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ABSTRACT For soccer managers, player selection lineups are a key process for better performance, both on financial and sports matters. However, to determine a quality solution to this problem it becomes more complex, as the number of alternatives and criteria increases and the number of viable solutions grows ex ponentially. This paper proposes a multicriteria method with genetic algorithm for the evaluation of soccer teams based on Brazilian Championship data. A team complementation percentage was calculated con sidering a total of 322 athletes and 18 criteria. The results presented a 3-6-1 format as the ideal for this case study, obtaining a team complementation value of 43.04%. The method adaptability for the decision-maker is highlighted, showing it was possible to determinate the most complementary team according to the desired tactical formation and importance attributed for each criterion.

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ABSTRACT Composition of probabilistic preferences is applied here together with life cycle assessment in the evaluation of sewage sludge treatment scenarios. The computations are based on the transformation of preferences for the alternatives elicited applying each criterion into probabilities of being the best. Different forms of probabilistic composition are applied and the possibility of interaction between factors is considered. The results are compared to results previously obtained with different forms of composition modeling the interaction or assuming linearity. Eight scenarios combining different processing techniques and leading to distinct end-uses are compared. These scenarios are ranked combining probabilities of preference according to five environmental impact factors: water use, energy consumption, carbon footprint, human toxicity potential and terrestrial ecotoxicity potential. In the large spectrum of views that the probabilistic approach provides, evidence is found favoring a system that includes recovery of energy to be used in a dryer and in a cement kiln.

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ABSTRACT This paper presents a robust deterministic method for the treatment of uncertainty in decision-making systems based on Sonar Method. It introduces uncertainty into mathematical models as interval numbers. This work proposes an interactive approach that identifies the efficient vertices of the Multiobjective Linear Programming (MOLP), where some or all the coefficients of the objective functions, constraints or limits of the constraints are interval of real numbers. The method identifies robust solutions to MOLP under uncertainty, showing how the interactive approach presented in this paper can provide the possibility of exploring in new decision support methodologies.

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ABSTRACT In this paper, we propose a new heuristic strategy to solve linear integer mathematical problems. The strategy begins by finding the optimal solution of the continuous associated problem and the simplex directions from that optimal solution. A total of n − m problems are generated and solved by the strategy, where m is the number of constraints and n is the number of variables of the problem. The best solution to those problems is the solution to the original problem. Several instance problems were randomly generated to validate the strategy, and our strategy finds good solutions in 80% of the instances. We also tested the proposed strategy with instances of the MIPLIB 2017. We compare a total of 39 instances and on average our strategy performed 47% fewer iterations than the solver, in 34 of 39 instances, the strategy found good solutions.

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ABSTRACT Stochastic production frontier models are widely used in microeconometrics and, in the last decades, have been proven to be versatile in their range of applications. However, there are few studies concerning endogeneity in stochastic production frontier models. Here we present two stochastic production frontier models with endogenous variables based on the main distributions for the technical inefficiency. We also derive analytic gradient vectors to obtain the best performance at a reasonable computational time cost. The methodology presented here is based on one and two-step maximum likelihood estimation, allows for endogeneity and heteroscedasticity in relation to one or both error terms, and is implemented in R language. Finally, we illustrate an application with municipal data from the Brazilian agricultural census. The results show that capital dominates the production function, credit access and technical assistance are endogenous, and income concentration seems to impede productive inclusion through the more intensive use of technology.

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ABSTRACT Human Resource Allocation (HRA) can be defined as the way professionals are distributed across the organization’s tasks, given that each individual has his/her own set of characteristics, and that each task has specific needs. Thus, this paper puts forward a mathematical programming model for allocating human resources that considers employees’ formal qualifications and experience and the possibility of employees sharing tasks in each project. The proposed mathematical model was designed and implemented according to a set of heuristics based on a Greedy Search (GS), a Genetic Algorithm, a Cosine Pigeon- Inspired Optimizer and an Iterated Local Search (ILS), to solve small, medium and large random instances. Thus, it was verified which of the heuristics had the best performance according to certain indicators, such as resolution time and average quality of the solutions found. Finally, they were also compared with the optimal solution obtained for small and medium-sized instances, with the best average results to ILS, although these are not too far from those of the GS.

