1,794 research outputs found

    Supply chain management: An opportunity for metaheuristics

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    In today’s highly competitive and global marketplace the pressure on organizations to find new ways to create and deliver value to customers grows ever stronger. In the last two decades, logistics and supply chain has moved to the center stage. There has been a growing recognition that it is through an effective management of the logistics function and the supply chain that the goal of cost reduction and service enhancement can be achieved. The key to success in Supply Chain Management (SCM) require heavy emphasis on integration of activities, cooperation, coordination and information sharing throughout the entire supply chain, from suppliers to customers. To be able to respond to the challenge of integration there is the need of sophisticated decision support systems based on powerful mathematical models and solution techniques, together with the advances in information and communication technologies. The industry and the academia have become increasingly interested in SCM to be able to respond to the problems and issues posed by the changes in the logistics and supply chain. We present a brief discussion on the important issues in SCM. We then argue that metaheuristics can play an important role in solving complex supply chain related problems derived by the importance of designing and managing the entire supply chain as a single entity. We will focus specially on the Iterated Local Search, Tabu Search and Scatter Search as the ones, but not limited to, with great potential to be used on solving the SCM related problems. We will present briefly some successful applications.Supply chain management, metaheuristics, iterated local search, tabu search and scatter search

    On the Complexities of the Design of Water Distribution Networks

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    Water supply is one of the most recognizable and important public services contributing to quality of life. Water distribution networks WDNs are extremely complex assets. A number of complex tasks, such as design, planning, operation, maintenance, and management, are inherently associated with such networks. In this paper, we focus on the design of a WDN, which is a wide and open problem in hydraulic engineering. This problem is a large-scale combinatorial, nonlinear, nonconvex, multiobjective optimization problem, involving various types of decision variables and many complex implicit constraints. To handle this problem, we provide a synergetic association between swarm intelligence and multiagent systems where human interaction is also enabled. This results in a powerful collaborative system for finding solutions to such a complex hydraulic engineering problem. All the ingredients have been integrated into a software tool that has also been shown to efficiently solve problems from other engineering fields.This work has been developed with the support of the project IDAWAS, DPI2009-11591, of the Direccion General de Investigacion of the Ministerio de Educacion y Ciencia, and ACOMP/2010/146 of the Conselleria d'Educacio of the Generalitat Valenciana. The first author is also indebted to the Universitat Politecnica de Valencia for the sabbatical leave granted during the first semester of 2011. The use of English in this paper was revised by John Rawlins.Izquierdo Sebastián, J.; Montalvo Arango, I.; Pérez García, R.; Matías, A. (2012). On the Complexities of the Design of Water Distribution Networks. Mathematical Problems in Engineering. 