Decision-making in a fuzzy environment

Decision making where goals or constraints are not sharply defined boundaries and fuzzy using dynamic programmin

Multistage scenario-based interval-stochastic programming for planning water resources allocation

In this study, a multistage scenario-based interval-stochastic programming (MSISP) method is developed for water-resources allocation under uncertainty. MSISP improves upon the existing multistage optimization methods with advantages in uncertainty reflection, dynamics facilitation, and risk analysis. It can directly handle uncertainties presented as both interval numbers and probability distributions, and can support the assessment of the reliability of satisfying (or the risk of violating) system constraints within a multistage context. It can also reflect the dynamics of system uncertainties and decision processes under a representative set of scenarios. The developed MSISP method is then applied to a case of water resources management planning within a multi-reservoir system associated with joint probabilities. A range of violation levels for capacity and environment constraints are analyzed under uncertainty. Solutions associated different risk levels of constraint violation have been obtained. They can be used for generating decision alternatives and thus help water managers to identify desired policies under various economic, environmental and system-reliability conditions. Besides, sensitivity analyses demonstrate that the violation of the environmental constraint has a significant effect on the system benefit

Energy and environmental systems planning under uncertainty-An inexact fuzzy-stochastic programming approach

In this study, an inexact fuzzy-stochastic energy model (IFS-EM) is developed for planning energy and environmental systems (EES) management under multiple uncertainties. In the IFS-EM, methods of interval parameter fuzzy linear programming (IFLP) and multistage stochastic programming with recourse (MSP) are introduced into a mixed-integer linear programming (MILP) framework, such that the developed model can tackle uncertainties described in terms of interval values, fuzzy sets and probability distributions. Moreover, it can reflect dynamic decisions for facility-capacity expansion and energy supply over a multistage context. The developed model is applied to a case of planning regional-scale energy and environmental systems to demonstrate its applicability, where three cases are considered based on different energy and environmental management policies. The results indicate that reasonable solutions have been generated. They are helpful for supporting: (a) adjustment or justification of allocation patterns of regional energy resources and services, (b) formulation of local policies regarding energy consumption, economic development and environmental protection, and (c) in-depth analysis of tradeoffs among system cost, satisfaction degree and environmental requirement under multiple uncertainties. (C) 2010 Elsevier Ltd. All rights reserved

A Novel Euler's Elastica based Segmentation Approach for Noisy Images via using the Progressive Hedging Algorithm

Euler's Elastica based unsupervised segmentation models have strong capability of completing the missing boundaries for existing objects in a clean image, but they are not working well for noisy images. This paper aims to establish a Euler's Elastica based approach that properly deals with random noises to improve the segmentation performance for noisy images. We solve the corresponding optimization problem via using the progressive hedging algorithm (PHA) with a step length suggested by the alternating direction method of multipliers (ADMM). Technically, all the simplified convex versions of the subproblems derived from the major framework of PHA can be obtained by using the curvature weighted approach and the convex relaxation method. Then an alternating optimization strategy is applied with the merits of using some powerful accelerating techniques including the fast Fourier transform (FFT) and generalized soft threshold formulas. Extensive experiments have been conducted on both synthetic and real images, which validated some significant gains of the proposed segmentation models and demonstrated the advantages of the developed algorithm

Solution Approaches for the Management of the Water Resources in Irrigation Water Systems with Fuzzy Costs

