Application of Mathematical Programming to the Plywood Design and Manufacturing Problem

Plywood manufacture includes two fundamental stages. The first is to peel or separate logs into veneer sheets of different thicknesses. The second is to assemble veneer sheets into finished plywood products. At the first stage a decision must be made as to the number of different veneer thicknesses to be peeled and what these thicknesses should be. At the second stage, choices must be made as to how these veneers will be assembled into final products to meet certain constraints while minimizing wood loss. These decisions present a fundamental management dilemma. Costs of peeling, drying, storage, handling, etc. can be reduced by decreasing the number of veneer thicknesses peeled. However, a reduced set of thickness options may make it infeasible to produce the variety of products demanded by the market or increase wood loss by requiring less efficient selection of thicknesses for assembly. In this paper the joint problem of veneer choice and plywood construction is formulated as a nonlinear integer programming problem. A relatively simple optimal solution procedure is developed that exploits special problem structure. This procedure is examined on data from a British Columbia plywood mill. Restricted to the existing set of veneer thicknesses and plywood designs used by that mill, the procedure generated a solution that reduced wood loss by 79 percent, thereby increasing net revenue by 6.86 percent. Additional experiments were performed that examined the consequences of changing the number of veneer thicknesses used. Extensions are discussed that permit the consideration of more than one wood species.

Size optimization of a cantilever beam under deformation-dependent loads with application to wheat stalks

In this paper, we consider the optimization of the cross-section profile of a cantilever beam under deformation-dependent loads. Such loads are encountered in plants and trees, cereal crop plants such as wheat and corn in particular. The wind loads acting on the grain-bearing spike of a wheat stalk vary with the orientation of the spike as the stalk bends; this bending and the ensuing change in orientation depend on the deformation of the plant under the same load.The uprooting of the wheat stalks under wind loads is an unresolved problem in genetically modified dwarf wheat stalks. Although it was thought that the dwarf varieties would acquire increased resistance to uprooting, it was found that the dwarf wheat plants selectively decreased the Young's modulus in order to be compliant. The motivation of this study is to investigate why wheat plants prefer compliant stems. We analyze this by seeking an optimal shape of the wheat plant's stem, which is modeled as a cantilever beam, by taking the large deflection of the stem into account with the help of co-rotational finite element beam modeling. The criteria considered here include minimum moment at the fixed ground support, adequate stiffness and strength, and the volume of material. The result reported here is an example of flexibility, rather than stiffness, leading to increased strength.

Supersymmetric Solution Of Gauge Hierarchy Problem

Some recent developments with respect to the resolution of the gauge hierarchy problem in grand unified theories by supersymmetry are presented. A general argument is developed to show how global supersymmetry maintains the stability of the different mass-scales under perturbative effects.

A Branch and Bound Algorithm for a Transportation Type Problem with Piecewise Linear Convex Objective Function

A branch and bound type algorithm is presented in this paper to the problem of finding a transportation schedule which minimises the total transportation cost, where the transportation cost over each route is assumed to be a piecewice linear continuous convex function with increasing slopes. The algorithm is an extension of the work done by Balachandran and Perry, in which the transportation cost over each route is assumed to beapiecewise linear discontinuous function with decreasing slopes. A numerical example is solved illustrating the algorithm.

On the Transform Method of Solution of an External Crack Problem

The breakdown of the usual method of Fourier transforms in the problem of an external line crack in a thin infinite elastic plate is discovered and the correct solution of this problem is derived using the concept of a generalised Fourier transform of a type discussed first by Golecki [1] in connection with Flamant's problem.

The buffering effect of selection, optimization, and compensation strategy use on the relationship between problem solving demands and occupational well-being: A daily diary study

This study investigated within-person relationships between daily problem solving demands, selection, optimization, and compensation (SOC) strategy use, job satisfaction, and fatigue at work. Based on conservation of resources theory, it was hypothesized that high SOC strategy use boosts the positive relationship between problem solving demands and job satisfaction, and buffers the positive relationship between problem solving demands and fatigue. Using a daily diary study design, data were collected from 64 administrative employees who completed a general questionnaire and two daily online questionnaires over four work days. Multilevel analyses showed that problem solving demands were positively related to fatigue, but unrelated to job satisfaction. SOC strategy use was positively related to job satisfaction, but unrelated to fatigue. A buffering effect of high SOC strategy use on the demands-fatigue relationship was found, but no booster effect on the demands-satisfaction relationship. The results suggest that high SOC strategy use is a resource that protects employees from the negative effects of high problem solving demands.