2012:1-25. https://doi.org/10.1155/2012/9479611252012Goulter, I. C., & Coals, A. V. (1986). Quantitative Approaches to Reliability Assessment in Pipe Networks. 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Pressure-Driven Demand and Leakage Simulation for Water Distribution Networks. Journal of Hydraulic Engineering, 134(5), 626-635. doi:10.1061/(asce)0733-9429(2008)134:5(626)Montalvo, I., Izquierdo, J., Pérez, R., & Tung, M. M. (2008). Particle Swarm Optimization applied to the design of water supply systems. Computers & Mathematics with Applications, 56(3), 769-776. doi:10.1016/j.camwa.2008.02.006Montalvo, I., Izquierdo, J., Pérez, R., & Iglesias, P. L. (2008). A diversity-enriched variant of discrete PSO applied to the design of water distribution networks. Engineering Optimization, 40(7), 655-668. doi:10.1080/03052150802010607Montalvo, I., Izquierdo, J., Pérez-García, R., & Herrera, M. (2010). Improved performance of PSO with self-adaptive parameters for computing the optimal design of Water Supply Systems. Engineering Applications of Artificial Intelligence, 23(5), 727-735. doi:10.1016/j.engappai.2010.01.015Martínez, J. B. (2010). 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Journal of Water Resources Planning and Management, 127(4), 206-213. doi:10.1061/(asce)0733-9496(2001)127:4(206)Kalungi, P., & Tanyimboh, T. T. (2003). Redundancy model for water distribution systems. Reliability Engineering & System Safety, 82(3), 275-286. doi:10.1016/s0951-8320(03)00168-6Morgan, D. R., & Goulter, I. C. (1985). Optimal urban water distribution design. Water Resources Research, 21(5), 642-652. doi:10.1029/wr021i005p00642Walters, G. A., & Knezevic, J. (1989). Discussion of « Reliability‐Based Optimization Model for Water Distribution Systems » by Yu‐Chun Su, Larry W. Mays, Ning Duan, and Kevin E. Lansey (December, 1987, Vol. 113, No. 12). Journal of Hydraulic Engineering, 115(8), 1157-1158. doi:10.1061/(asce)0733-9429(1989)115:8(1157)LOGANATHAN, G. V., SHERALI, H. D., & SHAH, M. P. (1990). A TWO-PHASE NETWORK DESIGN HEURISTIC FOR MINIMUM COST WATER DISTRIBUTION SYSTEMS UNDER A RELIABILITY CONSTRAINT. Engineering Optimization, 15(4), 311-336. doi:10.1080/03052159008941160Bouchart, F., & Goulter, I. (1991). Reliability Improvements in Design of Water Distribution Networks Recognizing Valve Location. Water Resources Research, 27(12), 3029-3040. doi:10.1029/91wr00590Gupta, R., & Bhave, P. R. (1994). Reliability Analysis of Water‐Distribution Systems. Journal of Environmental Engineering, 120(2), 447-461. doi:10.1061/(asce)0733-9372(1994)120:2(447)Xu, C., & Goulter, I. C. (1999). Reliability-Based Optimal Design of Water Distribution Networks. Journal of Water Resources Planning and Management, 125(6), 352-362. doi:10.1061/(asce)0733-9496(1999)125:6(352)Su, Y., Mays, L. W., Duan, N., & Lansey, K. E. (1987). Reliability‐Based Optimization Model for Water Distribution Systems. Journal of Hydraulic Engineering, 113(12), 1539-1556. doi:10.1061/(asce)0733-9429(1987)113:12(1539)Cullinane, M. J., Lansey, K. E., & Mays, L. W. (1992). Optimization‐Availability‐Based Design of Water‐Distribution Networks. Journal of Hydraulic Engineering, 118(3), 420-441. doi:10.1061/(asce)0733-9429(1992)118:3(420)Vamvakeridou-Lyroudia, L. S., Walters, G. A., & Savic, D. A. (2005). Fuzzy