Linear Programming Analysis Research Articles

Can Optimal Combinations of Local Foods Achieve the Nutrient Density of the F100 Catch‐up Diet for Severe Malnutrition?

F100 is a fortified milk-based food used as a standard therapy for severe malnutrition. Our aim was to assess whether optimal combinations of local foods in Ghana, Bangladesh, and Latin America could achieve the nutrient density levels of F100 and, if that was unachievable, to identify the key limiting nutrients. In all of the analyses, a published list of population-specific foods (n = 59) and maximum food portions were used. The nutrient densities of individual foods were calculated to identify nutrient-dense foods and potential limiting nutrients. The feasibility of formulating diets that achieved the nutrient density of F100, for each region individually and for all regions combined, was explored by the use of linear programming analysis (4 models), which minimized the total grams of food while respecting model constraints on diet energy and nutrients, phytate:zinc molar ratio, and maximum food portion sizes. For vitamin E, riboflavin, zinc, and copper, fewer than 5 foods achieved the nutrient density of F100. All 4 linear programming model solutions were unfeasible, indicating that in all regions, community-based home-prepared rehabilitation diets for severely malnourished children will not achieve the nutrient densities of F100. In model solutions, the densities of vitamin E, riboflavin, zinc, copper, calcium, thiamin, and niacin were unachievable, indicating they are potential key problem nutrients. Optimal combinations of local foods are unlikely to achieve the nutrient density of F100, especially for vitamin E, riboflavin, thiamin, niacin, zinc, calcium, and copper. Before home-prepared rehabilitation diets with nutrient densities lower than those of F100 are promoted, it is important to establish their clinical efficacy.

Probabilistic Analysis of Linear Programming Decoding

We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in correcting a constant fraction of errors with high probability. The fraction of correctable errors guaranteed by our analysis surpasses previous non-asymptotic results for LDPC codes, and in particular exceeds the best previous finite-length result on LP decoding by a factor greater than ten. This improvement stems in part from our analysis of probabilistic bit-flipping channels, as opposed to adversarial channels. At the core of our analysis is a novel combinatorial characterization of LP decoding success, based on the notion of a generalized matching. An interesting by-product of our analysis is to establish the existence of ``probabilistic expansion'' in random bipartite graphs, in which one requires only that almost every (as opposed to every) set of a certain size expands, for sets much larger than in the classical worst-case setting.

Multi-parametric sensitivity analysis in piecewise linear fractional programming

In this paper, we study multi-parametric sensitivity analysis forprogramming problems with the piecewise linear fractional objective function in the tolerance region. We construct critical regions for simultaneous and independent perturbations in the objective function coefficients and in the right-hand-side vector of the given problem. Necessary and sufficient conditions are derived to classify perturbation parameters as 'focal' and 'non-focal'. Non-focal parameters can be deleted from the analysis, because of their low sensitivity in practice. Theoretical results are illustrated with the help of a numerical example.

Determining optimal maize-based enterprise in soba local government area of Kaduna State, Nigeria

This study was designed to determine the optimal maize-based enterprise in soba local government area of Kaduna state, Nigeria. Data were collected from a survey conducted with 200 farmers in eight districts in the local government area. Results of the dominance analysis showed that maize/cowpea enterprise dominated the other enterprises because it had the highest gross margin and lowest total variable cost. The linear programming analysis indicated that a gross margin of N56,920.30 was obtained in the planned farm as against N26,282.00, per hectare of maize/cowpea in the unplanned farm. The study also indicates that Maize/cowpea enterprise was the most competitive enterprise in the study area. Labour and land were the most limiting resources. Agro-Science Vol. 6 (2) 2007: pp. 28-32

Sensitivity analysis in linear semi-infinite programming: Perturbing cost and right-hand-side coefficients

This paper analyzes the effect on the optimal value of a given linear semi-infinite programming problem of the kind of perturbations which more frequently arise in practical applications: those which affect the objective function and the right-hand-side coefficients of the constraints. In particular, we give formulae which express the exact value of a perturbed problem as a linear function of the perturbation.

Ten years of sustainability evaluation using the MESMIS framework: Lessons learned from its application in 28 Latin American case studies

This paper focuses on sustainability evaluation and, more specifically, it describes and analyses the Indicator-based Framework for Evaluation of Natural Resource Management Systems (MESMIS, its Spanish acronym), ten years after its development. This framework fulfilled a pioneering role by proposing an integrated interdisciplinary approach to assess sustainability of peasant NRMS. Results of a thorough analysis of 28 case studies are presented, to seek improvement to the methods. The MESMIS approach is acceptable to a wide range of systems and to stakeholders; it has greatly assisted in sustainability evaluation and has increased understanding of the complexity of such systems, making it a significant tool for sustainability evaluation. The degree to which MESMIS and evaluation in general was shown to be an effective tool in reaching more sustainable systems depended mainly on the type of participation applied; additional guidance and information on participation is essential. Improvement possibilities are further directed to exploration and incorporation into the framework of 'new' tools that have proved valuable for the monitoring and integration of indicators (i.e.simulation models, linear programming and trade-off analysis), tools capable of assessing effects of management on indicators in the long term and thereby increasing the understanding of system attributes.

