Simultaneous column-and-row generation for large-scale linear programs with column-dependent-rows

In this paper, we develop a simultaneous column-and-row generation algorithm that could be applied to a general class of large-scale linear programming problems. These problems typically arise in the context of linear programming formulations with exponentially many variables. The defining property for these formulations is a set of linking constraints, which are either too many to be included in the formulation directly, or the full set of linking constraints can only be identified, if all variables are generated explicitly. Due to this dependence between columns and rows, we refer to this class of linear programs as problems with column-dependent-rows. To solve these problems, we need to be able to generate both columns and rows on-the-fly within an efficient solution approach. We emphasize that the generated rows are structural constraints and distinguish our work from the branch-and-cut-and-price framework. We first characterize the underlying assumptions for the proposed column-and-row generation algorithm. These assumptions are general enough and cover all problems with column-dependent-rows studied in the literature up until now to the best of our knowledge. We then introduce in detail a set of pricing subproblems, which are used within the proposed column-and-row generation algorithm. This is followed by a formal discussion on the optimality of the algorithm. To illustrate the proposed approach, the paper is concluded by applying the proposed framework to the multi-stage cutting stock and the quadratic set covering problems

Simultaneous column-and-row generation for large-scale linear programs with column-dependent-rows

In this paper, we develop a simultaneous column-and-row generation algorithm for a general class of large-scale linear programming problems. These problems typically arise in the context of linear programming formulations with exponentially many variables. The defining property for these formulations is a set of linking constraints. These constraints are either too many to be included in the formulation directly, or the full set of linking constraints can only be identified, if all variables are generated explicitly. Due to this dependence between columns and rows, we refer to this class of linear programs as problems with column-dependent-rows. To solve these problems, we need to be able to generate both columns and rows on the fly within an efficient solution method. We emphasize that the generated rows are structural constraints and distinguish our work from the branch-and-cut-and-price framework. We first characterize the underlying assumptions for the proposed column-and-row generation algorithm and then introduce the associated set of pricing subproblems in detail. The proposed methodology is demonstrated on numerical examples for the multi-stage cutting stock and the quadratic set covering problems

A note on "A LP-based heuristic for a time-constrained routing problem"

In their paper, Avella et al. (2006) investigate a time-constrained routing problem. The core of the proposed solution approach is a large-scale linear program that grows both row- and column-wise when new variables are introduced. Thus, a column-and-row generation algorithm is proposed to solve this linear program optimally, and an optimality condition is presented to terminate the column-and-row generation algorithm. We demonstrate by using Lagrangian duality that this optimality condition is incorrect and may lead to a suboptimal solution at termination

A note on "A LP-based heuristic for a time-constrained routing problem"

Avella et al. (2006) [Avella, P., D'Auria, B., Salerno, S. (2006). A LP-based heuristic for a time-constrained routing problem. European Journal of Operational Research 173:120-124] investigate a time-constrained routing (TCR) problem. The core of the proposed solution approach is a large-scale linear program (LP) that grows both row- and column-wise when new variables are introduced. Thus, a column-and-row generation algorithm is proposed to solve this LP optimally, and an optimality condition is presented to terminate the column-and-row generation algorithm. We demonstrate that this optimality condition is incorrect and may lead to a suboptimal solution at termination. We identify the source of this error and discuss how the generic column-and-row generation algorithm proposed by Muter et al. (2010) may be applied to this TCR problem in order to solve the proposed large-scale LP correctly

The preparation and characterization of some metal complexes with tridentate ONO ligand derived from phenyl hydrazine

The phenyl hydrazine was react readily with acetic acid chloride in [1:2] ratio in alkyl of ethanolic solution, and refluxe for five hours to produce a new ligand of (N-Carboxymethyl-N-phenyl-hydrazino)-acetic acid [H2L]

Kontribusi Supervisi Akedemik Kepala Sekolah, Kompetensi Guru Dalam Penyusunan Administrasi Pembelajaran Dan Motivasi Kerja Guru Terhadap Implementasi Kurikulum Tingkat Satuan Pendidikan Pada SMA Negeri Bertaraf Internasional Di Kabupaten

