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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]

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]

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]

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]

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]

• 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]

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]

Abstract: In several recent investigations dealing with the economic order quantity with permissible delay in payments, the following assumptions are made: (A) The supplier always offers the retailer fully permissible delay in payments independent of the order quantity. (B) The annual interest which is charged per dollar in stocks by the supplier is higher than the annual interest earned on investment per dollar. (C) The unit purchase cost c is the same as the selling price s per unit. Huang [1] generalizes the concept of fully permissible delay in payments by advocating that the supplier would offer the retailer partially permissible delay in payments where the order quantity is smaller than a predetermined quantity to relax the assumption (A). Motivated essentially by Huang’s work [1], the main purpose of this paper is twofold as stated below: (P1) This paper will extend Huang’s work [1] by establishing new inventory models without having the assumptions (B) and (C) to match the real world situation. (P2) This paper will present new solution procedures different from those of Huang [1]. Among other things, these new solution procedures will show that those of Huang [1] will cause misuses under some circumstances. Several numerical examples illustrate the fact that the percentages of the cost penalty (PCP) of misuses are terribly high in some cases. [Copyright &y& Elsevier]

Abstract: This paper develops a model for determining ordering/trade-credit policy of a supply chain, where one supplier sells a product to a retailer, who faces a deterministic demand, and may offer the retailer two types of trade credit contracts: a “one-part” or a “two-part” contract. We discuss the existence of the optimal solution to the model, and provide a simple algorithm for finding the optimal ordering and trade credit policy of two members. We specify the conditions under which it is beneficial in reducing operational cost for the supplier to offer the two trade credit contracts. Through numerical experiments, we reveal that it is more superior in reducing operational cost for the supplier to offer a two-part credit than to offer a one-part credit, which can be extended to a multi-part credit. The sensitivity analysis is presented at the end of the paper. [Copyright &y& Elsevier]

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]

Abstract: This paper is to resolve the VRPTW and the inventory control decision problem simultaneously since both the vehicle routing decision with time windows and the inventory control decision affect each other and must be considered together. A mathematical model of inventory routing problem with time windows (IRPTW) is proposed. Since finding the optimal solution(s) for IRPTW is a NP-hard problem, this paper proposes a two-phase heuristic method. The first phase is to find the initial solution. The second phase is to improve the solution adopting the variable neighborhood tabu search (VNTS) selecting better neighborhood solutions, to obtain the optimal solution. Moreover, the proposed method was compared with three other heuristic methods. The experimental results indicate that the proposed method is better than the three other methods in terms of average supply chain cost (transportation cost, time window violation penalty cost and inventory cost). [Copyright &y& Elsevier]

Abstract: This paper transfers the classic frequency-based transit assignment method of Spiess and Florian to containers demonstrating its promise as the basis for a global maritime container assignment model. In this model, containers are carried by shipping lines operating strings (or port rotations) with given service frequencies. An origin–destination matrix of full containers is assigned to these strings to minimize sailing time plus container dwell time at the origin port and any intermediate transhipment ports. This necessitated two significant model extensions. The first involves the repositioning of empty containers so that a net outflow of full containers from any port is balanced by a net inflow of empty containers, and vice versa. As with full containers, empty containers are repositioned to minimize the sum of sailing and dwell time, with a facility to discount the dwell time of empty containers in recognition of the absence of inventory. The second involves the inclusion of an upper limit to the maximum number of container moves per unit time at any port. The dual variable for this constraint provides a shadow price, or surcharge, for loading or unloading a container at a congested port. Insight into the interpretation of the dual variables is given by proposition and proof. Model behaviour is illustrated by a simple numerical example. The paper concludes by considering the next steps toward realising a container assignment model that can, amongst other things, support the assessment of supply chain vulnerability to maritime disruptions. [Copyright &y& Elsevier]

Abstract: Production quality in the food production supply chain is studied in this paper. The deficiencies of quality monitoring that exist in traceability systems are analyzed. An abnormality diagnosis algorithm, pre-warning method and structure of pre-warning system are presented. Four abnormal data types in supply chain are analyzed, they are substandard abnormality, over-range abnormality, abnormal distribution and abnormal tendency. All the detection data of the whole supply chain are monitored timely and pre-warned. The production abnormality of the logistics unit is diagnosed and automatically warned, and the decision support information is given. A standard hierarchy evaluation indicator system for abnormalities is developed in this paper. A mathematical model for abnormality detection is developed by combining radial base function (RBF) neural network, fuzzy control, and statistical analysis methods. This model is used in detecting and recognizing different types of abnormalities in the food production supply chain, especially hidden problems. The simulation results show that the proposed pre-warning system can effectively identify abnormal data types, and accurately determine whether a warning should be issued, depending on the warning level when an abnormality is detected by the system. The pre-warning system for food production supply chain performs well and effectively. [ABSTRACT FROM AUTHOR]

