2,787 research outputs found
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
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
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
On the degeneracy phenomenon for nonlinear optimal control problems with higher index state constraints
Relatório Técnico do Núcleo de Investigação Officina Mathematica.Necessary conditions of optimality (NCO) play an important role in
optimization problems. They are the major tool to select a set of
candidates to minimizers. In optimal control theory, the NCO
appear in the form of a Maximum Principle (MP). For certain
optimal control problems with state constraints, it might happen
that the MP are unable to provide useful information --- the set of
all admissible solutions coincides with the set of candidates that
satisfy the MP. When this happens, the MP is said to degenerate. In
the recent years, there has been some literature on fortified forms
of the MP in such way that avoid degeneracy. These fortified forms
involve additional hypotheses --- Constraint Qualifications.
Whenever the state constraints have higher index (i.e. their first
derivative with respect to time does not depend on control), the
current constraint qualifications are not adequate. So, the main
purpose here is fortify the maximum principle for optimal control
problems with higher index constraints, for which there is a need to
develop new constraint qualifications. The results presented here are
a generalization to nonlinear problems of a previous work.The financial support from Projecto FCT POSC/EEA-SRI/61831/2004 is
gratefully acknowledged
A line-binned treatment of opacities for the spectra and light curves from neutron star mergers
The electromagnetic observations of GW170817 were able to dramatically
increase our understanding of neutron star mergers beyond what we learned from
gravitational waves alone. These observations provided insight on all aspects
of the merger from the nature of the gamma-ray burst to the characteristics of
the ejected material. The ejecta of neutron star mergers are expected to
produce such electromagnetic transients, called kilonovae or macronovae.
Characteristics of the ejecta include large velocity gradients, relative to
supernovae, and the presence of heavy -process elements, which pose
significant challenges to the accurate calculation of radiative opacities and
radiation transport. For example, these opacities include a dense forest of
bound-bound features arising from near-neutral lanthanide and actinide
elements. Here we investigate the use of fine-structure, line-binned opacities
that preserve the integral of the opacity over frequency. Advantages of this
area-preserving approach over the traditional expansion-opacity formalism
include the ability to pre-calculate opacity tables that are independent of the
type of hydrodynamic expansion and that eliminate the computational expense of
calculating opacities within radiation-transport simulations. Tabular opacities
are generated for all 14 lanthanides as well as a representative actinide
element, uranium. We demonstrate that spectral simulations produced with the
line-binned opacities agree well with results produced with the more accurate
continuous Monte Carlo Sobolev approach, as well as with the commonly used
expansion-opacity formalism. Additional investigations illustrate the
convergence of opacity with respect to the number of included lines, and
elucidate sensitivities to different atomic physics approximations, such as
fully and semi-relativistic approaches.Comment: 27 pages, 22 figures. arXiv admin note: text overlap with
arXiv:1702.0299
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