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ABSTRACT Account receivable can help companies expand sales and reduce inventory; however, bad debt in account receivable is not uncommon, and it dramatically occupies company funds. Therefore, the study on the problems existing in managing the account receivable of a company is necessary. For this reason, the selection of a final accounts receivable strategy needs to consider at least two factors of importance: decision-maker preferences and fuzzy preference information in the decision criteria. In this paper, a multicriteria approach for ranking a set of accounts receivable strategies in a company is proposed, and the case of a Mexican regional company is presented. The proposed model considers all the above factors. The approach uses the ELECTRE III method to obtain a recommendation per the decision maker’s preferences. The results showed that the most preferred alternative is visiting an account receivable executive at home and agreement calls. Insights gained from this applied research had practical implications for the decision- maker, including a better understanding of the problem and its value, reflected in a credit management department setup.

Resumo em Inglês:

ABSTRACT Two integer linear programming models are developed for the unrestricted vehicle routing problem with two-dimensional loading constraints. The first one is a complete model, and the other uses valid inequalities to guarantee that routes are connected and respect the two-dimensional loading constraints. The models are solved with a branch-and-cut algorithm. Computational experiments on benchmark instances showed the complete model has allowed optimal solutions for 5% of the instances, while the second model optimally solved 64% of the instances. Given the superior performance of the second model, we adapted it to handle the sequential variant of the problem, which is harder, and then optimal solutions were obtained for 46% of the instances within the given time limit. The second model compared with a branch-and-cut algorithm from the literature found identical or better solutions for all the instances.

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ABSTRACT In this paper, we consider a skew-generalized inverse Weibull probability distribution for repetitive acceptance sampling plans based on truncated life tests with known shape parameter. The design parameters such as sample size and acceptance numbers are evaluated by considering the median life time of the test units as a quality parameter under the constraint of two risks, known as the producer’s risk and consumer’s risk at a certain level. We explained the proposed method with the help of tables for different values of the known parameter. The skew-generalized inverse Weibull distribution fits better a real data set considered than the generalized inverse Weibull distribution. Comparison between the proposed plan and the single sampling plan is presented.

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ABSTRACT Military issues have great relevance worldwide since they affect the security and sovereignty of nations. In this context, the application of Multicriteria Decision Analysis (MCDA) methods is important because accurate decision-making is the deciding factor for success, which can reduce expenses and increase defense capacity. This paper aims to present a literature review on the main applications of MCDA in the military area, considering the tactical, operational and strategic spheres. The methodology includes a bibliometric study and literature review of documents from the Scopus and Web of Science databases. The bibliometric study identified the document type, language, year of publication, authors, author network, author’s publications, affiliation, keyword clusters, the field of knowledge, country and the main applied MCDA methods in military problems. The literature review allows us to verify that, as well as in other areas of knowledge, the Analytic Hierarchy Process (AHP) is the most applied MCDA method in the military area.

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ABSTRACT This research develops a production function to evaluate the teams’ efficiency in the Colombian professional soccer league. The designed methodology uses the concepts of structural equations and Data Envelope Analysis. In the development of the research, primary information associated with the sports and financial performance of the 20 Colombian Professional soccer teams was collected, with which a structural equation model was established that was empirically validated to evaluate the efficiency of each football team finally holistically. As result of this research, it can be pointed out that the proposed PLS structural model validates the hypotheses about the relationships between the latent variables. Similarly, the results show that the best Colombian soccer teams for the analyzed period are Medellín, Tolima, Nacional, and Junior.

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ABSTRACT In this paper we explore a Bayesian approach for stable distributions in presence of covariates. This class of distribution has great flexibility for fitting asymmetric and heavy-tailed empirical data. These models are commonly used for data sets in finance and insurance. In this paper we show that these distributions can also be used to fit clinical data. Since there is not an analytical form for the density probability function which implies in serious difficulties to obtain the maximum likelihood estimators for the parameters, we use Bayesian methods with data augmentation techniques to get the inferences of interest. In this study we also discuss the choice of different prior distributions for the parameters considering regression models for the location and scale parameters of the stable distribution. We use MCMC (Markov Chain Monte Carlo) algorithms to generate samples from the posterior distributions in order to evaluate the point and interval estimators. A great simplification is obtained using the OpenBugs software. Two real data examples illustrate the applicability of the proposed modeling approach.

