Bilevel models on the competitive facility location problem

Facility location and allocation problems have been a major area of research for decades, which has led to a vast and still growing literature. Although there are many variants of these problems, there exist two common features: finding the best locations for one or more facilities and allocating demand points to these facilities. A considerable number of studies assume a monopolistic viewpoint and formulate a mathematical model to optimize an objective function of a single decision maker. In contrast, competitive facility location (CFL) problem is based on the premise that there exist competition in the market among different firms. When one of the competing firms acts as the leader and the other firm, called the follower, reacts to the decision of the leader, a sequential-entry CFL problem is obtained, which gives rise to a Stackelberg type of game between two players. A successful and widely applied framework to formulate this type of CFL problems is bilevel programming (BP). In this chapter, the literature on BP models for CFL problems is reviewed, existing works are categorized with respect to defined criteria, and information is provided for each work.WOS:000418225000002Scopus - Affiliation ID: 60105072Book Citation Index- Science - Book Citation Index- Social Sciences and HumanitiesArticle; Book ChapterOcak2017YÖK - 2016-1

Metaheuristic and matheuristic approaches for multi-objective optimization problems in process engineering : application to the hydrogen supply chain design

Complex optimization problems are ubiquitous in Process Systems Engineering (PSE) and are generally solved by deterministic approaches. The treatment of real case studies usually involves mixed-integer variables, nonlinear functions, a large number of constraints, and several conflicting criteria to be optimized simultaneously, thus challenging the classical methods. The main motivation of this research is therefore to explore alternative solution methods for addressing these complex multiobjective optimization problems related to the PSE area, focusing on the recent advances in Evolutionary Computation. If multiobjective evolutionary algorithms (MOEAs) have proven to be robust for the solution of multiobjective problems, their performance yet strongly depends on the constraint-handling techniques for the solution of highly constrained problems. The core of innovation of this research is the adaptation of metaheuristic-based tools to this class of PSE problems. For this purpose, a two-stage strategy was developed. First, an empirical study was performed in the perspective of comparing different algorithmic configurations and selecting the best to provide a high-quality approximation of the Pareto front. This study, comprising both academic test problems and several PSE applications, demonstrated that a method using the gradient-based mechanism to repair infeasible solutions consistently obtains the best results, in particular for handling equality constraints. Capitalizing on the experience from this preliminary numerical investigation, a novel matheuristic solution strategy was then developed and adapted to the problem of Hydrogen Supply Chain (HSC) design that encompasses the aforementioned numerical difficulties, considering both economic and environmental criteria. A MOEA based on decomposition combined with the gradient-based repair was first explored as a solution technique. However, due to the important number of mass balances (equality constraints), this approach showed a poor convergence to the optimal Pareto front. Therefore, a novel matheuristic was developed and adapted to this problem, following a bilevel decomposition: the upper level (discrete) addresses the HSC structure design problem (facility sizing and location), whereas the lower level (Linear Programming problem) solves the corresponding operation subproblem (production and transportation). This strategy allows the development of an ad-hoc matheuristic solution technique, through the hybridization of a MOEA (upper level) with a LP solver (lower level) using a scalarizing function to deal with the two objectives considered. The numerical results obtained for the Occitanie region case study highlight that the hybrid approach produces an accurate approximation of the optimal Pareto front, more efficiently than exact solution methods. Finally, the matheuristic allowed studying the HSC design problem with more realistic assumptions regarding the technologies used for hydrogen synthesis, the learning rates capturing the increasing maturity of these technologies over time and nonlinear relationships for the computation of Capital and Operational Expenditures (CAPEX and OPEX) for the hydrogen production facilities. The resulting novel model, with a non-convex, bi-objective mixed-integer nonlinear programming (MINLP) formulation, can be efficiently solved through minor modifications in the hybrid algorithm proposed earlier, which finds its mere justification in the determination of the timewise deployment of sustainable hydrogen supply chains

