Linear Programming Analysis Research Articles

Characterization of Proton Binding Properties of Extracellular Polymeric Substances in an Expanded Granular Sludge Bed Using Linear Programming Analysis

Characterization of Proton Binding Properties of Extracellular Polymeric Substances in an Expanded Granular Sludge Bed Using Linear Programming Analysis

S0830301 昭和基地マイクログリッドのエンジン発電機の最適運用計画に関する検討

The ship Shirase in charge of transporting fuel and research equipment to the Japanese Showa Base in the Antarctica is approaching its loading capacity limit due to the increasing research activities and new requirements for ambient comfort in the base. Also, due to the negative effects of the emissions caused by the burning of fossil fuels, the increasing utilization of renewable energy and the reduction of fuel consumption represent important challenges. In order to reduce fuel consumption and to increase the utilization of renewable energy, we are considering the implementation of a microgrid for the base named the Showa Base Microgrid (SBMG). In this work, the microgrid is considered to be composed, together with the solar and wind generators, of distributed engine generators, a seawater source heat pump and electric thermal storage heaters, and an operation plan is implemented. In this work, as analysis methods, we propose a mixed integer linear programming (Analysis A) and genetic algorithm (GA) (Analysis B). For these two methods, the amounts of fuel consumption are calculated, and the difference between the amounts of fuel consumption for each method, together with the differences in operation for the engine generators are evaluated.

Complementary feeding recommendations based on locally available foods in Indonesia.

Affordable, locally contextual complementary feeding recommendations (CFRs) that take into account cultural diversity and differences in food availability will be more likely to result in long-term improvements in complementary feeding practices than general recommendations. More objective approaches, such as linear programming (LP), have been recommended to identify optimal but CFRs to meet nutrient requirements given local food availability, food patterns, food portions, and cost. To present results of our previous studies in which we developed CFRs using LP and to provide an example of how these CFRs can be put into practice in a community intervention trial in Indonesia. Dietary data were obtained using single 24-hour dietary recall or 1-day weighed diet record combined with 1-day 24-hour recall and 5-day food intake tally. With the use of the LP approach, nutrient intakes were optimized while ensuring that a realistic diet was selected by using constraints such as the diet's energy content, food patterns, food portions, and cost. The price per 100 g of edible portion was obtained from market surveys in two or three local markets in each study area. LP analysis was performed using Super Solver in MS Excel or Optifood software. Iron, zinc, calcium, and niacin were problem nutrients in all age groups of children (6 to 8, 9 to 11, and 12 to 23 months) in both rural and periurban areas, except among children of higher socioeconomic status in urban areas. Thiamin and folate were also problem nutrients found in some settings. Animal-source foods (meat, fish, poultry, and eggs [MFPE] and fortified foods were the nutrient-dense foods identified by LP to fill the nutrient gaps of these problem nutrients. Iron, calcium, zinc, niacin, and potentially folate and thiamine are typical "problem nutrients" in complementary foods of Indonesian children. However, the extent of dietary inadequacy varies across age groups, area, and socioeconomic level. MFPE and fortified foods can improve micronutrient adequacy in complementary feeding diets and should be promoted in CFRs.

Linear programming analysis of the R-parity violation within EDM-constraints

The constraint on the $R$-parity violating supersymmetric interactions is discussed in the light of current experimental data of the electric dipole moment of neutron, $^{129}$Xe , $^{205}$Tl, and $^{199}$Hg atoms, and YbF and ThO molecules. To investigate the constraints without relying upon the assumption of the dominance of a particular combination of couplings over all the rest, an extensive use is made of the linear programming method in the scan of the parameter space. We give maximally possible values for the EDMs of the proton, deuteron, $^3$He nucleus, $^{211}$Rn, $^{225}$Ra, $^{210}$Fr, and the $R$-correlation of the neutron beta decay within the constraints from the current experimental data of the EDMs of neutron, $^{129}$Xe, $^{205}$Tl, and $^{199}$Hg atoms, and YbF and ThO molecules using the linear programming method. It is found that the $R$-correlation of the neutron beta decay and hadronic EDMs are very useful observables to constrain definite regions of the parameter space of the $R$-parity violating supersymmetry.