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ABSTRACT If scarce resources are not used efficiently, welfare could be increased without any cost. Efficiency metrics have a long tradition in economics. However, measures of spatial efficiency (SE) are far less common in the literature. In health care, SE is crucial to guarantee population’s access to health care providers. We develop a metric of SE of Primary Health Care Centres (PHCCs) location based on the comparison of the minimum distances users must travel to reach a PHCC, considering their current location, against the distances they should travel if all PHCCs were optimally located. We apply this metric to assess the spatial efficiency of the PHCCs of Bahía Blanca City (Argentina). To determine the optimal location of the centres we used a capacitated P-Median model. The annual demand for medical consultations of each demand node was estimated by adjusting the number of inhabitants of that node by a socioeconomic index.

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ABSTRACT This paper presents a methodology for evaluating public investments in railway infrastructure based on the theory of real options, using the binomial model combined with dynamic programming procedures and Monte Carlo simulation. This modelling was proposed in order to overcome the inefficiencies in the evaluation process of projects conducted by the Brazilian public agencies, as pointed out by World Bank studies. According to these studies, there is evidence that the various managerial and regulatory instances of the Brazilian government have been limited to applying classical analysis techniques, considering only the discounted cash flow indicators, instead of paying more attention to risk issues, as well as to the possibilities of managerial flexibility. The proposed analytical procedures are recommended to support infrastructure investment decisions that can be transferred to the private sector or to guide the formation of public-private partnerships (PPPs).

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ABSTRACT The knapsack problem is basic in combinatorial optimization and possesses several variants and expansions. In this paper, we focus on the multi-objective stochastic quadratic knapsack problem with random weights. We propose a Multi-Objective Memetic Algorithm With Selection Neighborhood Pareto Local Search (MASNPL). At each iteration of this algorithm, crossover, mutation, and local search are applied to a population of solutions to generate new solutions that would constitute an offspring population. Then, we use a selection operator for the best solutions to the combined parent and offspring populations. The principle of the selection operation relies on the termination of the non-domination rank and the crowding distance obtained respectively by the Non-dominated Sort Algorithm and the Crowding-Distance Computation Algorithm. To evaluate the performance of our algorithm, we compare it with both an exact algorithm and the NSGA-II algorithm. Our experimental results show that the MASNPL algorithm leads to significant efficiency.

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ABSTRACT MCDM methods have been proposed to select, rank, classify, or describe alternatives based on the process of pairwise comparison. While the typologies of MCDM methods present in the literature usually are focused on their amalgamation phase, this paper proposes a typology for classifying MCDM methods based on the rationality of their pairwise comparison procedures. Accordingly, four discriminants were used to provide support in choosing MCDM methods based on the typology proposed. The proposed typology allows the analyst to identify the type of rationality from MCDM methods that best fits the multicriteria problem.

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ABSTRACT We propose two-dimensional representations for the efficient frontier for two different Network DEA (NDEA) models. Both representations follow a previous study that developed a generalization of the two-dimensional representation method for the classic DEA using a new form of linearization. The graphical representation of the efficient frontier allows managers and decision-makers unfamiliar with linear programming and DEA to understand the results obtained simply and clearly. In this study, we can obtain graphs that provide information about the efficiencies of each DMU. Furthermore, for the NDEA with an efficiency decomposition approach, it is possible to obtain a graph to evaluate the technical efficiency for each stage, as well as for the overall efficiency. The NDEA model based on efficiency composition only produces one graph. However, this unique representation shows the stage-level and the overall process level information within the same graph.

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ABSTRACT In this paper, we investigate the bi-objective multiperiod one-dimensional cutting stock problem that seeks to minimize the cost of production associated with the total length of cut objects (waste) and the inventory costs related to objects and items. A mathematical model is presented and heuristically solved by a column generation method. Computational tests were performed using the Weighted Sum method, the ε-Constraint method and a variation of the Benson method. The Pearson correlation coefficient was calculated in order to investigate the trade-off between the conflicting objectives of the problem. The results confirmed a strong negative correlation between the objective functions of the problem. All the applied scalar methods were able to find multiple efficient solutions for the problem in a reasonable computational time; however, the ε-Constraint and the modified Benson methods performed better.