Suomen maatalouden tuottamat kasvihuonekaasujen päästöt eri politiikkaskenaarioissa

Climate change is the single biggest environmental problem in the world at the moment. Although the effects are still not fully understood and there is considerable amount of uncertainty, many na-tions have decided to mitigate the change. On the societal level, a planner who tries to find an eco-nomically optimal solution to an environmental pollution problem seeks to reduce pollution from the sources where reductions are most cost-effective. This study aims to find out how effective the instruments of the agricultural policy are in the case of climate change mitigation in Finland. The theoretical base of this study is the neoclassical economic theory that is based on the assumption of a rational economic agent who maximizes his own utility. This theoretical base has been widened towards the direction clearly essential to the matter: the theory of environmental eco-nomics. Deeply relevant to this problem and central in the theory of environmental economics are the concepts of externalities and public goods. What are also relevant are the problems of global pollution and non-point-source pollution. Econometric modelling was the method that was applied to this study. The Finnish part of the AGMEMOD-model, covering the whole EU, was used for the estimation of the development of pollution. This model is a seemingly recursive, partially dynamic partial-equilibrium model that was constructed to predict the development of Finnish agricultural production of the most important products. For the study, I personally updated the model and also widened its scope in some relevant matters. Also, I devised a table that can calculate the emissions of greenhouse gases according to the rules set by the IPCC. With the model I investigated five alternative scenarios in comparison to the base-line scenario of Agenda 2000 agricultural policy. The alternative scenarios were: 1) the CAP reform of 2003, 2) free trade on agricultural commodities, 3) technological change, 4) banning the cultivation of organic soils and 5) the combination of the last three scenarios as the maximal achievement in reduction. The maximal achievement in the alternative scenario 5 was 1/3 of the level achieved on the base-line scenario. CAP reform caused only a minor reduction when com-pared to the base-line scenario. Instead, the free trade scenario and the scenario of technological change alone caused a significant reduction. The biggest single reduction was achieved by banning the cultivation of organic land. However, this was also the most questionable scenario to be real-ized, the reasons for this are further elaborated in the paper. The maximal reduction that can be achieved in the Finnish agricultural sector is about 11 % of the emission reduction that is needed to comply with the Kyoto protocol.

The avocado problem solver field guide

This guide has been produced to assist Australian avocado growers and others involved in the avocado supply chain to identify the wide range of pests, diseases, nutrient deficiencies and toxicitites, and other disorders that may affect orchards and the quality of fruit reaching the consumer

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Considering gambling involvement in the understanding of problem gambling: A large cross-sectional study of an Australian population

Instead of regarding a particular type of gambling activity (for example, electronic gambling machines, table games) as an isolated factor for problem gambling, recent research suggests that gambling involvement (for example, as measured by the number of different types of gambling activities played) should also be considered. Using a large sample of the Victorian adult population, this study found that the strength of association between problem gambling and the type of gambling reduced after adjusting for gambling involvement. This finding supports recent research that gambling involvement is an important factor in assessing the risk of problem gambling. The study also provides insights into the measurements of gambling involvement and provides alternative statistical modelling to analyse problem gambling.

On the bottleneck linear programming problem

In this paper, the results on primal methods for Bottleneck Linear Programming (BLP) problem are briefly surveyed, the primal method is presented and the degenerate case related to Bottleneck Transportation Problem (BTP) is explicitly considered. The algorithm is based on the idea of using auxiliary coefficients as is done by Garfinkel and Rao [6]. The modification presented for the BTP rectifies the defect in Hammer's method in the case of degenerate basic feasible solution. Illustrative numerical examples are also given.

Two-Impurity Kondo Problem

The two-impurity Kondo problem is studied by use of perturbative scaling techniques. The physics is determined by the interplay between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the two impurity spins and the Kondo effect. In particular, for a strong ferromagnetic RKKY interaction the susceptibility exhibits three structures as the temperature is lowered, corresponding to the ferromagnetic locking together of the two impurity spins followed by a two-stage freezing out of their local moments by the conduction electrons due to the Kondo effect.

A time minimising transportation problem with quality dependent time

The usual assumption made in time minimising transportation problem is that the time for transporting a positive amount in a route is independent of the actual amount transported in that route. In this paper we make a more general and natural assumption that the time depends on the actual amount transported. We assume that the time function for each route is an increasing piecewise constant function. Four algorithms - (1) a threshold algorithm, (2) an upper bounding technique, (3) a primal dual approach, and (4) a branch and bound algorithm - are presented to solve the given problem. A method is also given to compute the minimum bottle-neck shipment corresponding to the optimal time. A numerical example is solved illustrating the algorithms presented in this paper.

Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.