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• The model allocates safety stocks in supply chains at minimum cost. • An MIQCP reformulation with piecewise approximation greatly improves computational efficiency. • The piecewise function yields an improved estimation for the fill rates. • The GSM is extended to handle non-normally distributed demands. • Real-world case studies solved to optimality within few seconds of computational time. This paper presents a Multi-Echelon Inventory Optimization (MEIO) framework, based on the Guaranteed-Service Model (GSM), to allocate safety stocks across a supply chain with several locations and products, minimizing costs while meeting service level objectives. Extending previous work by Achkar et al. (2023), this paper enhances the Mixed-Integer Quadratically Constrained Program (MIQCP) with a highly efficient solution approach. The model introduces a piecewise linear approximation, significantly improving computational efficiency and the accuracy of the approximation for the fill rate function. It also introduces a different and more efficient approach to account for stochastic lead times using a discrete function. Moreover, an extension of the approach to account for non-normally distributed demands is proposed. The model is applied to several instances of a real-world case study from a pharmaceutical company, with more than 7300 product-location combinations, showing that optimal solutions can be obtained within few seconds of computational time. [ABSTRACT FROM AUTHOR]

Due to increasing air pollution, which is a consequence of the environmental effects of production in various industries, green supply chain management (GSCM) has attracted the attention of both scholars and practitioners. Green supplier selection is an important problem in GSCM and seeks to satisfy a firm's environmental goals as well as its economic targets. In this paper, for the first time, a green supplier selection problem considering both green and non-green evaluation criteria in a closed-loop supply chain is studied, and a cap-and-trade mechanism as a way of controlling the air pollution caused by manufacturers is proposed. To solve this particular problem, we propose a multi-objective robust optimization (RO) model. This specific model is an effective approach to handle uncertainty. A numerical example using randomly generated data, accompanied by subsequent discussion of the proposed approach, is deployed to validate the model. The results prove that the developed model for green supplier selection is able to effectively enhance the decision-making process of the experts. By illustrating the trade-off in robustness between the model and proposed solutions, as well as the effect of the deviation penalty on the closeness of results to the achieved solution, we show how firms can make optimal decisions when assigning the parameters. Furthermore, analyses show that decreasing the allowance amount (cap) and increasing the allowance prices in the cap-and-trade system escalate the firms' costs, but lower the amount of carbon released. Finally, we show that the cap-and-trade mechanism results in a better solution in terms of the total utility of the supply chain compared to the penalty-based system for a specific range of carbon allowance. • This paper generalizes the green supplier selection and order allocation problem. • A mathematical model for the problem is developed. • A robust optimization approach to handle the model uncertainty is developed. • The impact of changes in model parameters on the objective functions is analyzed. • The cap-and-trade mechanism is compared with a penalty-based mechanism. [ABSTRACT FROM AUTHOR]

Microalgae is one of the most promising feedstocks for biofuel production because it yields the high content of sugar and oil. In order to help to develop this nascent industry, this paper proposes a mixed integer linear programming (MILP) model for planning and designing a microalgae-based biobutanol supply chain network. The goal of this study is minimizing the fixed cost of constructing required facilities, transportation costs, and operational costs (harvesting, pretreatment, treatment, and energy conversion). This paper considers supply, production, distribution, and addresses a multi-period model. Since the volume of harvested and dried algae cannot be determined accurately, a fuzzy programming approach is employed to address uncertainties. Additionally, a data envelopment analysis (DEA) method is used to reduce the complexity of solving the proposed model. The applicability of the model is evaluated through a real case study of Iran. • An MILP model is proposed for planning and designing a microalgae-based biobutanol supply chain network. • The model minimizes fixed costs of constructing required facilities, transportation costs, and operational costs. • A fuzzy programming approach is employed to address with uncertainties. • A DEA method is used to reduce the complexity of solving the proposed model. [ABSTRACT FROM AUTHOR]

• We develop a mathematical programming model for scheduling turnaround maintenance activities for a network of plants in a supply chain. • We propose a heuristic algorithm for solving the model when the network has large number of plants. • A case study petrochemical supply chain is used to demonstrate the utilization of the model and the effectiveness of the heuristic. Turnaround (TAM) is a periodic maintenance in which plants are shutdown to conduct inspections, repairs, preventive maintenance and overhauls. The shutdown periods range from three to four weeks and prolonging this period is expensive and therefore requires effective planning. The primary purpose of this paper is to develop a mathematical programming model to coordinate and plan TAM for several plants in an integrated supply chain network. A secondary objective is to develop a heuristic algorithm for solving the model when the network has large number of plants. The model and the algorithm are developed, tested and applied on a case study petrochemical supply chain. The exact algorithm takes 8.3 times the time of the heuristic. In addition the heuristic algorithm provides near optimal solution in much shorter time. The developed model provides a tool to plan TAM for several plants in an integrated supply in an optimal fashion. [ABSTRACT FROM AUTHOR]

