Second-stage Model Research Articles

Waste Electrical and Electronic Equipment Recycling with Capacity Constraints and Demand Forecast Updating

Waste electrical and electronic equipment (WEEE) recycling plays an important role in the control of environmental pollution and sustainable use of resources. With great government incentives, third-party recycling enterprises emerge as a bridge in the formal WEEE recycle supply chain. To help the supply chain operate stably, we investigate the optimal recycle planning for the third-party recycling enterprises considering capacity constraints and demand forecast updating. A two-stage stochastic programming model is formulated. A closed-form optimal solution for the second-stage model is derived based on KKT conditions. The sampling average approximation method and genetic algorithm are combined to solve the first-stage model. A numerical study is conducted to validate the proposed model and solution.

Integrating relational systems theory with ethical leadership: how ethical leadership relates to employee turnover intentions

PurposeAs ethical leadership has advanced as a construct, the degree to which healthy relational systems explain its effect on employee outcomes has been understudied. With this manuscript we conceptualize and test a model based on a Relational Systems approach to ethical leadership and its relationship with conflict and turnover intentions.Design/methodology/approachTwo studies were conducted to test our hypothesized first- and second-stage moderated mediation model. In Study 1, online surveys were completed by 168 working adults across two different time points. Study 2 extended Study 1 by surveying 115 working adults across three time points using the Mechanical Turk platform.FindingsThe indirect relationship between ethical leadership and turnover intentions via relationship conflict was conditional based on follower moral identity. The negative influence of ethical leadership on relationship conflict and, in turn, turnover intentions was stronger for followers who had higher moral identities. In addition, our findings suggest that leader holding behaviors strengthen the negative indirect effects of ethical leadership on turnover intentions.Originality/valueThis paper demonstrates the usefulness of a Relational Systems theoretical approach to understanding ethical leadership. Specifically, ethical leaders, through their desire and ability to help employees feel known and not alone at work, are better able to reduce relationship conflict and, in turn, reduce employees' desire to leave the organization.

Estimating PM2.5 Concentrations in Contiguous Eastern Coastal Zone of China Using MODIS AOD and a Two-Stage Random Forest Model

Abstract The coarse Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol optical depth (AOD) product (spatial resolution: 3 km) retrieved by the dark-target algorithm always generates the missing values when being adopted to estimate the ground-level PM2.5 concentrations. In this study, we developed a two-stage random forest using MODIS 3-km AOD to obtain the PM2.5 concentrations with full coverage in a contiguous coastal developed region, i.e., Yangtze River delta–Fujian–Pearl River delta (YRD–FJ–PRD) region of China. A first-stage random forest–integrated six meteorological fields was employed to predict the missing values of AOD product, and the combined AOD (i.e., random forest–derived AOD and MODIS 3-km AOD) incorporated with other ancillary variables were developed for predicting PM2.5 concentrations within a second-stage random forest model. The results showed that the first-stage random forest could explain 94% of the AOD variability over YRD–FJ–PRD region, and we achieved a site-based cross validation (CV) R2 of 0.87 and a time-based CV R2 of 0.85. The full-coverage PM2.5 concentrations illustrated a spatial pattern with annual-mean PM2.5 of 46, 40, and 35 μg m−3 in YRD, PRD, and FJ, respectively, sharing the same trend with previous studies. Our results indicated that the proposed two-stage random forest model could be effectively used for PM2.5 estimation in different areas.

A machine learning based two-stage clinical decision support system for predicting patients\u2019 discontinuation from opioid use disorder treatment: retrospective observational study

