeling results.

A scenario-based modeling approach for emergency evacuation management and risk analysis under multiple uncertainties

Nuclear emergency evacuation is important to prevent radioactive harms by hazardous materials and to limit the accidents’ consequences; however, uncertainties are involved in the components and processes of such a management system. In the study, an interval-parameter joint-probabilistic integer programming (IJIP) method is developed for emergency evacuation management under uncertainties. Optimization techniques of interval-parameter programming (IPP) and joint-probabilistic constrained (JPC) programming are incorporated into an integer linear programming framework, so that the approach can deal with uncertainties expressed as joint probability and interval values. The IJIP method can schedule the optimal routes to guarantee the maximum population evacuated away from the effected zone during a finite time. Furthermore, it can also facilitate post optimization analysis to enhance robustness in controlling system violation risk imposed on the joint-probabilistic constraints. The developed method has been applied to a case study of nuclear emergency management; meanwhile, a number of scenarios under different system conditions have been analyzed. It is indicated that the solutions are useful for evacuation management practices. The result of the IJIP method can not only help to raise the capability of disaster responses in a systematic manner, but also provide an insight into complex relationships among evacuation planning, resources utilizations, policy requirements and system risks.

Hot Discharges/Feeds between Plants To Combine Utility Streams for Heat Integration

A sharp increase in worldwide energy requirements has forced people to exploit novel energy conservation technologies and new alternative energies. Heat integration, as a method of saving energy, is proposed in this paper in the form of integrating multiple hot discharges/feeds between plants and utility streams to reduce utility requirements and increase steam production for the total site. T–Q graphic methods are proposed to coordinate the temperatures of multiple hot discharges/feeds between plants and the steam production. The grand composite curve (GCC), the composite curve of the streams employed for hot discharges/feeds, and the curve of steam generation are combined into the T–Q diagram to obtain an insight into the interrelationship between these streams. A bilevel mixed integer linear programming (MILP) framework is presented to minimize the total hot and cold utilities of the up and down plants and to maximize the steam generation in the total site. The first level of the programming framework is formulated to target the utility requirements, and the second level of the programming framework is formulated to maximize the steam production. Two examples are investigated to demonstrate the performance of the proposed method, and the results show a decrease in the total hot and cold utilities of the up and down plants and also indicate an increase in steam production.

Collision monitoring and optimal collision avoidance manoeuvre for formation flying satellites

PurposeThe purpose of this paper is to evaluate the safety of formation flying satellites, and propose a method for practical collision monitoring and collision avoidance manoeuvre.Design/methodology/approachA general formation description method based on relative orbital elements is proposed, and a collision probability calculation model is established. The formula for the minimum relative distance in the crosstrack plane is derived, and the influence of J2 perturbation on formation safety is analyzed. Subsequently, the optimal collision avoidance manoeuvre problem is solved using the framework of linear programming algorithms.FindingsThe relative orbital elements are illustrative of formation description and are easy to use for perturbation analysis. The relative initial phase angle between the in‐plane and cross‐track plane motions has considerable effect on the formation safety. Simulations confirm the flexibility and effectiveness of the linear programming‐based collision avoidance manoeuvre method.Practical implicationsThe proposed collision probability method can be applied in collision monitoring for the proximity operations of spacecraft. The presented minimum distance calculation formula in the cross‐track plane can be used in safe configuration design. Additionally, the linear programming method is suitable for formation control, in which the initial and terminal states are provided.Originality/valueThe relative orbital elements are used to calculate collision probability and analyze formation safety. The linear programming algorithms are extended for collision avoidance, an approach that is simple, effective, and more suitable for on‐board implementation.

Algorithmic determination of the maximum possible earnings for investment strategies

This paper proposes a new method for determining the upper bound of any investment strategy's maximum profit, applied in a given time window [0,T]. This upper bound is defined once all the prices are known at time T and therefore represents the ex-post maximum efficiency of any investment strategy determined during the relevant time interval. This approach allows us to gauge in absolute terms those behaviors defined through atomic “buy” and “sell” actions, and can be extended to more complex strategies. We show that, even in the ex-post framework, establishing this upper bound when transaction costs are implemented is extremely complex. We first describe this problem using a linear programming framework. Thereafter, we propose to embed this question in a graph theory framework and to show that determining the best investment behavior is equivalent to identifying an optimal path in an oriented, weighted, bipartite network or a weighted, directed, acyclic graph. We illustrate this method using real world data and introduce a new theory about absolute optimal behavior in the financial world.

AN IMPROVED MODEL FOR ASSESSING THE FDH-COST EFFICIENCY

Recently Leleu [A linear programming framework for free disposal hull (FDH) technologies and cost functions: Primal and dual models] presented a linear model for assessing the FDH-cost function with various returns to scale assumptions. He stated that economic inefficiency can be computed as the ratio of the observed cost to the minimum cost and, as usual, the allocative inefficiency is computed as the ratio between the economic and the technical inefficiencies. In this paper, we propose a modified model with various returns to scale assumptions that has fewer constraints and variables than Leleu's model and obtains the FDH-cost efficiency directly. Reducing nm constraints and nm variables, where n is the number of DMUs and m is the number of inputs, leads to the computational advantage of our model over that of Leleu.

An interval full-infinite programming approach for energy systems planning under multiple uncertainties

An interval full-infinite programming regional energy model (IFIP-REM) is developed in this study for supporting energy systems management under uncertainty. IFIP-REM integrates full-infinite programming (FIP) into an interval linear programming (ILP) framework. The IFIP is capable of addressing multiple uncertainties existing in related costs, impact factors and system objectives (expressed as determinates, crisp interval values and functional intervals). The modeling approach inherits the advantages of ILP and FIP, and allows uncertainties and decision-makers’ aspirations to be directly communicated into the optimization process and resulting solutions. The developed method is applied to an energy planning system, where pollutant emissions are desired to be controlled. The results indicate that reasonable solutions can be generated and used to support the obtained interval solutions of IFIP-REM model, and the solutions can be used for generating decision alternatives and thus help decision makers identify desired policies under various economic and system constraints to coordinate the conflict interactions among economic cost, system efficiency, pollutant mitigation and energy-supply security.

A theoretical framework for optimal cooperative networking in multiradio multichannel wireless networks

A wide range of next generation wireless networks are based on the multiradio multichannel (MR-MC) network model. A full exploration of the MR-MC wireless network capacity incurs challenging cooperative networking issues including transmission cooperation, resource allocation cooperation, and cross-layer protocol cooperation. In this article, rather than focus on protocol designs for specific cooperative networking issues, we present a generic theoretical framework that could guide the protocol or algorithm development to approach the maximum network capacity. Based on our multidimensional conflict graph (MDCG) tool, we could achieve a cross-layer linear programming framework to study the optimal cooperative networking in two complementary aspects: optimal network dimensioning and throughput-optimal control. While certain NP-hard computing issues hindered the MR-MC network optimization for a long time, the MDCG-based framework can readily generate simple polynomial and distributed algorithms with guaranteed capacity region.

“An Integer Programming Power Optimization in Storage Systems”

This paper presents a linear integer programming framework for effective power management in storage systems. A sample memory system with different data banks is considered for optimal energy consumption during data operations by manipulating the data among banks. The memory bank four-level power state schemes, namely, active, stand-by, nap, and power down states, are included for superior power management of the storage system by formulating a linear integer optimization framework that includes plausible data manipulations, energy consumption levels, data migration, and compression options. The numerical results illustrate the efficiency of the proposed framework in terms of power management of storage systems with respect to available approaches with two-level power state operations.