This paper proposes a production and differential pricing decision model in a two-echelon supply chain that involves a demand from two or more market segments. In this framework, the retailer is allowed to set different prices during the planning horizon. While integrated production-marketing management has been a key research issue in supply chain management for a long time, little attention has been given to set prices and marketing expenditures in integrated multi-site (parallel) manufacturing systems and multiple demand classes. Generally, the presence of multiple demand classes induced by different market segments may impose demand leakage and then change production plan and ordering policies throughout the supply chain system. To tackle this problem, this paper develops a novel approach in order to provide an optimal aggregate production and marketing plan by interconnecting the sales channels of the retailer and demand. A non-linear model is established to determine optimal price differentiation, marketing expenditures and production plans of manufacturing sites in a multi-period, multi-product and multi-sale channels production planning problem by maximizing total profit of the supply chain. To handle the model and obtain solutions, we propose an efficient analytical model based upon convex hulls. Finally, we apply the proposed procedure to a clothing company in order to show usefulness and significance of the model and solution method. [ABSTRACT FROM AUTHOR]

[Display omitted] • This paper considers quality integration in a coordinated model of project scheduling and material transportation. • This model coordinates quality concepts in internal processes, customer-related processes, and supplier-related processes. • In this study, we assume that both renewable and non-renewable resources influence the quality of project activities. • In our model, material transportation is modeled using MDOVRP to meet the needs of project-oriented organizations. This study aims to investigate how quality integration affects a joint model of multi-project scheduling and material transportation. Therefore, the research problem not only considers the quality of project activities, but also focuses on quality in processes related to suppliers and customers. Accordingly, this study considers the quality of materials as a factor when determining the suppliers in a project-based organization. Furthermore, unlike the existing studies, it also assumes that the rework-time of projects depends on the quality of materials. The research problem is addressed using a mixed integer linear programming model, which minimizes the total normalized cost (TNC) as a measure of the balance between supply chain costs. Contrary to previous models, this model examines the simultaneous impacts of renewable and nonrenewable resources on project quality. Also, the material transportation is modeled based on the "multi-depot open vehicle routing problem" to increase the model's applicability in real conditions. In order to solve the research problem, a tabu search algorithm is applied, which is verified based on instances of different sizes. Then, the proposed model is compared with one of the similar models in the literature to determine its efficiency. Additionally, a real-world case study is utilized to show the model application. The results show that the quality concept in the suggested model leads to more appropriate materials and shorter routes for transportation. Therefore, quality integration in this model reduces the total normalized cost by improving projects' delays and transportation costs. [ABSTRACT FROM AUTHOR]

In response to global warming, it is urgent to control and reduce greenhouse gas (GHG) emissions, especially from the supply chain perspective. The most often discussed topic in this domain indicates that emission trading scheme (ETS) could be employed as one of policy instruments for supply chain emissions management. Via mathematical models, scholars have shown that the employment of emission trading is affecting supply chain performances (both environmental and economic) in different levels. However, previous literature focus on the cost-effectiveness analysis only from the mathematical aspect. To provide policy-makers and companies with the theoretical bases on this hot topic, it is significant to discuss how ETS, one of market-based instruments, could be imposed in the context of supply chain from the mechanical point of view. By incorporating ideas from relevant literature, this paper generates two concepts/modes in imposing ETS on supply chain: jointly imposed supply chain emission trading (e.g., jointly imposed SC-ETS) and separately imposed supply chain emission trading (e.g., separately imposed SC-ETS). It illustrates the working principles of both concepts/modes and conducts a sandbox example to analyze the cost-effectiveness of them. Furthermore, this paper discusses the challenges and opportunities of implementing two modes from practical aspects. Results of quantitative analysis and discussion show that for the sake of both policy-makers and supply chain companies, the separately imposed SC-ETS allowing selling permits would be so far the better mode to manage supply chain GHG emissions compared to the jointly imposed SC-ETS. [ABSTRACT FROM AUTHOR]

