The Learning of the Mathematical Models to Aid Decision Making in the High Level Engineering Schools?

At present, in the University curricula in most countries, the decision theory and the mathematical models to aid decision making is not included, as in the graduate program like in Doctored and Master´s programs. In the Technical School of High Level Agronomic Engineers of the Technical University of Madrid (ETSIA-UPM), the need to offer to the future engineers training in a subject that could help them to take decisions in their profession was felt. Along the life, they will have to take a lot of decisions. Ones, will be important and others no. In the personal level, they will have to take several very important decisions, like the election of a career, professional work, or a couple, but in the professional field, the decision making is the main role of the Managers, Politicians and Leaders. They should be decision makers and will be paid for it. Therefore, nobody can understand that such a professional that is called to practice management responsibilities in the companies, does not take training in such an important matter. For it, in the year 2000, it was requested to the University Board to introduce in the curricula an optional qualified subject of the second cycle with 4,5 credits titled " Mathematical Methods for Making Decisions ". A program was elaborated, the didactic material prepared and programs as Maple, Lingo, Math Cad, etc. installed in several IT classrooms, where the course will be taught. In the course 2000-2001 this subject was offered with a great acceptance that exceeded the forecasts of capacity and had to be prepared more classrooms. This course in graduate program took place in the Department of Applied Mathematics to the Agronomic Engineering, as an extension of the credits dedicated to Mathematics in the career of Engineering.

Task classification and decision processes in monitoring behaviour

Task classification is introduced as a method for the evaluation of monitoring behaviour in different task situations. On the basis of an analysis of different monitoring tasks, a task classification system comprising four task 'dimensions' is proposed. The perceptual speed and flexibility of closure categories, which are identified with signal discrimination type, comprise the principal dimension in this taxonomy, the others being sense modality, the time course of events, and source complexity. It is also proposed that decision theory provides the most complete method for the analysis of performance in monitoring tasks. Several different aspects of decision theory in relation to monitoring behaviour are described. A method is also outlined whereby both accuracy and latency measures of performance may be analysed within the same decision theory framework. Eight experiments and an organizational study are reported. The results show that a distinction can be made between the perceptual efficiency (sensitivity) of a monitor and his criterial level of response, and that in most monitoring situations, there is no decrement in efficiency over the work period, but an increase in the strictness of the response criterion. The range of tasks exhibiting either or both of these performance trends can be specified within the task classification system. In particular, it is shown that a sensitivity decrement is only obtained for 'speed' tasks with a high stimulation rate. A distinctive feature of 'speed' tasks is that target detection requires the discrimination of a change in a stimulus relative to preceding stimuli, whereas in 'closure' tasks, the information required for the discrimination of targets is presented at the same point In time. In the final study, the specification of tasks yielding sensitivity decrements is shown to be consistent with a task classification analysis of the monitoring literature. It is also demonstrated that the signal type dimension has a major influence on the consistency of individual differences in performance in different tasks. The results provide an empirical validation for the 'speed' and 'closure' categories, and suggest that individual differences are not completely task specific but are dependent on the demands common to different tasks. Task classification is therefore shovn to enable improved generalizations to be made of the factors affecting 1) performance trends over time, and 2) the consistencv of performance in different tasks. A decision theory analysis of response latencies is shown to support the view that criterion shifts are obtained in some tasks, while sensitivity shifts are obtained in others. The results of a psychophysiological study also suggest that evoked potential latency measures may provide temporal correlates of criterion shifts in monitoring tasks. Among other results, the finding that the latencies of negative responses do not increase over time is taken to invalidate arousal-based theories of performance trends over a work period. An interpretation in terms of expectancy, however, provides a more reliable explanation of criterion shifts. Although the mechanisms underlying the sensitivity decrement are not completely clear, the results rule out 'unitary' theories such as observing response and coupling theory. It is suggested that an interpretation in terms of the memory data limitations on information processing provides the most parsimonious explanation of all the results in the literature relating to sensitivity decrement. Task classification therefore enables the refinement and selection of theories of monitoring behaviour in terms of their reliability in generalizing predictions to a wide range of tasks. It is thus concluded that task classification and decision theory provide a reliable basis for the assessment and analysis of monitoring behaviour in different task situations.

