Industrial Engineering

Permanent URI for this collectionhttps://hdl.handle.net/10679/45

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    ArticlePublication
    A novel collection optimisation solution maximising long-term profits: a case study in an international bank
    (Taylor & Francis, 2017-10-02) Duman, Ekrem; Ecevit, F.; Çakır, Ç.; Altan, O.; Industrial Engineering; DUMAN, Ekrem
    When customers fail to pay the amount they owe to their bank related with a credit product (credit cards, overdraft accounts or instalment loans), the bank starts the collection process. This process typically lasts for a particular amount of time after which the customer is labelled as defaulted and a litigation period is launched. Banks try to minimise the percentage of credit exposure that goes to litigation since it negatively affects the bank’s profitability. Accordingly, they take various actions to maximise the collections before litigation. In this study, we approach this problem from a different perspective as we maximise not the short-term collections but the long-term revenues from customers by incorporating the churn effects of these actions in our modelling. © 2018 Informa UK Limited, trading as Taylor & Francis Group.
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    Conference ObjectPublication
    International roaming traffic optimization with call quality
    (SciTePress, 2019) Şahin, Ahmet; Demirel, Kenan Cem; Albey, Erinç; Gürsun, Gonca; Industrial Engineering; ALBEY, Erinç; Şahin, Ahmet; Demirel, Kenan Cem; Gürsun, Gonca
    In this study we focus on a Steering International Roaming Traffic (SIRT) problem with single service that concerns a telecommunication’s operators’ agreements with other operators in order to enable subscribers access services, without interruption, when they are out of operators’ coverage area. In these agreements, a subscriber’s call from abroad is steered to partner operator. The decision for which each call will be forwarded to the partner is based on the user’s location (country/city), price of the partner operator for that location and the service quality of partner operator. We develop an optimization model that considers agreement constraints and quality requirements while satisfying subscribers demand over a predetermined time interval. We test the performance of the proposed approach using different execution policies such as running the model once and fixing the roaming decisions over the planning interval or dynamically updating the decisions using a rolling horizon approach. We present a rigorous trade off analysis that aims to help the decision maker in assessing the relative importance of cost, quality and ease of implementation. Our results show that steering cost is decreased by approximately 25% and operator mistakes are avoided with the developed optimization model while the quality of the steered calls is kept above the base quality level.
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    Book PartPublication
    Contributions to humanitarian and non-profit operations: Equity impacts on modeling and solution approaches
    (Springer, 2019-09-14) Koyuncu, Burcu Balçık; Smilowitz, K.; Industrial Engineering; KOYUNCU, Burcu Balçık
    Equity has been acknowledged as an important concern in designing and managing humanitarian and non-profit operations over the past decade. Given the significant demands for relief supplies created by a disaster and the scarcity of resources (such as supplies, vehicles, equipment), it is inevitable that some needs will be satisfied later than others, and effective prioritization is crucial. Relief organizations are faced with the challenge of finding ways to deliver resources in an equitable way to increase the chances of survival of people. These issues also emerge in the operations of non-profit organizations that allocate distribute scarce resources. Important contributions have been made by women in studying equity in humanitarian and non-profit operations, both in terms of practical insights and methodological advances. In this chapter, we review key papers written by women, which have advanced the literature in characterizing equity in humanitarian and non-profit operations and exploring the methodological implications of equity.
  • ArticlePublicationOpen Access
    Robust reformulations of ambiguous chance constraints with discrete probability distributions
    (Balikesir University, 2019) Yanıkoğlu, İhsan; Industrial Engineering; YANIKOĞLU, Ihsan
    This paper proposes robust reformulations of ambiguous chance constraints when the underlying family of distributions is discrete and supported in a so-called ``p-box'' or ``p-ellipsoidal'' uncertainty set. Using the robust optimization paradigm, the deterministic counterparts of the ambiguous chance constraints are reformulated as mixed-integer programming problems which can be tackled by commercial solvers for moderate sized instances. For larger sized instances, we propose a safe approximation algorithm that is computationally efficient and yields high quality solutions. The associated approach and the algorithm can be easily extended to joint chance constraints, nonlinear inequalities, and dependent data without introducing additional mathematical optimization complexity to that of the original robust reformulation. In numerical experiments, we first present our approach over a toy-sized chance constrained knapsack problem. Then, we compare optimality and computational performances of the safe approximation algorithm with those of the exact and the randomized approaches for larger sized instances via Monte Carlo simulation.
