With supply chains becoming increasingly extended, the uncertainties in the upstream production process can greatly affect the material flows that aim toward meeting the uncertain demands at the downstream. We analyze a two-location system in which the upstream production facility experiences random capacities and the downstream store faces random demands. Different from the widely used approach that seeks the decomposition of the profit function based on the echelon inventories, our approach builds on the notions of stochastic functions, in particular, the stochastic linearity in midpoint and the directionally concave order. With these notions, we establish the concavity and submodularity of the profit functions in the transformed decision variables. In general, it is optimal to follow a two-level state-dependent threshold policy such that an order is issued at a location if and only if the inventory position of that location is below the corresponding threshold. In the special case where the salvage values are linear in the ending inventories, the profit function becomes separable in the inventory positions, and the optimal policy reduces to the echelon base-stock policy. The effect of the uncertain capacity and demand depends critically on whether the production capacity is limited or ample in relation to the demand. Only when the capacity and the demand do not differ much, the upstream facility carries positive inventory; otherwise, all units produced are shipped immediately toward the downstream. We further extend our analysis to systems with general stochastic production functions and with multiple locations.

Traditionally supply chain management has meant factories, assembly lines, warehouses, transportation vehicles, and time sheets. Modern supply chain management is a highly complex, multidimensional problem set with virtually endless number of variables for optimization. An Internet enabled supply chain may have just-in-time delivery, precise inventory visibility, and up-to-the-minute distribution-tracking capabilities. Technology advances have enabled supply chains to become strategic weapons that can help avoid disasters, lower costs, and make money. From internal enterprise processes to external business transactions with suppliers, transporters, channels and end-users marks the wide range of challenges researchers have to handle. The aim of this book is at revealing and illustrating this diversity in terms of scientific and theoretical fundamentals, prevailing concepts as well as current practical applications.

​The subject of this book is supply chain logistics planning optimization under multiple uncertainties, the key issue in supply chain management. Focusing on the strategic-alliance three-level supply chain, the model of supply chain logistics planning was established in terms of the market prices and the market requirements as random variables of manufactured goods with random expected value programming theory, and the hybrid intelligence algorithm solution model was designed. Aiming at the decentralized control supply chain, in which the nodes were unlimited expansion, the chance-constrained stochastic programming model was created in order to obtain optimal decision-making at a certain confidence level. In addition, the hybrid intelligence algorithm model was designed to solve the problem of supply chain logistics planning with the prices of the raw-materials supply market of the upstream enterprises and the prices of market demand for products of the downstream enterprises as random variables in the supply chain unit. Aimed at the three-stage mixed control supply chain, a logistics planning model was designed using fuzzy random programming theory with customer demand as fuzzy random variables and a hybrid intelligence algorithm solution was created. The research has significance both in theory and practice. Its theoretical significance is that the research can complement and perfect existing supply chain planning in terms of quantification. Its practical significance is that the results will guide companies in supply chain logistics planning in the uncertain environment.

Quantitative models and computer-based tools are essential for making decisions in today's business environment. These tools are of particular importance in the rapidly growing area of supply chain management. This volume is a unified effort to provide a systematic summary of the large variety of new issues being considered, the new set of models being developed, the new techniques for analysis, and the computational methods that have become available recently. The volume's objective is to provide a self-contained, sophisticated research summary - a snapshot at this point of time - in the area of Quantitative Models for Supply Chain Management. While there are some multi-disciplinary aspects of supply chain management not covered here, the Editors and their contributors have captured many important developments in this rapidly expanding field. The 26 chapters can be divided into six categories. Basic Concepts and Technical Material (Chapters 1-6). The chapters in this category focus on introducing basic concepts, providing mathematical background and validating algorithmic tools to solve operational problems in supply chains. Supply Contracts (Chapters 7-10). In this category, the primary focus is on design and evaluation of supply contracts between independent agents in the supply chain. Value of Information (Chapters 11-13). The chapters in this category explicitly model the effect of information on decision-making and on supply chain performance. Managing Product Variety (Chapters 16-19). The chapters in this category analyze the effects of product variety and the different strategies to manage it. International Operations (Chapters 20-22). The three chapters in this category provide an overview of research in the emerging area of International Operations. Conceptual Issues and New Challenges (Chapters 23-27). These chapters outline a variety of frameworks that can be explored and used in future research efforts. This volume can serve as a graduate text, as a reference for researchers and as a guide for further development of this field.

Biomass to Biofuel Supply Chain Design and Planning under Uncertainty: Concepts and Quantitative Methods explores the design and optimization of biomass-to-biofuel supply chains for commercial-scale implementation of biofuel projects by considering the problems and challenges encountered in real supply chains. By offering a fresh approach and discussing a wide range of quantitative methods, the book enables researchers and practitioners to develop hybrid methods that integrate the advantages and features of two or more methods in one decision-making framework for the efficient optimization of biofuel supply chains, especially for complex supply chain models. Combining supply chain management and modeling techniques in a single volume, the book is beneficial for graduate students who no longer need to consult subject-specific books alongside mathematical modeling textbooks. The book consists of two main parts. The first part describes the key components of biofuel supply chains, including biomass production, harvesting, collection, storage, preprocessing, conversion, transportation, and distribution. It also provides a comprehensive review of the concepts, problems, and opportunities associated with biofuel supply chains, such as types and properties of the feedstocks and fuel products, decision-making levels, sustainability concepts, uncertainty analysis and risk management, as well as integration of biomass supply chain with other supply chains. The second part focuses on modeling and optimization of biomass-to-biofuel supply chains under uncertainty, using different quantitative methods to determine optimal design. Proposes a general multi-level framework for the optimal design and operation of biomass-to-biofuel supply chains through quantitative analysis and modeling, including different biomass and waste biomass feedstock, production pathways, technology options, transportation modes, and final products Explores how modeling and optimization tools can be utilized to address sustainability issues in biofuel supply chains by simultaneously assessing and identifying sustainable solutions Presents several case studies with different regional constraints to evaluate the practical applicability of different optimization methods and compares their performance in real-world situations Includes General Algebraic Modeling System (GAMS) codes for solving biomass supply chain optimization problems discussed in different chapters

This book presents the latest developments in optimization and optimal control models; exact, approximate and hybrid methods; and their applications in lean and green supply chains. It examines supply chain network design and modeling, closed loop supply chains, and lean, green, resilient and agile or responsive networks, and also discusses corporate social responsibility and occupational health and safety. It particularly focuses on supply chain management under uncertainty – employing stochastic or nonlinear modeling, simulation based studies and optimization – multi-criteria decision-making and applications of fuzzy set theory, and covers various aspects of supply chain management such as risk management, supplier selection or the design of automated warehouses. Lastly, using experimental applications and practical case studies, it shows the impact of lean and green applications on vehicle/fleet management and operations management.