Mathematical Programming Procedure Research Articles

Household Effective Demand for Electricity in Ghana: Analysis and Implication for Tariffs

Outcomes of most developing country projects to secure inclusive growth through electricity provision appear to hinge on available information regarding households’ response to electricity. To provide the needed information for policy, this study assessed the determinants of household electricity demand and estimated the mean willingness to pay for electricity by households in Ghana. The study used a Contingent Valuation modelling procedure involving over 3000 households to derive an effective demand function for electricity in Ghana. This was done through a national household survey. A mathematical programming analytical procedure was employed to fully account for the block pricing tariff system used in Ghana. The study found that Ghanaian households are willing to pay a monthly mean electricity tariff of 50.40 Ghana cedis (US$11.56), which is lower than the average monthly tariff of 73.67 Ghana cedis (US$16.90) paid by households. Thus, the average tariff paid by households monthly is 46% higher than the mean willingness to pay. The study also found that the highest impact determinants of demand for electricity in Ghana were affordability of tariffs, usage of electrical appliances, and availability of electricity, respectively. This study employs a mathematical programming procedure to determine the mean willingness to pay for electricity in Ghana. This procedure is theoretically more robust than the often-used differential calculus approach since it incorporates the block pricing of electricity in Ghana, which the calculus approach ignores. Also, it uses the largest and most inclusive known sample, specifically designed to elicit households’ willingness to pay for electricity in Ghana. The study is also unique in its findings.

A non-standard numerical method for finite element modelling of tensile cracks in quasi-brittle material

In this paper, a non-standard finite element (FE) method, coupled with a mathematical programming procedure, is presented to simulate initiation and propagation of in-plane tensile cracks in quasi-brittle material. Potential crack lines are defined and limited by the FE edges. The cracks are considered as localized plastic deformations imposed at the nodes along the potential crack paths. Crack opening is detected at each node by a limit value of tensile force normal to the crack direction. When the limit value is reached, a cohesive crack starts, following a linear softening branch. The mechanical model is such that no remeshing neither the introduction of interfaces is necessary to describe the discontinuity between elements, as usually required in standard FE approaches. The non-linear solution of the structural problem is obtained using a mathematical programming procedure based on the solution of a parametric linear complementarity problem (PLCP). The main advantage of the PLCP formulation is its ability to manage structural configurations in which instability and multiplicity of solutions are possible, providing one solution even at points characterized by a not-positive-semidefinite Hessian matrix. Simple numerical simulations are presented with the aim to test the method and the solution procedures.

Integration of a Combined Cycle Power Plant with MED-RO Desalination Based on Conventional and Advanced Exergy, Exergoeconomic, and Exergoenvironmental Analyses

The ever-increasing world population, change in lifestyle, and limited natural water and energy resources have made industrial seawater desalination plants the leading contenders for cost-efficient freshwater production. In this study, the integration of a combined cycle power plant (CCPP) with multi-effect distillation (MED) and reverse osmosis (RO) desalination units is investigated through comprehensive conventional and advanced exergy, exergoeconomic, and exergoenvironmental analyses. Firstly, the thermodynamic modelling of the CCPP is performed by using a mathematical programming procedure. Then, a mathematical model is developed for the integration of the existing CCPP plant with MED and RO desalination units. Finally, conventional and advanced exergy, exergoeconomic, and exergoenvironmental analyses are carried out to assess the main performance parameters of the integrated CCPP and MED-RO desalination system, as well as to identify potential technical, economic, and environmental improvements. A case study is presented based on the Shahid Salimi Neka power plant located at the north of Iran along the Caspian Sea. The mathematical modelling approach for the integrated CCPP and MED-RO desalination system is solved in MATLAB, and the results are validated via Thermoflex software. The results reveal an increase of 3.79% in fuel consumption after the integration of the CCPP with the desalination units. The exergy efficiency of the integrated system is 42.7%, and the highest cost of exergy destruction of the combustion chamber is 1.09 US$ per second. Economic and environmental analyses of the integrated system also show that gas turbines present the highest investment cost of 0.047 US$ per second. At the same time, MED exhibits the highest environmental impact rate of 0.025 points per second.