Quantifying the metabolic capabilities of engineered Zymomonas mobilis using linear programming analysis

BackgroundThe need for discovery of alternative, renewable, environmentally friendly energy sources and the development of cost-efficient, "clean" methods for their conversion into higher fuels becomes imperative. Ethanol, whose significance as fuel has dramatically increased in the last decade, can be produced from hexoses and pentoses through microbial fermentation. Importantly, plant biomass, if appropriately and effectively decomposed, is a potential inexpensive and highly renewable source of the hexose and pentose mixture. Recently, the engineered (to also catabolize pentoses) anaerobic bacterium Zymomonas mobilis has been widely discussed among the most promising microorganisms for the microbial production of ethanol fuel. However, Z. mobilis genome having been fully sequenced in 2005, there is still a small number of published studies of its in vivo physiology and limited use of the metabolic engineering experimental and computational toolboxes to understand its metabolic pathway interconnectivity and regulation towards the optimization of its hexose and pentose fermentation into ethanol.ResultsIn this paper, we reconstructed the metabolic network of the engineered Z. mobilis to a level that it could be modelled using the metabolic engineering methodologies. We then used linear programming (LP) analysis and identified the Z. mobilis metabolic boundaries with respect to various biological objectives, these boundaries being determined only by Z. mobilis network's stoichiometric connectivity. This study revealed the essential for bacterial growth reactions and elucidated the association between the metabolic pathways, especially regarding main product and byproduct formation. More specifically, the study indicated that ethanol and biomass production depend directly on anaerobic respiration stoichiometry and activity. Thus, enhanced understanding and improved means for analyzing anaerobic respiration and redox potential in vivo are needed to yield further conclusions for potential genetic targets that may lead to optimized Z. mobilis strains.ConclusionApplying LP to study the Z. mobilis physiology enabled the identification of the main factors influencing the accomplishment of certain biological objectives due to metabolic network connectivity only. This first-level metabolic analysis model forms the basis for the incorporation of more complex regulatory mechanisms and the formation of more realistic models for the accurate simulation of the in vivo Z. mobilis physiology.

Added sugars displaced the use of vital nutrients in the National Food Stamp Program Survey.

Recent increases in consumption of added sugars in the US can reduce intake of vital nutrients and increase the overall energy intakes. A comprehensive framework is necessary for addressing the controversy surrounding the effects of added sugars on nutrient intakes while controlling for dietary knowledge, behavioral factors, and total energy intakes, especially among low-income households. This paper analyzed the proximate determinants of 1-wk availability (or use) of added sugars by 913 households participating in the National Food Stamp Program Survey conducted in 1996-97. In addition, households' use of protein; fiber; calcium; iron; beta-carotene; vitamins A, C, E, B-6, and B-12; folic acid; and potassium were explained by socioeconomic and behavioral factors and by added sugars use. Linear programming analyses were conducted for assessing the effects of food prices on added sugars use. Participation in Supplemental Food Program for Women, Infants and Children program, food stamp benefits, and consumption of low-fat diets were associated (P<0.05) with lower added sugars use. Furthermore, greater use of added sugars significantly lowered households' uses of protein; iron; vitamins A, C, B-6, and B-12; and potassium. Behavioral and socioeconomic variables such as adopting a low-fat diet, consuming fruits and vegetables, saving money at grocery stores, frequency of shopping trips, skipping meals, and food insecurity were often important predictors of nutrient use. Overall, the results indicated that added sugars should be discouraged in dietary guidelines, because their adverse effects on diet quality were evident in this low-income population.

Conversion to organic arable farming in The Netherlands: A dynamic linear programming analysis

Several studies show that organic farming is more profitable than conventional farming. However, in reality not many farmers convert to organic farming. Policy makers and farmers do not have clear insight into factors which hamper or stimulate the conversion to organic farming. The objective of this paper is to develop a dynamic linear programming model to analyse the effects of different limiting factors on the conversion process of farms over time. The model is developed for a typical arable farm in The Netherlands central clay region, and is based on two static liner programming models (conventional and organic). The objective of the model is to maximise the net present value over a 10-year planning horizon. The results of the analysis of a basic scenario show that conversion to organic farming is more profitable than staying conventional. In order to arrive at the actual profitable phase of organic farming, the farmer has to pass through the economically difficult 2-year conversion period. Sensitivity analysis shows that if depreciation is 25% higher than conventional fixed costs due to machinery made superfluous by conversion, conversion is less profitable than staying conventional. Also the availability of hired labour, which can be constrained in peak periods, has a strong effect on the cropping plan and the amount of area converted. Further analysis shows that a slight drop (2%) in organic prices lowers the labour income of the farmer and makes conversion less profitable than conventional farming. For farmers, a minimum labour income can be required to ‘survive’. The analysis shows that constraint on minimum labour income makes stepwise conversion the best way for farmers to overcome economic difficulties during conversion.

