Abstract
This paper addresses the joint scheduling of production operations, transport tasks, and storage/retrieval activities in flexible job shop systems where the production operations and transport tasks can be done by one of the several resources available. Jobs need to be retrieved from storage and delivered to a load/unload area, from there, they are transported to and between the machines where their operations are processed on. Once all operations of a job are processed, the job is taken back to the load/unload area and then returned to the storage cell. Therefore, the problem under study requires, concurrently, solving job routing, machine scheduling, transport allocation, vehicle scheduling, and shuttle schedule. To this end, we propose a hybrid biased random-key genetic algorithm (BRKGA) in which the mutation operator resorts to six local search heuristics. The computational experiments conducted on a set of benchmark instances show the effectiveness of the proposed mutation operator.

Abstract
In this work, we consider a classic international trade model with two countries and one firm in each country. The game has two stages: in the first stage, the governments of each country use their welfare functions to choose their tariffs either: (a) competitively (Nash equilibrium) or (b) cooperatively (social optimum); in the second stage, firms competitively choose (Nash) their home and export quantities under Cournot-type competition conditions. In a previous publication we compared the competitive tariffs with the cooperative tariffs and we showed that the game is one of the two following types: (i) prisoner's dilemma (when the competitive welfare outcome is dominated by the cooperative welfare outcome); or (ii) a lose-win dilemma (an asymmetric situation where only one of the countries is damaged in the cooperative welfare outcome, whereas the other is benefited). In both scenarios, their aggregate cooperative welfare is larger than the aggregate competitive welfare. The lack of coincidence of competitive and cooperative tariffs is one of the main difficulties in international trade calling for the establishment of trade agreements. In this work, we propose a welfare-balanced trade agreement where: (i) the countries implement their cooperative tariffs and so increase their aggregate welfare from the competitive to the cooperative outcome; (ii) they redistribute the aggregate cooperative welfare according to their relative competitive welfare shares. We analyse the impact of such trade agreement in the relative shares of relevant economic quantities such as the firm's profits, consumer surplus, and custom revenue. This analysis allows the countries to add other conditions to the agreement to mitigate the effects of high changes in these relative shares. Finally, we introduce the trade agreement index measuring the gains in the aggregate welfare of the two countries. In general, we observe that when the gains are higher, the relative shares also exhibit higher changes. Hence, higher gains demand additional caution in the construction of the trade agreement to safeguard the interests of the countries.

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We consider a continuous lifetime model for investor whose lifetime is a random variable. We assume the investor has an access to the social welfare system, the financial market and the life insurance market. The investor aims to find the optimal strategies that maximize the expected utility obtained from consumption, investing in the financial market, buying life insurance, registering in the social welfare system, the size of his estate in the event of premature death and the size of his fortune at time of retirement if he lives that long. We use dynamic programming techniques to derive a second-order nonlinear partial differential equation whose solution is the maximum objective function. We use special case of discounted constant relative risk aversion utilities to find an explicit solutions for the optimal strategies. Finally, we have shown a numerical solution for the problem under consideration and study some properties for the optimal strategies.

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We show that in finite settings with identical firms and consumers, asymmetric pure price equilibria with positive profits exist. We consider a price competition duopoly for a homogeneous product. Demand stems from a second-stage consumption game at posted prices, with consumers' behavior impacted by negative network effects. We characterize equilibrium prices and demand. In all subgame-perfect pure price equilibria, both firms have positive profits, and in some, firms charge different prices.

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