Multiobjective Optimization of Water Distribution Networks. Journal of Water Resources Planning and Management, 131(6), 467-476. doi:10.1061/(asce)0733-9496(2005)131:6(467)Montalvo, I., Izquierdo, J., Schwarze, S., & Pérez-García, R. (2010). Multi-objective particle swarm optimization applied to water distribution systems design: An approach with human interaction. Mathematical and Computer Modelling, 52(7-8), 1219-1227. doi:10.1016/j.mcm.2010.02.017Izquierdo, J., Montalvo, I., Pérez, R., & Fuertes, V. S. (2008). Design optimization of wastewater collection networks by PSO. Computers & Mathematics with Applications, 56(3), 777-784. doi:10.1016/j.camwa.2008.02.007Dong, Y., Tang, J., Xu, B., & Wang, D. (2005). An application of swarm optimization to nonlinear programming. Computers & Mathematics with Applications, 49(11-12), 1655-1668. doi:10.1016/j.camwa.2005.02.006Jin, Y.-X., Cheng, H.-Z., Yan, J., & Zhang, L. (2007). New discrete method for particle swarm optimization and its application in transmission network expansion planning. Electric Power Systems Research, 77(3-4), 227-233. doi:10.1016/j.epsr.2006.02.016Arumugam, M. S., & Rao, M. V. C. (2008). On the improved performances of the particle swarm optimization algorithms with adaptive parameters, cross-over operators and root mean square (RMS) variants for computing optimal control of a class of hybrid systems. Applied Soft Computing, 8(1), 324-336. doi:10.1016/j.asoc.2007.01.010Izquierdo, J., Montalvo, I., Pérez, R., & Fuertes, V. S. (2009). Forecasting pedestrian evacuation times by using swarm intelligence. Physica A: Statistical Mechanics and its Applications, 388(7), 1213-1220. doi:10.1016/j.physa.2008.12.008Herrera, M., Izquierdo, J., Montalvo, I., García-Armengol, J., & Roig, J. V. (2009). Identification of surgical practice patterns using evolutionary cluster analysis. Mathematical and Computer Modelling, 50(5-6), 705-712. doi:10.1016/j.mcm.2008.12.026Molina, J., Santana, L. V., Hernández-Díaz, A. G., Coello Coello, C. A., & Caballero, R. (2009). g-dominance: Reference point based dominance for multiobjective metaheuristics. European Journal of Operational Research, 197(2), 685-692. doi:10.1016/j.ejor.2008.07.01510.1029/89WR02879. (2010). Water Resources Research. doi:10.1029/89wr02879Savic, D. A., & Walters, G. A. (1997). Genetic Algorithms for Least-Cost Design of Water Distribution Networks. Journal of Water Resources Planning and Management, 123(2), 67-77. doi:10.1061/(asce)0733-9496(1997)123:2(67)Zecchin, A. C., Simpson, A. R., Maier, H. R., & Nixon, J. B. (2005). Parametric Study for an Ant Algorithm Applied to Water Distribution System Optimization. IEEE Transactions on Evolutionary Computation, 9(2), 175-191. doi:10.1109/tevc.2005.844168Yurong Liu, Zidong Wang, Jinling Liang, & Xiaohui Liu. (2009). Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays. IEEE Transactions on Neural Networks, 20(7), 1102-1116. doi:10.1109/tnn.2009.2016210Jinling Liang, Zidong Wang, & Xiaohui Liu. (2009). State Estimation for Coupled Uncertain Stochastic Networks With Missing Measurements and Time-Varying Delays: The Discrete-Time Case. IEEE Transactions on Neural Networks, 20(5), 781-793. doi:10.1109/tnn.2009.2013240Zidong Wang, Yao Wang, & Yurong Liu. (2010). Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays. 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    A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

