Operational Research

The growing concern regarding global sustainability is increasingly evident in the construction sector due to the large amounts of waste produced. This work aims to develop a new approach in order to plan an efficient recycling network for Construction and Demolition Waste (CDW). The approach is based on the methodology of Process Systems Engineering (PSE), allowing an appropriate problem systematization and the definition of flows of materials between the network nodes. The developed mixed-integer linear programming (MILP) model is a tool to support CDW management in assessing the recycling network from a regulatory perspective (minimizing the total cost). Various scenarios can be defined and sensitivity analyses performed, making the aforementioned assessment clear regarding location, types and capacities of the new processes to be installed. The model was applied to the 211 parishes that comprise the Lisbon Metropolitan Area (LMA), in Portugal, but due to its generic formulation can be applied elsewhere at regional or national level. Results show a preference for direct deposition in landfills and the fact that high quality recycling processes are not, at present, economically viable for the LMA.

We aim to investigate a new class of games, where each player’s set of strategies is a union of polyhedra. These are called integer programming games. To motivate our work, we describe some practical examples suitable to be modeled under this paradigm. We analyze the problem of determining whether or not a Nash equilibria exists for an integer programming game, and demonstrate that it is complete for the second level of the polynomial hierarchy.

This paper is a study in Reverse Logistics (RL) that aims to analyse the reverse flow of medications with expired dates, in the pharmacies of the Campania region in Italy. The main objective is to analyse the final destination of medications that are not sold and are collected in pharmacies. The analysis of how the company responsible for the collection of the medications works was made using semi-structured interviews, and a subsequent factor analysis of the collected data. The pharmacies of the main cities of this region were investigated, in order to understand their importance in this process, as well as to understand their main difficulties and challenges. A statistical analysis of the data allowed us to verify how pharmacies are accustomed to the current legislation and are aware of the importance of their role in the RL of the medications that are not sold due to expired date. It was observed that pharmacies are very satisfied with the company responsible for the collection and referral of medications and their materials to an adequate final destination. Both of them work in tune, respond well to current legislation and respect the environment.

This paper presents a penalty approach for globally solving nonsmooth and nonconvex mixed-integer nonlinear programming (MINLP) problems. Both integrality constraints and general nonlinear constraints are handled separately by hyperbolic tangent penalty functions. Proximity from an iterate to a feasible promising solution is enforced by an oracle penalty term. The numerical experiments show that the proposed oracle-based penalty approach is effective in reaching the solutions of the MINLP problems and is competitive when compared with other strategies.

The home healthcare routing problem (HHRP) refers to the problem of allocating and routing caregivers to care-dependent people at their homes. It has been mostly tackled in the literature as a rich vehicle routing problem with time windows. This paper proposes a biased-randomized heuristic, based on the well-known savings heuristic, to solve the HHRP. The algorithm is tested in small but real-case instances where patients’ visits may occur more than once a day and, in such cases, all the visits have to be performed by the same caregiver. The results show the algorithm provides good quality results in reasonably low computing times.

The adequate training of health workforce in the field of excessive alcohol consumption is essential to provide health professionals with the necessary tools for an adequate provision of care, thus leading to a decrease in alcohol consumption. Proper planning of such training is thus essential, but literature in this area is still scarce. This paper proposes an optimization model based on mathematical programming for supporting the planning of health workforce training in the field of excessive alcohol consumption in National Health Service-based countries – the \({\textit{WFTM}}^{alcohol}\). The model aims at informing on (i) how many health professionals (physicians and nurses) should be trained per year and health unit, and (ii) which training packages should be available per year. The model allows exploring the impact of considering different objectives relevant in this sector, including the minimization of costs and the maximization of multiple performance indicators. Acknowledging that several sources of uncertainty may affect planning decisions, a sensitivity analysis on key parameters of the model is performed. To illustrate the applicability of the model, a case study based on the Oeste Sul ACES in Lisbon is analyzed. Results confirm that there is a shortage of trained professionals in this field in Portugal.