Sensitivity analysis of linear programming in the presence of correlation among right-hand side parameters or objective function coefficients

In the literature, sensitivity analysis of linear programming (LP) has been widely studied. However, only some very simple and special cases were considered when right-hand side (RHS) parameters or objective function coefficients (OFC) correlate to each other. In the presence of correlation when one parameter changes, other parameters vary, too. Here principal component analysis is used to convert the correlation of the LP homogenous parameters into functional relations. Then, using the derivatives of the functional relations, it is possible to perform classical sensitivity analysis for the LP with correlation among RHS parameters or OFC. The validity of the devised method is corroborated by open literature examples having correlation among homogenous parameters.

The role of non-Archimedean epsilon in finding the most efficient unit: With an application of professional tennis players

The determination of a single efficient decision making unit (DMU) as the most efficient unit has been attracted by decision makers in some situations. Some integrated mixed integer linear programming (MILP) and mixed integer nonlinear programming (MINLP) data envelopment analysis (DEA) models have been proposed to find a single efficient unit by the optimal common set of weights. In conventional DEA models, the non-Archimedean infinitesimal epsilon, which forestalls weights from being zero, is useless if one utilizes the well-known two-phase method. Nevertheless, this approach is inapplicable to integrated DEA models. Unfortunately, in some proposed integrated DEA models, the epsilon is neither considered nor determined. More importantly, based on this lack some approaches have been developed which will raise this drawback.In this paper, first of all some drawbacks of these models are discussed. Indeed, it is shown that, if the non-Archimedean epsilon is ignored, then these models can neither find the most efficient unit nor rank the extreme efficient units. Next, we formulate some new models to capture these drawbacks and hence attain assurance regions. Finally, a real data set of 53 professional tennis players is applied to illustrate the applicability of the suggested models.

A mathematical model proposal for cost-effective course planning in large hierarchical organizations

Hierarchical organizations, especially in government agencies, are known by their pyramidal structures and continuous training needs resulting from promotions and/or assignments. Using scientific and rational methods in the job analysis/description, recruitment/selection, assignment, performance appraisal and career planning functions of human resource management (HRM) process decreases training costs. In this study, we develop a new chain of methodologies (the cost-effective course planning model (CECPM)) to decrease training costs and increase the level of specialization. This methodology is implemented in the following steps of the HRM process: (1) the job analysis/description step, where our Mission Description Matrix defines in measurable units the amount of training needed for an employee assigned to a position, (2) the career matrix step, where the minimum training costs for an employee’s career path are determined using our network-flow model and (3) the assignment step, where we propose a decision support system composed of an analytical hierarchy process, linear programming and Pareto optimality analysis. The results indicate that our proposed system ensures minimum training needs while satisfying person-to-position compatibility and personnel’s preferences.

Identifying the anchor points in DEA using sensitivity analysis in linear programming

In this paper, the anchor points in DEA, as an important subset of the set of extreme efficient points of the production possibility set (PPS), are studied. A basic definition, utilizing the multiplier DEA models, is given. Then, two theorems are proved which provide necessary and sufficient conditions for characterization of these points. The main results of the paper lead to a new interesting connection between DEA and sensitivity analysis in linear programming theory. By utilizing the established theoretical results, a successful procedure for identification of the anchor points is presented.

The use of linear programming to determine whether a formulated complementary food product can ensure adequate nutrients for 6- to 11-month-old Cambodian infants

A new software tool, Optifood, developed by the WHO and based on linear programming (LP) analysis, has been developed to formulate food-based recommendations. This study discusses the use of Optifood for predicting whether formulated complementary food (CF) products can ensure dietary adequacy for target populations in Cambodia. Dietary data were collected by 24-h recall in a cross-sectional survey of 6- to 11-mo-old infants (n = 78). LP model parameters were derived from these data, including a list of foods, median serving sizes, and dietary patterns. Five series of LP analyses were carried out to model the target population's baseline diet and 4 formulated CF products [WinFood (WF), WinFood-Lite (WF-L), Corn-Soy-Blend Plus (CSB+), and Corn-Soy-Blend Plus Plus (CSB++)], which were added to the diet in portions of 33 g/d dry weight (DW) for infants aged 6-8 mo and 40 g/d DW for infants aged 9-11 mo. In each series of analyses, the nutritionally optimal diet and theoretical range, in diet nutrient contents, were determined. The LP analysis showed that baseline diets could not achieve the Recommended Nutrient Intake (RNI) for thiamin, riboflavin, niacin, folate, vitamin B-12, calcium, iron, and zinc (range: 14-91% of RNI in the optimal diets) and that none of the formulated CF products could cover the nutrient gaps for thiamin, niacin, iron, and folate (range: 22-86% of the RNI). Iron was the key limiting nutrient, for all modeled diets, achieving a maximum of only 48% of the RNI when CSB++ was included in the diet. Only WF and WF-L filled the nutrient gap for calcium. WF-L, CSB+, and CSB++ filled the nutrient gap for zinc (9- to 11-mo-olds). The formulated CF products improved the nutrient adequacy of complementary feeding diets but could not entirely cover the nutrient gaps. These results emphasize the value of using LP to evaluate special CF products during the intervention planning phase. The WF study was registered at controlled-trials.com as ISRCTN19918531.