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    Book PartPublication
    A decomposition-based heuristic for a waste cooking oil collection problem
    (Springer, 2020-01-01) Gültekin, Ceren; Ölmez, Ömer Berk; Koyuncu, Burcu Balçık; Ekici, Ali; Özener, Okan Örsan; Industrial Engineering; KOYUNCU, Burcu Balçık; EKİCİ, Ali; ÖZENER, Okan Örsan; Gültekin, Ceren; Ölmez, Ömer Berk
    Every year, a tremendous amount of waste cooking oil (WCO) is produced by households and commercial organizations, which poses a serious threat to the environment if disposed improperly. While businesses such as hotels and restaurants usually need to have a contract for their WCO being collected and used as a raw material for biodiesel production, such an obligation may not exist for households. In this study, we focus on designing a WCO collection network, which involves a biodiesel facility, a set of collection centers (CCs), and source points (SPs) each of whom represents a group of households. The proposed locationrouting problem (LRP) determines: (i) the CCs to be opened, (ii) the number of bins to place at each CC, (iii) the assignment of each SP to one of the accessible CCs, and (iv) the vehicle routes to collect the accumulated oil from the CCs. We formulate the problem as a mixed-integer mathematical model and solve it by using commercial solvers by setting a 1-h time limit. We also propose a decompositionbased heuristic and conduct a computational study. Our decomposition algorithm obtains the same or better solutions in 95% of all the test instances compared to the proposed mathematical model.
  • ArticlePublicationOpen Access
    A predictive multistage postdisaster damage assessment framework for drone routing
    (Wiley, 2024-01) Adsanver, Birce; Göktürk, Elvin Çoban; Koyuncu, Burcu Balçık; Industrial Engineering; GÖKTÜRK, Elvin Çoban; Adsanver, Birce
    This study focuses on postdisaster damage assessment operations supported by a set of drones. We propose a multistage framework, consisting of two phases applied iteratively to rapidly gather damage information within an assessment period. In the initial phase, the problem involves determining areas to be scanned by each drone and the optimal sequence for visiting these selected areas. We have adapted an electric vehicle routing formulation and devised a variable neighborhood descent heuristic for this phase. In the second phase, information collected from the scanned areas is employed to predict the damage status of the unscanned areas. We have introduced a novel, fast, and easily implementable imputation policy for this purpose. To evaluate the performance of our approach in real-life disasters, we develop a case study for the expected 7.5 magnitude earthquake in Istanbul, Turkey. Our numerical study demonstrates a significant improvement in response time and priority-based metrics.
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    ArticlePublication
    Production planning with flexible manufacturing systems under demand uncertainty
    (Taylor & Francis, 2024) Elyasi, M.; Özener, Başak Altan; Ekici, Ali; Özener, Okan Örsan; Economics; Industrial Engineering; ÖZENER, Başak Altan; EKİCİ, Ali; ÖZENER, Okan Örsan
    This paper delves into the impacts of an ongoing global crisis on the resilience of supply chains. Furthermore, it proposes measures to address and mitigate the disruptions caused by the prevailing uncertainties. For example, while the economy has started to recover after the pandemic and demand has increased, companies have not fully returned to their pre-pandemic levels. To enhance their supply chain resilience and effectively manage disruptions, one viable strategy is the implementation of flexible/hybrid manufacturing systems. This research is motivated by the specific requirements of Vestel Electronics, a household appliances company, which seeks a flexible/hybrid manufacturing production setup involving dedicated machinery to meet regular demand and the utilisation of flexible manufacturing system (FMS) to handle surges in demand. We employ a scenario-based approach to model demand uncertainty, enabling the company to make immediate and adaptive decisions that take advantage of the cost-effectiveness of standard production and the responsiveness of FMS. To solve the problem, we propose a heuristic algorithm based on column generation. The numerical results demonstrate that our optimisation model provides solutions with an average optimality gap of less than 6% while also reducing the average cost of standard production schemes without FMS by over 12%.
