Publications 2019

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21.  Logistic operations in a hospital: a multi-item inventory distribution problem with heterogeneous fleet

Agra, Agostinho and Cerveira, Adelaide and Requejo, Cristina

Pharmaceutical Supply Chains - Medicines Shortages. Lecture Notes in Logistics

Springer

A multi-item inventory distribution problem motivated by a practical case study occurring in the logistic operations of a hospital is considered. There, a single warehouse supplies several nursing wards. The distribution of medical products is done by two different teams of workers using a heterogeneous fleet, that is, the available vehicles have different capacities and different structures required to be used in specific nursing wards. The goal is to define a weekly distribution plan of medical products ensuring a balanced workload of both working teams and satisfying all the required constraints (inventory capacities, safety stock levels, vehicle capacities, etc.) that minimizes the total number of visits to locations. A mixed integer formulation is presented and several improvements are discussed. This is a NP-hard problem hardly solved to optimality within a reasonable amount of time, and more so for real size instances, with hundreds to few thousand of products. To circumvent this issue, a matheuristic is proposed to solve the problem. Finally, computational tests are reported and discussed.

ria.ua.pt | doi | Peer Reviewed

20.  Smart grid topology designs

Carroll, Paula and Requejo, Cristina

Proceedings of the 9th International Network Optimization Conference (INOC 2019)

OpenProceedings

This paper addresses supports for evolving design demands of electricity low voltage networks in urban areas. Innovations in how electricity is generated and supplied are required to support transformation of energy systems in response to climate change. We describe a MIP model to support grid upgrade decisions in the context of an energy community in an existing urban setting. We evaluate the MIP model on an adaption of an IEEE radial network benchmark instance augmented with geographic data. We present interesting computational results which suggest additional arcs to be added. Our results highlight potential research opportunities for the network optimisation community to facilitate the desired energy systems transformation challenge.

ria.ua.pt | doi | Peer Reviewed

Articles


19.  New bounds for the signless Laplacian spread

Andrade, Enide and Dahl, Geir and Leal, Laura and Robbiano, María

Linear Algebra and its Applications

Elsevier

Let $G$ be an undirected simple graph. The signless Laplacian spread of $G$ is defined as the maximum distance of pairs of its signless Laplacian eigenvalues. This paper establishes some new bounds, both lower and upper, for the signless Laplacian spread. Several of these bounds depend on invariant parameters of the graph. We also use a minmax principle to find several lower bounds for this spectral invariant.

ria.ua.pt | doi | Peer Reviewed

18.  Combinatorial Perron parameters for trees

Andrade, Enide and Ciardo, Lorenzo and Dahl, Geir

Linear Algebra and its Applications

Elsevier

The notion of combinatorial Perron value was introduced in [2]. We continue the study of this parameter and also introduce a new parameter πe(M) which gives a new lower bound on the spectral radius of the bottleneck matrix M of a rooted tree. We prove a bound on the approximation error for πe(M). Several properties of these two parameters are shown. These ideas are motivated by the concept of algebraic connectivity. A certain extension property for the combinatorial Perron value is shown and it allows us to define a new center concept for caterpillars. We also compare computationally this new center to the so-called characteristic set, i.e., the center obtained from algebraic connectivity.

ria.ua.pt | doi | Peer Reviewed

17.  Algorithmic determination of immobile indices in convex SIP problems with polyhedral index sets

Kostyukova, O.I. and Tchemisova, T.V.

INFOR, Information Systems and Operational Research

Taylor & Francis

The concepts of immobile indices and their immobility orders are objective and important characteristics of feasible sets of semi-infinite programming (SIP) problems. They can be used for the formulation of new efficient optimality conditions without constraint qualifications. Given a class of convex SIP problems with polyhedral index sets, we describe and justify a finite constructive algorithm (algorithm DIIPS) that allows to find in a finite number of steps all immobile indices and the corresponding immobility orders along the feasible directions. This algorithm is based on a representation of the cones of feasible directions in the polyhedral index sets in the form of linear combinations of extremal rays and on the approach proposed in our previous papers for the cases of immobile indices’ sets of simpler structures. A constructive procedure of determination of the extremal rays is described, and an example illustrating the application of the DIIPS algorithm is provided.