Abstract: Global enterprises require extended logistics operations that integrate channel intermediaries into the network. The method for deriving integrated models for logistics hubs that improve the efficiency of manufacturers’ global operations is the focus of this paper. Under government sponsorship, six industrial logistics hubs were implemented by leading manufacturing sectors across Taiwan over a five year period from 2004 until 2008. Each industry sector had unique industry characteristics, business strategies, and logistics models. Therefore, this paper describes how generalized and quick to implement integrated logistics hubs are developed by studying the successful reference models and systems used by six independent industrial sectors. The research results provide a field tested method for deriving integrated logistics hub models in different manufacturing economies with notes that provide sufficient methodological detail for repeating the construction of logistics hubs in other manufacturing economies. [ABSTRACT FROM AUTHOR]

Abstract: Supply chains are multifaceted structures focusing on the integration of all the factors involved in the overall process of production and distribution of end products to the customers. Growing interest in supply chain systems has highlighted the need to adopt appropriate approaches that can ensure the efficient management of their complexity, enormity and broadness of scope. With the main aim of supply chain management being to optimise the performance of supply chains, attention is mainly drawn to the development of modelling frameworks that can be utilised to analyse and comprehend the dynamic behaviour of supply chains. While there have been only a few supply chain modelling attempts reported in the literature, this paper proposes a modelling framework that is used to simulate the operation of a supply chain network of moderate complexity. The proposed model comprises four echelons and is build around a central medium-sized manufacturing company operating as a typical Make-to-Order (MTO) system. The developed model was built using a systems dynamics (SD) approach. The operations performed within a supply chain are a function of a great number of key variables which often seem to have strong interrelationships. The ability of understanding the network as a whole, analysing the interactions between the various components of the integrated system and eventually supplying feedback without de-composing it make systems dynamics an ideal methodology for modelling supply chain networks. The objective of the paper is to model the operation of the supply chain network under study and obtain a true reflection of its behaviour. The modelling framework is also used to study the performance of the system under the initial conditions considered and compare it with that obtained by running the system under eight different scenarios concerning commonly addressed real-life operational conditions. The modelling effort has focused on measuring the supply chain system performance in terms of key metrics such as inventory, WIP levels, backlogged orders and customer satisfaction at all four echelons. The study concludes with the analysis of the obtained results and the conclusions drawn from contrasting the system’s performance under each investigated scenario to that of the benchmark model. [Copyright &y& Elsevier]

[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]

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]

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]

Abstract: In a recent paper, Chiu et al. [Intra-supply chain system with multiple sales locations and quality assurance, Expert Systems with Applications, http://dx.doi.org/10.1016/j.eswa.2012.11.008] used the mathematical modeling and differential calculus to derive the optimal replenishment lot-size and shipment policy that minimizes overall costs for a specific intra-supply chain system. This paper proposes a two-phase straightforward algebraic approach to replace the use of calculus on the cost function for determining the optimal production-shipment policy for such a specific system. This alternative approach enables practitioners who may not have sufficient knowledge of calculus to manage the real-world intra-supply chain systems more effectively. [Copyright &y& Elsevier]

The increase in the consumption of resources in the past decade has caused an increase in the interest of the international academic community in the challenges to reduce such rapid consumption of resources. Every year, many researchers propose different methods by which resource consumption can be reduced. Material, equipment, and process refinement are vivid examples of such efforts. While these innovations can be very helpful, in several cases, however, they can be very costly and greatly time-consuming. In addition, decision-makers tend to tackle the problem of resource consumption, while maintaining the proper level of service. Thus, in this paper, we propose a new bi-objective mathematical model by which we can reduce the consumption of resources and energy, as well as decrease the tardiness penalty in a supply chain scheduling and vehicle routing problem. The model demonstrates that finding the proper production (assembly) sequence, assignment of orders to vehicles and vehicle routing, will enable us to reduce resource consumption. A new Non-dominated Sorting Genetic Algorithm based on shaking and local search strategies of Variable Neighborhood Search algorithm is also developed to solve the proposed problem. Several criteria are introduced and defined to assess the performance of the proposed algorithm. Results demonstrate the out-performance of the proposed algorithm compared with the classic non-dominated sorting genetic algorithm II. We also propose a method that allows decision makers to make an informed decision to choose a proper sequence of jobs and routes that create a trade-off between resource consumption and the tardiness penalty. [ABSTRACT FROM AUTHOR]