In this paper, an improved mathematical model is proposed to solve the multi-echelon biomass supply chain synthesis problem, including processing hubs selection, biomass allocation design and transportation mode selection, with the consideration of vehicle capacity constraint (weight and volume). On top of that, carbon emission penalty is introduced in the model in order to evaluate the environmental impact in the supply chain. The entire problem is modelled through mixed integer non-linear programming with the aim of maximising the overall profit, at the same time ensuring the minimal CO 2 emission. A comparative study between the model developed in the previous work (vehicle capacity constraint and environmental performance are not considered) and the current improved model is carried out to compare the reliability of the outcomes. Both models are illustrated by using a same case study in Johor, Malaysia. In order to fill the gap of lacking user-friendly decision-making tool for the transportation design in supply chain management, a novel graphical decision-making tool, called smart vehicle selection diagram is proposed in this paper. The diagrams are constructed based on the optimised results obtained from the formulated model. The user manual for the proposed decision-making tool is given in this paper. Besides, five sets of sensitivity analysis are conducted to identify the sensitivity of the assumed realistic factors (i.e. terrain profile, weather changes, traffic congestion, fuel price fluctuation and individual environmental preference) to the optimal results obtained from the proposed tools. This paper shows the potential of the proposed tools in providing rigid optimal solution for the proposed research problem. Finally, several potential future works is suggested in this paper to fill up some of the remaining research gaps. [ABSTRACT FROM AUTHOR]

Shelf-life (SL) prediction and Least Shelf-life First Out (LSFO) stock strategy are important factors in perishable food supply chain in order to reduce quality and economic losses. In particular, distribution represents one of the main critical phases in logistic chain management and only the introduction of monitoring procedure can allow a reduction in food losses. Literature shows several mathematical models for analysing the changes in food quality using environmental/product parameters. However, these models can be very useful decision support tools only if the abovementioned parameters can be processed in real time. This paper focuses on technologies and applications to acquire and monitor changes in product shelf life using different SL predictive models. The paper includes a case study on a simulated transportation of strawberries, using a prototype of Smart Logistic Unit equipped with a GPS module for real time positioning of the truck, a 3G connection as communication system for remote quality supervision, and a shelf life prediction algorithm based on four different models and implemented on a webGIS platform. [ABSTRACT FROM AUTHOR]

Highlights • We model a new quantity discounts supply chain planning problem. • The model is very hard to solve using leading commercial solvers. • We develop MIP-based local search algorithms for our problem. • We apply our model to a realistic food supply chain. • We show the efficiency of our algorithms in getting high quality solutions quickly. Abstract Supplier selection with quantity discounts has been an active research problem in the literature. In this paper, we focus on a new real-world quantity discounts scheme, where suppliers are selected in the beginning of a strategic planning period (e.g., 5 years). Monthly orders are placed from the selected suppliers, but the quantity discounts are based on the aggregated annual order quantities. We incorporate this type of cost structure in a multi-period, multi-product, multi-echelon supply chain planning problem, and develop a mixed integer linear programming (MIP) model for it. Our model is highly intractable; leading commercial solvers cannot construct high quality feasible solutions for realistic instances even after multiple hours of solution time. We develop an algorithm that constructs an initial feasible solution and a large neighborhood search method that combines two customized iterative algorithms based on MIP-based local search and improves such solution. We report numerical results for a food supply chain application and show the efficiency of using our methodology in getting very high quality primal solutions quickly. [ABSTRACT FROM AUTHOR]

Abstract Given the high variability of both quantity and condition of the returns, closed-loop supply chains depend on a mix of remanufactured and new components. Effectively managing the combined flow of returned and new components is imperative to minimize total system costs. This paper proposes a model that helps manage the flow of returns by determining the incentives to offer returners, while simultaneously determining a capacity contract with the supplier of new components. The model considers returns from multiple sources, where each source has different characteristics in terms of the quantity and condition of its returns. The model also accounts for uncertainties from the return sources, as well as the new components supplier. Such uncertainties result in a failure to meet the demand for components, incurring loss costs. Sensitivity analyses of a numerical example were conducted to illustrate the model and gain further insights. The results demonstrate noteworthy relationships between supplier-related costs and those associated with not meeting the required demand, as well as their influence on the incentives to offer and the supplier's capacity contract. Highlights • Components can be sourced new or remanufactured from multiple return sources. • Model determines the capacity to contract from the new component supplier. • Model determines the optimal incentive for each return source. • Costs include losses due to a lack of remanufactured components. • Major interactions exist among incentives, contract capacity and loss costs. [ABSTRACT FROM AUTHOR]