Petroleum Supply Chains (PSC) networks are complex organizations, strongly affected by competition, environmental regulation and market uncertainty. To improve profits and reduce costs and risks, companies may use mathematical programming for strategic, tactical and operational planning. The current paper identifies the research opportunities and presents our contributions with respect to the strategic and tactical planning of multiple entity, echelon, product, and transportation PSCs, under the context of crude costs, product prices, and customer demand uncertainties. In order to address these gaps, four mixed integer linear programming (MILP) models were developed, namely the individualistic, collaborative, multi-objective stochastic, and robust optimization MILPs. A detailed pricing structure and a piecewise linearization function determine the collaborative economy of scale multi-entity costs, tariffs and prices per route, location and product. A stochastic programming MILP integrates an augmented \(\epsilon \)-constraint algorithm to simultaneously maximize the expected net present value (ENPV) and minimize risk represented through selected measures. The robust optimization MILP optimizes the worst-case profits considering the crude costs, product prices, and customer demand uncertainties. Test results are presented for the Portuguese downstream PSC.

This paper aims to analyse the bi-directional relationship between technical efficiency, as a measure of companies’ performance, and capital structure, under the agency cost theory as well as the pecking order and trade-off theory, to explain the capital structure decisions. The technical efficiency was estimated by the DEA method and corrected by using a suitable bootstrap to obtain statistical inferences. To test the agency cost hypothesis, asymmetric information hypothesis, risk-efficiency hypothesis and franchise value hypothesis (under pecking order and trade off theories framework), two models were applied using some determinants of capital structure such as size, profitability, tangibility, liquidity as control and explanatory variables through a truncated regression with bootstrapping. From an initial sample of 1024 small and medium sized companies from the interior of Portugal, for the period 2006–2009, a subsample of 210 SMEs from secondary and tertiary sectors was selected. The results suggest that medium sized companies have higher average bias-corrected efficiency than small companies; that short-term leverage is positively related to efficiency and that the companies in the sample follow pecking order theory.

This work proposes a multi-criteria decision making approach to help assessing and selecting suppliers in the olive oil sector. Olive oil is a protected agricultural product, by region and origin certificate. Therefore to select a supplier, it is of utter importance to inspect and test (taste, colour, smell, density, among others) the olive oil in addition to the supplying company. The identification of possible suppliers was done in two stages: firstly, the region of origin from which to choose possible suppliers was identified and then potential suppliers were evaluated on a set of characteristics for which minimum threshold values were set. From this study, which is not part of the research reported here, we were able to identify the suppliers of interest. Due to the several characteristics and characteristic dimensions used to choose a supplier we resort to the Analytic Hierarchy Process to rank them, this way allowing for a better choice. The rank obtained is robust as the top ranked supplier remains the same for any reasonable change in the criteria weighs and in the evaluation of the suppliers on each criterion. The involved company found the results of value, as well as the lessons learned by addressing the supplier evaluation problem using a more systematic approach.

The process of diffusing viral marketing campaigns through social networks can be modeled under concepts of mathematical epidemiology. Based on a Susceptible-Infected-Recovered (SIR) epidemiological model, the benefits of optimal control theory on the diffusion of a real viral advertisement are studied. Two optimal control strategies that could help marketers to maximize the spread of information and minimize the costs associated to it in optimal time windows are analyzed and compared. The uniqueness of optimality system is proved. Numerical simulations show that high investment costs in publicity strategies do not imply high overall levels of information diffusion. This paper contributes to the current literature by studying a viral marketing campaign using real numerical data.

This paper presents an exploratory approach to study and identify the main characteristics of the two-dimensional strip packing problem (2D-SPP). A large number of variables was defined to represent the main problem characteristics, aggregated in six groups, established through qualitative knowledge about the context of the problem. Coefficient correlation are used as a quantitative measure to validate the assignment of variables to groups. A principal component analysis (PCA) is used to reduce the dimensions of each group, taking advantage of the relations between variables from the same group. Our analysis indicates that the problem can be reduced to 19 characteristics, retaining most part of the total variance. These characteristics can be used to fit regression models to estimate the strip height necessary to position all items inside the strip.

The process of contagiousness spread modelling is well-known in epidemiology. However, the application of spread modelling to banking market is quite recent. In this work, we present a system of ordinary differential equations, simulating data from the largest European banks. Then, an optimal control problem is formulated in order to study the impact of a possible measure of the Central Bank in the economy. The proposed approach enables qualitative specifications of contagion in banking obtainment and an adequate analysis and prognosis within the financial sector development and macroeconomy as a whole. We show that our model describes well the reality of the largest European banks. Simulations were done using MATLAB and BOCOP optimal control solver, and the main results are taken for three distinct scenarios.