Smoothed analysis of integer programming

We present a probabilistic analysis of integer linear programs (ILPs). More specifically, we study ILPs in a so-called smoothed analysis in which it is assumed that first an adversary specifies the coefficients of an integer program and then (some of) these coefficients are randomly perturbed, e.g., using a Gaussian or a uniform distribution with small standard deviation. In this probabilistic model, we investigate structural properties of ILPs and apply them to the analysis of algorithms. For example, we prove a lower bound on the slack of the optimal solution. As a result of our analysis, we are able to specify the smoothed complexity of classes of ILPs in terms of their worst case complexity. This way, we obtain polynomial smoothed complexity for packing and covering problems with any fixed number of constraints. Previous results of this kind were restricted to the case of binary programs.

Livestock carrying capacity evaluation in an integrated farming system: A case study from the mid-hills of Nepal

The crop livestock integrated farming system practiced in hilly regions of developing countries largely depends on the ecosystem as a whole. More especifically, the livestock component of the farming system relies heavily on natural resources such as forest, grazing and agricultural land for the supply of feed and fodder. The importance of animals as agents of nutrient recycling, sources of rural energy in terms of draft power and fuel, as well as being major contributors to the farm economy, has resulted in an increased population of ruminants in these regions, creating a threat to the sustainability and productivity of these land resources. This paper is an attempt to evaluate the livestock carrying capacity of land resources and to formulate the optimum herd size compatible with the differently resourced farm categories within the sub-watershed region of the mid-hills in Nepal. Our analysis reveals that the livestock carrying capacity of the land resources at the watershed level is 11696 Livestock Units (LU), whereas current stocking is 12985 LU, suggesting an overstocking of 1289 LU at the watershed level. Total feed supply from different sources is 12668 mt/yr whereas current Total Digestive Nutrient (TDN) demand is 14060 mt/yr, a negative balance of 1393 mt/yr. The excess livestock at the sub-watershed level directly implies excess livestock holding, producing a poor nutritional status for the farm household. Linear programming analysis reveals that the farmers of large, medium and small category farms can optimize their livestock holding by a combination of 3 LU buffaloes and 4 LU goats, 2 LU buffaloes and 4 LU goats and 1 LU buffaloes and 4.4 LU goats, thus giving maximum return to the farm family without exerting pressure on fragile natural resources.

Model Checking Linear Programs with Arrays

In previous work we proposed Linear Programs as a fine grained model for imperative programs, and showed how the model checking procedure used in SLAM can be generalised to a model checking procedure for Linear Programs. In this paper we show that our model checking procedure for linear programs can be extended in such a way to support the analysis of linear programs featuring a symbol for undefined values and conditional expressions. This extension is particularly important as it paves the way to the construction of model checking procedures for wider classes of imperative programs such as, e.g., linear programs with arrays. We provide a detailed account of a symbolic model checking procedure for this extended class of linear programs, discuss its implementation in the eureka tool, and present experimental results that confirm its effectiveness in the analysis of linear programs with arrays.

SHORT-TERM SCHEDULING OF CHEMICAL PROCESS INCLUDING UNCERTAINTY

This paper addresses the short-term scheduling of chemical process with uncertainty considerations. A multiobjective robust optimization method is proposed to identify Pareto optimal solutions, where Normal boundary intersection (NBI) technique is utilized in order to trace the Pareto optimal surface in the objective space, on which each point represents a trade-off between the various objectives. The issue is also addressed using parametric mixed integer linear programming (pMILP) analysis where uncertain parameters are present on the right hand side (RHS) of the constraints. For the case of multiple uncertain parameters, a new algorithm of multiparametric linear programming (mpLP) is proposed that does not require the construction of the LP tableaus but relies on the comparison between solutions at leaf nodes. Given the range of uncertain parameters, the output of this proposed framework is a set of optimal integer solutions and their corresponding critical regions and optimal functions.