Biofuel production from agricultural waste has been identified as a promising strategy in the field of renewable energy. This topic involves complex mathematical modeling tasks such as feedstock characteristics, biorefinery location, capacity strategy and material flows. This paper proposes a Multiple Objective Mixed Integer Linear Programming model (MOMILP) for the design of a sustainable supply chain using multiple agricultural residues. The proposed comprehensive model is utilized in a case study in Colombia, using coffee crop residues. Computational results show the model’s robustness as a decision-making tool, which allows the projection of a flexible supply chain structure in the long term. [ABSTRACT FROM AUTHOR]

In today's business world, oil companies cannot be productive and competitive, and thus, will not survive without taking the supply chain management concepts into account. Consequently, the management of a crude oil supply chain (COSC) is increasingly receiving substantial importance. The growing number of papers and books on this topic is a further witness of this fact. To foster insight into issues intertwined with COSC problems, this paper is devoted to an extensive review of mathematical programming models in this context. The classification approach for this review is based on a taxonomy framework. In this framework, ongoing and emerging challenges surrounding the strategic and tactical decisions of COSC problems are investigated. As a main goal, the gaps of literature are analyzed to recommend possible research directions. [ABSTRACT FROM AUTHOR]

The paper considers a three-echelon supply chain which consists of one supplier, one manufacturer and one retailer for trading a single product. The market demand at the retailer is influenced by the retail price and the quality of the product. The quality of the finished product at the manufacturer depends on the supplier’s raw material quality. We analyze the model for both deterministic and stochastic demand patterns. We first study the centralized and decentralized systems, and then the decentralized system with a sub-supply chain coordination strategy (where the manufacturer chooses to merge with either the supplier or the retailer and then acts as a single entity) and the two-level retail fixed mark-up (RFM) strategy. In the case of the two-level RFM strategy, the manufacturer and the retailer use fixed mark ups over the supplier’s wholesale price. The proposed models are demonstrated through numerical examples. It is observed from the numerical study that the two-level RFM strategy is superior to the sub-supply chain coordination strategy. Further, the two-level RFM strategy in the stochastic demand scenario is not as effective as in the deterministic demand scenario. [ABSTRACT FROM AUTHOR]

In this paper, we develop a decisional framework and a mathematical model for the sustainable design of biodiesel supply chain networks (BSCND). We consider a broad group of sustainable aims, i.e. standard economic goals (revenue and logistics costs of BSCND), environmental issues based on a biodiesel production life cycle assessment (LCA), and the social incidental aspects (e.g. crime control, political stability, and community attitude, among others). The framework begins with a simulation of the biodiesel production system, feeding later, with suitable input parameters and suitable solutions, and a macro-location model designed to establish the regional positioning of biofuel conversion plants. Optimal regions are used as initial feasible solution space for the proposed micro-location model. In this part of the framework, we introduce an adaptation of Extended Goal Programming to rank the best municipalities (definitive locations) emphasizing the social aspects under consideration. The framework application is set up in the following Colombian context: first generation biodiesel production from palm oil feedstock. Our computational results indicate that the Colombian city of Rionegro (in the Santader region) is the most sustainable location for a new biodiesel plant. [ABSTRACT FROM AUTHOR]

This paper shows a multi-objectives mixed-integer non-linear programming (MINLP) model for a petrochemical supply chain under uncertainty environments, namely disruption risks and less knowledge of parameters. In this model, two efficient queuing systems are applied in nylon plastic manufacturing and recycling centers, in which a Jackson network is also used. The aims are to minimize the average tardiness to deliver products, total cost and transportation cost. In addition the developed model specifies the optimal locations for a new distribution center (DC), collection center and disposal center as well as the optimal allocation of customer zones to each DC. This model is solved in three stages: (1) a Jackson network determines the queuing parameters, (2) an Lp -metric approach makes the multi-objectives into a single objective, and (3) an efficient Lagrangian relaxation based on a sub-gradient approach solves the presented model. Additionally, a real case study is shown in details to depict the application of the presented model. At the end, the sensitivity analyses are carried out to check the optimal objectives by changing the important parameters. [ABSTRACT FROM AUTHOR]