Survey on Ten Years of Multi-Depot Vehicle Routing Problems: Mathematical Models, Solution Methods and Real-Life Applications

A crucial practical issue encountered in logistics management is the circulation of final products from depots to end-user customers. When routing and scheduling systems are improved, they will not only improve customer satisfaction but also increase the capacity to serve a large number of customers minimizing time. On the assumption that there is only one depot, the key issue of distribution is generally identified and formulated as VRP standing for Vehicle Routing Problem. In case, a company having more than one depot, the suggested VRP is most unlikely to work out. In view of resolving this limitation and proposing alternatives, VRP with multiple depots and multi-depot MDVRP have been a focus of this paper. Carrying out a comprehensive analytical literature survey of past ten years on cost-effective Multi-Depot Vehicle Routing is the main aim of this research. Therefore, the current status of the MDVRP along with its future developments is reviewed at length in the paper

Medición de la eficiencia y la productividad: Aspectos computacionales

Programa de Doctorado en Economía (DECiDE)The purpose of efficiency and productivity problems is based on evaluating whether the use of the resources available (inputs) by a company or public institution (in general, any decision-making unit) corresponds or not with the optimal way of operating in such a way as to generate the largest possible number of outputs. To carry out this type of calculations, several mathematical models have already been proposed in the specialized literature that can be used, all of which are based on Mathematical Programming problems, and, in particular, some of them correspond to Mixed Integer Linear Programming problems (MILP). These types of problems combine several types of variables, continuous and discrete, in the same mathematical model as well as numerous restrictions, depending on the nature of the problem; features that can make the resolution process somewhat difficult. In addition, it is worth noting that these problems tend to be combinatorial in practice (NP-hard). Throughout this work, the analysis and study will focus on a field within the area of Operations Research called Data Envelopment Analysis (DEA), whose main objective is the estimation of production frontiers and the measurement of productive efficiency. Different optimization models belonging to this field will be put to the test in this thesis from a purely computational perspective, being solved through different techniques, both 2 exact and approximate, analyzing the performance and the difficulty of the same. The main objective of this work does not lie in the development and modeling of new problems in the field of DEA, but in how to achieve optimal solutions in a reasonable time for certain problems of a combinatorial nature, given that being NP-hard type problems, as the size of the problem grows, so does the difficulty of obtaining optimal solutions, especially in a short time. At this point, we will focus on the study and design of approximation techniques, known in the literature as Metaheuristics, closely linked to Machine Learning or Artificial Intelligence methodologies. In addition to these methodologies, based on learning and improving the solutions obtained, parallelization techniques have also been incorporated, capable of efficiently reducing the time needed to obtain optimal solutions in complex problems.La finalidad de los problemas de eficiencia y productividad se basan en evaluar si el uso de los recursos (entradas o inputs, en inglés) disponibles por parte de una empresa o institución pública (en general, cualquier unidad tomadora de decisiones) se corresponde o no con la forma óptima