Dynamic decision networks for decision-making in self-adaptive systems:a case study

Bayesian decision theory is increasingly applied to support decision-making processes under environmental variability and uncertainty. Researchers from application areas like psychology and biomedicine have applied these techniques successfully. However, in the area of software engineering and speci?cally in the area of self-adaptive systems (SASs), little progress has been made in the application of Bayesian decision theory. We believe that techniques based on Bayesian Networks (BNs) are useful for systems that dynamically adapt themselves at runtime to a changing environment, which is usually uncertain. In this paper, we discuss the case for the use of BNs, speci?cally Dynamic Decision Networks (DDNs), to support the decision-making of self-adaptive systems. We present how such a probabilistic model can be used to support the decision making in SASs and justify its applicability. We have applied our DDN-based approach to the case of an adaptive remote data mirroring system. We discuss results, implications and potential bene?ts of the DDN to enhance the development and operation of self-adaptive systems, by providing mechanisms to cope with uncertainty and automatically make the best decision.

Optimal release strategies for biological control agents: an application of stochastic dynamic programming to population management

1. Establishing biological control agents in the field is a major step in any classical biocontrol programme, yet there are few general guidelines to help the practitioner decide what factors might enhance the establishment of such agents. 2. A stochastic dynamic programming (SDP) approach, linked to a metapopulation model, was used to find optimal release strategies (number and size of releases), given constraints on time and the number of biocontrol agents available. By modelling within a decision-making framework we derived rules of thumb that will enable biocontrol workers to choose between management options, depending on the current state of the system. 3. When there are few well-established sites, making a few large releases is the optimal strategy. For other states of the system, the optimal strategy ranges from a few large releases, through a mixed strategy (a variety of release sizes), to many small releases, as the probability of establishment of smaller inocula increases. 4. Given that the probability of establishment is rarely a known entity, we also strongly recommend a mixed strategy in the early stages of a release programme, to accelerate learning and improve the chances of finding the optimal approach.

Using stochastic dynamic programming to determine optimal fire management for Banksia ornata

1. A model of the population dynamics of Banksia ornata was developed, using stochastic dynamic programming (a state-dependent decision-making tool), to determine optimal fire management strategies that incorporate trade-offs between biodiversity conservation and fuel reduction. 2. The modelled population of B. ornata was described by its age and density, and was exposed to the risk of unplanned fires and stochastic variation in germination success. 3. For a given population in each year, three management strategies were considered: (i) lighting a prescribed fire; (ii) controlling the incidence of unplanned fire; (iii) doing nothing. 4. The optimal management strategy depended on the state of the B. ornata population, with the time since the last fire (age of the population) being the most important variable. Lighting a prescribed fire at an age of less than 30 years was only optimal when the density of seedlings after a fire was low (< 100 plants ha(-1)) or when there were benefits of maintaining a low fuel load by using more frequent fire. 5. Because the cost of management was assumed to be negligible (relative to the value of the persistence of the population), the do-nothing option was never the optimal strategy, although lighting prescribed fires had only marginal benefits when the mean interval between unplanned fires was less than 20-30 years.

The use of stochastic dynamic programming in optimal landscape reconstruction for metapopulations

A decision theory framework can be a powerful technique to derive optimal management decisions for endangered species. We built a spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren (Stipiturus malachurus intermedius), a critically endangered Australian bird. Using diserete-time Markov,chains to describe the dynamics of a metapopulation and stochastic dynamic programming (SDP) to find optimal solutions, we evaluated the following different management decisions: enlarging existing patches, linking patches via corridors, and creating a new patch. This is the first application of SDP to optimal landscape reconstruction and one of the few times that landscape reconstruction dynamics have been integrated with population dynamics. SDP is a powerful tool that has advantages over standard Monte Carlo simulation methods because it can give the exact optimal strategy for every landscape configuration (combination of patch areas and presence of corridors) and pattern of metapopulation occupancy, as well as a trajectory of strategies. It is useful when a sequence of management actions can be performed over a given time horizon, as is the case for many endangered species recovery programs, where only fixed amounts of resources are available in each time step. However, it is generally limited by computational constraints to rather small networks of patches. The model shows that optimal metapopulation, management decisions depend greatly on the current state of the metapopulation,. and there is no strategy that is universally the best. The extinction probability over 30 yr for the optimal state-dependent management actions is 50-80% better than no management, whereas the best fixed state-independent sets of strategies are only 30% better than no management. This highlights the advantages of using a decision theory tool to investigate conservation strategies for metapopulations. It is clear from these results that the sequence of management actions is critical, and this can only be effectively derived from stochastic dynamic programming. The model illustrates the underlying difficulty in determining simple rules of thumb for the sequence of management actions for a metapopulation. This use of a decision theory framework extends the capacity of population viability analysis (PVA) to manage threatened species.