Estimation of capital requirements in downturn conditions via the CBV model: Evidence from the Greek banking sector

One of the main drawbacks of the original CreditRisk+ methodology is that it models the default rates of the sectors (e.g. industry) as independently distributed random variables. Such an assumption has been considered as unrealistic and various approaches have been proposed in order to overcome this issue. To the best of our knowledge, such approaches have not been applied to portfolios associated with periods characterized by severe downturn economic conditions. In our work, apart from the standard CreditRisk+ model, we have also implemented two recent approaches that allow the dependence between sector default rates and can account for macroeconomic factors and have fed each model with portfolio data from a major Greek bank spanning the period 2008–2015. Based on our empirical analysis, it became evident that among the three models only the CBV model, incorporating a nonlinear (and nonconvex) mathematical programming procedure, could follow the pace of the crisis and provided realistic estimations regarding the credit risk capital required. Finally, it is shown that the economic capital estimates derived by that model could have been used as an early warning indicator for the banking crisis (at least for the case of Greece) that may begin within the next couple of years, since there is a clear correlation between the model estimations and the values of well-established early warning indicators for banking crises.

Customer-driven investment decisions in existing multiple sales channels: A downstream supply chain analysis

A supply chain employing multiple sales channels, needs to continually enhance these channels for achieving competitive advantage. The purpose of this paper is to provide a channel-level benefit-cost analysis, through an integration of operations and marketing perspectives to ultimately provide a systematic procedure for optimal investment decisions towards improving existing sales channels. This study is motivated by the decision for improvement, on the part of many established firms that typically utilize multiple channel structures. In pursuing our objective, an analytic network process (ANP), that considers both customer priorities and demand correlations among channels, is suggested, for obtaining customer input data. Utilizing a proposed benefit-cost ratio metric for each channel, incorporating customer input information, as well as relevant operating costs, we outline a mathematical programming procedure for determining the optimal allocation of a limited investment budget among these channels. Our suggested methodological approach is illustrated by a realistic numerical example and some selected sensitivity analysis.

Optimization of 4th generation distributed district heating system: Design and planning of combined heat and power

Abstract This study applies a mathematical programming procedure to model the optimal design and planning of a new district which satisfies two features of the 4th generation district heating systems: energy reciprocity and on-site generation. The aim of the computational model is to investigate the effect of energy reciprocity (energy exchange among the buildings) as well as to find the best way to select the equipment among various candidates (capacities), the pipeline network among the buildings, and their electrical connections. The objective function includes the annualized overall capital and operation costs for the district along with the benefits of selling electricity to the grid. The distributed energy supply consists of heating, cooling, and power networks, several CHP technologies, solar array, chillers, and auxiliary boilers. The performance of the model for poly-generation was evaluated for designing the new part of Suurstoffi district situated in Risch Rotkreuz, Switzerland with seven residential and office complexes under four different scenarios. Allowing heat exchange among the buildings leads to 25% reduction in total annualized cost and 5% reduction in emission compared to the conventional districts. Removing the network and installation of PV and CHPs results in 9% reduction in emission and 11% reduction in cost. Simultaneous heat and electricity exchange results in a higher reduction in total annualized cost equal to 40% of the base scenario.

A fast mathematical programming procedure for simultaneous fitting of assembly components into cryoEM density maps.