de operar de dicha entidad, generando la mayor cantidad de salidas posible (outputs en inglés). Para llevar a cabo este tipo de cálculos, varios modelos matemáticos han sido ya planteados en la literatura especializada que pueden ser utilizados, teniendo en común todos ellos que están basados en problemas de Programación Matemática, y, en particular, algunos de ellos se corresponden con problemas de Programación Matemática Lineal Mixta (Mixed Integer Linear Programming en inglés – MILP). Este tipo de problemas combinan en un mismo modelo matemático varios tipos de variables, continuas y discretas, así como numerosas restricciones, dependiendo de la naturaleza del problema, siendo estas restricciones características que pueden hacer que el proceso de resolución resulte ser algo difícil. Además, cabe destacar la característica de que estos problemas suelen ser en la práctica de tipo combinatorio (NP-duros). A lo largo de este trabajo, el análisis y el estudio se va a centrar en un campo dentro del área de Investigación Operativa denominado Análisis Envolvente de Datos (Data Envelopment Analysis en inglés - DEA), cuyo principal objetivo es el de la estimación de fronteras de producción y la medición de la eficiencia productiva. Diferentes modelos de optimización pertenecientes a este ámbito serán puestos a prueba en esta tesis desde una perspectiva puramente computacional, siendo resueltos a través de diferentes técnicas, tanto exactas como de aproximación, analizando el rendimiento y la dificultad del mismo. El objetivo principal de este trabajo no reside en el desarrollo y modelado de nuevos problemas en el ámbito del DEA, sino en cómo conseguir soluciones óptimas y eficientes en un tiempo razonable para ciertos problemas de naturaleza combinatoria, dado que al ser problemas de tipo NP-duro, a medida que el tamaño del problema crece, también lo hace la dificultad de obtener soluciones óptimas, sobre todo en un tiempo reducido. En este punto, centraremos la atención en el estudio y diseño de técnicas de aproximación, conocidas en la literatura como Metaheurísticas, estando muy ligadas a metodologías de Machine Learning o Artificial Inteligence. Además de estas metodologías, basadas en el aprendizaje y la mejora de las soluciones obtenidas, también se han incorporado técnicas de paralelismo, capaces de reducir de forma eficiente el tiempo necesario para obtener soluciones óptimas en problemas complejos

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application

Overview of Dynamic Facility Layout Planning as a Sustainability Strategy

[EN] The facility layout design problem is significantly relevant within the business operations strategies framework and has emerged as an alternate strategy towards supply chain sustainability. However, its wide coverage in the scientific literature has focused mainly on the static planning approach and disregarded the dynamic approach, which is very useful in real-world applications. In this context, the present article offers a literature review of the dynamic facility layout problem (DFLP). First, a taxonomy of the reviewed papers is proposed based on the problem formulation current trends (related to the problem type, planning phase, planning approach, number of facilities, number of floors, number of departments, space consideration, department shape, department dimensions, department area, and materials handling configuration); the mathematical modeling approach (regarding the type of model, type of objective function, type of constraints, nature of market demand, type of data, and distance metric), and the considered solution approach. Then, the extent to which recent research into DFLP has contributed to supply chain sustainability by addressing its three performance dimensions (economic, environmental, social) is described. Finally, some future research guidelines are provided.This research was funded by the Spanish Ministry of Science, Innovation and Universities Project CADS4.0, grant number RTI2018-101344-B-I00; and the Valencian Community ERDF Programme 2014-2020, grant number IDIFEDER/2018/025.Pérez-Gosende, P.; Mula, J.; Díaz-Madroñero Boluda, FM. (2020). Overview of Dynamic Facility Layout Planning as a Sustainability Strategy. Sustainability. 