[EN] Currently, the management of water networks is key to increase their sustainability. This fact implies that water managers have to develop tools that ease the decision-making process in order to improve the efficiency of irrigation networks, as well as their exploitation costs. The present research proposes a mathematical programming model to optimize the selection of the water sources and the volume over time in water networks, minimizing the operation costs as a function of the water demand and the reservoir capacity. The model, which is based on fuzzy methods, improves the evaluation performed by water managers when they have to decide about the acquisition of the water resources under uncertain costs. Different fuzzy solution approaches have been applied and assessed in terms of model complexity and computational efficiency, showing the solution accomplished for each one. A comparison between different methods was applied in a real water network, reaching a 20% total cost reduction for the best solution.Sanchis, R.; Díaz-Madroñero Boluda, FM.; López Jiménez, PA.; Pérez-Sánchez, M. (2019). Solution Approaches for the Management of the Water Resources in Irrigation Water Systems with Fuzzy Costs. Water. 11(12):1-22. https://doi.org/10.3390/w11122432S1221112Biswas, A. K. (2004). Integrated Water Resources Management: A Reassessment. Water International, 29(2), 248-256. doi:10.1080/02508060408691775Pahl-Wostl, C. (2006). Transitions towards adaptive management of water facing climate and global change. Water Resources Management, 21(1), 49-62. doi:10.1007/s11269-006-9040-4Wu, K., & Zhang, L. (2014). Progress in the Development of Environmental Risk Assessment as a Tool for the Decision-Making Process. Journal of Service Science and Management, 07(02), 131-143. doi:10.4236/jssm.2014.72011Hernández-Bedolla, J., Solera, A., Paredes-Arquiola, J., Pedro-Monzonís, M., Andreu, J., & Sánchez-Quispe, S. (2017). The Assessment of Sustainability Indexes and Climate Change Impacts on Integrated Water Resource Management. Water, 9(3), 213. doi:10.3390/w9030213Hunink, J., Simons, G., Suárez-Almiñana, S., Solera, A., Andreu, J., Giuliani, M., … Bastiaanssen, W. (2019). A Simplified Water Accounting Procedure to Assess Climate Change Impact on Water Resources for Agriculture across Different European River Basins. Water, 11(10), 1976. doi:10.3390/w11101976Pérez-Sánchez, M., Sánchez-Romero, F., Ramos, H., & López-Jiménez, P. (2016). Modeling Irrigation Networks for the Quantification of Potential Energy Recovering: A Case Study. Water, 8(6), 234. doi:10.3390/w8060234Corominas, J. (2010). Agua y energía en el riego, en la época de la sostenibilidad. Ingeniería del agua, 17(3). doi:10.4995/ia.2010.2977Romero, L., Pérez-Sánchez, M., & Amparo López-Jiménez, P. (2017). Improvement of sustainability indicators when traditional water management changes: a case study in Alicante (Spain). AIMS Environmental Science, 4(3), 502-522. doi:10.3934/environsci.2017.3.502Davies, E. G. R., & Simonovic, S. P. (2011). Global water resources modeling with an integrated model of the social–economic–environmental system. Advances in Water Resources, 34(6), 684-700. doi:10.1016/j.advwatres.2011.02.010ALCAMO, J., DÖLL, P., HENRICHS, T., KASPAR, F., LEHNER, B., RÖSCH, T., & SIEBERT, S. (2003). Development and testing of the WaterGAP 2 global model of water use and availability. Hydrological Sciences Journal, 48(3), 317-337. doi:10.1623/hysj.48.3.317.45290Sanchis, R., & Poler, R. (2019). Enterprise Resilience Assessment—A Quantitative Approach. Sustainability, 11(16), 4327. doi:10.3390/su11164327Rahaman, M. M., & Varis, O. (2005). Integrated water resources management: evolution, prospects and future challenges. Sustainability: Science, Practice and Policy, 1(1), 15-21. doi:10.1080/15487733.2005.11907961Markantonis, V., Reynaud, A., Karabulut, A., El Hajj, R., Altinbilek, D., Awad, I. M., … Bidoglio, G. (2019). Can the Implementation of the Water-Energy-Food Nexus Support Economic Growth in the Mediterranean Region? The Current Status and the Way Forward. Frontiers in Environmental Science, 7. doi:10.3389/fenvs.2019.00084Food and Agriculture Organization (FAO)www.fao.orgDirective 2000/60/EC of the European Parliament and of the Councilhttps://eur-lex.europa.eu/eli/dir/2000/60/ojNamany, S., Al-Ansari, T., & Govindan, R. (2019). Sustainable energy, water and food nexus systems: A focused review of decision-making tools for efficient resource management and governance. Journal of Cleaner Production, 225, 610-626. doi:10.1016/j.jclepro.2019.03.304Archibald, T. W., & Marshall, S. E. (2018). Review of Mathematical Programming Applications in Water Resource Management Under Uncertainty. Environmental Modeling & Assessment, 23(6), 753-777. doi:10.1007/s10666-018-9628-0Chen, S., Shao, D., Gu, W., Xu, B., Li, H., & Fang, L. (2017). An interval multistage water allocation model for crop different growth stages under inputs uncertainty. Agricultural Water Management, 186, 