Regional adjustments in grain production : a linear programming analysis : mathematical models, proofs, methods of data collection and estimation, and supplementary tables /

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An integrated scheduling problem of PCB components on sequential pick-and-place machines:mathematical models and heuristic solutions

This paper formulates several mathematical models for determining the optimal sequence of component placements and assignment of component types to feeders simultaneously or the integrated scheduling problem for a type of surface mount technology placement machines, called the sequential pick-andplace (PAP) machine. A PAP machine has multiple stationary feeders storing components, a stationary working table holding a printed circuit board (PCB), and a movable placement head to pick up components from feeders and place them to a board. The objective of integrated problem is to minimize the total distance traveled by the placement head. Two integer nonlinear programming models are formulated first. Then, each of them is equivalently converted into an integer linear type. The models for the integrated problem are verified by two commercial packages. In addition, a hybrid genetic algorithm previously developed by the authors is adopted to solve the models. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total traveling distance.

A short-term production scheduling methodology for open-pit mines

A multi-resource multi-stage scheduling methodology is developed to solve short-term open-pit mine production scheduling problems as a generic multi-resource multi-stage scheduling problem. It is modelled using essential characteristics of short-term mining production operations such as drilling, sampling, blasting and excavating under the capacity constraints of mining equipment at each processing stage. Based on an extended disjunctive graph model, a shifting-bottleneck-procedure algorithm is enhanced and applied to obtain feasible short-term open-pit mine production schedules and near-optimal solutions. The proposed methodology and its solution quality are verified and validated using a real mining case study.

An open pit multistage mine production scheduling model for drilling, blasting and excavating operations

This paper proposes a new multi-resource multi-stage scheduling problem for optimising the open-pit drilling, blasting and excavating operations under equipment capacity constraints. The flow process is analysed based on the real-life data from an Australian iron ore mine site. The objective of the model is to maximise the throughput and minimise the total idle times of equipment at each stage. The following comprehensive mining attributes and constraints have been considered: types of equipment; operating capacities of equipment; ready times of equipment; speeds of equipment; block-sequence-dependent movement times of equipment; equipment-assignment-dependent operation times of blocks; distances between each pair of blocks; due windows of blocks; material properties of blocks; swell factors of blocks; and slope requirements of blocks. It is formulated by mixed integer programming and solved by ILOG-CPLEX optimiser. The proposed model is validated with extensive computational experiments to improve mine production efficiency at the operational level. The model also provides an intelligent decision support tool to account for the availability and usage of equipment units for drilling, blasting and excavating stages.

MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

Mathematical models for the arrangement and the cleaning of the river basin and surroundings of the river sandy grounds to its passage by the city of Salta (Argentina)

The province of Salta is located the Northwest of Argentina in the border with Bolivia, Chile and Paraguay. Its Capital is the city of Salta that concentrates half of the inhabitants of the province and has grown to 600000 hab., from a small active Spanish town well founded in 1583. The city is crossed by the Arenales River descending from close mountains at North, source of water and end of sewers. But with actual growing it has become a focus of infection and of remarkable unhealthiness. It is necessary to undertake a plan for the recovery of the river, directed to the attainment of the well-being and to improve the life?s quality of the Community. The fundamental idea of the plan is to obtain an ordering of the river basin and an integral management of the channel and its surroundings, including the cleaning out. The improvement of the water?s quality, the healthiness of the surroundings and the improvement of the environment, must go hand by hand with the development of sport activities, of relaxation, tourism, establishment of breeding grounds, kitchen gardens, micro enterprises with clean production and other actions that contribute to their benefit by the society, that being a basic factor for their care and sustainable use. The present pollution is organic, chemical, industrial, domestic, due to the disposition of sweepings and sewer effluents that affects not only the flora and small fauna, destroying the biodiversity, but also to the health of people living in their margins. Within the plan it will be necessary to consider, besides hydric and environmental cleaning and the prevention of floods, the planning of the extraction of aggregates, the infrastructure and consolidation of margins works and the arrangement of all the river basin. It will be necessary to consider the public intervention at state, provincial and local level, and the private intervention. In the model it has been necessary to include the sub-model corresponding to the election of the entity to be the optimal instrument to reach the proposed objectives, giving an answer to the social, environmental and economic requirements. For that the authors have used multi-criteria decision methods to qualify and select alternatives, and for the programming of their implementation. In the model the authors have contemplated the short, average and long term actions. They conform a Paretooptimal alternative which secures the ordering, integral and suitable management of the basin of the Arenales River, focusing on its passage by the city of Salta.

