Fuzzy mixed integer programming model for medium-term planning in a closed-loop supply chain with remanufacturing option

Cell formation problem mainly addresses how machines should be grouped and parts be processed in cells. In dynamic environments, product mix and demand are changed in each period of the planning horizon. Incorporating such assumption in the model increases flexibility of the system to meet customers' requirements. In this model, to ensure the reliability of the system in presence of unreliable machines, alternative routing process as well as buffer storage are considered to reduce detrimental effects of machine failure. This problem is presented by a nonlinear mixed integer programming model attempting to minimize the overall cost of the system. To solve the model in large scale for practical purposes, a genetic algorithm approach is adopted as the model belongs to NP-hard class of problems. Sensitivity analysis is used to show the validity of the proposed model. Besides, numerical examples are used both, for small-sized and large- sized instances to show the efficiency of the method in finding near optimal solution.

An integrated sustainable partner selection approach with closed-loop supply chain network configuration

PurposeSome essential issues about modeling of reverse logistics (RL) systems and product recovery networks include consideration of the qualities of the returned products, taking into account uncertainty and integrating the forward and reverse flows. The purpose of this paper is to develop the integrated RL model, which focuses on the control of inventory and production planning problems in a case of uncertainty in demand, quantities and qualities of returns.Design/methodology/approachThe model involves a forward production route, three alternative recovery routes and a disposal route. Various levels of qualities are considered for returned products. A fuzzy mixed integer programming model (FMIP) is developed to provide a solution for the problems of production planning and inventory control. After maximizing the satisfaction degree, different solutions can have the same maximum. Moreover, policies that use all recovery routes and reduce the overall uncertainty have no chance to be chosen. To tackle these problems, a two-phase approach method is applied.FindingsAccording to the results of the numerical example, using different and appropriate recovery options based on the quality of returns can significantly decrease the recovery costs. Similarly, it is shown that the two-phase approach can be an effective and efficient method to reach a satisfactory solution for such problems.Originality/valueIn this study, after maximizing the FMIP model, a two-phase approach ‒ as a novel optimization technique in this research ‒ is employed to achieve a desirable solution.

The complexity of closed-loop supply chain makes the operation of logistics system more dependent on logistics network, so the facility location-allocation problem in closed-loop supply chains has been the most important problem in the supply chain management with reverse logistics. The Facility location-allocation problem in designing closed-loop supply chains is analyzed in this paper at first, and then the mathematical model is formulated. In the model the logistics network is shared by forward logistics and reverse logistics, and the demanded quantities is considered as stochastic variable. The objective of the model is to optimize the total cost of the closed-loop supply chain. Because the formulated model is NP-hard, genetic local search algorithm is designed to solve the problem. The local search is used in the algorithm to improve the search effectiveness. Simulations based on numerical examples show that the proposed mathematical model and the algorithm are effective.

ABSTRACTA generalized interval fuzzy mixed integer programming model is proposed for the multimodal freight transportation problem under uncertainty, in which the optimal mode of transport and the optimal amount of each type of freight transported through each path need to be decided. For practical purposes, three mathematical methods, i.e. the interval ranking method, fuzzy linear programming method and linear weighted summation method, are applied to obtain equivalents of constraints and parameters, and then a fuzzy expected value model is presented. A heuristic algorithm based on a greedy criterion and the linear relaxation algorithm are designed to solve the model.

In the last decade, planning of closed-loop supply chains in different strategic, tactical, and operational levels has attracted many interests due to economic reasons, environmental challenges, and government legislations. This paper presents a novel linear programming model for the integrated production and distribution planning in closed-loop supply chains under uncertainty. The proposed model involves multi-product and multi-period which considers multiple transportation modes, direct or indirect shipments, advertising costs, and several customer zones for different types of products and also attempts to integrate production and distribution plans in the forward and reverse sides of the closed-loop supply chain, simultaneously. To deal with uncertain input data, a robust optimization counterpart based on polyhedral uncertainty set is developed to obtain optimal solutions immunizing the problem for any realization of uncertain parameters in the given polyhedral uncertainty set. Computation results for a numerical example under different scenarios are discussed to give insights about the features of the proposed robust optimization model in handling the uncertainty of parameters. Finally, some sensitivity analyses are performed to show the behaviour of the robust and deterministic models respect to changes of uncertainty levels of parameters as well as the amounts of important parameters such as demands and returns.