Environmental Sustainability is one of the ‘Grand Challenges’ for manufacturing success in the 21st century. The present article mainly focuses on energy use during the manufacturing steps used for assembling products. In particular, industry still needs systematic and reliable ways to capture information for ultimately accounting for energy efficiency in manufacturing processes. For that purpose, an information model in the form of a formal ontology was created using information elements as building blocks, which emerge from manufacturing process models, supply chain operations, manufacturing process parameters, 3D form features and exergy-based thermodynamic analysis. These information elements were integrated by means of semantic relationships in an ontology. Once this information model was constructed, an application example of a welded hull panel assembly was used for verification of the model's representativeness and completeness. Results show that it is feasible to correlate all required data by means of semantic relationships for estimating energy efficiency indicators prior to physical prototyping, or ultimately comparing different alternatives for manufacturing processes regarding energy efficiency. However, manufacturing processes must be described in detail in order to allow energy efficiency analyses. In addition, geometric models need to be able to represent form features that can best relate to specific manufacturing process parameters. And finally, energy efficiency indicators, such as the degree-of-perfection can be derived from a comprehensive thermodynamic analysis, to be performed in each individual process step. Results indicate it is possible to provide an information structure for the calculation of the degree-of- perfection associated with an exergy-based thermodynamic analysis in assembly processes. Therefore, it has the potential to serve as a basis for a unifying framework for developing software applications that could allow the calculation of the degree of perfection in manufacturing operations. In addition, the resulting information model may facilitate data integration in the extended enterprise environment as well as the development of standards that can lead to seamless interoperability of manufacturing information systems. This paper presents the means by which energy efficiency can be accessed directly from an integrated semantic model, and opens the possibility to be extended for many different sorts of manufacturing processes. [ABSTRACT FROM AUTHOR]

Forward and reverse supply chains form a closed-loop supply chain. In this paper, a mathematical model is proposed for a closed-loop supply chain network by considering global factors, including exchange rates and customs duties. The model is a multi-objective mixed-integer linear programming model under uncertain demand. A solution approach based on fuzzy programming is developed for solving the optimization problem. The model is then applied in a network, which is located in Southwestern Ontario, Canada. A sensitivity analysis is provided to validate the model. This model considers global factors, multiobjectives, and uncertainty simultaneously in a closed-loop supply chain network. [ABSTRACT FROM AUTHOR]

This paper proposes a novel hybrid BSC-DEA framework for performance evaluation in sustainable supply chains. The proposed DEA model is capable of dealing with both qualitative and quantitative indicators while accounting for desirable and undesirable indicators. A tailored network DEA model involving a set of comprehensive sustainability indicators is applied to rank different supply chains from sustainability viewpoint to find the efficient and benchmarked units at each echelon. Then, sustainability indicators are classified into four groups according to BSC perspectives to help policy makers and top managers to have a more comprehensive and thorough understanding of the sustainability with respect to the long- and short term strategies. Finally, a number of sensitivity analyses are performed to identify the effective factors and strengths and weaknesses of each supply chain are identified based on BSC perspectives. To demonstrate the capabilities of the proposed approach, this framework is implemented for performance evaluation of plastic recycling companies in Mazandaran and Golestan provinces of Iran and some helpful managerial insights are derived from the numerical results. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model for the design of a non-cooperative supply chain where transportation activities are provided by logistics companies. We consider a four-layer network comprised of manufacturers, retailers, customers, and logistics service providers (LSPs). In this problem, manufacturers, retailers, and LSPs do not collaborate or engage in any type of bargaining strategy among one other. Instead, they compete to supply products to customers at demand markets, while each agent seeks to maximize his own profit. LSPs compete among themselves to provide logistics (transportation/warehousing) services to manufacturers. It is considered that manufacturers, LSPs, and retailers collaborate to maximize services. Normally this problem cannot be modeled as an optimization problem, so we use a variational inequality approach to formulate it. To the best of our knowledge, this important problem, which helps evaluate options and make decisions when logistics activities are provided by LSPs, has not been modeled in the literature and this constitutes our main contribution. The model determines the optimal level of production for each manufacturer, the flow of products between manufacturers and retailers, the flow of products to be handled by each logistics service provider and the flow of products between retailers and demand markets in a non-cooperative environment. Numerous experiments are presented and adapted from test examples that are available in the literature, while results and important findings are discussed. [ABSTRACT FROM AUTHOR]