A novel approach for sensitivity analysis in linear programs with trapezoidal fuzzy numbers

There are several methods in the literature to deal with the sensitivity analysis of fuzzy linear programming (FLP) problems. In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, a new method is proposed to handle the sensitivity analysis of that kind of FLP problems in which the elements of the coefficient matrix of the constraints are represented by real numbers, and the remaining parameters are represented by symmetric trapezoidal fuzzy numbers. To the best of our knowledge, till now there is no method in the literature to deal with the sensitivity analysis of such FLP problems without converting them to the crisp linear programming problems. The advantages of the proposed method over existing methods are discussed. To illustrate the approach a numerical example is examined by using the proposed method and the obtained results are discussed. The method is easy to understand and to apply for dealing with the sensitivity analysis of the same problems occurring in real life situations.

Matching socio-economic and environmental efficiency of wood-residues energy chain: a partial equilibrium model for a case study in Alpine area

Abstract Combining the economics and the environmental and social aspects of bioenergy chain implementation is a difficult task, particularly for wood fuel production. Multiple aspects, such as financial analysis, technology development, natural resource exploitation and avoided environmental pollution, must be considered simultaneously. Thus, decision support models seem to be the proper tools for the overall definition of strategies in the wood energy sector. The objective of this study has been to develop a partial equilibrium model able to quantify the socio-economic and environmental effects of policy, technology and best biomass allocation scenarios on the forest residue chain. The model, based on multi-objective linear programming and spatial analysis, considers the financial benefits/losses and the potential trends of three compartments: sawmills, forest enterprises and energy plants. In addition, the model computes avoided emissions for bioheat and bioelectricity production and introduces an impact indicator for the road transport of biomass. Model outputs are defined using a multi criteria approach. The main results stress the importance of both environmental parameters and the implementation of organic Rankine cycle technology for the optimization of the entire bioenergy chain. The model was tested in an Italian Alpine region (province of Trento).

Performance Analysis of Classification Methods and Alternative Linear Programming Integrated with Fuzzy Delphi Feature Selection

Among various statistical and data mining discriminant analysis proposed so far for group classification, linear programming discriminant analysis have recently attracted the researchers' interest. This study evaluates multi-group discriminant linear programming (MDLP) for classification problems against well-known methods such as neural networks, support vector machine, and so on. MDLP is less complex compared to other methods and does not suffer from local optima. However, sometimes classification becomes infeasible due to insufficient data in databases such as in the case of an Internet Service Provider (ISP) small and medium-sized market considered in this research. This study proposes a fuzzy Delphi method to select and gather required data. The results show that the performance of MDLP is better than other methods with respect to correct classification, at least for small and medium-sized datasets.

Designing appropriate complementary feeding recommendations: tools for programmatic action.

Suboptimal complementary feeding practices contribute to a rapid increase in the prevalence of stunting in young children from age 6 months. The design of effective programmes to improve infant and young child feeding requires a sound understanding of the local situation and a systematic process for prioritizing interventions, integrating them into existing delivery platforms and monitoring their implementation and impact. The identification of adequate food-based feeding recommendations that respect locally available foods and address gaps in nutrient availability is particularly challenging. We describe two tools that are now available to strengthen infant and young child-feeding programming at national and subnational levels. ProPAN is a set of research tools that guide users through a step-by-step process for identifying problems related to young child nutrition; defining the context in which these problems occur; formulating, testing, and selecting behaviour-change recommendations and nutritional recipes; developing the interventions to promote them; and designing a monitoring and evaluation system to measure progress towards intervention goals. Optifood is a computer-based platform based on linear programming analysis to develop nutrient-adequate feeding recommendations at lowest cost, based on locally available foods with the addition of fortified products or supplements when needed, or best recommendations when the latter are not available. The tools complement each other and a case study from Peru illustrates how they have been used. The readiness of both instruments will enable partners to invest in capacity development for their use in countries and strengthen programmes to address infant and young child feeding and prevent malnutrition.