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ABSTRACT One of the strategies used to optimize production processes is to define the best layout. For this, the relative positioning of the various equipment, areas, or functional activities inside the company is studied. Proper arrangement of facilities will result in shorter process times and higher productivity. In general, the objective function of the facility layout problem (FLP) is to reduce the total material handling cost. Although over six decades have been passed since the first work on FLP modeling was published, research on many aspects of this problem is still in an early stage and needs to be further explored, which motivated this study. In this paper, the unequal area of rectangular blocks with fixed dimensions and input/output points are considered for FLPs. Four new mixed-integer programming (MIP) models based on previous research formulations are developed. Then, a mathematical optimization approach based on the linearization of the models is applied. An algorithm that solves the linearized MIP model by CPLEX setting a time limit for the solution obtained excellent results for different test problems when compared to those reported in the literature.

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ABSTRACT The vertex enumeration problem of a polyhedron P in ℜn , given by m inequalities, is widely discussed in the literature. In this work it is introduced a new algorithm to solve it. The algorithm is based on lexicographic pivoting and the worst-case time complexity is Omm+n2×minm,n which is OmnVP for the case of non-degenerate polyhedra, where VP is the number of vertices of P. The proposed algorithm was coded in Matlab and numerical experiments performed for several randomly generated problems show its efficiency.

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ABSTRACT The use of the Multicriteria Decision Support Hybrid Algorithm for Decision Making Processes with Discrete Alternatives, acronym THOR, requires from the decision maker, during the judgment insertion stage, a significant amount of information that needs to be valued, which may cause the decision maker great cognitive fatigue. Therefore, this article aims to reformulate the THOR algorithm, in the judgment insertion stage, based on the inclusion of a fuzzy measurement scale, allowing the decision maker to express only a single value judgment. This reformulation follows the three steps of a fuzzy system: fuzzification, fuzzy inference and defuzzification. In addition, a comparative analysis is performed between the THOR algorithm and its new version based on the construction of the fuzzy scale. It should be noted that its reformulation does not compromise the methodological efficiency of the THOR algorithm, it only reduces the complexity of decision making.

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ABSTRACT Optimization benchmarks are tools for the validation and comparison of algorithms. Routing benchmarks are particularly relevant to industry. However, there are few available VRP benchmarks based on realistic situations. This research creates a set of multi-objective (three objectives) instances for a length- constrained variant of VRP. The instances model a realistic case of mail delivery performed by mail carriers on foot in the Brazilian city of Rio Claro. A new graph of the city road map was created, and mail carriers’ activities were estimated. Streets were assigned with distinct probability densities to receive deliveries. This research produces 80 mail delivery instances with up to 50,000 deliveries per instance. Finally, bounds for a set of instances were produced. The instances are publicly available for the community to test, compare and validate multi-objective optimization algorithms.

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ABSTRACT Background: The inventory control practice of deteriorating food products that are subject to an expiration date is a challenging process. Inappropriate inventory control practice leads to substantial waste of products and significant holding and purchasing costs. Purpose: This paper aims to develop an inventory control model-based Genetic Algorithm (GA) to minimize the Total Annual Inventory Cost (TAIC) function developed explicitly for the proposed model. Methodology: GA is used and tailored to provide the best reorder level of deteriorating food products. A case study of one of the five-star hotels in Iraq is conducted, followed by a sensitivity analysis study to validate the proposed model for varying reorder levels. Results and Conclusion: A minimum inventory cost is obtained with an optimum reorder level achieved by running GA. It is concluded that the optimal reorder level provided by the proposed GA minimized the monthly inventory cost of products.