86-97. doi:10.1016/j.agwat.2017.03.001Xie, Y. L., Xia, D. H., Huang, G. H., Li, W., & Xu, Y. (2015). A multistage stochastic robust optimization model with fuzzy probability distribution for water supply management under uncertainty. Stochastic Environmental Research and Risk Assessment, 31(1), 125-143. doi:10.1007/s00477-015-1164-8Heumesser, C., Fuss, S., Szolgayová, J., Strauss, F., & Schmid, E. (2012). Investment in Irrigation Systems under Precipitation Uncertainty. Water Resources Management, 26(11), 3113-3137. doi:10.1007/s11269-012-0053-xPereira-Cardenal, S. J., Mo, B., Riegels, N. D., Arnbjerg-Nielsen, K., & Bauer-Gottwein, P. (2015). Optimization of Multipurpose Reservoir Systems Using Power Market Models. Journal of Water Resources Planning and Management, 141(8), 04014100. doi:10.1061/(asce)wr.1943-5452.0000500Kumari, S., & Mujumdar, P. P. (2017). Fuzzy Set–Based System Performance Evaluation of an Irrigation Reservoir System. Journal of Irrigation and Drainage Engineering, 143(5), 04017002. doi:10.1061/(asce)ir.1943-4774.0001155Jairaj, P. G., & Vedula, S. (2000). Water Resources Management, 14(6), 457-472. doi:10.1023/a:1011117918943Li, M., Guo, P., Singh, V. P., & Zhao, J. (2016). Irrigation Water Allocation Using an Inexact Two-Stage Quadratic Programming with Fuzzy Input under Climate Change. JAWRA Journal of the American Water Resources Association, 52(3), 667-684. doi:10.1111/1752-1688.12415Bozorg-Haddad, O., Malmir, M., Mohammad-Azari, S., & Loáiciga, H. A. (2016). Estimation of farmers’ willingness to pay for water in the agricultural sector. Agricultural Water Management, 177, 284-290. doi:10.1016/j.agwat.2016.08.011Raju, K. S., & Duckstein, L. (2003). Multiobjective fuzzy linear programming for sustainable irrigation planning: an Indian case study. Soft Computing - A Fusion of Foundations, Methodologies and Applications, 7(6), 412-418. doi:10.1007/s00500-002-0230-6Regulwar, D. G., & Gurav, J. B. (2012). Sustainable Irrigation Planning with Imprecise Parameters under Fuzzy Environment. Water Resources Management, 26(13), 3871-3892. doi:10.1007/s11269-012-0109-yMula, J., Poler, R., & Garcia-Sabater, J. P. (2008). Capacity and material requirement planning modelling by comparing deterministic and fuzzy models. International Journal of Production Research, 46(20), 5589-5606. doi:10.1080/00207540701413912Díaz-Madroñero, M., Mula, J., Jiménez, M., & Peidro, D. (2016). A rolling horizon approach for material requirement planning under fuzzy lead times. International Journal of Production Research, 55(8), 2197-2211. doi:10.1080/00207543.2016.1223382Mula, J., Poler, R., & Garcia, J. P. (2006). MRP with flexible constraints: A fuzzy mathematical programming approach. Fuzzy Sets and Systems, 157(1), 74-97. doi:10.1016/j.fss.2005.05.045Mula, J., Poler, R., & Garcia-Sabater, J. P. (2007). Material Requirement Planning with fuzzy constraints and fuzzy coefficients. Fuzzy Sets and Systems, 158(7), 783-793. doi:10.1016/j.fss.2006.11.003Díaz-Madroñero, M., Mula, J., & Jiménez, M. (2014). Fuzzy goal programming for material requirements planning under uncertainty and integrity conditions. International Journal of Production Research, 52(23), 6971-6988. doi:10.1080/00207543.2014.920115Pérez-Sánchez, M., Díaz-Madroñero, M., Díaz-Madroñero, D.-M., … Josefa, J. (2017). Mathematical Programming Model for Procurement Selection in Water Irrigation Systems. A Case Study. Journal of Engineering Science and Technology Review, 10(6), 154-162. doi:10.25103/jestr.106.19Herrera, F., & Verdegay, J. L. (1995). Three models of fuzzy integer linear programming. European Journal of Operational Research, 83(3), 581-593. doi:10.1016/0377-2217(93)e0338-xHerrera, F., & Verdegay, J. L. (1996). Fuzzy boolean programming problems with fuzzy costs: A general study. Fuzzy Sets and Systems, 81(1), 57-76. doi:10.1016/0165-0114(94)00324-6Alavidoost, M. H., Babazadeh, H., & Sayyari, S. T. (2016). An interactive fuzzy programming approach for bi-objective straight and U-shaped assembly line balancing problem. Applied Soft Computing, 40, 221-235. doi:10.1016/j.asoc.2015.11.025Torabi, S. A., & Hassini, E. (2008). An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets and Systems, 159(2), 193-214. doi:10.1016/j.fss.2007.08.010Yager, R. R. (1981). A procedure for ordering fuzzy subsets of the unit interval. Information Sciences, 24(2), 143-161. doi:10.1016/0020-0255(81)90017-7Lai, Y.-J., & Hwang, C.-L. (1992). A new approach to some possibilistic linear programming problems. Fuzzy Sets and Systems, 49(2), 121-133. doi:10.1016/0165-0114(92)90318-xZimmermann, H.-J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45-55. doi:10.1016/0165-0114(78)90031-3Selim, H., & Ozkarahan, I. (2006). A supply chain distribution network design model: An interactive fuzzy goal programming-based solution approach. The International Journal of Advanced Manufacturing Technology, 36(3-4), 401-418. doi:10.1007/s00170-006-0842-6Bellman, R. E., & Zadeh, L. A. (1970). Decision-Making in a Fuzzy Environment. Management Science, 17(4), B-141-B-164. doi:10.1287/mnsc.17.4.b14