ria.ua.pt | doi | Peer Reviewed

16.  Invisibility in billiards is impossible in an infinite number of directions

Plakhov, Alexander and Roshchina, Vera

Journal of Dynamical and Control Systems

Springer

We show that the maximum number of directions of invisibility in a planar billiard defined in the exterior of a piecewise smooth body is at most finite.

ria.ua.pt | doi | Peer Reviewed

15.  Local properties of the surface measure of convex bodies

Plakhov, Alexander

Journal of Convex Analysis

Heldermann Verlag

It is well known that any measure in S^2 satisfying certain simple conditions is the surface measure of a bounded convex body in R^3. It is also known that a local perturbation of the surface measure may lead to a nonlocal perturbation of the corresponding convex body. We prove that, under mild conditions on the convex body, there are families of perturbations of its surface measure forming line segments, with the original measure at the midpoint, corresponding to {it local} perturbations of the body. Moreover, there is, in a sense, a huge amount of such families. We apply this result to Newton's problem of minimal resistance for convex bodies.

ria.ua.pt | Peer Reviewed

14.  Boris Rufimovich Vainberg

Lakshtanov, Evgeny and Egorov, Yu. V. and A. I. Komech and Kuchment, P. A. and Maz'ya, V. G. and Molchanov, S. A. and Novikov, R. G. and Freidlin, M. I.

Russian Mathematical Surveys

Turpion

Boris R. Vainberg was born on March 17, 1938, in Moscow. His father was a Lead Engineer in an aviation design institute. His mother was a homemaker. From early age, Boris was attracted to mathematics and spent much of his time at home and in school working through collections of practice problems for the Moscow Mathematical Olympiad. His first mathematical library consisted of the books he received as one of the prize-winners of these olympiads.

ria.ua.pt | doi | Peer Reviewed

13.  Designing lasing and perfectly absorbing potentials

Lakshtanov, Evgeny and Vainberg, Boris and Konotop, Vladimir

Physical Review A

American Physical Society

Existence of a spectral singularity (SS) in the spectrum of a Schrödinger operator with a non-Hermitian potential requires exact matching of parameters of the potential. We provide a necessary and sufficient condition for a potential to have a SS at a given wavelength. It is shown that potentials with SSs at prescribed wavelengths can be obtained by a simple and effective procedure. In particular, the developed approach allows one to obtain potentials with several SSs and with SSs of the second order, as well as potentials obeying a given symmetry, say, PT -symmetric potentials. We illustrate all these opportunities with examples. We also describe splitting of a second-order SS under change of the potential parameters, and discuss possibilities of experimental observation of SSs of different orders.

ria.ua.pt | doi | Peer Reviewed

12.  Bounds for different spreads of line and total graphs

Andrade, Enide and Lenes, Eber and Mallea-Zepeda, Exequiel and Robbiano, María and Rodríguez Z., Jonnathan

Linear Algebra and its Applications

Elsevier

In this paper we explore some results concerning the spread of the line and the total graph of a given graph. A sufficient condition for the spread of a unicyclic graph with an odd girth to be at most the spread of its line graph is presented. Additionally, we derive an upper bound for the spread of the line graph of graphs on $n$ vertices having a vertex (edge) connectivity at most a positive integer $k$. Combining techniques of interlacing of eigenvalues, we derive lower bounds for the Laplacian and signless Laplacian spread of the total graph of a connected graph. Moreover, for a regular graph, an upper and lower bound for the spread of its total graph is given.

ria.ua.pt | doi | Peer Reviewed

11.  Solution of the initial value problem for the focusing Davey-Stewartson II system

Lakshtanov, E. and Vainberg, B.

Contemporary Mathematics

American Mathematical Society

We consider a focusing Davey-Stewartson system and construct the solution of the Cauchy problem in the possible presence of exceptional points (and/or curves).

ria.ua.pt | doi | Peer Reviewed

10.  AAD: breaking the primal barrier

Goloubentsev, Dmitri and Lakshtanov, Evgeny

Wilmott

Wiley

In this article we present a new approach for automatic adjoint differentiation (AAD) with a special focus on computations where derivatives ∂F(X) ∂X are required for multiple instances of vectors X. In practice, the presented approach is able to calculate all the differentials faster than the primal (original) C++ program for F.

ria.ua.pt | Peer Reviewed

9.  Faithful permutation representations of toroidal regular maps

Fernandes, Maria Elisa and Piedade, Cláudio Alexandre

Journal of Algebraic Combinatorics

Springer Verlag

In this paper we list all possible degrees of a faithful transitive permutation representation of the group of symmetries of a regular map of types ${4,4}$ and ${3,6}$ and we give examples of graphs, called CPR-graphs, representing some of these permutation representations.

ria.ua.pt | doi | Peer Reviewed

8.  An overview of (k,t)-regular sets and their applications

Cardoso, Domingos M.