Uncertain coalitional game deals with situations in which the transferable payoffs are uncertain variables. The uncertain core has been proposed as the solution of uncertain coalitional game. This paper goes further by presenting two definitions of uncertain Shapley value: expected Shapley value and α -optimistic Shapley value. Meanwhile, some characterizations of the uncertain Shapley value are investigated. Finally, as an application, uncertain Shapley value is used to solve a profit allocation problem of supply chain alliance. [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]

Business stability, quality, safety, supply chain flexibility and cost optimization have an increasing role in companies that strive to stay and survive in the market competition. A wise supplier choice becomes ever more important prerequisite for the success of any company. This paper presents a novel hybrid model for supplier assessment and selection, based on hybrid solution including genetic algorithm (GA) and harmony search algorithm (HSA). The chosen data set presents original data which is used for assessment in “Lames” company. The results show that HSA & GA value constraint model is slightly more restricted than other discussed models, and separates, much better and with greater precision, poor companies from the good ones in business environment. [ABSTRACT FROM AUTHOR]

Abstract: As today’s consumers are more and more concerned with the environmental impacts of products and services they buy, enterprises have been more and more concerned with “green operations”. One of the key aspects of green logistics management is reverse logistics. This paper shows how the potential of managing reverse logistics flows can be implemented in the agro-industrial sector. As an example, the palm oil supply chain is considered. This study is carried out under the focus of the “closed-loop supply chain (CLSC) framework” in which forward and backward product flows are considered simultaneously. A mathematical model is proposed in order to represent the dynamic interaction between flows. The objective function considers energy, cost and economic profits. Different implementation scenarios of recovery processes are proposed and interactions between direct and reverse flows in the chain are evaluated. Results are analyzed using proper statistical tools, showing that the simultaneous analysis of direct and reverse flows positively impact the net economic profits in this complex supply chain of the agro-industrial sector. [Copyright &y& Elsevier]

Abstract: Tandem queues are widely used in mathematical modeling of random processes describing the operation of manufacturing systems, supply chains, computer and telecommunication networks. Although there exists a lot of publications on tandem queueing systems, analytical research on tandem queues with non-Markovian input is very limited. In this paper, the results of analytical investigation of two-node tandem queue with arbitrary distribution of inter-arrival times are presented. The first station of the tandem is represented by a single-server queue with infinite waiting room. After service at the first station, a customer proceeds to the second station that is described by a single-server queue without a buffer. Service times of a customer at the first and the second server have PH (Phase-type) distributions. A customer, who completes service at the first server and meets a busy second server, is forced to wait at the first server until the second server becomes available. During the waiting period, the first server becomes blocked, i.e., not available for service of customers. We calculate the joint stationary distribution of the system states at the embedded epochs and at arbitrary time. The Laplace–Stieltjes transform of the sojourn time distribution is derived. Key performance measures are calculated and numerical results presented. [Copyright &y& Elsevier]

Abstract: An organization's environmental performance is affected by its suppliers' environmental performance, and selecting green suppliers is a strategic decision in order to be more competitive in today's global market. The supplier selection problem involves several quantitative and qualitative criteria. In the supplier selection process, if suppliers have limited capacity or other constraints, it is necessary to determine the best supplier and order quantity of each supplier. In this paper, we present an integrated approach, of fuzzy multi attribute utility theory and multi-objective programming, for rating and selecting the best green suppliers according to economic and environmental criteria and then allocating the optimum order quantities among them. At first, the fuzzy analytic hierarchy process and fuzzy technique for order preference by similarity to ideal solution is applied in order to analyze the importance of multiple criteria by incorporating experts' opinion and to determine the best green suppliers. Next, multi-objective linear programming is used to consider and to formulate various constraints such as quality control, capacity, and other objectives. The objective of the mathematical model is simultaneously to maximize the total value of purchasing and to minimize the total cost of purchasing. To handle the subjectivity of decision makers' preferences, fuzzy logic has been applied. The efficiency and application of the proposed approach has been illustrated with a case study in an automobile manufacturing company. The obtained results help firms establish a systematic approach for tackling green supplier selection and order allocation problems in a realistic situation. Finally managerial implications, conclusions, and directions for additional research are introduced. [Copyright &y& Elsevier]