Monitoring Infection Risk for Air and Soil Borne Fungal Plant Pathogens using Antibody and DNA Techniques and Mathematical Models describing Environmental Parameters

Economic losses resulting from disease development can be reduced by accurate and early detection of plant pathogens. Early detection can provide the grower with useful information on optimal crop rotation patterns, varietal selections, appropriate control measures, harvest date and post harvest handling. Classical methods for the isolation of pathogens are commonly used only after disease symptoms. This frequently results in a delay in application of control measures at potentially important periods in crop production. This paper describes the application of both antibody and DNA based systems to monitor infection risk of air and soil borne fungal pathogens and the use of this information with mathematical models describing risk of disease associated with environmental parameters.

Application of mathematical models to mycotoxins children risk assessment: a case study of Portuguese children exposure to co-occurring mycotoxins in processed cereal-based foods

People, animals and the environment can be exposed to multiple chemicals at once from a variety of sources, but current risk assessment is usually carried out based on one chemical substance at a time. In human health risk assessment, ingestion of food is considered a major route of exposure to many contaminants, namely mycotoxins, a wide group of fungal secondary metabolites that are known to potentially cause toxicity and carcinogenic outcomes. Mycotoxins are commonly found in a variety of foods including those intended for consumption by infants and young children and have been found in processed cereal-based foods available in the Portuguese market. The use of mathematical models, including probabilistic approaches using Monte Carlo simulations, constitutes a prominent issue in human health risk assessment in general and in mycotoxins exposure assessment in particular. The present study aims to characterize, for the first time, the risk associated with the exposure of Portuguese children to single and multiple mycotoxins present in processed cereal-based foods (CBF). Portuguese children (0-3 years old) food consumption data (n=103) were collected using a 3 days food diary. Contamination data concerned the quantification of 12 mycotoxins (aflatoxins, ochratoxin A, fumonisins and trichothecenes) were evaluated in 20 CBF samples marketed in 2014 and 2015 in Lisbon; samples were analyzed by HPLC-FLD, LC-MS/MS and GC-MS. Daily exposure of children to mycotoxins was performed using deterministic and probabilistic approaches. Different strategies were used to treat the left censored data. For aflatoxins, as carcinogenic compounds, the margin of exposure (MoE) was calculated as a ratio of BMDL (benchmark dose lower confidence limit) to the aflatoxin exposure. The magnitude of the MoE gives an indication of the risk level. For the remaining mycotoxins, the output of exposure was compared to the dose reference values (TDI) in order to calculate the hazard quotients (ratio between exposure and a reference dose, HQ). For the cumulative risk assessment of multiple mycotoxins, the concentration addition (CA) concept was used. The combined margin of exposure (MoET) and the hazard index (HI) were calculated for aflatoxins and the remaining mycotoxins, respectively. 71% of CBF analyzed samples were contaminated with mycotoxins (with values below the legal limits) and approximately 56% of the studied children consumed CBF at least once in these 3 days. Preliminary results showed that children exposure to single mycotoxins present in CBF were below the TDI. Aflatoxins MoE and MoET revealed a reduced potential risk by exposure through consumption of CBF (with values around 10000 or more). HQ and HI values for the remaining mycotoxins were below 1. Children are a particularly vulnerable population group to food contaminants and the present results point out an urgent need to establish legal limits and control strategies regarding the presence of multiple mycotoxins in children foods in order to protect their health. The development of packaging materials with antifungal properties is a possible solution to control the growth of moulds and consequently to reduce mycotoxin production, contributing to guarantee the quality and safety of foods intended for children consumption.

Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.