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    ArticlePublication
    Developing a national pandemic vaccination calendar under supply uncertainty
    (Elsevier, 2024-04) Karakaya, Sırma; Koyuncu, Burcu Balçık; Industrial Engineering; KOYUNCU, Burcu Balçık; Karakaya, Sırma
    During the COVID-19 pandemic, many countries faced challenges in developing and maintaining a reliable national pandemic vaccination calendar due to vaccine supply uncertainty. Deviating from the initial calendar due to vaccine delivery delays eroded public trust in health authorities and the government, hindering vaccination efforts. Motivated by these challenges, we address the problem of developing a long-term national pandemic vaccination calendar under supply uncertainty. We propose a novel two-stage mixed integer programming model that considers critical factors such as multiple doses, varying dosing schemes, and uncertainties in vaccine delivery timing and quantity. We present an efficient aggregation-based algorithm to solve this complex problem. Additionally, we extend our model to allow for dynamic adjustments to the vaccine schedule in response to mandatory policy changes, such as modifications to dose intervals, during ongoing vaccinations. We validate our model based on a case study developed by using real COVID-19 vaccination data from Norway. Our results demonstrate the advantages of the proposed stochastic optimization approach and heuristic algorithm. We also present valuable managerial insights through extensive numerical analysis, which can aid public health authorities in preparing for future pandemics.
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    ArticlePublication
    Neural network estimators for optimal tour lengths of traveling salesperson problem instances with arbitrary node distributions
    (Informs, 2024) Varol, Taha; Özener, Okan Örsan; Albey, Erinç; Industrial Engineering; ÖZENER, Okan Örsan; ALBEY, Erinç; Varol, Taha
    It is essential to solve complex routing problems to achieve operational efficiency in logistics. However, because of their complexity, these problems are often tackled sequentially using cluster-first, route-second frameworks. Unfortunately, such two-phase frameworks can suffer from suboptimality due to the initial phase. To address this issue, we propose leveraging information about the optimal tour lengths of potential clusters as a preliminary step, transforming the two-phase approach into a less myopic solution framework. We introduce quick and highly accurate Traveling Salesperson Problem (TSP) tour length estimators based on neural networks (NNs) to facilitate this. Our approach combines the power of NNs and theoretical knowledge in the routing domain, utilizing a novel feature set that includes node-level, instance-level, and solution-level features. This hybridization of data and domain knowledge allows us to achieve predictions with an average deviation of less than 0.7% from optimality. Unlike previous studies, we design and employ new instances replicating real-life logistics networks and morphologies. These instances possess characteristics that introduce significant computational costs, making them more challenging. To address these challenges, we develop a novel and efficient method for obtaining lower bounds and partial solutions to the TSP, which are subsequently utilized as solution-level predictors. Our computational study demonstrates a prediction error up to six times lower than the best machine learning (ML) methods on their training instances and up to 100 times lower prediction error on out-of-distribution test instances. Furthermore, we integrate our proposed ML models with metaheuristics to create an enumeration-like solution framework, enabling the improved solution of massive scale routing problems. In terms of solution time and quality, our approach significantly outperforms the state-of-the-art solver, demonstrating the potential of our features, models, and the proposed method.
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    ArticlePublication
    Operations research approaches for improving coordination, cooperation, and collaboration in humanitarian relief chains: A framework and literature review
    (Elsevier, 2023) Adsanver, B.; Koyuncu, Burcu Balçık; Bélanger, V.; Rancourt, M. E.; Industrial Engineering; KOYUNCU, Burcu Balçık
    Given the considerable number of actors in the humanitarian space, coordination is essential for successful disaster response. Furthermore, the sheer size of challenges and limited resources increasingly highlight the need for improved cooperation and collaboration in humanitarian supply chains. A significant number of studies in the literature explore the 3Cs (coordination, cooperation and collaboration), using conceptual, empirical and analytical methods. This paper aims to provide an overview and analysis of the Operations Research (OR) approaches that support decision making for improved 3Cs in humanitarian relief chains and to identify future research directions. To achieve this aim, we first present a holistic view of the discussions in the literature and derive a conceptual framework for 3C mechanisms in humanitarian operations. Based on our framework, we analyse studies that develop OR methods to address the design and management of 3C mechanisms in humanitarian relief chains. We also identify current gaps and future research directions.