BackgroundBuprenorphine is a widely used treatment option for patients with opioid use disorder (OUD). Premature discontinuation from this treatment has many negative health and societal consequences.ObjectiveTo develop and evaluate a machine learning based two-stage clinical decision-making framework for predicting which patients will discontinue OUD treatment within less than a year. The proposed framework performs such prediction in two stages: (i) at the time of initiating the treatment, and (ii) after two/three months following treatment initiation.MethodsFor this retrospective observational analysis, we utilized Massachusetts All Payer Claims Data (MA APCD) from the year 2013 to 2015. Study sample included 5190 patients who were commercially insured, initiated buprenorphine treatment between January and December 2014, and did not have any buprenorphine prescription at least one year prior to the date of treatment initiation in 2014. Treatment discontinuation was defined as at least two consecutive months without a prescription for buprenorphine. Six machine learning models (i.e., logistic regression, decision tree, random forest, extreme-gradient boosting, support vector machine, and artificial neural network) were tested using a five-fold cross validation on the input data. The first-stage models used patients’ demographic information. The second-stage models included information on medication adherence during the early phase of treatment based on the proportion of days covered (PDC) measure.ResultsA substantial percentage of patients (48.7%) who started on buprenorphine discontinued the treatment within one year. The area under receiving operating characteristic curve (C-statistic) for the first stage models varied within a range of 0.55 to 0.59. The inclusion of knowledge regarding patients’ adherence at the early treatment phase in terms of two-months and three-months PDC resulted in a statistically significant increase in the models’ discriminative power (p-value < 0.001) based on the C-statistic. We also constructed interpretable decision classification rules using the decision tree model.ConclusionMachine learning models can predict which patients are most at-risk of premature treatment discontinuation with reasonable discriminative power. The proposed machine learning framework can be used as a tool to help inform a clinical decision support system following further validation. This can potentially help prescribers allocate limited healthcare resources optimally among different groups of patients based on their vulnerability to treatment discontinuation and design personalized support systems for improving patients’ long-term adherence to OUD treatment.

Entrepreneurial sensing capabilities: the stimulating role of cross-cultural experience

PurposeDrawing on image theory, the authors investigate how and when cross-cultural experience cultivates two core entrepreneurial sensing capabilities: opportunity recognition and creative behavior.Design/methodology/approachThe authors develop and test a second-stage moderated mediation model across two studies. Study 1 consists of a sample of prospective entrepreneurs from the UK using perceptual scale measures (n = 153). Building on this, core findings are replicated using task-based measures on a sample of US participants (n = 342).FindingsResults show that cross-cultural experience is positively related to both entrepreneurial sensing capabilities through the mediating role of self-image fluidity. No support is found for the moderating role of regulatory focus orientations.Research limitations/implicationsThese findings contribute to the burgeoning literature on multicultural experience and initiating skills in nascent venturing by providing insight on the mechanisms and boundary conditions relevant for entrepreneurial capabilities to emerge.Practical implicationsThe results reinforce the need for educators, policymakers, and entrepreneurs to facilitate and encourage opportunities for cross-cultural and overseas experiences as they are influential for stimulating entrepreneurial skills.Originality/valuePositive linkages between international mobility and entrepreneurial activity are of continued interest, yet individual-level mechanisms that explain this have been limited. The authors find that exposure to foreign cultures is potent for entrepreneurship as it can stimulate flexibility and exploration of the self-image and break frames of reference. This fosters greater tendencies for opportunity recognition and creative behaviors.

Music Signal Recognition Based on the Mathematical and Physical Equation Inversion Method

Digitization and analysis processing technology of music signals is the core of digital music technology. The paper studies the music signal feature recognition technology based on the mathematical equation inversion method, which is aimed at designing a method that can help music learners in music learning and music composition. The paper firstly studies the modeling of music signal and its analysis and processing algorithm, combining the four elements of music sound, analyzing and extracting the characteristic parameters of notes, and establishing the mathematical model of single note signal and music score signal. The single note recognition algorithm is studied to extract the Mel frequency cepstrum coefficient of the signal and improve the DTW algorithm to achieve single note recognition. Based on the implementation of the single note algorithm, we combine the note temporal segmentation method based on the energy-entropy ratio to segment the music score into single note sequences to realize the music score recognition. The paper then goes on to study the music synthesis algorithm and perform simulations. The benchmark model demonstrates the positive correlation of pitch features on recognition through comparative experiments and explores the number of harmonics that should be attended to when recognizing different instruments. The attention network-based classification model draws on the properties of human auditory attention to improve the recognition scores of the main playing instruments and the overall recognition accuracy of all instruments. The two-stage classification model is divided into a first-stage classification model and a second-stage classification model, and the second-stage classification model consists of three residual networks, which are trained separately to specifically identify strings, winds, and percussions. This method has the highest recognition score and overall accuracy.