Discrete Applied Mathematics

Elsevier

A (k,t)-regular set is a vertex subset S inducing a k-regular subgraph such that every vertex out of S has t neighbors in S. This article is an expository overview of the main results obtained for graphs with (k,t)-regular sets. The graphs with classical combinatorial structures, like perfect matchings, Hamilton cycles, efficient dominating sets, etc, are characterized by (k,t)-regular sets whose determination is equivalent to the determination of those classical combinatorial structures. The characterization of graphs with these combinatorial structures are presented. The determination of (k,t)-regular sets in a finite number of steps is deduced and the main spectral properties of these sets are described.

ria.ua.pt | doi | Peer Reviewed

7.  String C-group representations of alternating groups

Fernandes, Maria Elisa and Leemans, Dimitri

Ars Mathematica Contemporanea

We prove that for any integer n ≥ 12, and for every r in the interval [3, . . . , Floor((n−1)/2)], the group A_n has a string C-group representation of rank r, and hence that the only alternating group whose set of such ranks is not an interval is A_11.

ria.ua.pt | doi | Peer Reviewed

6.  More on geometry of Krein space C-numerical range

Guterman, Alexander and Lemos, Rute and Soares, Graça

Applied Mathematics and Computation

Elsevier

For n × n complex matrices A, C and H, where H is non-singular Hermitian, the Krein space C-numerical range of A induced by H is the subset of the complex plane given by {Tr(CU^[*]AU: U^{-1}= U^[*] )} with U^[*]=H^{-1}U*H the H-adjoint matrix of U. We revisit several results on the geometry of Krein space C-numerical range of A and in particular we obtain a condition for the Krein space C-numerical range to be a subset of the real line.

ria.ua.pt | doi | Peer Reviewed

5.  Comparing techniques for modelling uncertainty in a maritime inventory routing problem

Rodrigues, Filipe and Agra, Agostinho and Christiansen, Marielle and Hvattum, Lars Magnus and Requejo, Cristina

European Journal of Operational Research

Elsevier

Uncertainty is inherent in many planning situations. One example is in maritime transportation, where weather conditions and port occupancy are typically characterized by high levels of uncertainty. This paper considers a maritime inventory routing problem where travel times are uncertain. Taking into account possible delays in the travel times is of main importance to avoid inventory surplus or shortages at the storages located at ports. Several techniques to deal with uncertainty, namely deterministic models with inventory buffers; robust optimization; stochastic programming and models incorporating conditional value-at-risk measures, are considered. The different techniques are tested for their ability to deal with uncertain travel times for a single product maritime inventory routing problem with constant production and consumption rates, a fleet of heterogeneous vessels and multiple ports. At the ports, the product is either produced or consumed and stored in storages with limited capacity. We assume two-stages of decisions, where the routing, the visit order of the ports and the quantities to load/unload are first-stage decisions (fixed before the uncertainty is revealed), while the visit time and the inventory levels at ports are second-stage decisions (adjusted to the observed travel times). Several solution approaches resulting from the proposed techniques are considered. A computational comparison of the resulting solution approaches is performed to compare the routing costs, the amount of inventory bounds deviation, the total quantities loaded and unloaded, and the running times. This computational experiment is reported for a set of maritime instances having up to six ports and five ships.