Co-firing of biomass in fossil fuel-fired power plants is a mature technology option for reducing greenhouse gas emissions. Up to 10 % of fossil fuel energy input can be displaced by biomass without the need for major retrofits. Co-firing may be done directly or indirectly. However, direct co-firing has the disadvantage of being less flexible with the use of different types of biomass. Indirect co-firing, on the other hand, overcomes this limitation by using a gasifier which converts the biomass into syngas and biochar. The syngas can then be used for co-firing, while biochar can be applied to soil as a form of carbon sequestration. This process stores the carbon initially fixed by biomass through photosynthesis in the soil, and results in the net transfer of part of the carbon in biomass from the atmosphere to the soil. Biochar thus acts as a negative emissions technology with potential for scale-up in the near future. The utilization of biomass for co-firing in a fleet of thermal power plants can be optimized as a carbon management network, subject to biomass availability and the presence of suitable biochar sinks. In this work, a fuzzy mixed integer linear programming model is developed to minimize net carbon emissions in such a system, taking into account parametric uncertainties in the storage capacities of the biochar sinks. It is assumed that there is the option to use direct, indirect or no co-firing in each power plant in the system. The model is illustrated using a case study.

PurposeThe purpose of this paper is to unveil the circular economy (CE) values with an ultimate goal to provide tenets in a format or structure that can potentially be used for designing a circular, closed-loop supply chain and reverse logistics.Design/methodology/approachThis is desk-based research whose data were collected from relevant publication databases and other scientific resources, using a wide range of keywords and phrases associated with CE, reverse logistics, product recovery and other relevant terms. There are five main steps in the reformulation of CE principles: literature filtering, literature analysis, thematic analysis, value definition and value mapping.FindingsIn total, 15 CE values have been identified according to their fundamental concepts, behaviours, characteristics and theories. The values are grouped into principles, intrinsic attributes and enablers. These values can be embedded into the design process of product recovery management, reverse logistics and closed-loop supply chain.Research limitations/implicationsThe paper contributes to the redefinition, identification and implementation of the CE values, as a basis for the transformation from a traditional to a more circular supply chain. The reformulation of the CE values will potentially affect the way supply chain and logistics systems considering the imperatives of circularity may be designed in the future.Originality/valueThe reformulation principles, intrinsic attributes and enablers of CE in this paper is considered innovative in terms of improving a better understanding of the notion of CE and how CE can be applied in the context of modern logistics and supply chain management.

The ability of closed-loop supply chains (CLSC) and reverse logistics (RL) to improve the triple bottom line (economic, social and environmental values) has increased the development of design and management models for CLSCs and RL. Consequently, there exists an extensive body of literature dedicated to exploring these supply and logistics issues. This paper reviews recent and relevant literature on CLSC and RL with an emphasis on uncertainty, carbon emissions, greenness index, return product quality and reliability considerations. The selected references are organized, reviewed, and analyzed to establish valuable mapping to highlight major findings. Finally, the outcomes are synthesized, and the primary research gaps are emphasized, pointing toward potential avenues for future investigation. These findings reveal that research efforts must be directed towards the development of multi-criteria greenness indices and multi-objective robust optimization models for uncertain quality and reliability of returns.