Automated segmentation of knee articular cartilage: Joint deep and hand-crafted learning-based framework using diffeomorphic mapping

Segmentation of knee articular cartilage tissue (ACT) from 3D magnetic resonance images (MRIs) is a fundamental task in assessing knee osteoarthritis (KOA). However, automated ACT segmentation of knee cartilage is complicated by (1) the variability of pathological structures in terms of shape, size, spatial resolution and (2) the uncertainties in delineating inter- and intra-cartilage boundaries (possibly touching inter-cartilage surfaces, intensity inhomogeneity, cartilage loss due to disease progression). To address these problems, we propose a novel joint deep and hand-crafted learning-based (JD-HCl) framework. The fully automated segmentation pipeline is a combination of three main steps: 3D convolutional neural networks (CNNs), diffeomorphic mapping, and a conventional hand-crafted feature-based classification model. Firstly, the initial segmentation of knee ACT was drawn from preprocessed knee MRIs using 3D U-Net. Secondly, the spatial alignment in the image domain was carried out using diffeomorphic image registration derived from an estimate of the anatomical correspondences between the subjects and population-specific template. Finally, a tissue-specific hand-crafted feature set was extracted from the spatially aligned pre-segmented ACT region and combined with the semantic context priors obtained from 3D CNN model to develop the second-stage learning model. The proposed method was evaluated with two publicly available Osteoarthritis Initiative (OAI) datasets and one in-house MRI sequences from the Alfred hospital, Melbourne, Australia. The proposed JD-HCl framework produced strong Dice similarity coefficient (DSC), ranging between 97.4% and 98.5% (95% confidence interval) for all cartilage compartments at baseline to 97.2% and 98.5% (the 1-year follow-up) for OAI(-Imorphics) dataset, and 89.3% and 94.6% for OAI-ZIB validation dataset, respectively. Average correlations of cartilage volumes between manual and automatic segmentations were 0.9 and 0.83 for OAI-ZIB dataset, respectively, and 0.975, 0.995, and 0.99 for OAI(-Imorphics) validation datasets, respectively. In longitudinal studies, accurate segmentation of knee ACT using the proposed method produces reproducible cartilage volume, thickness measurements valuable for the study of KOA progression.

A National-Scale 1-km Resolution PM2.5 Estimation Model over Japan Using MAIAC AOD and a Two-Stage Random Forest Model

Satellite-based models for estimating concentrations of particulate matter with an aerodynamic diameter less than 2.5 μm (PM2.5) have seldom been developed in islands with complex topography over the monsoon area, where the transport of PM2.5 is influenced by both the synoptic-scale winds and local-scale circulations compared with the continental regions. We validated Multi-Angle Implementation of Atmospheric Correction (MAIAC) aerosol optical depth (AOD) with ground observations in Japan and developed a 1-km-resolution national-scale model between 2011 and 2016 to estimate daily PM2.5 concentrations. A two-stage random forest model integrating MAIAC AOD with meteorological variables and land use data was applied to develop the model. The first-stage random forest model was used to impute the missing AOD values. The second-stage random forest model was then utilised to estimate ground PM2.5 concentrations. Ten-fold cross-validation was performed to evaluate the model performance. There was good consistency between MAIAC AOD and ground truth in Japan (correlation coefficient = 0.82 and 74.62% of data falling within the expected error). For model training, the model showed a training coefficient of determination (R2) of 0.98 and a root mean square error (RMSE) of 1.22 μg/m3. For the 10-fold cross-validation, the cross-validation R2 and RMSE of the model were 0.86 and 3.02 μg/m3, respectively. A subsite validation was used to validate the model at the grids overlapping with the AERONET sites, and the model performance was excellent at these sites with a validation R2 (RMSE) of 0.94 (1.78 μg/m3). Additionally, the model performance increased as increased AOD coverage. The top-ten important predictors for estimating ground PM2.5 concentrations were day of the year, temperature, AOD, relative humidity, 10-m-height zonal wind, 10-m-height meridional wind, boundary layer height, precipitation, surface pressure, and population density. MAIAC AOD showed high retrieval accuracy in Japan. The performance of the satellite-based model was excellent, which showed that PM2.5 estimates derived from the model were reliable and accurate. These estimates can be used to assess both the short-term and long-term effects of PM2.5 on health outcomes in epidemiological studies.

