Computational results for Constrained Minimum Spanning Trees in Flow Networks

In this work, we address the problem of finding a minimum cost spanning tree on a single source flow network. The tree must span all vertices in the given network and satisfy customer demands at a minimum cost. The total cost is given by the summation of the arc setup costs and of the nonlinear flow routing costs over all used arcs. Furthermore, we restrict the trees of interest by imposing a maximum number of arcs on the longest arc emanating from the single source vertex. We propose a dynamic programming model an solution procedure to solve this problem exactly. Intensive computational experiments were performed using randomly generated test problems and the results obtained are reported. From them we can conclude that the method performance is independent of the type of cost functions considered and improves with the tightness of the constrains.Dynamic programming, network flows, constrained trees, general nonlinear costs

Real Options using Markov Chains: an application to Production Capacity Decisions

In this work we address investment decisions using real options. A standard numerical approach for valuing real options is dynamic programming. The basic idea is to establish a discrete-valued lattice of possible future values of the underlying stochastic variable (demand in our case). For most approaches in the literature, the stochastic variable is assumed normally distributed and then approximated by a binomial distribution, resulting in a binomial lattice. In this work, we investigate the use of a sparse Markov chain to model such variable. The Markov approach is expected to perform better since it does not assume any type of distribution for the demand variation, the probability of a variation on the demand value is dependent on the current demand value and thus, no longer constant, and it generalizes the binomial lattice since the latter can be modelled as a Markov chain. We developed a stochastic dynamic programming model that has been implemented both on binomial and Markov models. A numerical example of a production capacity choice problem has been solved and the results obtained show that the investment decisions are different and, as expected the Markov chain approach leads to a better investment policy.Flexible Capacity Investments, Real Options, Markov Chains, Dynamic Programming

A decision support system for TV self-promotion scheduling

This paper describes a Decision Support System (DSS) that aims to plan and maintain the weekly self-promotion space for an over the air TV station. The self-promotion plan requires the assignment of several self-promotion advertisements to a given set of available time slots over a pre-specified planning period. The DSS consists of a data base, a statistic module, an optimization module, and a user interface. The input data is provided by the TV station and by an external audiometry company, which collects daily audience information. The statistical module provides estimates based on the data received from the audiometry company. The optimization module uses a genetic algorithm that can find good solutions quickly. The interface reports the solution and corresponding metrics and can also be used by the decision makers to manually change solutions and input data. Here, we report mainly on the optimization module, which uses a genetic algorithm (GA) to obtain solutions of good quality for realistic sized problem instances in a reasonable amount of time. The GA solution quality is assessed using the optimal solutions obtained by using a branch-and-bound based algorithm to solve instances of small size, for which optimality gaps below 1% are obtained.This research had the support of COMPETE-FEDERPORTUGAL2020-POCI-NORTE2020-FCT funding via grants POCI-01-0145-FEDER 031447 and 031821, NORTE-01-0145-FEDER-000020, and PTDC-EEI-AUT-2933-2014|16858–TOCCATA

Optimal investment timing using Markov jump price processes

In this work, we address an investment problem where the investment can either be made immediately or postponed to a later time, in the hope that market conditions become more favourable. In our case, uncertainty is introduced through market price. When the investment is undertaken, a fixed sunk cost must be paid and a series of cash flows are to be received. Therefore, we are faced with an irreversible investment. Real options analysis provides an adequate framework for this type of problems by recognizing these two characteristics, uncertainty and irreversibility, explicitly. We describe algorithmic solutions for this type of problems by modelling market prices evolution by Markov jump processes.Irreversible investment, optimal stopping, dynamic programming, Markov jump processes

Shannon entropy of brain functional complex networks under the influence of the psychedelic Ayahuasca

The entropic brain hypothesis holds that the key facts concerning psychedelics are partially explained in terms of increased entropy of the brain's functional connectivity. Ayahuasca is a psychedelic beverage of Amazonian indigenous origin with legal status in Brazil in religious and scientific settings. In this context, we use tools and concepts from the theory of complex networks to analyze resting state fMRI data of the brains of human subjects under two distinct conditions: (i) under ordinary waking state and (ii) in an altered state of consciousness induced by ingestion of Ayahuasca. We report an increase in the Shannon entropy of the degree distribution of the networks subsequent to Ayahuasca ingestion. We also find increased local and decreased global network integration. Our results are broadly consistent with the entropic brain hypothesis. Finally, we discuss our findings in the context of descriptions of "mind-expansion" frequently seen in self-reports of users of psychedelic drugs.Comment: 27 pages, 6 figure

A decision support system for planning promotion time slots

We report on the development of a Decision Support System (DSS) to plan the best assignment for the weekly promotion space of a TV station. Each product to promote has a given target audience that is best reached at specific time periods during the week. The DSS aims to maximize the total viewing for each product within its target audience while fulfilling a set of constraints defined by the user. The purpose of this paper is to describe the development and successful implementation of a heuristic-based scheduling software system that has been developed for a major Portuguese TV station.Fundação para a Ciência e a Tecnologia (FCT)- FCT/POCI 2010/FEDER, Projecto POCTI/MAT/61842/2004Estação de Televisão SI

A genetic algorithm approach for the TV self-promotion assignment problem

We report on the development of a Genetic Algorithm (GA), which has been integrated into a Decision Support System to plan the best assignment of the weekly self-promotion space for a TV station. The problem addressed consists on deciding which shows to advertise and when such that the number of viewers, of an intended group or target, is maximized. The GA proposed incorporates a greedy heuristic to find good initial solutions. These solutions, as well as the solutions later obtained through the use of the GA, go then through a repair procedure. This is used with two objectives, which are addressed in turn. Firstly, it checks the solution feasibility and if unfeasible it is fixed by removing some shows. Secondly, it tries to improve the solution by adding some extra shows. Since the problem faced by the commercial TV station is too big and has too many features it cannot be solved exactly. Therefore, in order to test the quality of the solutions provided by the proposed GA we have randomly generated some smaller problem instances. For these problems we have obtained solutions on average within 1% of the optimal solution value