Opportunity cost of ad hoc marine reserve design decisions: an example from South Australia

Like many states and territories, South Australia has a legacy of marine reserves considered to be inadequate to meet current conservation objectives. In this paper we configured exploratory marine reserve systems, using the software MARXAN, to examine how efficiently South Australia's existing marine reserves contribute to quantitative biodiversity conservation targets. Our aim was to compare marine reserve systems that retain South Australia's existing marine reserves with reserve systems that are free to either ignore or incorporate them. We devised a new interpretation of irreplaceability to identify planning units selected more than could be expected from chance alone. This is measured by comparing the observed selection frequency for an individual planning unit with a predicted selection frequency distribution. Knowing which sites make a valuable contribution to efficient marine reserve system design allows us to determine how well South Australia's existing reserves contribute to reservation goals when representation targets are set at 5, 10, 15, 20, 30 and 50% of conservation features. Existing marine reserves that tail to contribute to efficient marine reserve systems constitute 'opportunity costs'. We found that despite spanning less than 4% of South Australian state waters, locking in the existing ad hoc marine reserves presented considerable opportunity costs. Even with representation targets set at 50%, more than halt of South Australia's existing marine reserves were selected randomly or less in efficient marine reserve systems. Hence, ad hoc marine reserve systems are likely to be inefficient and may compromise effective conservation of marine biodiversity.

Open-source software in operations research in engineering teaching

ENEGI 2013: Atas do 2º Encontro Nacional de Engenharia e Gestão Industrial, Universidade de Aveiro, 17 e 18 de maio de 2013, Aveiro, Portugal.

Metodologia multicritério na seleção de sistemas de informação na gestão da cadeia de abastecimento

Os sistemas de informação empresariais têm vindo nos últimos anos a afirmar- se como ferramentas essenciais no mercado cada vez mais competitivo em que as empresas se encontram. Pretende-se com este trabalho aplicar uma metodologia de apoio à tomada de decisão baseada num modelo decisão multicritério que permite a avaliação e seleção de um sistema de informação (SI) num determinado contexto. Para atingir esse objetivo foi utilizado o estudo de caso na empresa Proef, SGSP. Foi então realizada uma revisão bibliográfica sobre a gestão da cadeia de abastecimento, logística e teoria da decisão para dar suporte a todo o trabalho prático. Posteriormente foi aplicada a metodologia Multicritério para Apoio à seleção de SI – MMASSI/TI com base nos processos existentes na organização. Com recurso à aplicação informática foi obtido o sistema de informação mais adequado ao contexto de decisão, sendo este resultado avaliado através de uma análise de sensibilidade e robustez. Desta dissertação surgiram limitações e também recomendações futuras.

Bayesian classification criterion for forensic multivariate data

This study presents a classification criteria for two-class Cannabis seedlings. As the cultivation of drug type cannabis is forbidden in Switzerland, law enforcement authorities regularly ask laboratories to determine cannabis plant's chemotype from seized material in order to ascertain that the plantation is legal or not. In this study, the classification analysis is based on data obtained from the relative proportion of three major leaf compounds measured by gas-chromatography interfaced with mass spectrometry (GC-MS). The aim is to discriminate between drug type (illegal) and fiber type (legal) cannabis at an early stage of the growth. A Bayesian procedure is proposed: a Bayes factor is computed and classification is performed on the basis of the decision maker specifications (i.e. prior probability distributions on cannabis type and consequences of classification measured by losses). Classification rates are computed with two statistical models and results are compared. Sensitivity analysis is then performed to analyze the robustness of classification criteria.