Regularity is an important property of optimization problems. Various notions of regularity are known from the literature, being defined for different classes of problems. Usually, optimization methods are based on the optimality conditions, that in turn, often suppose that the problem is regular. Absence of regularity leads to theoretical and numerical difficulties, and solvers may fail to provide a trustworthy result. Therefore, it is very important to verify if a given problem is regular in terms of certain regularity conditions and in the case of nonregularity, to apply specific methods. On the other hand, in order to test new stopping criteria and the computational behaviour of new methods, it is important to have an access to sets of reasonably-sized nonregular test problems. The paper presents a generator that constructs nonregular Semidefinite Programming (SDP) instances with prescribed irregularity degrees and a database of nonregular test problems created using this generator. Numerical experiments using popular SDP solvers on the problems of the database are carried out and permit to conclude that the most popular SDP solvers are not efficient when applied to nonregular problems.

This paper presents a multi-objective optimization model for the buses fleet management problem. This model is solved using the Augmented Weighted Tchebycheff method. The aim is to minimize three objective functions, \(Z_1\) (CO\(_2\) emissions), \(Z_2\) (other types of emissions) and \(Z_3\) (total costs), for a bus fleet that uses four types of buses: diesel, electric bus, electric bus of fast charging, and Compressed Natural Gas (CNG). A public transport (PT) company of Joinville, Brazil, where it operates three different PT lines, owns the fleet. The respective data was modelled and optimized using the MS Excel solver. Results provided interesting insights concerning the most adequate strategy for bus selection according with public transport line characteristics and taking into account trade-off between costs and emissions. The results indicate that optimal solutions include the diesel in the Itinga line and the CNG in the South line. The electric bus is more adequate in the South-North line due to the large number of stops and low average speed. However, when the costs are disregarded, in some scenarios, the best option is the electric bus for all lines.

Logistic decisions involving the location of facilities in connection with vehicle routing appear in many contexts and applications. Given a set of potential distribution centers (DC) and a group of clients, the choice of which DC to open together with the design of a number of vehicle routes, satisfying clients’ demand, may define Location-Routing Problems (LRP). This paper contributes with a new method, the 4-Phase Method (4-PhM), to deal with Capacitated LRP. Relevant advantages of 4-PhM are its generality, the possibilities of handling Multiple-Criteria and of facing large dimension problems. This last aptitude is a consequence of the sectorization phases, which permit a simplification of the solution space. Sectors are constructed by two Simulated Annealing based procedures, and they follow SectorEl, a sectorization approach inspired by electrostatics. In the last phase, the results obtained are evaluated using multicriteria analysis. Here, decision makers play an important role by reflecting preferences in a pairwise comparison matrix of the Analytic Hierarchy Process. Computational results, based on randomly generated instances, confirm the expectations about 4-PhM and its potentiality to deal with LRP.

This paper proposes a decomposition approach combining heuristic algorithms and Mixed Integer Linear Programming (MILP) models to solve the long-term scheduling of a multiproduct pipeline connecting a single-source to multiple distribution centers. The solution considers many operational aspects, such as simultaneous deliveries, pipeline maintenance periods, deliveries of multiple products during the same pumping run, and rigorous inventory control. A long-term scheduling problem from the literature was solved to validate the proposed approach. This problem is composed of a straight pipeline connecting a refinery to 3 distribution centers and transporting 4 different oil derivatives. The approach was able to obtain an operational solution in less than half a minute of CPU time. Moreover, additional tests using the same scenario were executed in order to analyze the performance of the developed decomposition approach.

Sustainability is more than ever a central concern when deciding a company’s strategy. Stakeholders are continuously pressuring industries to further reduce their environmental impact. In order to achieve that, it is imperative to look for solutions across all of the company’s operations adopting a supply chain view. However, supply chains’ complexity makes this a challenging task. Analysing the sustainability of such complex systems requires the use of capable tools as are optimization models. Several of these models can be found in the literature, mostly focusing on specific issues or specific decisions in the supply chain. Therefore, a research gap is found in models capable of handling a wider variety of decisions. With this work a mixed integer linear programming model is used to demonstrate the impact of including more or less options/decisions on design and planning decisions, and on the environmental performance of a supply chain. A case-study based on a Portuguese pulp and paper company is analysed. The results obtained for different scenarios are examined.