12(19):1-16. https://doi.org/10.3390/su12198277S1161219Ghassemi Tari, F., & Neghabi, H. (2015). A new linear adjacency approach for facility layout problem with unequal area departments. Journal of Manufacturing Systems, 37, 93-103. doi:10.1016/j.jmsy.2015.09.003Kheirkhah, A., Navidi, H., & Messi Bidgoli, M. (2015). Dynamic Facility Layout Problem: A New Bilevel Formulation and Some Metaheuristic Solution Methods. IEEE Transactions on Engineering Management, 62(3), 396-410. doi:10.1109/tem.2015.2437195Altuntas, S., & Selim, H. (2012). 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International Journal of Physical Distribution & Logistics Management, 38(5), 360-387. doi:10.1108/09600030810882816Carter, C. R., & Washispack, S. (2018). Mapping the Path Forward for Sustainable Supply Chain Management: A Review of Reviews. Journal of Business Logistics, 39(4), 242-247. doi:10.1111/jbl.12196Roy, V., Schoenherr, T., & Charan, P. (2018). The thematic landscape of literature in sustainable supply chain management (SSCM). International Journal of Operations & Production Management, 38(4), 1091-1124. doi:10.1108/ijopm-05-2017-0260Barbosa-Póvoa, A. P., da Silva, C., & Carvalho, A. (2018). Opportunities and challenges in sustainable supply chain: An operations research perspective. European Journal of Operational Research, 268(2), 399-431. doi:10.1016/j.ejor.2017.10.036Tonelli, F., Evans, S., & Taticchi, P. (2013). Industrial sustainability: challenges, perspectives, actions. International Journal of Business Innovation and Research, 7(2), 143. doi:10.1504/ijbir.2013.052576Sánchez-Flores, R. B., Cruz-Sotelo, S. E., Ojeda-Benitez, S., & Ramírez-Barreto, M. E. (2020). Sustainable Supply Chain Management—A Literature Review on Emerging Economies. Sustainability, 12(17), 6972. doi:10.3390/su12176972Ford, S., & Despeisse, M. (2016). Additive manufacturing and sustainability: an exploratory study of the advantages and challenges. Journal of Cleaner Production, 137, 1573-1587. doi:10.1016/j.jclepro.2016.04.150Kamble, S. S., Gunasekaran, A., & Gawankar, S. A. (2018). Sustainable Industry 4.0 framework: A systematic literature review identifying the current trends and future perspectives. Process Safety and Environmental Protection, 117, 408-425. doi:10.1016/j.psep.2018.05.009Khuntia, J., Saldanha, T. J. V., Mithas, S., & Sambamurthy, V. (2018). Information Technology and Sustainability: Evidence from an Emerging Economy. Production and Operations Management, 27(4), 756-773. doi:10.1111/poms.12822Roy, S., Das, M., Ali, S. M., Raihan, A. S., Paul, S. K., & Kabir, G. (2020). Evaluating strategies for environmental sustainability in a supply chain of an emerging economy. Journal of Cleaner Production, 262, 121389. doi:10.1016/j.jclepro.2020.121389Morais, D. O. C., & Silvestre, B. S. (2018). Advancing social sustainability in supply chain management: Lessons from multiple case studies in an emerging economy. Journal of Cleaner Production, 199, 222-235. doi:10.1016/j.jclepro.2018.07.097Stindt, D. (2017). A generic planning approach for sustainable supply chain management - How to integrate concepts and methods to address the issues of sustainability? Journal of Cleaner Production, 153, 146-163. doi:10.1016/j.jclepro.2017.03.126MOSLEMIPOUR, G., LEE, T. S., & LOONG, Y. T. (2017). Performance Analysis of Intelligent Robust Facility Layout Design. Chinese Journal of Mechanical Engineering, 30(2), 407-418. doi:10.1007/s10033-017-0073-9Emami, S., & S. Nookabadi, A. (2013). Managing a new multi-objective model for the dynamic facility layout problem. The International Journal of Advanced Manufacturing Technology, 68(9-12), 2215-2228. doi:10.1007/s00170-013-4820-5Al Hawarneh, A., Bendak, S., & Ghanim, F. (2019). Dynamic facilities planning model for large scale construction projects. Automation in Construction, 98, 72-89. doi:10.1016/j.autcon.2018.11.021Pournaderi, N., Ghezavati, V. R., & Mozafari, M. (2019). Developing a mathematical model for the dynamic facility layout problem considering material handling system and optimizing it using cloud theory-based simulated annealing algorithm. SN Applied Sciences, 1(8). doi:10.1007/s42452-019-0865-xTuranoğlu, B., & Akkaya, G. (2018). A new hybrid heuristic algorithm based on bacterial foraging optimization for the dynamic facility layout problem. 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A Systematic Literature Review. Relationships between the Sharing Economy, Sustainability and Sustainable Development Goals. Sustainability, 12(17), 6744. doi:10.3390/su12176744Novais, L., Maqueira, J. M., & Ortiz-Bas, Á. (2019). A systematic literature review of cloud computing use in supply chain integration. Computers & Industrial Engineering, 129, 296-314. doi:10.1016/j.cie.2019.01.056Masi, D., Day, S., & Godsell, J. (2017). Supply Chain Configurations in the Circular Economy: A Systematic Literature Review. Sustainability, 9(9), 1602. doi:10.3390/su9091602Zavala-Alcívar, A., Verdecho, M.