Motivation: Single-particle cryo electron microscopy (cryoEM) typically produces density maps of macromolecular assemblies at intermediate to low resolution (∼5–30 Å). By fitting high-resolution structures of assembly components into these maps, pseudo-atomic models can be obtained. Optimizing the quality-of-fit of all components simultaneously is challenging due to the large search space that makes the exhaustive search over all possible component configurations computationally unfeasible.Results: We developed an efficient mathematical programming algorithm that simultaneously fits all component structures into an assembly density map. The fitting is formulated as a point set matching problem involving several point sets that represent component and assembly densities at a reduced complexity level. In contrast to other point matching algorithms, our algorithm is able to match multiple point sets simultaneously and not only based on their geometrical equivalence, but also based on the similarity of the density in the immediate point neighborhood. In addition, we present an efficient refinement method based on the Iterative Closest Point registration algorithm. The integer quadratic programming method generates an assembly configuration in a few seconds. This efficiency allows the generation of an ensemble of candidate solutions that can be assessed by an independent scoring function. We benchmarked the method using simulated density maps of 11 protein assemblies at 20 Å, and an experimental cryoEM map at 23.5 Å resolution. Our method was able to generate assembly structures with root-mean-square errors <6.5 Å, which have been further reduced to <1.8 Å by the local refinement procedure.Availability: The program is available upon request as a Matlab code package.Contact: alber@usc.edu and m.topf@cryst.bbk.ac.ukSupplementary information: Supplementary data are available at Bioinformatics Online.

Using mixed integer programming for solving the capacitated arc routing problem with vehicle/site dependencies with an application to the routing of residential sanitation collection vehicles

We present the Composite Approach for solving the Capacitated Arc Routing Problem with Vehicle/Site Dependencies (CARP-VSD). We also present two mixed integer programs, the Initial Fleet Mix Generator (IFM) and the Mathematical Programming Procedure (MPP), and a multi-criterion function called the Measure of Goodness. The IFM, MPP and Measure of Goodness are critical components of the Composite Approach. A key application area of the CARP-VSD is the routing of residential sanitation vehicles; throughout this paper, we derive parameters specific to this problem. In this paper, we describe the Composite Approach, the IFM, the MPP, the Measure of Goodness and work out several examples in detail.

Simulation of fracture in plain concrete modeled as a composite material

A composite model is used to represent the heterogeneity of plain concrete consisting of coarse aggregates, mortar matrix and the mortar-aggregate interface. The composite elements of plain concrete are modeled using triangular finite element units which have six interface nodes along the sides. Fracture is captured through a constitutive single branch softening-fracture law at the interface nodes, which bounds the elastic domain inside each triangular unit. The inelastic displacement at an interface node represents the crack opening or sliding displacement and is conjugate to the internodal force. The path-dependent softening behaviour is developed within a quasi-prescribed displacement control formulation. The crack profile is restricted to the interface boundaries of the defined mesh. No re-meshing is carried out. Solutions to the rate formulation are obtained using a mathematical programming procedure in the form of a linear complementary problem. An event by event solution strategy is adopted to eliminate solutions with simultaneous formation of softening zones in symmetric problems. The composite plain concrete model is compared to experimental results for the tensile crack growth in a Brazilian test and three-point bending tests on different sized specimens. The model is also used to simulate wedge-type shear-compression failure directly under the loading platen of a Brazilian test.

Minimum weight design of inhomogeneous rotating discs

There are numerous applications for gas turbine discs in the aerospace industry such as in turbojet engines. These discs normally work under high temperatures while subjected to high angular velocities. Minimizing the weight of such items in aerospace applications results in benefits such as low dead weights and lower costs. High speed of rotation causes large centrifugal forces in a disc and simultaneous application of high temperatures reduces disc material strength. Thus, the latter effects tend to increase deformations of the disc under the applied loads. In order to obtain a reliable disc analysis and arrive at the corresponding correct stress distribution, solutions should consider changes in material properties due to the temperature field throughout the disc. To achieve this goal, an inhomogeneous disc model with variable thickness is considered. Using the variable material properties method, stresses are obtained for the disc under rotation and a steady temperature field. In this paper this is done by modelling the rotating disc as a series of rings of different but constant properties. The optimum disc profile is arrived at by sequentially proportioning the thicknesses of each ring to satisfy the stress requirements. This method vis-à-vis a mathematical programming procedure for optimization shows several advantages. Firstly, it is simple iterative proportioning in each design cycle not requiring involved mathematical operations. Secondly, due to its simplicity it alleviates the necessity of certain simplifications that are common in so-called rigorous mathematical procedures. The results obtained, compared to those published in the literature show agreement and superiority. A further advantage of the proposed method is the independence of the end results from the initially assumed point in the iterative design routine, unlike most methods published so far.