Abstract: Order elements are often not punctually or synchronically provided in supply chain processes involving the convergence of different material flows (e.g., assemblies). This paper focuses on the development of a model for reviewing the timeliness and simultaneousness of these converging material flows. The model is validated by simulation studies as well as several practice based case studies. The application of this mathematical model allows the influence of critical supply processes on the logistic performance of the supply chain to be identified and quantified. Hence, measures to improve the logistic performance can be derived and their anticipated impact can be visualized. [Copyright &y& Elsevier]

Abstract: A closed-loop supply chain is a complex system in which node enterprises play important roles and exert great influence. Firstly, this paper established a collecting price game model for a close-loop supply chain system with a manufacturer and a retailer who have different rationalities. It assumed that the node enterprises took the marginal utility maximization as the basis of decision-making. Secondly, through numerical simulation, we analyzed complex dynamic phenomena such as the bifurcation, chaos and continuous power spectrum and so on. Thirdly, we analyzed the influences of the system parameters; this further explained the complex nonlinear dynamics behavior from the perspective of economics. The results have significant theoretical and practical application value. [Copyright &y& Elsevier]

Abstract: Huang (2010) [1] proposed an integrated inventory model with trade credit financing in which the vendor decides its production lot size while the buyer determines its expenditure to minimize the annual integrated total cost for both the vendor and the buyer. In this paper, we extend his integrated supply chain model to reflect the following four facts: (1) generated sales revenue is deposited in an interest-bearing account for the buyer, (2) the buyer’s interest earned is not always less than or equal to its interest charged, (3) the total number of shipments in one lot size is the vendor’s decision variable to minimize the cost, and (4) it is vital to have a discrimination term which can determine whether the buyer’s replenishment cycle time is less than the permissible delay period or not. We then derive the necessary and sufficient conditions to obtain the optimal solution, and establish some theoretical results to characterize the optimal solution. Finally, numerical examples are presented to illustrate the proposed model and its optimal solution. [Copyright &y& Elsevier]

Abstract: A closed-loop supply chain (CLSC) network consists of both forward and reverse supply chains. In this paper, a CLSC network is investigated which includes multiple plants, collection centres, demand markets, and products. To this aim, a mixed-integer linear programming model is proposed that minimizes the total cost. Besides, two test problems are examined. The model is extended to consider environmental factors by weighed sums and ε-constraint methods. In addition, we investigate the impact of demand and return uncertainties on the network configuration by stochastic programming (scenario-based). Computational results show that the model can handle demand and return uncertainties, simultaneously. [Copyright &y& Elsevier]

Abstract: Bioethanol produced from lignocellulosic feedstock show enormous potential as an economically and environmentally sustainable renewable energy source. Switchgrass (panicum virgatum) is considered as one of the best second generation feedstock for bioethanol production. In order to commercialize the production of switchgrass-based bioethanol, it is essential to design an efficient switchgrass-based bioethanol supply chain (SBSC) and effectively manage the logistics operation. This paper proposes an integrated mathematical model to determine the optimal comprehensive supply chain/logistics decisions to minimize the total SBSC cost by considering existing constraints. A case study based on North Dakota state (ND) in the United States illustrates the application of the proposed model. The results demonstrate that by using only 61% of the available marginal land for production of switchgrass feedstock, 100% of the annual gasoline energy equivalent requirement of ND can be economically and sustainably met from the produced bioethanol. Sensitivity analysis is conducted to provide insights for efficiently managing the entire SBSC and minimizing the total cost. [Copyright &y& Elsevier]