An effective decomposition algorithm for scheduling branched multiproduct pipelines

This article develops a novel two-stage algorithm for the detailed scheduling of branched multiproduct pipeline systems with a single refinery and multiple depots. It features continuous-time models allowing multiple batches to be injected/delivered over a slot. The first-stage model reduces the complexity by neglecting the lower flowrate limits, enforced by big-M constraints. The objective is to minimize the makespan. The second-stage model works with the first-stage assignments and with an extended time grid. Coupled with a backtracking mechanism, the proposed algorithm can significantly reduce computational time and improve the pipeline transportation capacity. We use four benchmark instances from the literature to test and validate the effectiveness and superiority of the method proposed in this paper. Compared to the literature, a new optimal solution is reported in one case, while the computational time is reduced by at least one order of magnitude in the other cases.

A low-complexity decision model for home energy management systems

A low-complexity decision model for a Home Energy Management System is proposed to follow demand trajectory sets received from a Demand Side Response aggregator. This model is designed to reduce its computational complexity and being solved by low performance processors using available Single-Board Computers as a proof of concept. To decrease the computational complexity is proposed a two-stage model, where the first stage evaluates the hourly appliance scheduling using a relaxed set of restrictions, and the second stage evaluates a reduced set of appliances in a intra-hourly interval with a detailed characterization of the scheduled appliance properties. Simulations results show the effectiveness of the proposed algorithm to follow trajectories for different sets of home appliances and operational conditions. For the studied cases, the model presents deviations in the demand for the 3.2% of the cases in the first-stage and a 12% for the second-stage model. Results show that the proposed model can schedule available appliances according to the demand aggregator requirements in a limited solving time with diverse hardware.

Effects of co-management on technical efficiency and environmental stressors: An application to small-scale shrimp polyculture in Indonesia

Shrimp polyculture is an important activity in South East Asia, providing a livelihood and food for small-scale farmers. However, farmers are facing challenges due to increasing environmental problems in rivers used as the primary source of water in aquaculture pond production. To deal with these challenges, farmers have organized co-management communities, which gives them a stronger voice among river users. This study investigates the effects of co-management on technical efficiency and environmental stressors using a second-stage Data Envelopment Analysis model. Environmental stressors are identified through interviews with 306 farmers in eight sub-districts, of which two are practicing co-management. The results show that farmers in areas with co-management have relatively high technical efficiency after taking other drivers into account. Furthermore, the farmer’s technical efficiency seems to be less affected by the identified environmental stressors. In conclusion, co-management could be used as a tool to improve technical efficiency and limit stress factors for farmers. It could be initiated by the farmers themselves or by policymakers and natural resource managers and could improve the livelihoods of small-scale shrimp polyculture farmers.

The Late Triassic Molasse Deposits in Central Jilin Province, NE China: Constraints on the Paleo-Asian Ocean Closure

This paper presents a new detailed study including zircon U-Pb-Hf isotopic, whole-rock geochemical and Sr-Nd isotopic analyses of conglomerate and granitic pebbles from the molasse deposits in central Jilin Province, NE China. These data are used to better constrain the Late Permian–Triassic tectonic evolution regarding particularly the final closure of the Paleo-Asian Ocean (PAO) along the Changhun-Yanji suture (CYS). Zircon U-Pb data indicate that the granitic pebbles formed in the end-Permian (254–253 Ma). The youngest detrital zircon age of 231 Ma from the conglomerate, and presence of the overlying Upper Triassic Sihetun Formation suggests that the molasse deposits on the Jin′gui Island formed during the Late Triassic. The end-Permian granitic rocks display high SiO2 (66.07–74.77 wt %), with low MgO (0.55–2.05 wt %) and Mg# (31.61–43.64) values, together with depleted Hf and Nd isotopic values (εHf(t) = +1.61 to +11.62; εNd(t) = +3.3 to +4.2; (87Sr/86Sr)i = 0.706458–0.706842) and juvenile second-stage Hf model ages (1148–512 Ma), suggesting that they were probably generated by the partial melting of a Meso-Neoproterozoic juvenile metabasaltic lower crust. They are characterized by enrichments in large ion lithophile elements (LILEs) and depletions in high field strength elements (HFSEs), with affinities to igneous rocks forming in a subduction-related setting. This, combined with regional coeval subduction-related magmatic rocks, indicates that the PAO still existed along the CYS. In addition, the identification of Late Triassic molasse deposits on the Jin′gui Island in this study, coupled with occurrences of many Early Triassic syn-collisional granitoids along the CYS, indicates that the final closure of the PAO took place prior to the Late Triassic.