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    ArticlePublication
    Multi-stage scenario-based stochastic programming for managing lot sizing and workforce scheduling at Vestel
    (Springer, 2023-12) Seyfishishavan, Seyed Amin; Yanıkoğlu, İhsan; Yılmaz, G.; Industrial Engineering; YANIKOĞLU, Ihsan; Seyfishishavan, Seyed Amin
    This study proposes a multi-stage stochastic production planning approach for a joint lot sizing and workforce scheduling problem under demand uncertainty. Scenario trees are used to model uncertainty in demand, and a multi-stage scenario-based stochastic linear program is developed. This model allows for both here-and-now and wait-and-see decisions providing flexibility for decision-makers to adjust production quantities according to the realized portion of demand and improve the overall effectiveness of production planning by better managing the number of active lines, workforce, and inventory levels. A matheuristic is developed for large-sized instances, which yields near-optimal solutions in practicable computation times. The proposed methods are demonstrated over a real data set taken from a Turkish home and professional appliances company, Vestel. The results show significant improvements in cost and CPU time performances for benchmark approaches, verifying the effectiveness of the proposed method.
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    Conference ObjectPublication
    Turkish cashier problem with time windows and its solution by Migrating bird optimization algorithm
    (IEEE, 2023) Bassaleh, Ahmad; Duman, Ekrem; Industrial Engineering; DUMAN, Ekrem; Bassaleh, Ahmad
    A new application of the traveling salesman problem referred to as the Turkish cashier problem (TCP) was recently introduced in literature. The problem revolved around a cashier that must visit several locations and return to his office. To complete his visits, he can use taxis or public transportation and the objective is to minimize the total transportation cost. To make this problem more practical, we took time into consideration by adding a soft time interval for each location obligating the cashier to make his visit within. If he fails to visit within the adequate time, a penalty must be paid. We name this problem as the TCP with time windows (TCPwTW). A metaheuristic algorithm known as the Migrating Birds Optimization (MBO) algorithm coupled with mathematical programming was developed to solve TCPwTW. We attempted to find the exact optimum using an exact solver where for complex problems, optimal solutions cannot be found. The quantitative study reveals that for problems having a loose time interval, the Solver serves as the best approach. On the other hand, for problems having tight time intervals, the best solutions can be obtained by the matheuristic.
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    Book PartPublication
    Post-disaster damage assessment using drones in a remote communication setting
    (Springer, 2023) Yücesoy, Ecem; Göktürk, Elvin Çoban; Koyuncu, Burcu Balçık; Industrial Engineering; GÖKTÜRK, Elvin Çoban; KOYUNCU, Burcu Balçık; Yücesoy, Ecem
    After a disaster event, obtaining fast and accurate information about the damaged built-in structure is crucial for planning life-saving response operations. Unmanned aerial vehicles (UAVs), known otherwise as drones, are increasingly utilized to support damage assessment activities as a part of humanitarian operations. In this study, we focus on a post-disaster setting where the drones are utilized to scan a disaster-affected area to gather information on the damage levels. The affected area is assumed to be divided into grids with varying criticality levels. We consider en-route recharge stations to address battery limitations and remote information transmission to a single operation center. We address the problem of determining the routes of a set of drones across a given assessment horizon to maximize the number of visited grids considering their criticality levels and transmit the collected assessment information as quickly as possible along the routes. We propose a mixed integer linear programming formulation to solve this problem and also adapt it to a setting where the information transmission is only possible at the end of the routes for comparison purposes. We propose performance metrics to evaluate the performance of our model and present results on small-sized instances with sensitivity analysis. We present results that highlight the tradeoff between attained coverage (visiting more grids) and response time (the timing of information transmission in the scanned areas). Moreover, we show the advantage of en-route data transmission compared to the setting with data transmission at the end of the routes.
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    ArticlePublication
    A column generation-based approach for the adaptive stochastic blood donation tailoring problem
    (Taylor & Francis, 2023) Elyasi, Milad; Özener, Okan Örsan; Yanıkoğlu, İhsan; Ekici, Ali; Dolgui, A.; Industrial Engineering; ÖZENER, Okan Örsan; YANIKOĞLU, Ihsan; EKİCİ, Ali; Elyasi, Milad
    Managing blood donations is a challenging problem due to the perishability of blood, limited donor pool, deferral time restrictions, and demand uncertainty. The problem addressed here combines two important aspects of blood supply chain management: the inventory control of blood products and the donation schedule. We propose a stochastic scenario-based reformulation of the blood donation management problem that adopts multicomponent apheresis and utilises donor pool segmentation into here-and-now and wait-and-see donors. We propose a flexible donation scheme that is resilient against demand uncertainty. This scheme enables more flexible donation schedules because wait-and-see donors may adjust their donation schedules according to the realised values of demand over time. We propose a column generation-based approach to solve the associated multi-stage stochastic donation tailoring problem. The numerical results show the effectiveness of the proposed optimisation model, which provides solutions with less than a 7% optimality gap on average with respect to a lower bound. It also improves the operational cost of the standard donation scheme that does not use wait-and-see donors by more than 18% on average. Utilising multicomponent apheresis and flexible wait-and-see donations are suggested for donation organisations because they yield significant cost reductions and resilient donation schedules.