ria.ua.pt | doi | Peer Reviewed

4.  A computational comparison of compact MILP formulations for the zero forcing number

Agra, Agostinho and Cerdeira, Jorge Orestes and Requejo, Cristina

Discrete Applied Mathematics

Elsevier

Consider a graph where some of its vertices are colored. A colored vertex with a single uncolored neighbor forces that neighbor to become colored. A zero forcing set is a set of colored vertices that forces all vertices to become colored. The zero forcing number is the size of a minimum forcing set. Finding the minimum forcing set of a graph is NP-hard. We give a new compact mixed integer linear programming formulation (MILP) for this problem, and analyse this formulation and establish relation to an existing compact formulation and to two variants. In order to solve large size instances we propose a sequential search algorithm which can also be used as a heuristic to derive upper bounds for the zero forcing number. A computational study using Xpress (a MILP solver) is conducted to test the performances of the discussed compact formulations and the sequential search algorithm. We report results on cubic, Watts-Strogatz and randomly generated graphs with 10, 20 and 30 vertices.

ria.ua.pt | doi | Peer Reviewed

3.  Suppliers selection problem with quantity discounts and price changes: a heuristic approach

Rodrigues, Filipe and Requejo, Cristina

RAIRO: Operations Research

EDP Sciences

This paper addresses a complex suppliers selection problem with multiple products, considering minimum package quantities, minimum order values related to delivery costs and discounted pricing schemes. Its main contribution is to present an integer linear programming (ILP) model for this suppliers selection problem as well as a model to analyse the impact of prices change. Furthermore, a hybrid heuristic and a genetic algorithm to obtain feasible solutions for this problem are presented. Several randomly generated examples are solved by using the above two models and the heuristic approaches. Experimental results demonstrate the robustness of the genetic algorithm and allow to realize which are the most important decisions in the suppliers selection problem.

ria.ua.pt | doi | Peer Reviewed

2.  Injective edge coloring of graphs

Cardoso, Domingos M. and Cerdeira, J. Orestes and Dominic, Charles and Cruz, J. Pedro

Filomat

Faculty of Sciences and Mathematics, University of Nis

Three edges $e_{1}, e_{2}$ and $e_{3}$ in a graph $G$ are consecutive if they form a path (in this order) or a cycle of lengths three. An injective edge coloring of a graph $G = (V,E)$ is a coloring $c$ of the edges of $G$ such that if $e_{1}, e_{2}$ and $e_{3}$ are consecutive edges in $G$, then $c(e_{1})neq c(e_3)$. The injective edge coloring number $chi_{i}^{'}(G)$ is the minimum number of colors permitted in such a coloring. In this paper, exact values of $chi_{i}^{'}(G)$ for several classes of graphs are obtained, upper and lower bounds for $chi_{i}^{'}(G)$ are introduced and it is proven that checking whether $chi_{i}^{'}(G)= k$ is NP-complete.

ria.ua.pt | doi | Peer Reviewed

Proceedings


1.  Problem based learning in a Biostatistics course

Cruz, J. P.

Proceeding of the 12th International Conference of Education, Research and Innovation

IATED Academy

We have introduced statistical problems, to be solved using the R software, into a Biostatistics course, in order to increase motivation for the field that requires a certain level of mathematical knowledge when most students are not always inspired for it. Our traditional class style used to be based only on slide presentations followed by pen and paper exercises with a calculator. Our aim was to complement this method with the use of software as a professional tool creating a active learning environment. Students came from Biology degree, Teaching of Geology and Biology degree and Marine Sciences degree. Each of the 200 students were presented with a total of four problems, during the semester, in the topics of Descriptive Statistics, Inference in One Variable, ANOVA and Simple Linear Regression. Students were requested to solve them at home and answer them in a form available in the “Moodle Inquiry” tool. Each student has his own different sample and also, questions were parameterized. For example, questions about Confidence Intervals were posed with different confidence levels (90%, 95% or 99%). Each students sees a different problem. Each of these has more than ten parameterized questions related to the same dataset exposed in the beginning of the text. Moodle doesn’t do this type of deliver different composed problems to each student so a small Python library was used to generate different problems and evaluate each individual student answer (numerical, textual or multiple choice types). To evaluate our methodology, we request students to “Share ideas, thoughts and constructive judgments about the Problems and also about the course” while students were working in the third Problem and also after the First Written Evaluation. The last and fourth Problem has been answered in class and students were requested to grade sentences in a five item Likert scale. Questions were about effort, time, help from other students and help from teacher. The analysis of answers suggest that the methodology of Problem Solving should be used again, with improvements, given the motivation and enthusiasm it promotes.

ria.ua.pt | Peer Reviewed
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