This article presents a project developed in a company’s quality department aiming at scheduling the nonconforming devices analysis’ process. The company faced a problem of low compliance with pre-established time requests, resulting in large fines paid to its customers of the automotive sector. In order to overcome this problem, scheduling tools were developed and tested, with the goal of minimizing the number of tardy tasks in identical parallel machines. The simulation of different scheduling rules allowed confirmation that the current prioritization rule is not the most effective one. Preliminary simulations were carried out using Lekin software [18], showing that other criteria promote better results. The use of a newly developed algorithm, combining two different criteria, resulted in a reduction of tardy tasks, thus decreasing tardiness fines paid to customers. Despite the preliminary status of present results, it is possible to foresee some improvements in the analysis process performance, by using decision making support tools based on scheduling algorithms. This way, a significant improvement on the number of analysis which fulfills the defined pre-requirements will be achieved.

Optimization problems that are motivated by real-world settings are often complex to solve. Bridging the gap between theory and practice in this field starts by understanding the causes of complexity of each problem and measuring its impact in order to make better decisions on approaches and methods. The Job-Shop Scheduling Problem (JSSP) is a well-known complex combinatorial problem with several industrial applications. This problem is used to analyse what makes some instances difficult to solve for a commonly used solution approach – Mathematical Integer Programming (MIP) – and to compare the power of an alternative approach: Constraint Programming (CP). The causes of complexity are analysed and compared for both approaches and a measure of MIP complexity is proposed, based on the concept of load per machine. Also, the impact of problem-specific global constraints in CP modelling is analysed, making proof of the industrial practical interest of commercially available CP models for the JSSP.

Car rental companies have the ability and potential to integrate their dynamic pricing decisions with their capacity decisions. Pricing has a significant impact on demand, while capacity, which translates fleet size, acquisition planning and fleet deployment throughout the network, can be used to meet this price-sensitive demand. Dynamic programming has been often used to tackle dynamic pricing problems and also to deal with similar integrated problems, yet with some significant differences as far as the inventory depletion and replenishment are considered. The goal of this work is to understand what makes the car rental problem different and hinders the application of more common methods. To do so, a discrete dynamic programming framework is proposed, with two different approaches to calculate the optimal-value function: one based on a Mixed Integer Non Linear Program (MINLP) and one based on a Constraint Programming (CP) model. These two approaches are analyzed and relevant insights are derived regarding the (in)ability of discrete dynamic programming to effectively tackle this problem within a rental context when realistically sized instances are considered.

In this paper, we describe a set of algorithms regarding real combinatorial optimization problems in the context of transportation of goods. These problems consist in the combination of the vehicle routing problem with the two-dimensional bin-packing problem, which is also known as the vehicle routing problem with two-dimensional loading constraints. We also analyzed two related problems, namely the elementary shortest path problem and the vehicle routing problem with mixed linehaul and backhaul customers. In both problems, two-dimensional loading constraints are explicitly considered. Two column generation based approaches are proposed for the vehicle routing problem with two-dimensional constraints. The elementary shortest path problem with two-dimensional constraints is addressed due to its importance in solving the subproblem of the column generation algorithms. To the best of our knowledge, we contribute with the first approach for this problem, through different constructive strategies to achieve feasible solutions, and a variable neighborhood search algorithm in order to search for improved solutions. In what concerns the vehicle routing problem with mixed linehaul and backhaul customers and two-dimensional loading constraints, different variable neighborhood search algorithms are proposed. All the proposed methods were implemented and experimentally tested. An exhaustive set of computational tests was conducted, using, for this purpose, a large group of benchmark instances. In some cases, a large set of benchmark instances was adapted in order to assess the quality of the proposed models.

This paper studies the definition of dynamic routes regarding the waste collection problem. Based on access to real-time information, provided by sensors located at waste bin containers, a Vehicle Routing Problem with Profits (VRPP) solution approach is developed. This aims for the maximization of waste collected while minimizing the total distance travelled, resulting in a maximization of profit. Different scenarios are studied, based on real data. The conclusions clearly show that the usage of real-time information on containers fill-levels, coupled with an optimization approach to define dynamic routes potentially increases the profit of waste management companies.

The purpose of this paper is to present the current understanding and conceptualization of the cargo stability constraint within the context of the Container Loading Problem. This problem is highly relevant in the transportation industry due to the increasing pressure for a more economically, environmentally and socially efficient and sustainable cargo transportation. Stability is one the most important practical relevant constraints in the Container Loading Problem due to its strong influence on the cargo arrangement. Stability is usually divided into stability during loading operations (static) and stability during transportation (dynamic). Two main contributions are made. Firstly, an overview of recent developments in the literature on the two types of stability, static and dynamic, is provided. Secondly, of opportunities for future research are identified.