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    Conference ObjectPublication
    Advancing home healthcare through machine learning: Predicting service time for enhanced patient care
    (IEEE, 2023) Selçuk, Yağmur Selenay; Göktürk, Elvin Çoban; Industrial Engineering; GÖKTÜRK, Elvin Çoban; Selçuk, Yağmur Selenay
    Providing healthcare services at home is crucial for patients who require long-term care or face mobility or other health-related constraints that prevent them from traveling to healthcare facilities. Effective data analysis techniques are needed to optimize these services to understand patient needs and allocate resources efficiently. Machine learning algorithms can analyze big datasets generated from home healthcare services to identify patterns, trends, and predictive factors. By utilizing these techniques, predictive models for service time can be developed, leading to improved patient outcomes, increased efficiency, and reduced costs. This study explores the significance of various features in predicting service time for home healthcare services by analyzing real-life data using data analysis techniques. By developing a correlation matrix, healthcare providers can examine the relationships between features as well as their connections with the target value, thereby providing valuable managerial insights into improving the quality of home healthcare services through enhanced predictions of service time.
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    ArticlePublication
    Healthcare inventory management in the presence of supply disruptions and a reliable secondary supplier
    (Springer, 2023-12) Shourabizadeh, H.; Kundakcıoğlu, Ömer Erhun; Bozkır, Cem Deniz Çağlar; Tüfekçi, Mihriban Büşra; Henry, A. C.; Industrial Engineering; KUNDAKCIOĞLU, Ömer Erhun; Bozkır, Cem Deniz Çağlar; Tüfekçi, Mihriban Büşra
    We study the inventory review policy for a healthcare facility to minimize the impact of inevitable drug shortages. Usually, healthcare facilities do not rely on a single source of supply, and alternative mechanisms are present. When the primary supplier is not available, items are produced in-house or supplied through another supplier, albeit with additional cost. Our aim in this study is to determine how optimal inventory parameters are adjusted depending on the availability of the primary supplier. We show that an approximation provides trivial results, yet fails to capture the nuances therein. Our proposed Markov chain model overcomes these issues, and numerical results illustrate the significant economic impact of inventory parameter optimization. Furthermore, we simulate uncertainty scenarios and provide sensitivity analyses concerning fixed ordering cost for the secondary supplier, shortage frequency, shortage duration, and demand rates.
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    ArticlePublication
    Electric bus fleet scheduling under travel time and energy consumption uncertainty
    (Elsevier, 2023-11) Avishan, Farzad; Yanıkoğlu, İhsan; Alwesabi, Y.; Industrial Engineering; YANIKOĞLU, Ihsan; Avishan, Farzad
    The public transportation system is experiencing a substantial shift due to the rapid expansion of electromobility infrastructure and operations. This transformation is anticipated to contribute to decarbonizing and promoting environmental sustainability significantly. Among the most pressing planning issues in this area is the optimization of operational and strategic costs associated with electric fleets, which has recently garnered the attention of researchers. This paper investigates the scheduling and procurement problem of electric fleets under travel time and energy consumption uncertainty. A novel mixed-integer linear programming model is proposed, which determines the number of buses required to cover all trips, yields the schedule of the trips, and creates bus charging plans. The robust optimization paradigm is employed to address uncertainty, and a new budget uncertainty set is introduced to control the robustness of the solution. The efficiency of the model is evaluated through an extensive Monte Carlo simulation. Additionally, a case study is conducted on the off-campus college transport network at Binghamton University to demonstrate the real-world applicability of the model. The numerical results have shown that ignoring uncertainty can lead to schedules where up to 48% of the trips are affected, which are either delayed or missed. The proposed approach can also be applied to other transportation networks with similar characteristics and uncertainties.