Planning Hydropower Production of Small Reservoirs Under Resources and System Knowledge Uncertainty

Available energy from water varies widely from season to season, depending on precipitation and streamflows, especially in small catchments. In addition, the reservoir operation problem is associated with the inability of operators to formulate crisp boundary conditions, due to uncertainty in knowledge. In this chapter, an approach for planning the operation of small multipurpose reservoir systems for hydropower generation and flood control under consideration of the stochastic nature of inflows and initial storage levels and allowed formulation of constraints with some range of uncertainty will be presented. The approach is based on joint chance constrained and fuzzy programming, which addresses the problem of including risk directly in the optimization. Therefore, the stochastic nature of inputs is incorporated directly in the model through the use of convolution of random variables. Furthermore, probabilistic/vague constraints and preassigned tolerance levels are used to transform the stochastic optimization problem into its deterministic equivalent. The approach searches for a control strategy, which maximizes the benefits acquired from hydropower generation and minimizes the economic losses incurred due to not meeting the required reliability levels from the various purposes served by the reservoir system. Besides the optimal reservoir release strategy, this approach also determines the optimal reliabilities of satisfying hydropower demand and flood control storage requirements. Therefore, this tool has some advantages in planning the operations of reservoirs in extreme hydrological events such as floods and droughts. The system is applied to the Wuyang small hydropower plants cascade in the People’s Republic of China

Review of mathematical models for production planning under uncertainty due to lack of homogeneity: proposal of a conceptual model