Increasing environmental concerns require businesses to become more responsive to products that either have been returned or that are at the end of their useful lives. Organization's responsiveness and their reactions toward life cycles of products are critical to achieve sustained success once fluctuations are recurrent and the business environments are turbulent. Life cycles are getting shorter, and efficient handling can save large amounts of cash since many materials can be extracted, reused, and redistributed. Reverse Logistics (RL) and Closed Loop Supply Chains (CLSC) have garnered growing interest as a way to manage this reverse flow of products in a cost effective way. It is discernible that the degree of complexity in closed loop networks is usually higher than open networks. In a closed loop supply chain network, the attempt is to ensure a smooth flow of materials as well as extracting the maximum value from returning and end-of-life goods. Reduction of waste and generating profit for enterprises are two paramount achievements through integrating forward and reverse logistics. By considering various proposed conceptual models for CLSC, in this study at first we present a comprehensive applicable conceptual model. Then, we specifically focus on a CLSC network, which includes multiple plants, collection centers, demand markets, and products. To this aim, a generalized proposed mixed-integer linear programming model is presented that minimizes the total cost. The objective is to know how many, which production plants and Return Processors (Collection sites) should be open, which products, and in which quantities should have stuck. The goal of this model is to minimize the supply chain waste and reduce supply chain costs. In such a way, the supply chain system can be agile, integrated, robust, and lean. The proposed model can be extended to consider more environmental factors. Moreover, the efficacy and efficiency of that have been validated by case study and numerical example.

PurposeThis study research contributes in fulfilling the gap by carrying out a systematic literature review (SLR) of contemporary research studies in closed-loop supply chain (CLSC). To the best of the author’s knowledge, an SLR rooted in bibliometric analysis has not been carried focusing on advent developments in CLSC. SLR employs scientific methodologies to select papers from standard databases. The SLR using advanced bibliometric and network analysis enables unveiling the key features of the contemporary literature.Design/methodology/approachThe author has analyzed over 333 documents published from 2008 and onward. Using the contemporary tools from bibliometric analysis tools, the author presented an exploratory analysis. A network analysis is utilized to visualize literature and create clusters for the cocited research studies, keywords and publication sources. A detailed multivariate analysis of most influential works published based top 100 articles via a cocitation matrix is done. The multivariate analysis used k-means clustering in which optimal number of clusters are estimated. The analysis is further extended by using a factor analysis, which enables determining the most influential clusters in the k-means clustering analysis.FindingsThe SLR using a bibliometric and network analysis enables unveiling the key features of the contemporary literature in CLSC. The author examined published research for influential authors, sources, region, among other key aspects. Network analysis enabled visualizing the clusters of cocited research studies, cowords and publication sources. Cluster analysis of cocited research studies is further explored using k-means clustering. Factor analysis extends findings by identifying most contributing grouping of research areas within CLSC research. Each clustering technique disclosed a unique grouping structure.Originality/valueCLSC has received considerable attention, and its core areas start with focusing on reverse logistics concepts relating reuse, recycling, remanufacturing, among others. Contemporarily, the studies have enhanced reverse logistics core functionalities interfaced with the other interesting avenues related to CO2 emission reduction, greening and environmental protection, sustainability, product design and governmental policies. Earlier studies have presented a literature review of CLSC; however, these reviews are commonly conducted in the traditional manner where the authors select papers based on their area of expertise, interest and experience. As such these reviews fall short in utilizing the advanced tools from bibliometric analysis.

Structured prediction is used in areas such as computer vision and natural language processing to predict structured outputs such as segmentations or parse trees. In these settings, prediction is performed by MAP inference or, equivalently, by solving an integer linear program. Because of the complex scoring functions required to obtain accurate predictions, both learning and inference typically require the use of approximate solvers. We propose a theoretical explanation to the striking observation that approximations based on linear programming (LP) relaxations are often tight on real-world instances. In particular, we show that learning with LP relaxed inference encourages integrality of training instances, and that tightness generalizes from train to test data.

<p style='text-indent:20px;'>This paper investigates decisions in a three-echelon closed-loop supply chain composed of one manufacturer, one retailer, and one third-party logistics provider (3PL), with the retailer being dominant. Inspired by game theory, we develop an equilibrium model for a retailer-led, closed-loop supply chain under logistics outsourcing. We derive the optimal forward and reverse logistics decisions of each supply chain member. This article analyzes the effects of market size, consumers' sensitivity to sales prices, the proportion of logistics costs, consumers' environmental awareness, and consumers' sensitivity to recycling prices on decision-making process. Finally, we provide a numerical example to verify the validity of our conclusions. Our results indicate that the higher the manufacturer's share in the forward logistics cost, the higher the sales price, the wholesale price, and the forward logistics service price, and the lower the order quantity. The higher the manufacturer's share in the reverse logistics costs, the lower the recycling price, the transfer price, and the recycling amount, and the higher the reverse logistics service price. Whether it is forward logistics or not, the higher the manufacturer's share in the logistics costs, the lower the profits of each member.</p>