Optimizing configuration and scheduling of double 40 ft dual-trolley quay cranes and AGVs for improving container terminal services

Meeting the individual needs of customers will increase the competitiveness of container terminals. This paper optimizes the configuration and scheduling of double 40 ft dual-trolley quay cranes (QCs) and automated guided vehicles (AGVs) to improve the service of a container terminal. A two-stage biobjective mixed integer programming model with the objectives of maximizing customer satisfaction, minimizing the ineffective time of AGVs, and minimizing the delay time of QCs is proposed. For the proposed model, the piecewise function in the first stage is linearized by adding constraints of special ordered sets, and the GUROBI software is used to solve it. Then, an improved nondominated sorting genetic algorithm-Ⅲ is applied that aims to efficiently solve the second-stage model. Numerical experiments are presented to verify the effectiveness of models and algorithms. The results demonstrate the rationality and validity of the method, which selects the configuration and scheduling scheme based on customer satisfaction. • The satisfaction of shipowner and cargo owners are analyzed. • The handling equipment are double 40 ft dual-trolley quay cranes and AGV. • A two-stage bi-objective mixed integer programming model is proposed. • The capacity constraints of transport platform and buffer bracket are considered. • The improved non-dominated sorting genetic algorithmⅡ is used to solve the model.

Intelligent multivariable air-quality forecasting system based on feature selection and modified evolving interval type-2 quantum fuzzy neural network.

Owing to the high nonlinearity and noise in the air quality index (AQI), tackling the uncertainties and fuzziness in the forecasting process is still a prevalent problem. Therefore, this study developed an intelligent hybrid air-quality forecasting system based on feature selection and a modified evolving interval type-2 quantum fuzzy neural network (eIT2QFNN), which provides accurate air-quality forecasting information by considering climate influencing factors. The main contributions of this study are as follows. The optimal input structure of the model is determined by the proposed second-stage feature-selection model, which can better extract the influencing variables and remove redundant information. Moreover, a novel multi-objective chaotic Bonobo optimizer algorithm is proposed to improve the eIT2QFNN. The modified eIT2QFNN implements AQI prediction by considering the importance of influencing variables that can cope with the uncertainties and fuzziness in the forecasting process. Finally, the Diebold-Mariano and modified Diebold-Mariano tests are employed to evaluate the performance of the proposed system. The experimental results demonstrate that our proposed system significantly improves the modeling performance in terms of high accuracy and compact structure, and can thus serve as an effective tool for air-quality management.

Inclusive leadership and employees’ voice behavior: A moderated mediation model

The number of studies dedicated to organizational inclusion is rapidly growing. Using relational leadership theory (RLT) as the overarching framework, the current study aimed to examine how inclusive leadership indirectly influences the voices of Chinese employees via leader-member exchange (LMX). The boundary conditions of these relationships were also explored by using employee achievement values as a potential moderator. A total of 814 full-time Chinese employees were recruited. The results showed that LMX mediated the positive effect of inclusive leadership on employee voice behaviors. Specifically, inclusive leadership enhanced LMX, and employees were then more likely to express ideas in front of supervisors. Moreover, achievement values moderated the positive linkage of LMX–voice. When building the high quality LMX relationships, employees with higher achievement values were more willing to speak up compared to their counterparts holding lower achievement values. We further found that the magnitude of the mediating effect of LMX on the relationship between inclusive leadership and voice also relied on employee achievement values (i.e., a second-stage moderated mediation model). This indicates that the indirect effect was stronger when the employees had higher achievement values. The conceptual and applied implications of our findings are also discussed.

A two-stage optimization approach on the decisions for prosumers and consumers within a community in the Peer-to-peer energy sharing trading

In the traditional power system, the end users are independent individuals without any interaction. While the development of communication and information technology brings many possibilities for the interaction and cooperation among these individuals. This study explores the interaction and cooperative relationship among the prosumers and consumers within a community in the Peer-to-peer (P2P) energy sharing trading. In the community, a customer would like to provide some payoffs to encourage other customers to exchange certain amounts of energy to obtain more profits. We propose a two-stage optimization approach on the optimal strategies to maximize their utilities in the P2P energy sharing trading. In the first-stage optimization model, the decision on whether to participate in the P2P energy sharing trading is obtained based on the maximization of social utility function. Meanwhile, the optimal amounts of exchanged energy also can be obtained. In the second-stage optimization model, we provide an analysis of the optimal associated trading payments based on a payments bargaining model. Both of the above two optimization problems are solved based on a distributed algorithm respectively. Moreover, we demonstrate that the customers who participate in P2P energy sharing trading can improve their utilities compared with an individual optimization method based on a case study.

