Polyhedral study of mixed integer sets arising from inventory problems

“Branch-and-cut” algorithm is one of the most efficient exact approaches to solve mixed integer programs. This algorithm combines the advantages of a pure branch-and-bound approach and cutting planes scheme. Branch-and-cut algorithm computes the linear programming relaxation of the problem at each node of the search tree which is improved by the use of cuts, i.e. by the inclusion of valid inequalities. It should be taken into account that selection of strongest cuts is crucial for their effective use in branch-and-cut algorithm. In this thesis, we focus on the derivation and use of cutting planes to solve general mixed integer problems, and in particular inventory problems combined with other problems such as distribution, supplier selection, vehicle routing, etc. In order to achieve this goal, we first consider substructures (relaxations) of such problems which are obtained by the coherent loss of information. The polyhedral structure of those simpler mixed integer sets is studied to derive strong valid inequalities. Finally those strong inequalities are included in the cutting plane algorithms to solve the general mixed integer problems. We study three mixed integer sets in this dissertation. The first two mixed integer sets arise as a subproblem of the lot-sizing with supplier selection, the network design and the vendor-managed inventory routing problems. These sets are variants of the well-known single node fixed-charge network set where a binary or integer variable is associated with the node. The third set occurs as a subproblem of mixed integer sets where incompatibility between binary variables is considered. We generate families of valid inequalities for those sets, identify classes of facet-defining inequalities, and discuss the separation problems associated with the inequalities. Then cutting plane frameworks are implemented to solve some mixed integer programs. Preliminary computational experiments are presented in this direction.

Distress Tolerance among Students Referred for Treatment Following Violation of Campus Cannabis Use Policy: Relations to Use, Problems, and Motivation

Students referred to treatment after violating campus drug policies represent a high-risk group. Identification of factors related to these students’ cannabis use could inform prevention and treatment efforts. Distress tolerance (DT) is negatively related to substance-related behaviors and may be related to high-risk cannabis use vulnerability factors that can impact treatment outcome. Thus, the current study tested whether DT was related to cannabis use frequency, cannabis-related problems, and motivation to change cannabis use among 88 students referred for treatment after violating campus cannabis policies. DT was robustly, negatively related to cannabis use and related problems. DT was also significantly, negatively correlated with coping, conformity, and expansion motives. DT was directly and indirectly related to cannabis problems via coping (not conformity or expansion) motives. Motives did not mediate the relation of DT to cannabis use frequency. DT may be an important target in treatment with students who violate campus cannabis policies.

Working with the complexities of adolescent mental health problems: applying Time‐limited Adolescent Psychodynamic Psychotherapy (TAPP)

This article discusses the application in a CAMHS setting of a distinctive intervention for adolescent mental health difficulties, Time‐limited Adolescent Psychodynamic Psychotherapy (TAPP). TAPP has been developed specifically for working with adolescents and the characteristic developmental and psychosocial complexities they present to mental health services. It is widely recognised that supporting the developmental process in adolescence is central to therapeutic interventions and the therapeutic aim of TAPP is to enable recovery of the capacity to meet developmental challenges. The key factors of TAPP are described, including the formulation and working with a developmental focus, the therapeutic stance, working with transference and counter‐transference, working with time limits, and the emphasis on engagement of adolescents in therapy in TAPP. The experiences of introducing and developing TAPP in the CAMHS service are discussed with two brief and one extended case examples and this leads to a discussion of the kinds of outcomes achieved. It is concluded that TAPP is a key and relevant intervention for adolescents in complex and vulnerable situations; further work will be undertaken to continue its application in these settings and to formally assess outcomes.

Removal of cyanobacteria and cyanotoxins from drinking water by powdered activated carbon adsorption/ultrafiltration

Tese dout., Ciências e Tecnologias do Ambiente, Universidade do Algarve, 2009

Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in

We study the Riemann boundary value problem , for analytic functions in the class of analytic functions represented by the Cauchy-type integrals with density in the spaces with variable exponent. We consider both the case when the coefficient is piecewise continuous and it may be of a more general nature, admitting its oscillation. The explicit formulas for solutions in the variable exponent setting are given. The related singular integral equations in the same setting are also investigated. As an application there is derived some extension of the Szegö-Helson theorem to the case of variable exponents.

Optimised search heuristics: combining metaheuristics and exact methods to solve scheduling problems

Tese dout., Matemática, Investigação Operacional, Universidade do Algarve, 2009

Comparison of on-line learning algorithms for RBF models in greenhouse environmental control problems

The problem with the adequacy of radial basis function neural networks to model the inside air temperature as a function of the outside air temperature and solar radiation, and the inside relative humidity in an hydroponic greenhouse is addressed.

Problems in the use of benzoic acid for estimating the internal pH of yeasts

Some yeasts have the peculiar ability to grow in the presence of weak acids at rather low pH. These conditions are predominant in preserved foods and beverages such as fruit concentrates, juices, wine, where these yeasts are responsible for spoilage. The main preservatives currently utilized by food industries are sorbic, propionic, benzoic acids and SO2. It is usually assumed that weak acids diffuse through the plasma membrane in the undissociated form. In the cytoplasm, where the pH is higher, dissociation occurs resulting in accumulation of the lipid-insoluble anion and internal acidification. This is probably a very general mechanism of preventing microbial growth in foods.

Prospects and Problems for Religious Education in England, 1967-1970: Curriculum Reform in Political Context

This article provides an historical case study of an abortive attempt to revise policy and legislation relating to Religious Education (RE) in English schools in the late 1960s and early 1970s. Drawing upon published sources, including parliamentary debates, as well as previously unutilised national archival sources from the Department of Education and Science, it comments upon events which have hitherto been omitted from the historiography of RE, but which help to contextualise significant changes in RE theory and practice at that time. Moreover, it demonstrates that the current parlous state of RE in schools is in part the result of latent and longstanding issues and problems, rather than a consequence of present-day government policy alone. Therefore, in reviewing and developing RE policies and practices, all stakeholders are urged to look more closely at both changes and continuities in the subject’s past and the contexts in which they occurred.

Ant colony system based approach to single machine scheduling problems: weighted tardiness scheduling problem

The paper introduces an approach to solve the problem of generating a sequence of jobs that minimizes the total weighted tardiness for a set of jobs to be processed in a single machine. An Ant Colony System based algorithm is validated with benchmark problems available in the OR library. The obtained results were compared with the best available results and were found to be nearer to the optimal. The obtained computational results allowed concluding on their efficiency and effectiveness.

Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.