Utilization of Duckweed (Lemna paucicostata) in Least-cost Feed Formulation for Broiler Starter: A Linear Programming Analysis

Utilization of Duckweed (Lemna paucicostata) in Least-cost Feed Formulation for Broiler Starter: A Linear Programming Analysis

A fresh view on the tolerance approach to sensitivity analysis in linear programming

The tolerance approach to sensitivity analysis in linear programming aims at finding a unique numerical value (tolerance) representing the maximum absolute perturbation which can be applied simultaneously and independently on each right-hand-side or objective coefficient without affecting the optimality of the given basis. Some extensions have been proposed in the literature, which allow for individual tolerances for each coefficient, thus enlarging the tolerance region. In this paper we review the main results concerning the approach, giving new and simpler proofs, and we propose an efficient geometric algorithm returning a tolerance region that is maximal with respect to inclusion. We compare our method with the existing ones on two examples, showing how a priori information can be naturally exploited by our algorithm to further enlarge individual tolerances.

Analysis of linear programming in model predictive control

The linear programming formulations of model predictive control are known to exhibit degenerate solution behavior. In this work, a multi-parametric linear programming technique is utilized to analyze the control laws that are generated from various linear programming based MPC routines. These various routines explore a number of factors, including objective function selection and constraint handling on the control laws generated from LP based MPC. A single input single output system is used to demonstrate that the use of input velocity penalties, input blocking, and ∞ -norm objective functions can limit or eliminate this undesirable behavior. Finally, a paper machine cross directional control problem is used to demonstrate the control laws generated from LP based MPC for a multivariable example.

Unifying Optimal Partition Approach to Sensitivity Analysis in Conic Optimization

We study convex conic optimization problems in which the right-hand side and the cost vectors vary linearly as functions of a scalar parameter. We present a unifying geometric framework that subsumes the concept of the optimal partition in linear programming (LP) and semidefinite programming (SDP) and extends it to conic optimization. Similar to the optimal partition approach to sensitivity analysis in LP and SDP, the range of perturbations for which the optimal partition remains constant can be computed by solving two conic optimization problems. Under a weaker notion of nondegeneracy, this range is simply given by a minimum ratio test. We discuss briefly the properties of the optimal value function under such perturbations.

Tolerance Sensitivity and Optimality Bounds in Linear Programming

Traditional sensitivity analysis in linear programming usually focuses on variations of one coefficient or term at a time. The tolerance approach was proposed to provide a decision maker with an effective and easy-to-use method to summarize the effects of simultaneous and independent changes in selected parameters. In particular, for variations of the objective function coefficients, the approach gives a maximum-tolerance percentage within which selected coefficients may vary from their estimated values (within a priori limits) while still retaining the same optimal basic feasible solution. Although an optimal solution may cease being optimal for variations beyond the maximum-tolerance percentage, it may still be close to optimal. Herein we characterize the potential loss of optimality for variations beyond the maximum-tolerance percentage as a maximum-regret function. We consider theoretical properties of this function and propose a method to compute a relevant portion of it.

Food-Based Dietary Guidelines Can Be Developed and Tested Using Linear Programming Analysis

Effective food-based dietary guidelines (FBDGs) are required to combat micronutrient deficiencies. This study aimed to develop a rigorous approach for designing population-specific FBDGs. A 4-phase approach based on linear programming analysis was used to design, test, and refine the FBDGs. This was illustrated for Malawian children. In phase I, the objective function minimized the difference in the energy contributed by different food groups between modeled and observed diets for 16 observed diet types, while preferentially selecting foods most often consumed. Constraints ensured nutrient adequacy and diet palatability. In phase II, the meal/snack patterns of the phase I modeled diets were examined to develop season-specific FBDGs. In phase III, the robustness of these FBDGs, for ensuring a nutritionally adequate diet, was tested. The objective function, in this analysis, minimized selected nutrient levels in the modeled diets (i.e., chose the "worst-case scenario"), while respecting the FBDGs, palatability, and energy constraints. The FBDGs were refined in phase IV. In the Malawian example used to illustrate our approach, the FBDGs promoted daily consumption of maize flour, small dry fish (>or=20 g), leaf relish, and 2-3 snacks. The last mentioned included mangoes, in the food-shortage season, and pumpkin in the food-plenty season. In addition, legume relish was recommended in the food-shortage season. The approach presented here can be used to design and then test the robustness of FBDGs for meeting nutrient recommendations.

Sensitivity Analysis and Uncertainty in Linear Programming

Linear programming (LP) is one of the great successes to emerge from operations research and management science. It is well developed and widely used. LP problems in practice are often based on numerical data that represent rough approximations of quantities that are inherently difficult to estimate. Because of this, most LP-based studies include a postoptimality investigation of how a change in the data changes the solution. Researchers routinely undertake this type of sensitivity analysis (SA), and most commercial packages for solving linear programs include the results of such an analysis as part of the standard output report. SA has shortcomings that run contrary to conventional wisdom. Alternate models address these shortcomings.