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    Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms

    State-of-the-art in aerodynamic shape optimisation methods

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    Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

    Optimisation of the concurrent product and process configuration: an approach to reduce computation time with an experimental evaluation

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    International audienceConcurrent configuration of a product and its associated production process is a challenging problem in customer/supplier relations dealing with customisable or configurable products. It gathers in a single model multiple choices and constraints which come simultaneously from products (choices of components or functionalities), from processes (choices of resources and quantities) and from their mutual interrelations. Considering this problem as a Constraint Satisfaction Problem (CSP), the aim of this article is to improve its optimisation, while considering multiple objectives. Using an existing evolutionary optimisation algorithm as a basis, we propose an approach that reduces the computation time required for optimisation. The idea is first to quickly compute a rough Pareto of solutions, then ask the user to select an area of interest, and finally to launch a second computation on this restricted area. After an introduction to the problem, the approach is explained and the algorithm adaptations are presented. Then various computation experiments results demonstrate that computation times are significantly reduced while keeping the optimality level

    Line Balancing Problem with Multi-Manned Workstations and Resource Constraints: The Case of Electronics Waste Disassembly

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    The increasing public awareness of environmental protection and the scarcity of rare earth elements have made closed-loop supply chains a necessity in many sectors. In particular, recycling components and parts from end-of-life consumer electronics have drawn the attention of both academics and practitioners. Disassembly line balancing improves the resource efficiency of recycling operations. This study proposes a new mathematical formulation and hybrid metaheuristics for solving the Disassembly Line Balancing Problem (DLBP) considering multi-manned workstations and resource constraints. The transformed AND/OR graph is used for prioritizing disassembly tasks in the modeling process. The method is applied for optimizing a real-world case of laptop disassembly to showcase the usefulness of the approach. The performance of the developed metaheuristics is compared to minimize the number of workstations, operators, and machines involved in the disassembly operations. Further, the results are analyzed through sensitivity analysis. This study concludes by providing practical insights and suggestions for the future development of DLBPs

    Numerical and Evolutionary Optimization 2020

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    This book was established after the 8th International Workshop on Numerical and Evolutionary Optimization (NEO), representing a collection of papers on the intersection of the two research areas covered at this workshop: numerical optimization and evolutionary search techniques. While focusing on the design of fast and reliable methods lying across these two paradigms, the resulting techniques are strongly applicable to a broad class of real-world problems, such as pattern recognition, routing, energy, lines of production, prediction, and modeling, among others. This volume is intended to serve as a useful reference for mathematicians, engineers, and computer scientists to explore current issues and solutions emerging from these mathematical and computational methods and their applications

    Multiobjective Coordination Models For Maintenance And Service Parts Inventory Planning And Control

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    In many equipment-intensive organizations in the manufacturing, service and particularly the defense sectors, service parts inventories constitute a significant source of tactical and operational costs and consume a significant portion of capital investment. For instance, the Defense Logistics Agency manages about 4 million consumable service parts and provides about 93% of all consumable service parts used by the military services. These items required about US1.9billionoverthefiscalyears19992002.Duringthesametime,theUSGeneralAccountabilityOfficediscoveredthat,intheUnitedStatesNavy,therewereabout3.7billionshipandsubmarinepartsthatwerenotneeded.TheFederalAviationAdministrationsaysthat26millionaircraftpartsarechangedeachyear.In2002,theholdingcostofservicepartsfortheaviationindustrywasestimatedtobeUS1.9 