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Aquaculture is a fast growth activity in the world, but needs continued improvement in the conduct of management. In this sense, we highlight the Amazon basin, which has important species of fish as Colossoma macropomum with incipient production to meet the demand of the consumer market. Since that problem identified, we applied a Markovian decision process aiming to develop an optimization system to maximize the yield of the C. macropomum aquaculture. Were used mathematical algorithms were simulated with layout scenarios with 5 and 10 ponds, representing different size aquaculture farms. The transition between the growth phases was considered a stochastic process to satisfy the Markov property as per a sequential queuing through growth phases. The main goal was to define the target weight mix for the market and their optimal levels that optimize the production. The highest profitabilities were US$9,608 and 15,385 for 5 and 10 ponds layout scenarios, respectively, with a target weight mix harvest of 0.5 kg and 1 kg; 0.5 kg, 1 kg and 2 kg, respectively. The results showed the number of months for discounted the fixed monthly cost, about the cycle time that lasted of 5, 7 and 11 months, as well as the optimization was defined with the time at the fingerlings stage fixed for 50 days, possible to be improved.

In general, the unit-demand envy-free pricing problem has proven to be APX-hard, but some special cases can be optimally solved in polynomial time. When substitution costs that form a metric space are included, the problem can be solved in O(n4) time, and when the number of consumers is equal to the number of items—all with a single copy so that each consumer buys an item—a O(n3) time method is presented to solve it. This work shows that the first case has similarities with the second, and, by exploiting the structural properties of the costs set, it presents a O(n2) time algorithm for solving it when a competitive equilibrium is considered or a O(n3) time algorithm for more general scenarios. The methods are based on a dynamic programming strategy, which simplifies the calculations of the shortest paths in a network; this simplification is usually adopted in the second case. The theoretical results obtained provide efficiency in the search for optimal solutions to specific revenue management problems.

We present a method for finding envy-free prices in a combinatorial auction where the consumers’ number n coincides with that of distinct items for sale, each consumer can buy one single item and each item has only one unit available. This is a particular case of the unitdemand envy-free pricing problem , and was recently revisited by Arbib et al. (2019). These authors proved that using a Fibonacci heap for solving the maximum weight perfect matching and the Bellman-Ford algorithm for getting the envy-free prices, the overall time complexity for solving the problem is O ( n 3 ) . We propose a method based on dynamic programming design strategy that seeks the optimal envyfree prices by increasing the consumers’ utilities, which has the same cubic complexity time as the aforementioned approach, but whose theoretical and empirical results indicate that our method performs faster than the shortest paths strategy, obtaining an average time reduction in determining optimal envy-free prices of approximately 48%.