Distributionally robust mixed integer linear programs: Persistency models with applications

In this paper, we review recent advances in the distributional analysis of mixed integer linear programs with random objective coefficients. Suppose that the probability distribution of the objective coefficients is incompletely specified and characterized through partial moment information. Conic programming methods have been recently used to find distributionally robust bounds for the expected optimal value of mixed integer linear programs over the set of all distributions with the given moment information. These methods also provide additional information on the probability that a binary variable attains a value of 1 in the optimal solution for 0–1 integer linear programs. This probability is defined as the persistency of a binary variable. In this paper, we provide an overview of the complexity results for these models, conic programming formulations that are readily implementable with standard solvers and important applications of persistency models. The main message that we hope to convey through this review is that tools of conic programming provide important insights in the probabilistic analysis of discrete optimization problems. These tools lead to distributionally robust bounds with applications in activity networks, vertex packing, discrete choice models, random walks and sequencing problems, and newsvendor problems.

AN ECONOMIC ASSESSMENT OF THE SUSTAINABILITY OF TRADITIONAL AGROFORESTRY SYSTEMS: THE CASE OF KANDYAN FOREST GARDENS

A feature of the Sri Lanka Forestry Sector Alaster Plan of 1995 is the promotionol conservation-oriented methods or forest management. In this contextagroforestry systems such as Kandyan forest gardens (KFCi.\) are important, since they are not only productive and relieve pressure on the naturalforests,but also conserve a rich collection of biodiversity. Although national policyseeks to promote agroforestry ill order to achieve nationally desirableobjectives. the successful adoption or this policy depends on the degree ofcongruence between different national objectives, the multiple objectives offarmers, and changing socio-economic conditions. The objective of this study was to make an economic assessment of KFCrs, front the point of vieH' ()/ theindividualfarmers who operate under changing and varied economic objectives.Data were collected by a field survey. using a structured questionnaire. Tabularanalvtical techniques were then used to describe important features of !'FCrs.The major technique used to find out how the structure ofhome gardens changeswith changing economic objectives was linear programming analysis by thejIIOT4. [) model. The results ofthe SIU(~V indicate that even under the conditionthat a farmer 's main objective is tv maximize the net present value (}lPI), homegardens can still be an important source of timber, because (?f their largecomponent 0/ multipurpose trees, which include species such as jak andcoconut. 717C binding constraint of the model is land; sensitivity analysis showedthat with an increase in the land area of KFGs, both the number of species andthe income increase.

Preemptive and non-preemptive generalized min sum set cover

In the (non-preemptive) Generalized Min Sum Set Cover Problem, we are given $$n$$ ground elements and a collection of sets $$\mathcal{S }= \{S_1, S_2, \ldots , S_m\}$$ where each set $$S_i \in 2^{[n]}$$ has a positive requirement $$\kappa (S_i)$$ that has to be fulfilled. We would like to order all elements to minimize the total (weighted) cover time of all sets. The cover time of a set $$S_i$$ is defined as the first index $$j$$ in the ordering such that the first $$j$$ elements in the ordering contain $$\kappa (S_i)$$ elements in $$S_i$$ . This problem was introduced by Azar et al. (2009) with interesting motivations in web page ranking and broadcast scheduling. For this problem, constant approximations are known by Bansal et al. (2010) and Skutella and Williamson (Oper Res Lett 39(6):433---436, 2011). We study the version where preemption is allowed. The difference is that elements can be fractionally scheduled and a set $$S$$ is covered in the moment when $$\kappa (S)$$ amount of elements in $$S$$ are scheduled. We give a 2-approximation for this preemptive problem. Our linear programming relaxation and analysis are completely different from the aforementioned previous works. We also show that any preemptive solution can be transformed into a non-preemptive one by losing a factor of 6.2 in the objective function. As a byproduct, we obtain an improved $$12.4$$ -approximation for the non-preemptive problem.