The responsible management of product return flows in production and inventory environments is a rapidly increasing requirement for companies. This can be attributed to economic, environmental and/or regulatory motivations. Mathematical modeling of such systems has assisted decision-making processes and provided a better understanding of the behavior of such production and inventory environments. Therefore, this paper reviews the literature on the modeling of reverse logistics inventory systems that are based on the economic order/production quantity (EOQ/EPQ) and the joint economic lot size (JELS) settings, so as to systematically analyze the mathematics involved in capturing the main characteristics of related processes. The literature is surveyed and classified according to the specific issues faced and modeling assumptions. Special attention is given to environmental issues. In addition, there are indications of the need for the mathematics of reverse logistics models to follow current trends in ‘greening’ inventory and supply-chain models. Finally, the modeling of waste disposal, greenhouse-gas emissions and energy consumption during production is considered as the most pressing priority for the future of reverse logistics models. An illustrative example for modeling reverse logistics inventory models with environmental implications is presented. [ABSTRACT FROM AUTHOR]

Electricity generated from forest-based biomass is an attractive source of renewable energy. However, the cost of generating heat and/or electricity from it is relatively high due to the low energy density of wood, high moisture content and variations in its quality and availability. Models have been developed to optimize the supply chain and reduce the cost per kilowatt hour generated. This paper focuses on incorporating uncertainty in the supply chain of such a model. The model considers the tactical supply chain planning of a power plant over a one-year time horizon with monthly time steps. Uncertain parameters which impact the net profit of the power plant include ‘biomass quality,’ namely moisture content and higher heating value, and ‘monthly available biomass’ from different suppliers. Robust optimization is used to model uncertainty in the quality of biomass. Then a hybrid, multi-stage, ‘stochastic programming-robust optimization’ model is presented in order to simultaneously include uncertainty in biomass quality and biomass availability. It is demonstrated that the hybrid model takes advantage of both modelling approaches to balance the profit estimates and the tractability to various circumstances. The model provides solution considering all instances of the uncertain parameters within the defined sets and scenario tree. The results revealed a major trade-off between profit and range of biomass quality. Profit decreased by up to 23% when there was ±13% variation in moisture content and ±5% change in higher heating value. The model achieved a biomass purchase cost that was lower than the current commercial costs at the power plant. Implementing the model could prevent production curtailment and undesirable fluctuation in storage levels which occurred in the past due to variations in biomass availability and quality. [ABSTRACT FROM AUTHOR]

Robust optimization has attracted great attention in recent decade owing to its ability to cope with risk and uncertainty in real-life optimization problems. Recently, the scope of robust optimization is extended into fuzzy mathematical programming by proposing robust possibilistic programming approach. As a complementary for robust possibilistic programming approach, this paper proposes different novel robust flexible programming and robust mixed possibilistic-flexible programming models. The advantages and strengths of the proposed models are described and a real-life problem is employed to show the efficiency and practicability of the propounded models against the traditional fuzzy programming approach. [ABSTRACT FROM AUTHOR]

Models for evaluating supply chain delivery performance commonly assume a Gaussian delivery time distribution when the true underlying delivery time probability density function (PDF) cannot be analytically determined. Recent research has identified limitations to using the Gaussian PDF and has demonstrated the advantages of using the asymmetric Laplace PDF to model a supply chain delivery time distribution. Current models which use the asymmetric Laplace to model a supply chain delivery time distribution are limited in their scope of application for modeling continuous improvement of delivery performance. In this paper we present a more robust asymmetrical Laplace delivery performance model which overcomes limitations found in the current set of models. A set of propositions for modeling delivery improvement in terms of both the mean and variance of the delivery time distribution are presented. The results of a set of 48 numerical examples conducted across a range of key input parameters are used to illustrate the delivery improvement capabilities of the model. [ABSTRACT FROM AUTHOR]

The application of sustainability principles into supply chains is an evolving research area currently suffering from a scarcity of established theories, models, and frameworks. There are at least two key reasons why it is difficult to build sustainability into the supply chain. First, there are numerous context dependent factors that either enable or hinder progress towards sustainability in a supply chain. There is a need to better understand how these factors affect the sustainability performance of supply chains. Second, implementing sustainability requires a triple bottom line approach, where improvements are pursued in the environmental, economic, and social dimensions of performance. These two challenges mean that implementing sustainability in a supply chain is a complex process that involves a large number of interacting factors. This paper contributes to efforts to overcome these challenges by proposing a mathematical model for assessing sustainability in the supply chain. The model is based on the notion that a probabilistic representation of sustainability can realistically account for its challenges. The development of the proposed model was guided by the need for ease of use, simplicity, and the ability to quickly provide feedback on the sustainability status of supply chains over time. [ABSTRACT FROM AUTHOR]