Abstract: In growing competitive markets, close cooperative strategies among the vendors and the buyers are essential to cut the joint inventory cost and to have less response time to the supply chain players. Recently, Yang et al. (2007) [2] have presented an integrated two-stage production–inventory model and used the classical differential calculus method to derive the optimal lot size for the vendor and the buyer, and the number of deliveries in supply chain. Moreover, numerous researchers adopted other algebraic methods to derive the optimal solution for inventory models. However, in these papers, the cost comparisons method and arithmetic–geometric mean inequality do not focus on explicitly developing the mathematical expressions for two-stage inventory system with the backorders. In this study, we extend the inventory model proposed by Yang et al. (2007) [2], and consider a three-variable inventory problem and present an alternative approach to determine the optimal replenishment policy for the integrated vendor–buyer inventory system with backordering utilizing the cost-difference rate comparison approach. [Copyright &y& Elsevier]

Abstract: In this paper three different types of rebate induced contract namely direct-rebate and revenue sharing contract; downward direct rebate contract; direct-rebate and effort sharing contract are proposed for supply chain coordination perspective. Effectiveness and flexibility of proposed contracts under linear and iso-elastic demand are discussed analytically. It is shown that under certain conditions both manufacturer and retailer can gain more profit by means of appropriate coordination contracts. Several important implications are derived analytically to point out relationship among characteristically different contracts. Results are illustrated with numerical examples. [Copyright &y& Elsevier]

Abstract: This paper focuses on the operational issues of a Two-echelon Single-Vendor–Multiple-Buyers Supply chain (TSVMBSC) under vendor managed inventory (VMI) mode of operation. The operational parameters for TSVMBSC model are: sales quantity and sales price that determine the channel profit of the supply chain, and contract price between the vendor and the buyer, which depends upon the understanding between the partners on their revenue sharing. The optimal sales quantity for each buyer in TSVMBC is determined using a mathematical model available in the literature. The optimal sales price, the optimal channel profit and contract price between the vendor and buyer are determined based on the optimal sales quantity determined. Particle Swarm Optimization (PSO) and a hybrid of Genetic Algorithm and Artificial Immune System (GA–AIS) are proposed to solve this TSVMBSC problem. These two algorithms are evaluated for their solution quality. The robustness of the algorithms with their parameters are also analyzed and presented. [Copyright &y& Elsevier]

Abstract: This paper presents a MCO (multi-criteria optimisation) of regional biomass supply chains for the conversion of biomass to energy through the simultaneous maximisation of economic performance and minimisation of the environmental and social FPs (footprints). The energy supply-chain model contains agricultural, pre-processing, processing, and distribution layers. An integrated model, previously developed by the authors, for regional biomass energy network optimisation is used as a basis, and now extended for simultaneous assessment of the supply-chain performance based on LCA (Life cycle assessment). Several total FPs are introduced for “cradle” to “grave” evaluation, which, besides direct, comprises also indirect effects caused by products’ substitutions. In the MCO approach, the annual profit is maximised against each FP generating different sets of Pareto optimal solutions, one for each FP. With this approach the aggregation of different environmental and/or social pressures is thus avoided. The results indicate that total FPs enable the obtaining of more realistic solutions, than in those cases when only direct FPs are considered. More profitable and less environmentally harmful solutions can be gained with significant reduction in total carbon and total energy FPs. [Copyright &y& Elsevier]

Abstract: Assessment of both economical and environmental performance of biofuel supply chains is crucial to have a complete view of the future implications of those systems. This paper presents a multi-objective, static modelling framework for the optimisation of hybrid first/second generation biofuel supply chains. Using the proposed modelling framework, different aspects are analysed including the potential GHG savings, the impact of carbon tax on the economic and environmental performance of a biofuel supply chain, the trade-off between the economic and environmental objectives and the maximum bioethanol throughput that can be achieved at different cap levels on the total supply chain cost. The trade-off between the conflicting objectives is analysed by solving the proposed multi-objective model using the ɛ-constraint method. In addition, the impact of technological learning on the economic and environmental performance of the supply chain throughout time is also analysed using a multi-period model developed based on the proposed static optimisation framework. Bioethanol production in the UK using hybrid first/second generation technologies is considered as the case study to highlight the model applicability. [Copyright &y& Elsevier]

Abstract: This paper proposes a retailer collection model whereby the retailer collects end-of-life products and the manufacturer cooperates with a third-party firm to handle used products, and a non-retailer collection model whereby a third-party firm is subcontracted by the manufacturer for collection work. While the return rate, manufacturer’s profits, and channel members’ total profits of the retailer collection model are not always superior to those of the non-retailer collection model, we find that the retail collection model analytically outperforms when the third-party firm is a non-profit organization for recycling and disposal. [Copyright &y& Elsevier]