billion over the fiscal years 1999-2002. During the same time, the US General Accountability Office discovered that, in the United States Navy, there were about 3.7 billion ship and submarine parts that were not needed. The Federal Aviation Administration says that 26 million aircraft parts are changed each year. In 2002, the holding cost of service parts for the aviation industry was estimated to be US50 billion. The US Army Institute of Land Warfare reports that, at the beginning of the 2003 fiscal year, prior to Operation Iraqi Freedom the aviation service parts alone was in excess of US1billion.Thissituationmakesthemanagementoftheseitemsaverycriticaltacticalandstrategicissuethatisworthyoffurtherstudy.Thekeychallengeistomaintainhighequipmentavailabilitywithlowservicecost(e.g.,holding,warehousing,transportation,technicians,overhead,etc.).Forinstance,despitereportingUS1 billion. This situation makes the management of these items a very critical tactical and strategic issue that is worthy of further study. The key challenge is to maintain high equipment availability with low service cost (e.g., holding, warehousing, transportation, technicians, overhead, etc.). For instance, despite reporting US10.5 billion in appropriations spent on purchasing service parts in 2000, the United States Air Force (USAF) continues to report shortages of service parts. The USAF estimates that, if the investment on service parts decreases to about US$5.3 billion, weapons systems availability would range from 73 to 100 percent. Thus, better management of service parts inventories should create opportunities for cost savings caused by the efficient management of these inventories. Unfortunately, service parts belong to a class of inventory that continually makes them difficult to manage. Moreover, it can be said that the general function of service parts inventories is to support maintenance actions; therefore, service parts inventory policies are highly related to the resident maintenance policies. However, the interrelationship between service parts inventory management and maintenance policies is often overlooked, both in practice and in the academic literature, when it comes to optimizing maintenance and service parts inventory policies. Hence, there exists a great divide between maintenance and service parts inventory theory and practice. This research investigation specifically considers the aspect of joint maintenance and service part inventory optimization. We decompose the joint maintenance and service part inventory optimization problem into the supplier s problem and the customer s problem. Long-run expected cost functions for each problem that include the most common maintenance cost parameters and service parts inventory cost parameters are presented. Computational experiments are conducted for a single-supplier two-echelon service parts supply chain configuration varying the number of customers in the network. Lateral transshipments (LTs) of service parts between customers are not allowed. For this configuration, we optimize the cost functions using a traditional, or decoupled, approach, where each supply chain entity optimizes its cost individually, and a joint approach, where the cost objectives of both the supplier and customers are optimized simultaneously. We show that the multiple objective optimization approach outperforms the traditional decoupled optimization approach by generating lower system-wide supply chain network costs. The model formulations are extended by relaxing the assumption of no LTs between customers in the supply chain network. Similar to those for the no LTs configuration, the results for the LTs configuration show that the multiobjective optimization outperforms the decoupled optimization in terms of system-wide cost. Hence, it is economically beneficial to jointly consider all parties within the supply network. Further, we compare the model configurations LTs versus no LTs, and we show that using LTs improves the overall savings of the system. It is observed that the improvement is mostly derived from reduced shortage costs since the equipment downtime is reduced due to the proximity of the supply. The models and results of this research have significant practical implications as they can be used to assist decision-makers to determine when and where to pre-position parts inventories to maximize equipment availability. Furthermore, these models can assist in the preparation of the terms of long-term service agreements and maintenance contracts between original equipment manufacturers and their customers (i.e., equipment owners and/or operators), including determining the equitable allocation of all system-wide cost savings under the agreement