Numerical simulation of quasibrittle fracture in concrete

A triangular unit, constructed from constant strain triangles with nodes along its sides and not at the vertex, is developed for the simulation of fracture in quasibrittle materials. Fracture is modelled through a constitutive softening–fracture law at the interface nodes, with the material within the triangular unit remaining linear elastic. The inelastic displacement at an interface node represents the crack opening, which is related to the conjugate inter-nodal force by the appropriate softening relationship. The path-dependent softening behaviour is solved in nonholonomic rate form within a quasiprescribed displacement formulation. At each event in the loading history, all equilibrium solutions for the prescribed mesh can be established and the critical equilibrium path with the minimum increment of external work adopted. The crack profile or trajectory is restricted in that it can only follow the interface boundaries of the defined mesh. No remeshing is carried out. Solutions to the nonholonomic rate formulation are obtained using a mathematical programming procedure based on the solution of an LCP. Several examples are given and compared, where possible, with published results. The advantage of this formulation is that branching and interacting cracks can be tracked subject to the limitations of the prescribed mesh.

Numerical simulation of quasibrittle fracture in concrete

A triangular unit, constructed from constant strain triangles with nodes along its sides and not at the vertex, is developed for the simulation of fracture in quasibrittle materials. Fracture is modelled through a constitutive softening–fracture law at the interface nodes, with the material within the triangular unit remaining linear elastic. The inelastic displacement at an interface node represents the crack opening, which is related to the conjugate inter-nodal force by the appropriate softening relationship. The path-dependent softening behaviour is solved in nonholonomic rate form within a quasiprescribed displacement formulation. At each event in the loading history, all equilibrium solutions for the prescribed mesh can be established and the critical equilibrium path with the minimum increment of external work adopted. The crack profile or trajectory is restricted in that it can only follow the interface boundaries of the defined mesh. No remeshing is carried out. Solutions to the nonholonomic rate formulation are obtained using a mathematical programming procedure based on the solution of an LCP. Several examples are given and compared, where possible, with published results. The advantage of this formulation is that branching and interacting cracks can be tracked subject to the limitations of the prescribed mesh.

A mathematical programming procedure for the choice problematic

In the framework of a Multicriterion Approach to the Choice Problematic, the kernel concept, which is highly inspired from that of the efficient set, is very often used. This concept generally leads to some difficulties related to its existence and uniqueness. This paper proposes a Mathematical Programming based Procedure which originates from an index matrix of valued relations of global preference or outranking in order to assist the selection of “dominating” alternative(s).

Primal/Dual Positive Math Programming: Illustrated Through an Evaluation of the Impacts of Market Resistance to Genetically Modified Grains

AbstractThe goal of Howitt's positive mathematical programming procedure is to calibrate a mathematical programming model so that it will reproduce a set of base data for the primal variables. This article develops an analogous procedure allowing one to specify the levels of both primal and dual variables. This article also sheds light on a potential ambiguity of Howitt's procedure (with attendant policy evaluation impacts). The procedure is illustrated through application to an equilibrium displacement model focused on evaluating the consequences of the reluctance of U.S. trading partners to accept genetically modified crop products for U.S. production patterns and net farm income.