Penelitian ini bertujuan untuk mengetahui besarnya kontribusi (1) supervisiAkademik kepala sekolah, (2) kompetensi guru dalam penyusunan administrasipembelajaran, (3) motivasi kerja guru baik secara tunggal, maupun simultanterhadap implementasi Kurikulum Tingkat Satuan Pendidikan .Populasi subyek penelitian ini adalah seluruh guru SMA RSBI di KabupatenGianyar yang berjumlah 125 orang, (study sensus), Semua anggota populasidijadikan responden, pemelitian ini menggunakan rancangan ex-post facto.melibatkan tiga variable bebas, Supervisi Akedemik Kepala Sekolah, KompetensiGuru Dalam Penyusunan Administrasi Pembelajaran dan Motivasi Kerja Guru.Data dikumpulkan dengan kuesioner. Data dianalisis dengan analisis regresisederhana,regresi ganda dan korelasi. parsialHasil analisis terhadap Implementasi KTSP ditemukan: (1) terdapatkontribusi yang signifikan supervisi akademik kepala sekolah melalui persamaanregresi Y = 24,577 + 0,508X1 dengan kontribusi sebesar 25,90% dan sumbanganefektif sebesar 17,30%, (2) terdapat kontribusi yang signifikan kompetensi gurudalam penyusunan administrasi pembelajaran melalui persamaan regresi Y =27,114+ 0,458X2 dengan kontribusi sebesar 21,10% dan sumbangan efektifsebesar 11,20%, (3) terdapat kontribusi yang signifikan motivasi kerja gurumelalui persamaan regresi Y = 35,534+ 0,289X3 dengan kontribusi sebesar 8,40%dan sumbangan efektif sebesar 5,50%, dan (4) terdapat kontribusi yang signifikansecara bersama-sama antara supervisi akademik kepala sekolah, kompetensi gurudalam penyusunan administrasi pembelajaran, dan motivasi kerja guru terhadapimplementasi KTSP pada SMA Negeri bertaraf Internasional di KabupatenGianyar melalui persamaan regresi Y = 11,256+ 0,341X1 + 0,244X2 +0,190X3dengan Freg = 20,781 (p<0,05) dengan sumbangan efektif sebesar 34%. Dengan demikian ketiga variabel tersebut dapat dijadikan prediktor tingkatkecenderungan implementasi KTSP sekolah pada SMA bertaraf Internasional diKabuapten Gianyar

The Application of a Statistical Model Investigating Reactive Oxygen Species in Premature Ageing Syndromes

The premature ageing syndromes Hutchison-Gilford Progeria Syndrome (HGPS) and Restrictive Dermopathy (RD) are rare genetic disorders that result in greatly accelerated ageing. RD is neonatal fatal, whereas children suffering from HGPS age approximately 8 times faster than normal individuals and die during their second decade of life -usually from either stroke or heart disease. The underlying genetic causes of these diseases affect the post-translational processing of the protein lamin A. Lamin A is a Class V intermediate filament protein which resides in the cell nucleus, where it forms a cage-like structure against mechanical strain and is involved in transcriptional regulation, protecting the cell’s genome from damage. HGPS is caused by a mutation in LMNA, the gene encoding lamin A, which results in a truncated mutant protein termed progerin. RD, on the other hand, has genetic roots in the mutation of the metalloprotease Zmpste24, which has a vital role in the processing of prelamin A. The mutation results in the accumulation of immature prelamin A at the nuclear membrane. As a result of increased understanding of the defects in HGPS arising from LMNA mutations a number of therapeutic routes are currently being trialled, but with little success. Work in my supervisor’s laboratory has suggested that defective forms of lamin A may lead to the production of reactive oxygen species (ROS) in cells. ROS can cause a range of damage in cells including DNA damage. This type of damage eventually leads to cellular senescence which is thought to be a precursor to normal ageing. The results put forth here suggest that primary dermal fibroblasts from these premature ageing syndromes show defects in both DNA damage repair and ROS buffering ability. This is shown from my statistical modelling of immunofluorescence data showing DNA double strand break repair over time. RD and HGPS fibroblasts showed persistent γ-H2AX foci after DNA damage induction with oxidative stress, yet showed improved repair after induction with a direct DNA break inducing agent, etoposide. Proliferative markers indicated a reduced proliferative capacity in premature ageing fibroblasts, which was heightened after treatment with oxidative stress. Taken together these results suggest that RD and HGPS fibroblasts more readily enter a state of cellular senescence when exposed to oxidising conditions than control fibroblasts from both and young and old donors. Phenotypical aberrant cellular morphology associated with these diseases was shown to be independent of the defect in ROS buffering ability, supporting evidence showing improvements in abnormal nuclear shape by treatment with farnesyltransferase inhibitors (FTIs) have little impact on the DNA damage repair defects associated with these diseases. From the results here, N-acetyl cysteine (NAC), a powerful antioxidant, has shown to be effective in reducing the proportion of irreparable DNA damage in HGPS and RD fibroblasts. It has also been shown to increase repair rates by actively reducing ROS levels as detected by flow cytometry. NAC treatment therefore shows beneficial properties in treating certain phenotypes associated with progeria and may require consideration as a cooperative form of treatment. The implications of these results are that HGPS is a useful model for normal ageing as fibroblasts from an elderly donor showed signs not dissimilar to those of HGPS, albeit in milder form. These included an increase in the number of persistent γ-H2AX foci and increased ROS levels. This suggests that activation of the HGPS cryptic splice site in normal ageing may account for increased age-associated genomic instability Thus it is tempting to speculate that lamin A is a modulator of both premature and normal ageing through its regulation of cellular oxidative damage