• A multi scenario and multi objective optimization strategy is presented. • The effect of biogas demand and biomass availability in a supply chain are studied. • Uncertainty in the model is considered. • Economic and environmental balance for the solutions are obtained. This paper explores the impact of biomass availability and biogas demand on the economic and environmental performance of a biogas supply chain. A mixed-integer nonlinear programming model is proposed in a multi-objective form, then the problem is reformulated as a single objective problem with a multi-scenario strategy solution and a CVaR approach. The uncertainty associated with biomass availability and biogas demand is obtained from historical data of the central-western region of Mexico. Two case studies are presented to show the applicability of the proposed mathematical model to minimize the criteria gap in economic and environmental functions and to obtain cumulative probability graphs. The results showed that it is possible to minimize the gap between the objective functions, aiding the decision-making process. The average annual profit is at least 1,740,600 € with annual emissions of 292,440 tons of CO 2. Image, graphical abstract [ABSTRACT FROM AUTHOR]

With the growing level of public environmental consciousness, sustainability has become an important issue in the area of supply chain management. This paper focuses on a channel coordination problem in a two-echelon sustainable supply chain involving one socially responsible manufacturer and one fair-minded retailer. Constructing mathematical models to characterize the problem, four particular contracts are developed to investigate the environmental performance and channel profit under the framework of two non-cooperative contracts: wholesale price and two-part tariff, and two cooperative contracts: Nash bargaining and Rubinstein bargaining. Theoretical analysis verified by numerical experiments shows that the wholesale price contract performs worse than the other three in terms of the carbon emission per unit product and channel profit. In addition, the two-part tariff contract can partially coordinate the supply chain, whereas both bargaining contracts can achieve perfect coordination to provide outcomes of the centralized decision. Comparing with the fair-neutral scenarios, we find that the fairness behavior promotes the retailer's profit, but reduces the manufacturer's profit under different contracts. Sensitivity analysis reveals that with intensified fairness concerns, the sustainability level and channel profit diminish under non-cooperative contracts, but remain the same under cooperative contracts. The Nash bargaining and Rubinstein bargaining contracts are robust to the degree of the retailer's fairness behavior and could be the best choice for the socially responsible manufacturer. • A channel coordination issue in a two-echelon sustainable supply chain is studied. • Four contracts are developed to examine the impact of retailer's fairness behavior. • Fairness behavior worsens wholesale price contract compared to two-part tariff one. • Nash and Rubinstein bargaining contracts are robust to levels of fairness concerns. • Both bargaining contracts achieve perfect coordination in reducing carbon emission. [ABSTRACT FROM AUTHOR]

We consider a supply chain supernetwork constrained by stringent carbon policy of mandatory cap, the purpose of which is to examine how stringent carbon regulations and operational decision modes jointly influnce the profitability and emission control of the system. We show that two key aspects of caps sharing schemes and decision modes eventually constitute four basic configurations of operations environment. Drawing on these configurations, this paper formulates novel carbon-capped mathematical gaming models to portray the supply chain supernetwork operations, which is then transformed into equivalent ones based on variational inequality approach and solved by devising augmented algorithms. The algorithms empower us to conduct typical computational experiments to compare supply chain performances resulting from diverse scenarios. The results reveal that only when the mandatory cap is set in intermediate level rather than excessively mild or tight can it be effective to balance system profitability and emission control well. Furthermore, regardless of decision modes, caps sharing scheme can always incur more system profit than the nonsharing scheme, while this rule does not apply to total carbon emission. Specifically, it is illustrated that properly changing the combination of decision mode and cap scheme can achieve Pareto improvement on low-carbon supernetwork performances (i.e. increasing profit and reducing emission), which is however dependent on the emission intensities contrast of all emitting firms. This study provides the advanced analytical framework and new insights for better understanding the joint impact of stringent (mandatory) cap policies and decision modes on supply chain performances. We shed light on that properly adjusting the cap tightness and the combination of decision mode and cap-sharing scheme may achieve Paretoly improvement for individual profits and particularly attain win-win result for system profit and emission abatement. [ABSTRACT FROM AUTHOR]