[EN] Lack of homogeneity in the product (LHP) appears in some production processes that confer heterogeneity in the characteristics of the products obtained. Supply chains with this issue have to classify the product in different homogeneous subsets, whose quantity is uncertain during the production planning process. This paper proposes a generic framework for reviewing in a unified way the literature about production planning models dealing with LHP uncertainty. This analysis allows the identification of similarities among sectors to transfer solutions between them and gaps existing in the literature for further research. The results of the review show: (1) sectors affected by LHP inherent uncertainty, (2) the inherent LHP uncertainty types modelled, and (3) the approaches for modelling LHP uncertainty most widely employed. Finally, we suggest a conceptual model reflecting the aspects to be considered when modelling the production planning in sectors with LHP in an uncertain environment.This research was initiated within the framework of the project funded by the Ministerio de Economía y Competitividad [Ref. DPI2011-23597] entitled ‘Methods and models for operations planning and order management in supply chains characterised by uncertainty in production due to the lack of product uniformity’ (PLANGES-FHP) already finished. After, the project leading to this application has received funding from the European Union’s research and innovation programme under the H2020 Marie Skłodowska-Curie Actions with the grant agreement No 691249, Project entitled ’Enhancing and implementing Knowledge based ICT solutions within high Riskand Uncertain Conditions for Agriculture Production Systems’ (RUC-APS).Mundi, I.; Alemany Díaz, MDM.; Poler, R.; Fuertes-Miquel, VS. (2019). 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González-Araya, M. C. Gripe, and S. V. Rodrıguez. 2014. “A Mixed Integer Linear Program for Operational Planning in a Meat Packing Plant.” Accessed January 15, 2015. http://www.researchgate.net/profile/Victor_Albornoz/publication/268687089_A_Mixed_Integer_Linear_Program_for_Operational_Planning_in_a_Meat_Packing_Plant/links/547382bf0cf29afed60f55c7.pdf.José Alem, D., & Morabito, R. (2012). Production planning in furniture settings via robust optimization. Computers & Operations Research, 39(2), 139-150. doi:10.1016/j.cor.2011.02.022Alemany, M. M. E., Lario, F.-C., Ortiz, A., & Gómez, F. (2013). Available-To-Promise modeling for multi-plant manufacturing characterized by lack of homogeneity in the product: An illustration of a ceramic case. Applied Mathematical Modelling, 37(5), 3380-3398. doi:10.1016/j.apm.2012.07.022Alemany, M., Ortiz, A., & Fuertes-Miquel, V. S. (2018). A decision support tool for the order promising process with product homogeneity requirements in hybrid Make-To-Stock and Make-To-Order environments. Application to a ceramic tile company. Computers & Industrial Engineering, 122, 219-234. doi:10.1016/j.cie.2018.05.040Alfalla-Luque, R., Medina-Lopez, C., & Dey, P. K. (2012). Supply chain integration framework using literature review. Production Planning & Control, 24(8-9), 800-817. doi:10.1080/09537287.2012.666870Al-Othman, W. B. E., Lababidi, H. M. S., Alatiqi, I. M., & Al-Shayji, K. (2008). Supply chain optimization of petroleum organization under uncertainty in market demands and prices. European Journal of Operational Research, 189(3), 822-840. doi:10.1016/j.ejor.2006.06.081Al-Shammari, A., & Ba-Shammakh, M. S. (2011). Uncertainty Analysis for Refinery Production Planning. Industrial & Engineering Chemistry Research, 50(11), 7065-7072. doi:10.1021/ie200313rAmaro, A. C. S., & Barbosa-Póvoa, A. P. F. D. (2009). The effect of uncertainty on the optimal closed-loop supply chain planning under different partnerships structure. Computers & Chemical Engineering, 33(12), 2144-2158. doi:10.1016/j.compchemeng.2009.06.003ARAS, N., BOYACI, T., & VERTER, V. (2004). The effect of categorizing returned products in remanufacturing. IIE Transactions, 36(4), 319-331. doi:10.1080/07408170490279561Aydin, R., Kwong, C. K., Geda, M. W., & Okudan Kremer, G. E. (2017). Determining the optimal quantity and quality levels of used product returns for remanufacturing under multi-period and uncertain quality of returns. The International Journal of Advanced Manufacturing Technology, 94(9-12), 4401-4414. doi:10.1007/s00170-017-1141-0Bakhrankova, K., Midthun, K. T., & Uggen, K. T. (2014). Stochastic optimization of operational production planning for fisheries. Fisheries Research, 157, 147-153. doi:10.1016/j.fishres.2014.03.018Banasik, A., Kanellopoulos, A., Claassen, G. D. H., Bloemhof-Ruwaard, J. 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Fuzzy C-means-based scenario bundling for stochastic service network design

Stochastic service network designs with uncertain demand represented by a set of scenarios can be modelled as a large-scale two-stage stochastic mixed-integer program (SMIP). The progressive hedging algorithm (PHA) is a decomposition method for solving the resulting SMIP. The computational performance of the PHA can be greatly enhanced by decomposing according to scenario bundles instead of individual scenarios. At the heart of bundle-based decomposition is the method for grouping the scenarios into bundles. In this paper, we present a fuzzy c-means-based scenario bundling method to address this problem. Rather than full membership of a bundle, which is typically the case in existing scenario bundling strategies such as k-means, a scenario has partial membership in each of the bundles and can be assigned to more than one bundle in our method. Since the multiple bundle membership of a scenario induces overlap between the bundles, we empirically investigate whether and how the amount of overlap controlled by a fuzzy exponent would affect the performance of the PHA. Experimental results for a less-than-truckload transportation network optimization problem show that the number of iterations required by the PHA to achieve convergence reduces dramatically with large fuzzy exponents, whereas the computation time increases significantly. Experimental studies were conducted to find out a good fuzzy exponent to strike a trade-off between the solution quality and the computational time