Kinematical shakedown analysis with temperature-dependent yield stress

This paper describes a direct shakedown analysis of structures subjected to variable thermal and mechanical loading. The classical kinematical shakedown theorem is modified to be implemented with any displacement-based finite elements. The plastic incompressibility condition is imposed by the penalty function method. The shakedown limit is found via a non-linear mathematical programming procedure. Two numerical shakedown methods are developed and implemented to provide alternative numerical means. The temperature-dependent material model is included in theoretical and numerical calculation in a simple way. Its effect on shakedown limit is investigated. The numerical examination for some pressure vessel structures subjected to thermal and mechanical loading shows a satisfying precision and efficiency of the methods presented. Copyright © 2001 John Wiley & Sons, Ltd.

A mathematical programming procedure for selecting crops for mixed-cropping schemes

We have developed a new solution procedure for a mathematical — linear programming (LP) — model that can be optimized to obtain an optimum crop combination for a mixed-cropping scheme. Unlike two earlier solution procedures for this model, the new procedure does not involve the enumeration of all possible crop combinations or crop-subgroups obtainable from any set of crops under consideration for mixed-cropping. This makes it far more efficient. Instead of formulating and solving all LP problems associated with all possible crop-subgroups — as in one of the existing procedures — the new procedure formulates and solves a few LP problems with respect to a few crop-subgroups selected systematically. Many hypothetical crop-selection problems are simulated and solved to demonstrate the superiority of the procedure over the existing ones.

Consecutive train components analysis for inverse position of spherical wrist robot's manipulators

An original method for inverse position analysis of spherical wrist robot's manipulators is illustrated. This method is based on dividing the manipulator into a set of master train components. Mathematical governing equations are derived and used in a general mathematical programming procedure to determine the inverse position of spherical wrist robot's manipulators. The principle of superposition is applied and two numerical examples are presented to illustrate the approach. The results indicate that the technique is simple when it is compared with the other ones available. Also, it is found that the given approach reduces the computational time by a great extent.

A comparison of two approaches to fitting directed graphs to nonsymmetric proximity measures

Two algorithms for fitting directed graphs to nonsymmetric proximity data are compared. The first approach, termed MAPNET, is a direct extension of a mathematical programming procedure for fitting undirected graphs to symmetric proximity data presented by Klauer and Carroll (1989). For a user-specified number of links, the algorithm seeks to provide the connected network that gives the least-squares approximation of the proximity data with the specified number of links, allowing for linear transformations of the data. The mathematical programming approach is compared to the NETSCAL method for fitting directed graphs (Hutchinson 1989), using the Monte Carlo methods and data sets employed by Hutchinson.

Production planning in stochastic demand environments

The effects of fluctuating demand on production and inventory levels are important in manufacturing resource planning. Thus, the focus of this paper is on aggregate production planning of manufacturing resources in order to satisfy stochastic demand for a family of products, to minimize total costs that include production and inventory holding costs over a rolling horizon. If it is assumed that, in a commercial setting, the demands are fixed, then the production plans generated by a mathematical programming procedure are not responsive to the actual fluctuations of stochastic demand in each time period. The situation discussed here considers the case where demands are normally distributed with means and variances that are sequentially revised as new observations of demand are received over time. This assumption allows the probabilistic constraint to be converted to an equivalent linearly-constrained deterministic model. Extensions to the normality assumption are discussed. Other ideas, such as optimal control theory, learning and adaptive signal processing extensions, are discussed as well.

Kinematic analysis of robot's manipulators using consecutive analysis of train components

A useful method for kinematic analysis of robot's manipulators is presented. For the purpose of kinematic analysis, the manipulator is treated as a number of master train components. For each master train component, geometric constitutive equations for use in kinematic analysis are developed. The kinematic analysis of robot's manipulators are performed as parts of the master components using a mathematical programming procedure and the principle of superposition. The analysis is followed in sequence from one train component to another as they form the entire robot's manipulator. Numerical examples are presented to illustrate the proposed technique. Results are compared with the Denavit and Hartenberg approach.