A three-system approach that integrates DEA, BSC, and AHP for museum evaluation

This paper proposes to measure the museums performance with a model that combines the Data Envelopment Analysis (DEA) and Balanced Scorecard (BSC) methodologies with a third method, the analytic hierarchy process (AHP), which is often used to support decision making. Starting from the two-stage DEA–BSC model of Basso et al. (Omega Int J Manag Sci 81:67–84, 2018), which integrates DEA and BSC, we explore the advantages to consider also the AHP methodology, with the aim to include the judgement of some museums’ experts on the relative importance of the BSC perspectives in the performance evaluation model. A first approach uses directly the AHP priorities derived from the judgements expressed by the museums’ experts interviewed to determine the weights to aggregate the four BSC performance scores into an overall performance indicator. A second approach uses the judgments of the museums’ experts indirectly to introduce proper restrictions on the output weights of the second-stage DEA model. With this approach, we overcome the problem arising from the dispersion of the preferences within the group of experts, that may heavily affects the first approach. Both approaches proposed in this contribution are applied to the case study of the municipal museums of Venice.

Integration of Moderation and Mediation in a Latent Variable Framework: A Comparison of Estimation Approaches for the Second-Stage Moderated Mediation Model.

An increasing number of studies have focused on models that integrate moderation and mediation. Four approaches can be used to test integrated mediation and moderation models: path analysis (PA), product indicator analysis (PI, constrained approach and unconstrained approach), and latent moderated structural equations (LMS). To the best of our knowledge, few studies have compared the performances of PA, PI, and LMS in evaluating integrated mediation and moderation models. As a result, it is difficult for applied researchers to choose an appropriate method in their data analysis. This study investigates the performance of different approaches in analyzing the models, using the second-stage moderated mediation model as a representative model to be evaluated. Four approaches with bootstrapped standard errors are compared under different conditions. Moreover, LMS with robust standard errors and Bayesian estimation of LMS and PA were also considered. Results indicated that LMS with robust standard errors is the superior evaluation method in all study settings. And PA estimates could be severely underestimated as they ignore measurement errors. Furthermore, it is found that the constrained PI and unconstrained PI only provide acceptable estimates when the multivariate normal distribution assumption is satisfied. The practical guidelines were also provided to illustrate the implementation of LMS. This study could help to extend the application of LMS in psychology and social science research.

Should I Represent You? Abusive Management and Supervisor Organizational Embodiment

In effort to extend supervisor organizational embodiment (SOE) research, we integrate social exchange and psychological detachment theories to examine and explain how abusive management impacts SOE. Consistent with social exchange theory, we propose that when supervisors experience abusive management (i.e., middle-level supervisors being abused by upper-level managers), they reciprocate in kind negatively with an unfavorable desire to embody the organization. We also position and find support that supervisor feelings of violation (FOV) mediates the relationship between abusive management and SOE. Additionally, supervisor turnover intentions, which are an indicator of supervisors’ psychological detachment from the organization, are considered as a moderator of the influence of FOV on SOE such that high turnover intentions strengthen the negative relationship. Results from a multi-source field study support our proposed second-stage moderated-mediation model. Implications for research and practice are discussed.

Mathematical optimization approach for facility layout on several rows

The facility layout problem is concerned with finding an arrangement of non-overlapping indivisible departments within a facility so as to minimize the total expected flow cost. In this paper we consider the special case of multi-row layout in which all the departments are to be placed in three or more rows, and our focus is on, for the first time, solutions for large instances. We first propose a new mixed integer linear programming formulation that uses continuous variables to represent the departments’ location in both x and y coordinates, where x represents the position of a department within a row and y represents the row assigned to the department. We prove that this formulation always achieves an optimal solution with integer values of y, but it is limited to solving instances with up to 13 departments. This limitation motivates the application of a two-stage optimization algorithm that combines two mathematical optimization models by taking the output of the first-stage model as the input of the second-stage model. This algorithm is, to the best of our knowledge, the first one in the literature reporting solutions for instances with up to 100 departments.