-J., & Alfaro-Saiz, J.-J. (2020). A Conceptual Framework to Manage Resilience and Increase Sustainability in the Supply Chain. Sustainability, 12(16), 6300. doi:10.3390/su12166300Li, K., Rollins, J., & Yan, E. (2017). Web of Science use in published research and review papers 1997–2017: a selective, dynamic, cross-domain, content-based analysis. Scientometrics, 115(1), 1-20. doi:10.1007/s11192-017-2622-5Kulturel-Konak, S., & Konak, A. (2014). A large-scale hybrid simulated annealing algorithm for cyclic facility layout problems. Engineering Optimization, 47(7), 963-978. doi:10.1080/0305215x.2014.933825Madhusudanan Pillai, V., Hunagund, I. B., & Krishnan, K. K. (2011). Design of robust layout for Dynamic Plant Layout Problems. Computers & Industrial Engineering, 61(3), 813-823. doi:10.1016/j.cie.2011.05.014Peng, Y., Zeng, T., Fan, L., Han, Y., & Xia, B. (2018). An Improved Genetic Algorithm Based Robust Approach for Stochastic Dynamic Facility Layout Problem. Discrete Dynamics in Nature and Society, 2018, 1-8. doi:10.1155/2018/1529058McKendall, A. R., & Hakobyan, A. (2010). Heuristics for the dynamic facility layout problem with unequal-area departments. European Journal of Operational Research, 201(1), 171-182. doi:10.1016/j.ejor.2009.02.028Yang, C.-L., Chuang, S.-P., & Hsu, T.-S. (2010). A genetic algorithm for dynamic facility planning in job shop manufacturing. The International Journal of Advanced Manufacturing Technology, 52(1-4), 303-309. doi:10.1007/s00170-010-2733-0Abedzadeh, M., Mazinani, M., Moradinasab, N., & Roghanian, E. (2012). Parallel variable neighborhood search for solving fuzzy multi-objective dynamic facility layout problem. The International Journal of Advanced Manufacturing Technology, 65(1-4), 197-211. doi:10.1007/s00170-012-4160-xGuan, X., Dai, X., Qiu, B., & Li, J. (2012). A revised electromagnetism-like mechanism for layout design of reconfigurable manufacturing system. Computers & Industrial Engineering, 63(1), 98-108. doi:10.1016/j.cie.2012.01.016Jolai, F., Tavakkoli-Moghaddam, R., & Taghipour, M. (2012). A multi-objective particle swarm optimisation algorithm for unequal sized dynamic facility layout problem with pickup/drop-off locations. International Journal of Production Research, 50(15), 4279-4293. doi:10.1080/00207543.2011.613863Kia, R., Baboli, A., Javadian, N., Tavakkoli-Moghaddam, R., Kazemi, M., & Khorrami, J. (2012). Solving a group layout design model of a dynamic cellular manufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealing. Computers & Operations Research, 39(11), 2642-2658. doi:10.1016/j.cor.2012.01.012McKendall, A. R., & Liu, W.-H. (2012). New Tabu search heuristics for the dynamic facility layout problem. International Journal of Production Research, 50(3), 867-878. doi:10.1080/00207543.2010.545446Hosseini-Nasab, H., & Emami, L. (2013). A hybrid particle swarm optimisation for dynamic facility layout problem. International Journal of Production Research, 51(14), 4325-4335. doi:10.1080/00207543.2013.774486Kaveh, M., Dalfard, V. M., & Amiri, S. (2013). A new intelligent algorithm for dynamic facility layout problem in state of fuzzy constraints. Neural Computing and Applications, 24(5), 1179-1190. doi:10.1007/s00521-013-1339-5KIA, R., JAVADIAN, N., PAYDAR, M. M., & SAIDI-MEHRABAD, M. (2013). A SIMULATED ANNEALING FOR INTRA-CELL LAYOUT DESIGN OF DYNAMIC CELLULAR MANUFACTURING SYSTEMS WITH ROUTE SELECTION, PURCHASING MACHINES AND CELL RECONFIGURATION. Asia-Pacific Journal of Operational Research, 30(04), 1350004. doi:10.1142/s0217595913500048Mazinani, M., Abedzadeh, M., & Mohebali, N. (2012). Dynamic facility layout problem based on flexible bay structure and solving by genetic algorithm. The International Journal of Advanced Manufacturing Technology, 65(5-8), 929-943. doi:10.1007/s00170-012-4229-6Samarghandi, H., Taabayan, P., & Behroozi, M. (2013). Metaheuristics for fuzzy dynamic facility layout problem with unequal area constraints and closeness ratings. The International Journal of Advanced Manufacturing Technology, 67(9-12), 2701-2715. doi:10.1007/s00170-012-4685-zYu-Hsin Chen, G. (2013). A new data structure of solution representation in hybrid ant colony optimization for large dynamic facility layout problems. International Journal of Production Economics, 142(2), 362-371. doi:10.1016/j.ijpe.2012.12.012Bozorgi, N., Abedzadeh, M., & Zeinali, M. (2014). Tabu search heuristic for efficiency of dynamic facility layout problem. The International Journal of Advanced Manufacturing Technology, 77(1-4), 689-703. doi:10.1007/s00170-014-6460-9CHEN, G. Y.