Abstract
This paper addresses an extension of the flexible job shop scheduling problem by considering that jobs need to be moved around the shop-floor by a set of vehicles. Thus, this problem involves assigning each production operation to one of the alternative machines, finding the sequence of operations for each machine, assigning each transport task to one of the vehicles, and finding the sequence of transport tasks for each vehicle, simultaneously. Transportation is usually neglected in the literature and when considered, an unlimited number of vehicles is, typically, assumed. Here, we propose the first mixed integer linear programming model for this problem and show its efficiency at solving small-sized instances to optimality. In addition, and due to the NP-hard nature of the problem, we propose a local search based heuristic that the computational experiments show to be effective, efficient, and robust.

Abstract
In this paper we propose and analyze a game theoretical model regarding the dynamical interaction between government fiscal policy choices toward innovation and training (I&T), firm's innovation, and worker's levels of training and education. We discuss four economic scenarios corresponding to strict pure Nash equilibria: the government and I&T poverty trap, the I&T poverty trap, the I&T high premium niche, and the I&T ideal growth. The main novelty of this model is to consider the government as one of the three interacting players in the game that also allow us to analyse the I&T mixed economic scenarios with a unique strictly mixed Nash equilibrium and with I&T evolutionary dynamical cycles.

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We make two fits of an ODE system with 5 equations that model immune response by CD4 + T cells with the presence of regulatory T cells (Tregs). We fit the simulations to data regarding gp61 and NP309 epitopes from mice infected with lymphocytic choriomeningitis virus LCMV. We optimized parameters relating to: the T cell maximum growth rate; the T cell capacity; the T cell homeostatic level; and the ending time of the immune activation phase after infection. We quantitatively and qualitatively compare the obtained results with previous fits in the literature using different ODE models and we show that we are able to calibrate the model and obtain good fits describing the data. © 2021, Springer Nature Switzerland AG.

Abstract
We propose a refinement process of dynamic equilibria based on small random perturbations (SRPs) of the backward perfect foresight (bpf) equilibrium map in a class of one-step, forward-looking dynamic models. An equilibrium is selected if its stationary measure is the limit of the stationary measures associated with the processes generated by the SRPs of the bpf maps, as the perturbation size approaches 0. We show that, for full measure sets of parameter values of a large class of one-parameter families of unimodal bpf maps, only determinate cycles or the chaotic sunspot equilibrium defined by Araujo and Maldonado (2000) is selected. Two examples are provided illustrating such refinement process.

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Abstract