This work addresses a case study in an intercontinental supply chain. The problem emerges in a company in Angola dedicated to the trade of consumable goods for construction building and industrial maintenance. The company in Angola sends the replenishment needs to a Portuguese company, which takes the decision of which products and in which quantities will be sent by shipping container to the company in Angola. The replenishment needs include the list of products that reached the corresponding reorder point. The decision of which products and in which quantity should take into consideration a set of practical constraints: the maximum weight of the cargo, the maximum volume the cargo and financial constraints related with the minimum value that guarantees the profitability of the business and a maximum value associated with shipping insurance. A 2-stage hybrid method is proposed. In the first stage, an integer linear programming model is used to select the products that maximise the sales potential. In the second stage, a Container Loading Algorithm is used to effectively pack the selected products in the shipping container ensuring the geometrical constraints, and safety constraints such as weight limit and stability. A new set of problem instances was generated with the 2DCPackGen problem generator, using as inputs the data collected in the company. Computational results for the algorithm are presented and discussed. Good results were obtained with the solution approach proposed, with an average occupation ratio of 92% of the container and an average gap of 4% for the solution of the integer linear programming model.

This study discusses the application of Analytic Hierarchy Process (AHP) to support the decision-making regarding the destination of a batch of defective products. The alternatives of destination are rework or discard. Six criteria of analysis and comparison were used. The mathematical development of the model was performed in Excel, which allowed several interactions and simulations, giving greater reliability to its application. The study was developed in a Brazilian plant of a Japanese auto parts industry which supplies a world-renowned Japanese motorcycle manufacturer. The defective product is the steering column of one of the models that presented the weld bead displaced from the correct position. From a flow of analysis of quality problems, the AHP method was adapted and applied in this case study, using evaluation questions to establish the criteria for comparison. The evidence generated by the problem analysis promotes answers and determination of criteria weights according to the influences of the answers on the cost and the quality of the product in case of rework or disposal. The AHP method assisted the systematization of the decision process, allowing the developed system to be used in other quality problems involving the destination of defective products. The contribution of this work is the adaptation of the AHP method to the application of problems of this type, using questions and answers (information already existent in the analysis of quality problems). In continuation of this specific application, the format can be adapted to the reality of other companies with inclusion or exclusion of criteria and weightings as necessary, justified, either by the characteristic of the problem or by internal policies. The applied method assisted in the decision to discard the parts of the study.

This study aims to evaluate the economic efficiency of Nursing Homes owned by 96 Santas Casas da Misericórdia (SCM) and the determinants that influenced their efficiency in 2012 and 2013. The SCM are the oldest non-profit entities, which belong to Third Sector in Portugal, provide this social response and receive significant financial contributions annually from the state. The study is developed in two stages. In the first stage, the efficiency scores were calculated through the non-parametric DEA technique. In the second stage, Tobit regression is used to verify the effect of certain organizational variables on efficiency, namely the number of users and existence of Nursing Home chains. The results of the DEA model show that the efficiency average is 81.9%, and only 10 out of 96 Nursing Homes are efficient. Tobit regression shows that the number of users has a positive effect on the efficiency of Nursing Homes, whereas the existence of Nursing Home chains affects their efficiency negatively.

While planning to expand its tissue paper business, a Portuguese company aims to explore options regarding the design and planning of its supply chain accounting not only for economic objectives but also environmental and social concerns (the three pillars of sustainability). A multi-objective mixed integer linear programming model (MOMILP) is developed and applied to the company supply chain focusing on the supply of tissue paper to the United Kingdom market. Decisions to be taken include the network structure, entity location and capacity definition, transportation network definition, production and storage levels, and material flow planning. Additionally, it is important to decide whether or not to postpone the conversion to the final product to a location closer to the clients. The augmented epsilon-constraint method is applied to study the trade-off between the three pillars of sustainability and important managerial insights are derived from this study.

In this paper, two new extensions of TOPSIS method for Group decision makers and Interval data are presented. In particular, the behavior of some past contributions when using Nadir point at the place of anti ideal point is studied. Otherwise, through simulation studies and simulation, which are mainly based upon smart random instances, a comparison between four algorithms is carried out, its purpose is to show the most effective one.