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    ArticlePublication
    A non-clustered approach to platelet collection routing problem
    (Elsevier, 2023-12) Talebi Khameneh, R.; Elyasi, Milad; Özener, Okan Örsan; Ekici, Ali; Industrial Engineering; ÖZENER, Okan Örsan; EKİCİ, Ali; Elyasi, Milad
    One of the blood components that can be extracted from whole blood is the platelet, which has a wide range of uses in medical fields. Due to the perishable nature of platelets, it is recommended that the separation occurs within six hours after the donation. Moreover, platelets constitute less than one percent of the whole blood volume, yet they are highly demanded. Given the importance of platelets in healthcare, their perishability, and their limited supply, an effective platelet supply chain leans on well-managed whole blood collection operations. In this study, we consider a blood collection problem (BCP) focusing on the collection of whole blood donations from the blood donation sites (BDSs). Different from the basic form of BCP, we consider the processing time limit (PTL) of blood and arbitrary donation patterns of donors as well as relaxing the assumption of assigning each blood collection vehicle (BCV) to a set of BDSs. Therefore, we define the non-clustered maximum blood collection problem (NCMBCP) as a variant of BCP. In this study, we examine routing decisions for platelet collections while relaxing the clustering requirement from the BDSs, which results in a significant increase in the complexity of the problem. In order to solve the problem, we propose a hybrid genetic algorithm (HGA) and an invasive weed optimization (IWO) algorithm that provide considerable improvements over the best solution in the literature for the clustered variant of the problem and outperform it (on average) by 8.68% and 8.16%, respectively.
  • ArticlePublicationOpen Access
    A machine learning approach to deal with ambiguity in the humanitarian decision-making
    (Wiley, 2023-09) Grass, E.; Ortmann, J.; Koyuncu, Burcu Balçık; Rei, W.; Industrial Engineering; KOYUNCU, Burcu Balçık
    One of the major challenges for humanitarian organizations in response planning is dealing with the inherent ambiguity and uncertainty in disaster situations. The available information that comes from different sources in postdisaster settings may involve missing elements and inconsistencies, which can hamper effective humanitarian decision-making. In this paper, we propose a new methodological framework based on graph clustering and stochastic optimization to support humanitarian decision-makers in analyzing the implications of divergent estimates from multiple data sources on final decisions and efficiently integrating these estimates into decision-making. To the best of our knowledge, the integration of ambiguous information into decision-making by combining a cluster machine learning method with stochastic optimization has not been done before. We illustrate the proposed approach on a realistic case study that focuses on locating shelters to serve internally displaced people (IDP) in a conflict setting, specifically, the Syrian civil war. We use the needs assessment data from two different reliable sources to estimate the shelter needs in Idleb, a district of Syria. The analysis of data provided by two assessment sources has indicated a high degree of ambiguity due to inconsistent estimates. We apply the proposed methodology to integrate divergent estimates in making shelter location decisions. The results highlight that our methodology leads to higher satisfaction of demand for shelters than other approaches such as a classical stochastic programming model. Moreover, we show that our solution integrates information coming from both sources more efficiently thereby hedging against the ambiguity more effectively. With the newly proposed methodology, the decision-maker is able to analyze the degree of ambiguity in the data and the degree of consensus between different data sources to ultimately make better decisions for delivering humanitarian aid.
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    ArticlePublication
    Solving a new application of asymmetric TSP by modified migrating birds optimization algorithm
    (Springer, 2023-07) Duman, T.; Duman, Ekrem; Industrial Engineering; DUMAN, Ekrem
    In this study, we first introduce a new application of the asymmetric traveling salesman problem which is about a small restaurant with one cook and a single stove. Once a meal has started cooking on the stove, the cook prepares the next meal on the table where the preparation time is dependent on the previous meal prepared. For the solution of this problem, besides several simple construction algorithms and a new version of the simulated annealing (SA) algorithm, we focus on enhanced versions of the recently introduced migrating birds optimization (MBO) algorithm. The original MBO algorithm might suffer from early convergence. Here we introduce several different ways of handling this problem. The extensive numerical experimentation conducted shows the superiority of the enhanced MBO over the original MBO (about 2.62 per cent) and over the SA algorithm (about 1.05 per cent).