The electric energy consumption in passenger vehicles is rapidly increasing. To limit the associated increase in fuel consumption, an energy management system has been developed. This system exploits the fact that the losses in the internal combustion engine vary with the operating point, and uses the possibility to temporarily store electric energy in a battery, such that electric energy is only produced at moments when it is cheap to generate. To come to a practically applicable solution, a vehicle model is derived, containing only the component characteristics relevant for this application. The energy management problem is formulated as an optimization problem. The fuel consumption over a driving cycle is minimized, while respecting physical limitations of the components and maintaining an acceptable energy level of the battery. Several optimization methods are studied to come to a solution. The dynamic optimization problem is solved using Dynamic Programming. After rewriting it as a static optimization problem and approximating the cost function by a quadratic function, the problem is solved using Quadratic Programming, which requires less computation time. A real-time implementable strategy has been derived from the Quadratic Programming problem, that does not require a prediction of the future driving cycle. This strategy compares the current cost of producing electric energy with the estimated average cost. By adapting the average cost based on the energy level of the battery, it is ensured that the battery energy level will remain around the desired value. Simulations show that a fuel reduction up till 2% can be obtained on a conventional vehicle without major hardware changes. Higher reductions are possible on the exhaust emissions. To predict and explain the amount of fuel reduction that can be obtained with a given vehicle configuration, a set of engineering rules is derived based on typical component characteristics. Their results correspond reasonably well with the simulations. An advanced power net topology is studied which contains both a battery and an ultracapacitor that are connected by a DC-DC converter and a switch. Because of the increased complexity, this system is modeled using linear and piecewise linear approximations of the component characteristics, such that the energy management problem can be casted as a Linear Programming problem. The discrete switch makes it a Mixed Integer Linear Programming Problem. A realtime strategy, similar to the strategy for the conventional power net, has been derived. The addition fuel reduction that is obtained with the dual storage power net is small, because the maximum profit that can be obtained with an ideal lossless battery is not much higher than with a normal battery. Subsequently, hybrid electric vehicles are studied that use an Integrated Starter Generator which can be used for generating electric power and for vehicle propulsion. Several conSummary figurations are studied with respect to their potential fuel reduction. Configurations that enable start-stop operation of the engine obtain a much higher fuel reduction, up to 40%. The controllers are tested in real-time on a Hardware-in-the-Loop environment, where a vehicle simulation model is combined with existing electric components. It is shown that the electric power setpoints provided by an energy management strategy can be realized in practice.

PurposeThis paper presents a systematic literature review of the various aspects of reverse logistics (RL) and closed-loop supply chains (CLSC) in implementing and achieving circular economy (CE) motives. CE is identified as a method of embracing imperishability into the economic structure, helping shift from a linear to a condition leading to ecological and social benefits.Design/methodology/approachSystematic literature was used to review a total of 80 peer-reviewed articles are included in the study and covers different concepts related to the implementation of CE, such as cost-saving, network design, sustainable RL, waste management and extended producer responsibility.FindingsThe findings reveal that the research in the domain is in a growing phase, and in recent years, a lot of attention has been given by researchers across the globe. However, further research is required in crucial areas for the adoption of CE, such as retail reverse logistics, pharmaceutical industries and resource recycling industry.Practical implicationsThe study discusses the business needs and solutions for industries. Key enablers and barriers are listed along with the main activities involved in each sector in CLSC. Managers can design a pathway to decide which lever to use to overcome a particular challenge.Originality/valueThe work contributes theoretically by developing research themes in RL and CLSC practices applied to CE. It also provides theoretical and practical implications of the study, which can be used as a signboard for further research.