    A contribution to support decision making in energy/water sypply chain optimisation

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    The seeking of process sustainability forces enterprises to change their operations. Additionally, the industrial globalization implies a very dynamic market that, among other issues, promotes the enterprises competition. Therefore, the efficient control and use of their Key Performance Indicators, including profitability, cost reduction, demand satisfaction and environmental impact associated to the development of new products, is a significant challenge. All the above indicators can be efficiently controlled through the Supply Chain Management. Thus, companies work towards the optimization of their individual operations under competitive environments taking advantage of the flexibility provided by the virtually inexistent world market restrictions. This is achieved by the coordination of the resource flows, across all the entities and echelons belonging to the system network. Nevertheless, such coordination is significantly complicated if considering the presence of uncertainty and even more if seeking for a win-win outcome. The purpose of this thesis is extending the current decision making strategies to expedite these tasks in industrial processes. Such a contribution is based on the development of efficient mathematical models that allows coordinating large amount of information synchronizing the production and distribution tasks in terms of economic, environmental and social criteria. This thesis starts presents an overview of the requirements of sustainable production processes, describing and analyzing the current methods and tools used and identifying the most relevant open issues. All the above is always within the framework of Process System Engineering literature. The second part of this thesis is focused in stressing the current Multi-Objective solution strategies. During this part, first explores how the profitability of the Supply Chain can be enhanced by considering simultaneously multiple objectives under demand uncertainties. Particularly, solution frameworks have been proposed in which different multi-criteria decision making strategies have been combined with stochastic approaches. Furthermore, additional performance indicators (including financial and operational ones) have been included in the same solution framework to evaluate its capabilities. This framework was also applied to decentralized supply chains problems in order to explore its capabilities to produce solution that improves the performances of each one of the SC entities simultaneously. Consequently, a new generalized mathematical formulation which integrates many performance indicators in the production process within a supply chain is efficiently solved. Afterwards, the third part of the thesis extends the proposed solution framework to address the uncertainty management. Particularly, the consideration of different types and sources of uncertainty (e.g. external and internal ones) where considered, through the implementation of preventive approaches. This part also explores the use of solution strategies that efficiently selects the number of scenarios that represent the uncertainty conditions. Finally, the importance and effect of each uncertainty source over the process performance is detailed analyzed through the use of surrogate models that promote the sensitivity analysis of those uncertainties. The third part of this thesis is focused on the integration of the above multi-objective and uncertainty approaches for the optimization of a sustainable Supply Chain. Besides the integration of different solution approaches, this part also considers the integration of hierarchical decision levels, by the exploitation of mathematical models that assess the consequences of considering simultaneously design and planning decisions under centralized and decentralized Supply Chains. Finally, the last part of this thesis provides the final conclusions and further work to be developed.La globalización industrial genera un ambiente dinámico en los mercados que, entre otras cosas, promueve la competencia entre corporaciones. Por lo tanto, el uso eficiente de las los indicadores de rendimiento, incluyendo rentabilidad, satisfacción de la demanda y en general el impacto ambiental, representa un area de oportunidad importante. El control de estos indicadores tiene un efecto positivo si se combinan con la gestión de cadena de suministro. Por lo tanto, las compañías buscan definir sus operaciones para permanecer activas dentro de un ambiente competitivo, tomando en cuenta las restricciones en el mercado mundial. Lo anterior puede ser logrado mediante la coordinación de los flujos de recursos a través de todas las entidades y escalones pertenecientes a la red del sistema. Sin embargo, dicha coordinación se complica significativamente si se quiere considerar la presencia de incertidumbre, y aún más, si se busca exclusivamente un ganar-ganar. El propósito de esta tesis es extender el alcance de las estrategias de toma de decisiones con el fin de facilitar estas tareas dentro de procesos industriales. Estas contribuciones se basan en el desarrollo de modelos matemáticos eficientes que permitan coordinar grandes cantidades de información sincronizando las tareas de producción y distribución en términos económicos, ambientales y sociales. Esta tesis inicia presentando una visión global de los requerimientos de un proceso de producción sostenible, describiendo y analizando los métodos y herramientas actuales así como identificando las áreas de oportunidad más relevantes dentro del marco de ingeniería de procesos La segunda parte se enfoca en enfatizar las capacidades de las estrategias de solución multi-objetivo, durante la cual, se explora el mejoramiento de la rentabilidad de la cadena de suministro considerando múltiples objetivos bajo incertidumbres en la demanda. Particularmente, diferentes marcos de solución han sido propuestos en los que varias estrategias de toma de decisión multi-criterio han sido combinadas con aproximaciones estocásticas. Por otra parte, indicadores de rendimiento (incluyendo financiero y operacional) han sido incluidos en el mismo marco de solución para evaluar sus capacidades. Este marco fue aplicado también a problemas de cadenas de suministro descentralizados con el fin de explorar sus capacidades de producir soluciones que mejoran simultáneamente el rendimiento para cada uno de las entidades dentro de la cadena de suministro. Consecuentemente, una nueva formulación que integra varios indicadores de rendimiento en los procesos de producción fue propuesta y validada. La tercera parte de la tesis extiende el marco de solución propuesto para abordar el manejo de incertidumbres. Particularmente, la consideración de diferentes tipos y fuentes de incertidumbre (p.ej. externos e internos) fueron considerados, mediante la implementación de aproximaciones preventivas. Esta parte también explora el uso de estrategias de solución que elige eficientemente el número de escenarios necesario que representan las condiciones inciertas. Finalmente, la importancia y efecto de cada una de las fuentes de incertidumbre sobre el rendimiento del proceso es analizado en detalle mediante el uso de meta modelos que promueven el análisis de sensibilidad de dichas incertidumbres. La tercera parte de esta tesis se enfoca en la integración de las metodologías de multi-objetivo e incertidumbre anteriormente expuestas para la optimización de cadenas de suministro sostenibles. Además de la integración de diferentes métodos. Esta parte también considera la integración de diferentes niveles jerárquicos de decisión, mediante el aprovechamiento de modelos matemáticos que evalúan lasconsecuencias de considerar simultáneamente las decisiones de diseño y planeación de una cadena de suministro centralizada y descentralizada. La parte final de la tesis detalla las conclusiones y el trabajo a futuro necesario sobre esta línea de investigaciónPostprint (published version
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