-H., & LO, J.-C. (2014). DYNAMIC FACILITY LAYOUT WITH MULTI-OBJECTIVES. Asia-Pacific Journal of Operational Research, 31(04), 1450027. doi:10.1142/s0217595914500274Hosseini, S., Khaled, A. A., & Vadlamani, S. (2014). Hybrid imperialist competitive algorithm, variable neighborhood search, and simulated annealing for dynamic facility layout problem. Neural Computing and Applications, 25(7-8), 1871-1885. doi:10.1007/s00521-014-1678-xKia, R., Khaksar-Haghani, F., Javadian, N., & Tavakkoli-Moghaddam, R. (2014). Solving a multi-floor layout design model of a dynamic cellular manufacturing system by an efficient genetic algorithm. Journal of Manufacturing Systems, 33(1), 218-232. doi:10.1016/j.jmsy.2013.12.005Nematian, J. (2014). A robust single row facility layout problem with fuzzy random variables. The International Journal of Advanced Manufacturing Technology, 72(1-4), 255-267. doi:10.1007/s00170-013-5564-yPourvaziri, H., & Naderi, B. (2014). A hybrid multi-population genetic algorithm for the dynamic facility layout problem. Applied Soft Computing, 24, 457-469. doi:10.1016/j.asoc.2014.06.051Derakhshan Asl, A., & Wong, K. Y. (2015). Solving unequal-area static and dynamic facility layout problems using modified particle swarm optimization. Journal of Intelligent Manufacturing, 28(6), 1317-1336. doi:10.1007/s10845-015-1053-5Li, L., Li, C., Ma, H., & Tang, Y. (2015). An Optimization Method for the Remanufacturing Dynamic Facility Layout Problem with Uncertainties. Discrete Dynamics in Nature and Society, 2015, 1-11. doi:10.1155/2015/685408Ulutas, B., & Islier, A. A. (2015). Dynamic facility layout problem in footwear industry. Journal of Manufacturing Systems, 36, 55-61. doi:10.1016/j.jmsy.2015.03.004Zarea Fazlelahi, F., Pournader, M., Gharakhani, M., & Sadjadi, S. J. (2016). A robust approach to design a single facility layout plan in dynamic manufacturing environments using a permutation-based genetic algorithm. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 230(12), 2264-2274. doi:10.1177/0954405415615728Hosseini, S. S., & Seifbarghy, M. (2016). A novel meta-heuristic algorithm for multi-objective dynamic facility layout problem. RAIRO - Operations Research, 50(4-5), 869-890. doi:10.1051/ro/2016057Pourvaziri, H., & Pierreval, H. (2017). Dynamic facility layout problem based on open queuing network theory. European Journal of Operational Research, 259(2), 538-553. doi:10.1016/j.ejor.2016.11.011Tayal, A., & Singh, S. P. (2016). Integrating big data analytic and hybrid firefly-chaotic simulated annealing approach for facility layout problem. Annals of Operations Research, 270(1-2), 489-514. doi:10.1007/s10479-016-2237-xKumar, R., & Singh, S. P. (2017). A similarity score-based two-phase heuristic approach to solve the dynamic cellular facility layout for manufacturing systems. Engineering Optimization, 49(11), 1848-1867. doi:10.1080/0305215x.2016.1274205Liu, J., Wang, D., He, K., & Xue, Y. (2017). Combining Wang–Landau sampling algorithm and heuristics for solving the unequal-area dynamic facility layout problem. European Journal of Operational Research, 262(3), 1052-1063. doi:10.1016/j.ejor.2017.04.002Vitayasak, S., Pongcharoen, P., & Hicks, C. (2017). A tool for solving stochastic dynamic facility layout problems with stochastic demand using either a Genetic Algorithm or modified Backtracking Search Algorithm. International Journal of Production Economics, 190, 146-157. doi:10.1016/j.ijpe.2016.03.019Xiao, Y., Xie, Y., Kulturel-Konak, S., & Konak, A. (2017). A problem evolution algorithm with linear programming for the dynamic facility layout problem—A general layout formulation. Computers & Operations Research, 88, 187-207. doi:10.1016/j.cor.2017.06.025Li, J., Tan, X., & Li, J. (2018). Research on Dynamic Facility Layout Problem of Manufacturing Unit Considering Human Factors. Mathematical Problems in Engineering, 2018, 1-13. doi:10.1155/2018/6040561Vitayasak, S., & Pongcharoen, P. (2018). Performance improvement of Teaching-Learning-Based Optimisation for robust machine layout design. 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