Negotiating normativities: Counter narratives of lesbian queer world making in Cape Town

This thesis explores the different modes and meanings of queer world making (QWM) of lesbians in Cape Town. Through an analysis of in depth interviews and focus groups it reveals lesbians' constructions of their intersectional and permeable QWM through a series of counter narratives enacted in three interconnected socialities. Generational narratives reveal psycho-social processes of recognition of lesbian desire and coming into a lesbian subjectivity in a range of modes of QWM. Lesbian erotic world making centres their entitlement to enact sexual autonomy and sexual pleasure. Their counter narratives reveal how they simultaneously inhabit and extend normative gender regimes. Their productions of desire reveal a lesbian centred frame of sexual pleasure that extends the erotogenic body beyond the genitalia, innovates and transforms hegemonic libidinal zones, and extends phallocentric culture. Lesbian motherhood as a site of QWM reveals the participants' negotiations, conflict, stress and agency in relation to the 'good mother' discourse that undergirds mothering practices in South Africa. Their counter narratives reveal how they simultaneously resist and re-inscribe heteronormativity in their motherhood practice. Ironically, it is through publicly assuming their sexuality that they are they able to perform 'good motherhood'. They perform private resistance and public complicity with good mother ideologies; and simultaneously centre and destabilize the role of the father. They manage their 'difference' to the heterosexual norm by providing their children with tools to navigate heteronormativity, while simultaneously claiming being an unexceptional family. Their queer place making strategies in everyday spaces in Cape Town demonstrate how they rework racialised notions of belonging to incorporate the queer body (at times ephemerally) to make Cape Town home. Their creation of lesbian social networks and communities, embodied in lesbian social scenes and within their private homes, reveals how Cape Town is experienced as a hybrid space, their contrasting and competing narratives of the city revealing narratives of fractured belonging. QWM reveals how lesbians resist and (re)shape hegemonic identities, discourses and practices, revealing 'a mode of being in the world that is also inventing the world' (Muñoz, 1999: 121). QWM is about borderlands (Anzaldúa, 1987), where one lives within the possibility of multiple plotlines (Clandinin & Rosiek, 2006). Their queer life worlds are permeable to racialised heteronormativities. But their agency reveals multi-vocal and multivalent queer life worlds, enmeshed in the web of racialised, gendered, sexualised, aged and class-based hierarchies in Cape Town. There is no singular way of doing a lesbian subjectivity, no singular utopian notion of a lesbian community. Their differences are located in their varying political perspectives and their social positionalities of privilege and penalty, in short, how they position themselves within the 'politics of belonging' (Yuval Davis, 2006)

On the analysis of butter

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Algorithms for the One-Dimensional Two-Stage Cutting Stock Problem

In this paper, we consider a two-stage extension of one-dimensional cutting stock problem which arises when technical requirements inhibit cutting large stock rolls to demanded widths of finished rolls directly. Therefore, demands on finished rolls are fulfilled through two subsequent cutting processes, in which rolls produced in the former are used as input for the latter, while the number of stock rolls used is minimized. We tackle the pattern-based formulation of this problem which typically has a very large number of columns and constraints. The special structure of this formulation induces both a column-wise and a row-wise increase when solved by column generation. We design an exact simultaneous column-and-row generation algorithm whose novel element is a row-generating subproblem that generates a set of columns and rows. For this subproblem, which is modeled as an unbounded knapsack problem, we propose three algorithms: implicit enumeration, column generation which renders the overall methodology nested column generation, and a hybrid algorithm. The latter two are integrated in a well-known knapsack algorithm which forges a novel branch-and-price algorithm for the row-generating subproblem. Extensive computational experiments are conducted, and performances of the three algorithms are compared