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ABSTRACT The present research deals with the two-dimensional knapsack problem by considering the cutting of irregular items from a rectangular plate with defects. While the defects are only known at the time of cutting (in the future), we need first to select which items to produce from cutting the plate. The final items cannot have any defects and the goal is to maximize the profit from cutting the plate and producing the items. We propose a two-stage stochastic optimization model that makes use of a discrete set of scenarios with the realization of the plate defects. The first-stage decisions involve selecting items for cutting and possible production. The second-stage decisions consider the positioning of items in the plate given the scenarios with defects, and then the cancellation and non-production of some selected items, if any. We also extend this model to include a measure of risk, aiming at robust solutions. We perform computational tests on instances adapted from the literature that consider three types of defects, eight scenarios, and four cases for determining each scenario’s probability. The tests evaluate the impact of uncertainties on the problem by calculating the expected value of perfect information and the value of the stochastic solution. The results indicate a percentage reduction in the profit of up to 27.7%, on average, when considering a fully risk-averse decision-maker.

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ABSTRACT Fractional calculus is the branch of mathematics that studies the several possibilities of generalizing the derivative and integral of a function to noninteger order. Recent studies found in literature have confirmed the importance of fractional calculus for minimization problems. However, the study of fractional calculus in interior point methods for solving optimization problems is still new. In this study, inspired in applications of fractional calculus in many fields, was developed the so-called fractional order log barrier interior point algorithm by replacing some integer derivatives for the corresponding fractional ones on the first order optimality conditions of Karush-Kuhn-Tucker to solve polynomial regression models in the ℓ p −norm for 1 < p < 2. Finally, numerical experiments are performed to illustrate the proposed algorithm.

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ABSTRACT The direction of public policies plays an important role in society as a whole, especially in security, which, in addition to being considered a necessity for every citizen, is constitutionally guaranteed. This study presents the use of an unsupervised learning approach for the establishment of clusters among the municipalities in the State of Pernambuco, Brazil, considering some types of representative crimes, aiming to direct actions to prevent and fight crime in order to support policy makers. The k-means algorithm was used as the main tool in the study, using the software R 3.6.1, and recommendations for actions were directed to each of the obtained clusters. To demonstrate the direction, the grouping with the parameter k = 26 was used, referring to the State Security Integration Areas. The results show that the use of a clustering approach for the municipalities provides greater effectiveness in directing actions to combat and prevent crime, given that the municipalities that have the greatest similarities are grouped in the same cluster.

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ABSTRACT The two-dimensional cutting problem has a direct relationship with industry problems. There are several proposals to solve these problems. In particular, solution proposals using metaheuristics are the focus of this research. Thus, in this paper, we present a specialized biased random key genetic algorithm. Several tests were performed using known instances in the specific literature, and the results found by the metaheuristics proposed were, in many cases, equal or superior to the results already published in the literature. Another comparison of results presented in this paper is related to the results obtained by specialized metaheuristics and the results found by a mathematical model using commercial software. Once again, in this case, the genetic algorithm presented results equal to or very close to the optimum found by the mathematical model. In addition, the optimization proposal was extended to two-dimensional non-guillotine cutting without parts orientation.

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ABSTRACT In this paper, we present the integration of two problems related to the operations in a port terminal: the Berth Allocation Problem (BAP) integrated with the Machine Assignment Problem. We present a mixed-integer linear programming (MILP) formulation, capable of assigning and scheduling incoming vessels to berthing positions and the assignment of machines for handling the vessels. The machines can be quay cranes, mobile cranes, straddle carriers, forklifts, trucks, and any other machine. The problem aims to minimize the waiting time plus the handling time of the vessels. To solve the problem, we developed a heuristic algorithm, capable of solving a problem instance in seconds. To compare the results, we generate several instance problems based on real data and solve them with our MILP formulation implemented in a solver, our heuristic, and a First In First Out (FIFO) algorithm. The solver was able to find solutions only in small-scale instances, and the heuristic was able to find good solutions for all instances.

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ABSTRACT We consider the problem of finding the minimum uncovered area (trim loss) when tiling non- overlapping distinct integer-sided squares in an N × N square container such that the squares are placed with their edges parallel to those of the container. We find such trim losses and associated optimal packings for all container sizes N from 1 to 101, through an independently developed adaptation of Ian Gambini’s enumerative algorithm. The results were published as a new sequence to The On-Line Encyclopedia of Integer Sequences®. These are the first known results for optimal packings in non-decomposable squares.