Abstract
For the quadratic Hotelling model, we study the optimal localization and price strategies under incomplete information on the production costs of the firms. We compute explicitly the pure Bayesian-Nash price duopoly equilibrium and we prove that it does not depend upon the distributions of the production costs of the firms, except on their first moments. We find when the maximal differentiation is a local optimum for the localization strategy of both firms.

Abstract
This paper presents the development of Bubbles, a didactic robotic fish created within the scope of the European Project Semester offered by the School of Engineering of the Polytechnic of Porto. The robotic toy is intended to provide children with an appropriate set up to learn programming and become acquainted with technology. Consequently, Bubbles needs to appeal to young children and successfully blend fun with learning. The developer team, composed of five engineering students from different fields and nationalities, conducted multiple research and discussions to design Bubbles, while keeping the fish movements and programming simple. The fish body was created with a colourful appearance, ensuring floatability, waterproofness and including a tail, inspired on real life fish, for locomotion and to retain a fish-like appearance. Finally, the team designed a website where they share, in different languages, the blue-prints of the structure, the schematics of the control system, the list of material, including electronic components, the user assembly and operation manual as well as propose exploring activities.

Abstract
At a time when the need to reduce costs has become part of the day-to-day reality of all educational institutions, it is unthinkable to continue to manually perform those tasks (i.e., the creation of timetables) that can be automated and optimized. The automatic creation of timetables for educational institutions is one of the most studied problems by the scientific community. However, almost all studies have been based on very simplified models of reality that have no practical application. A realistic model of the problem, robust algorithms that are able to find valid solutions in highly restricted environments, and optimization methods that are able to quickly provide quality results are key factors to consider when attempting to solve this (real) problem faced by educational institutions. This paper presents a summary of the work performed by Bullet Solutions over the last few years, from the first stage of understanding and modelling the problem to the final analysis of the results obtained using the developed software under real conditions.

Abstract

Abstract
The importance of liquefied natural gas (LNG) is rising as demand for it grows rapidly and steadily due to growth in energy demand, the transition to a low carbon economy and the longer distances over which natural gas is now traded. Given its importance, this work proposes an optimization model that assists to decide on when and where LNG should be delivered by coordinating tanker type, assignment and routing, inventory management, contract obligations, arbitrage and uncommitted LNG. The model maximizes the profit mainly by taking advantage of price differences between different markets. The contributions of this work are twofold. First, following the analysis of expenses and revenues, a new mixed integer programming model for LNG liquefaction and shipping is proposed from a corporate finance perspective. Furthermore, a solution approach for it is implemented and tested. Second, the model is used to derive a short term trade policy for the Middle Eastern LNG producers regarding the spot sale of their uncommitted product to Japan or to the UK, namely to: dispatch to whichever market has the higher current spot price, regardless of the variability of the transport expenses.

Abstract
We present an exact method, based on an arc-flow formulation with side constraints, for solving bin packing and cutting stock problems-including multi-constraint variants-by simply representing all the patterns in a very compact graph. Our method includes a graph compression algorithm that usually reduces the size of the underlying graph substantially without weakening the model. Our formulation is equivalent to Gilmore and Gomory's, thus providing a very strong linear relaxation. However, instead of using column-generation in an iterative process, the method constructs a graph, where paths from the source to the target node represent every valid packing pattern. The same method, without any problem-specific parameterization, was used to solve a large variety of instances from several different cutting and packing problems. In this paper, we deal with vector packing, bin packing, cutting stock, cardinality constrained bin packing, cutting stock with cutting knife limitation, bin packing with conflicts, and other problems. We report computational results obtained with many benchmark test datasets, some of them showing a large advantage of this formulation with respect to the traditional ones.