Evaluation and optimization of the spatial organization of the petrochemical industry in China

The spatial organization of the Chinese petrochemical industry was optimized according to the status of development of the industry employing linear programming and ArcGIS spatial analysis tools. We first identified the indexes of the spatial organization of the petrochemical industry and established a comprehensive evaluation index system that includes four major categories and 11 indicators. The weight of each index was then determined by the analytical hierarchy process. Afterward, taking the 337 Chinese prefecture-level administrations as basic units and scientifically evaluating the potential comprehensive layout coefficients of the cities, 151 prefecture-level administrative units were selected as the basis for the choice of optimization sites with a linear programming model. Secondly, using the 151 prefecture-level administrative units and the maximum-coverage model, the optimal number and spatial distribution of refineries were identified for service radii of 100, 200 and 300 km. Thirdly, considering the actual distribution of China’s refineries, general rules for the number of refinery layout points and objective values were summarized, and 52 refinery layout points were selected for China. Finally, with ArcGIS spatial analysis tools, the spatial effect of the 52 optimal refinery layout points was simulated for the service scope and socioeconomic factors respectively, and the GDP and population data for each refinery layout point were then extracted within the service scope. On this basis and with estimation of the intensity of crude-oil consumption, final results were obtained for the optimal spatial organization of the Chinese refining capacity and ethylene production capacity.

AN ECONOMIC ASSESSMENT OF THE SUSTAINABILITY OF TRADITIONAL AGROFORESTRY SYSTEMS: THE CASE OF KANDYAN FOREST GARDENS

A feature of the Sri Lanka Forestry Sector Master Plan 1995 is the promotion conservation-oriented methods or forest management. In this context agroforestry systems such as Kandyan forest gardens (KFGs) are important,since they are not only productive and relieve pressure on the natural forests,but also conserve a rich collection of biodiversity. Although national policy seeks to promote agroforestry in order to achieve nationally desirable objectives, the successful adoption or this policy depends on the degree of congruence between different national objectives, the multiple objectives of farmers, and changing socio-economic conditions. The objective of this study was to make an economic assessment of KFGs, from the point of view of the individual farmers who operate under changing and varied economic objectives.Data were collected by a field survey. using a structured questionnaire. Tabular analytical techniques were then used to describe important features of KFGs.The major technique used to find out how the structure of home gardens changes with changing economic objectives was linear programming analysis by the MOTAD model. The results of the study indicate that even under the condition that a farmer 's main objective is to maximize the net present value (NPV), home gardens can still be an important source of timber, because of their large component of multipurpose trees, which include species such as jak and coconut. The binding constraint of the model is land; sensitivity analysis showed that with an increase in the land area of KFGs, both the number of species and the income increase.

Computation of polytopic invariants for polynomial dynamical systems using linear programming

This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given instant, it will remain in the set forever in the future. Polytopic invariants for polynomial systems can be verified by solving a set of optimization problems involving multivariate polynomials on bounded polytopes. Using the blossoming principle together with properties of multi-affine functions on rectangles and Lagrangian duality, we show that certified lower bounds of the optimal values of such optimization problems can be computed effectively using linear programs. This allows us to propose a method based on linear programming for verifying polytopic invariant sets of polynomial dynamical systems. Additionally, using sensitivity analysis of linear programs, one can iteratively compute a polytopic invariant set. Finally, we show using a set of examples borrowed from biological applications, that our approach is effective in practice.

Evaluating navigation safety for harbours in Taiwan:An empirical study

The purpose of this study is to develop a model to evaluate navigation safety for vessels sailing to Taiwanese commercial harbours, based on a dataset of marine casualties. In order to devise the practical model, linear programming and Data Envelopment Analysis (DEA) are applied to develop a DEA model algorithm. Firsly, a simplified DEA model structure is constructed with one input variable, eleven output variables and four decision-making units (DMUs). Then, a dataset of marine casualties are employed to obtain all variables, as well as to appraise the superiorities of all DMUs. Finally, utilising a DEA solver, the highest navigation safety for the DMUs can be evaluated. Furthermore, an empirical survey of navigation safety in Taiwanese commercial harbours is performed to appraise the systematic approach, ie, the DEA model. The results of this study show that: (1) Keelung and Kaohsiung are the most dangerous harbours; (2) Taiwan’s safest commercial harbour is Haulien, followed in ranking by Taichung, Kaohsiung and Keelung; (3) Based on the algorithm of the proposed DEA model, the results can reflect reality.