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Planning effective itineraries for tourists is a major problem that has been gaining attention over the last years. This paper proposes a new bi-objective integer linear programming model for this problem. Decisions include the choice of the best itinerary to be performed considering multi-period routing, time windows for the visited attractions and the choice of restaurants and hotels. The conflicting objectives considered are: (i) maximizing the level of service offered by the itinerary, and (ii) minimizing the total distance traveled. The problem resolution, even for small instances by exact methods, is limited. This motivated the proposition of a new customized MIP-heuristic based on decomposition, fix-and-optimize and MIP-start, to produce good-quality solutions with moderate computational effort. Tchebycheff's scalarization method was coupled to this heuristic and multiple compromise solutions were obtained. Extensive results with problem instances of different sizes and characteristics showed a good performance of this approach, capable of producing effective solutions within short runtimes. The analysis of the solutions indicated a strong conflict between the objectives, allowing the user to quantify the losses and gains when one criterion is prioritized over the other. A brief sensitivity analysis of some model parameters revealed interesting managerial insights. Some examples include quantifying the negative impacts in terms of the level of service offered by concentrating hotels and restaurants in the center of tourist attractions, increasing visit and transfer times between attractions and reducing the planning horizon for the entire itinerary. These aspects validate the potential of using this MIP model and applying this MIP-heuristic in real situations. • We propose an approach for touristic itinerary optimization planning. • The multi-period model optimizes two objectives: quality service and travel distances. • A new MIP heuristic is developed to determine fast and good-quality solutions. • A strong trade-off between the objectives was observed. • A brief sensitivity analysis showed the parameters that affect the objective values. [ABSTRACT FROM AUTHOR]

Sugarcane is one of the main commodities in the world economy. An important step in the sugarcane supply chain is the harvest stage, requiring the support of mathematical modeling and optimization tools. Integrating the process of choosing the areas for harvesting according to the sugarcane maturation with the formation of the harvesting fronts and associating them with machine relocation costs is challenging. This paper contributes with a novel integer mathematical model that considers these concerns using three conflicting objectives. The first is that the sugarcane should be harvested as close as possible to its maturity, considering the sugarcane should be harvested as close as possible to its maturity by considering a combined measure of temperature and time since planting. The second aims to minimize the number of harvest fronts. The third objective is to minimize the costs involved with the relocation of the harvesters that cut the cane. Different strategies for obtaining Pareto-optimal solutions were proposed using exact methods, including MIP start and a decomposition technique. In the worst case, solutions with tolerable integrality gaps were obtained (inferior to 3%) in less than 1.5 h. Computational tests in real case studies were conducted in the sugarcane industry in two countries, indicating strong trade-offs in the determined solutions. In the Brazilian case, harvesting as close to maturation as possible, for example, causes an increase of 158% in the number of harvest fronts and 47% in the transportation costs, considering the minimum values for these objectives. Other trade-offs were seen and discussed when one of the other objectives was prioritized. These different compromise solutions help the decision-makers choose the most appropriate harvesting schedule according to their preferences. • We propose a new MIP optimization model to determine the harvesting of sugarcane. • The model aims to optimize three conflicting objectives. • A new method of computing cane maturation is used: the concept of degree-days. • A procedure for determining Pareto solutions by exact methods is proposed. [ABSTRACT FROM AUTHOR]