Inference about the number of contributors to a DNA mixture: Comparative analyses of a Bayesian network approach and the maximum allele count method.

In the forensic examination of DNA mixtures, the question of how to set the total number of contributors (N) presents a topic of ongoing interest. Part of the discussion gravitates around issues of bias, in particular when assessments of the number of contributors are not made prior to considering the genotypic configuration of potential donors. Further complication may stem from the observation that, in some cases, there may be numbers of contributors that are incompatible with the set of alleles seen in the profile of a mixed crime stain, given the genotype of a potential contributor. In such situations, procedures that take a single and fixed number contributors as their output can lead to inferential impasses. Assessing the number of contributors within a probabilistic framework can help avoiding such complication. Using elements of decision theory, this paper analyses two strategies for inference on the number of contributors. One procedure is deterministic and focuses on the minimum number of contributors required to 'explain' an observed set of alleles. The other procedure is probabilistic using Bayes' theorem and provides a probability distribution for a set of numbers of contributors, based on the set of observed alleles as well as their respective rates of occurrence. The discussion concentrates on mixed stains of varying quality (i.e., different numbers of loci for which genotyping information is available). A so-called qualitative interpretation is pursued since quantitative information such as peak area and height data are not taken into account. The competing procedures are compared using a standard scoring rule that penalizes the degree of divergence between a given agreed value for N, that is the number of contributors, and the actual value taken by N. Using only modest assumptions and a discussion with reference to a casework example, this paper reports on analyses using simulation techniques and graphical models (i.e., Bayesian networks) to point out that setting the number of contributors to a mixed crime stain in probabilistic terms is, for the conditions assumed in this study, preferable to a decision policy that uses categoric assumptions about N.

The subjectivist interpretation of probability and the problem of individualisation in forensic science

This paper presents and discusses further aspects of the subjectivist interpretation of probability (also known as the 'personalist' view of probabilities) as initiated in earlier forensic and legal literature. It shows that operational devices to elicit subjective probabilities - in particular the so-called scoring rules - provide additional arguments in support of the standpoint according to which categorical claims of forensic individualisation do not follow from a formal analysis under that view of probability theory.

Proposta d'un model predictiu del risc d'ingrés hospitalari amb l'ús d'algoritmes bayesians

Model predictiu basat en xarxes bayesianes que permet identificar els pacients amb major risc d'ingrés a un hospital segons una sèrie d'atributs de dades demogràfiques i clíniques.

Strong minimax lower bounds for learning

Minimax lower bounds for concept learning state, for example, thatfor each sample size $n$ and learning rule $g_n$, there exists a distributionof the observation $X$ and a concept $C$ to be learnt such that the expectederror of $g_n$ is at least a constant times $V/n$, where $V$ is the VC dimensionof the concept class. However, these bounds do not tell anything about therate of decrease of the error for a {\sl fixed} distribution--concept pair.\\In this paper we investigate minimax lower bounds in such a--stronger--sense.We show that for several natural $k$--parameter concept classes, includingthe class of linear halfspaces, the class of balls, the class of polyhedrawith a certain number of faces, and a class of neural networks, for any{\sl sequence} of learning rules $\{g_n\}$, there exists a fixed distributionof $X$ and a fixed concept $C$ such that the expected error is larger thana constant times $k/n$ for {\sl infinitely many n}. We also obtain suchstrong minimax lower bounds for the tail distribution of the probabilityof error, which extend the corresponding minimax lower bounds.

Improved estimation of the covariance matrix of stock returns with an application to portofolio selection

This paper proposes to estimate the covariance matrix of stock returnsby an optimally weighted average of two existing estimators: the samplecovariance matrix and single-index covariance matrix. This method isgenerally known as shrinkage, and it is standard in decision theory andin empirical Bayesian statistics. Our shrinkage estimator can be seenas a way to account for extra-market covariance without having to specifyan arbitrary multi-factor structure. For NYSE and AMEX stock returns from1972 to 1995, it can be used to select portfolios with significantly lowerout-of-sample variance than a set of existing estimators, includingmulti-factor models.