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Industrial organizations often face difficulties in finding out the methods to meet ever increasing customer expectations and to remain competitive in the global market while maintaining controllable expenses. An effective and efficient green supply chain management (GSCM) can provide a competitive edge to the business. This paper focusses on the selection of green suppliers while simultaneously balancing economic, environmental and social issues.

In this study, it is assumed that two types of decision-makers (DMs), namely, the first level and second-level DMs operate at two separate groups in GSC. The first-level DMs always empathise to optimize carbon emissions, per unit energy consumption per product and per unit waste production, while the second-level DMs seek to optimize ordering costs, number of rejected units and number of late delivered units in the entire GSCM. In this paper, fuzzy goal programming (FGP) approach has been adopted to obtain compromise solution of the formulated problem by attaining the uppermost degree of each membership goal while reducing their deviational variables. Furthermore, demand has also been forecasted using exponential smoothing analysis. The model is verified on a real-time industrial case study.

This research enables DMs to analyse uncertainty scenarios in GSCM when information about different parameters are not known precisely.

The proposed model is restricted to vagueness only, however, DMs may need to consider probabilistic multi-choice scenarios also.

The proposed model is generic and can be applied for large-scale GSC environments with little modifications.

No prior attempt is made till date to present interval type-2 fuzzy sets in a multi-objective GSC environment where the DMs are at hierarchical levels. Interval type-2 fuzzy sets are considered as better ways to represent inconsistencies of human judgements, its incompleteness and imprecision more accurately and objectively. Also, crisp or deterministic forms of uncertain parameters have been obtained by taking expected value of the fuzzy parameters.

The purpose of this paper is to design petroleum products’ supply chain management, which includes efficient integration of suppliers, manufacturers, storehouses and retailers.

This paper proposes that a three-level supply chain will be turned into a bi-level supply chain of petroleum products by simultaneous integration of the middle level with the upstream and downstream levels. Also, it is integrally optimized by considering the multiple managerial flows' mutual results at various supply chain levels. Also, it is integrally optimized by considering the multiple managerial flows' mutual results at various supply chain levels.

The concepts of the design, structure and outputs are led by the model's solution. The model also responds to the variations in the market via coordination in the related decisions to the distribution, production and inventory issues, and also coordinating between the demands and production.

This paper has limited its analysis to definite values due to the over-expansion of calculations and analysis. Future works can study other aspects of the proposed model for a multi-level petroleum product supply chain in different states of certain parameters and time zones.

The designed model can directly and transparently help the oil managers and decision-makers lower the costs of manufacturing, distribution and sales with respect to the determined criteria.

This paper establishes that effectiveness of the dynamic petroleum materials supply chain design will increase by considering maintained and increased production costs and coordinate management flows at all levels by supply chain creation’s integration.

This paper aims to develop a grey decentralized bi-level multi-objective programming (MOP) model. A solution approach is also proposed for the given model. A production and transportation plan for a closed loop supply chain network under an uncertain environment and different scenarios is also developed.

In this paper, we combined grey linear programming (GLP) and fuzzy set theory to present a solution approach for the problem. The proposed model first solves the given problem using GLP. Membership functions for the decision variables under the control of the leader and for the goals are created. These membership functions are then used to generate the final solutions.

This paper provides insight for fomenting the decision-making process while providing a more flexible approach in uncertain logistics problems. The deviations of the final solution from the individual best solutions of the two levels are very little. These deviations can further be reduced by adjusting the tolerances associated with the decision variables under the control of the leader.

The proposed approach uses the concept of membership functions of linear form, and thus, requires less computational efforts while providing effective results. Most of the organizations exhibit decentralized decision-making under the presence of uncertainties. Therefore, the present study is helpful in dealing with such scenarios.

This is the first time, formulation of a decentralized bi-level multi-objective model under a grey environment is carried out as per the best knowledge of the authors. A solution approach is developed for bi-level MOP under grey uncertainty.

Supplier selection problem is the key process in decision making of supply chain management. An effective selection of vendors is heavily responsible for the success of any organization. Vendor selection problem (VSP) reflects a more practical view when the decision makers involved in the problem are present on different levels. Moreover, vendor selection consists of various random parameters to be dealt with in real life. The purpose of this paper is to present a decentralized bi-level VSP where demand and supply are normal random variables and objectives are fuzzy in nature. Decision makers are present at two levels and are called as leader and follower. As the next purpose, this paper extends and presents a solution approach for fuzzy bi-level multi-objective decision-making model with stochastic constraints. Different scenarios have been developed within a real-life case study based on different sets of controlling factors under the control of leader.

This study uses chance-constrained programming and fuzzy set theory to generate the results. Stochastic constraints are converted into deterministic constraints using chance-constrained programming. Decision variables in the bi-level VSP are partitioned between the two levels and considered as controlling factors. Membership functions based on fuzzy set theory are created for the goals and controlling factors and are used to obtain the overall satisfactory solutions. The model is tested on a real-life case study of a textile industry and different scenarios are constructed based on the choice of leader’s controlling factors.

Results showed that the approach is quite helpful as it generates efficient results producing a good level of satisfaction for the decision makers of both the levels. Results showed that on choosing the vendors that are associated with worst values in terms of associated costs, vendor ratings and quota flexibilities as controlling factors by the leaders, the level of satisfaction achieved is highest. The level of satisfaction of solution is lowest for the scenario when the leader chooses to control the decision variables associated with vendors that are profiled with minimum vendor ratings. Results also showed that higher availability of materials and budget with vendors proved helpful in obtaining quota allocations. Different scenarios generate different results along with different values of satisfaction degrees and objective values which shows the flexible feature of the approach based on leader’s choice of controlling factors. Numerical results showed that the leader’s control can be effectively incorporated maintaining satisfaction levels of the followers under various scenarios or conditions.

The paper makes a certain contribution toward the study of vendor selection existing in a hierarchical manner under uncertain environment. A wide set of data of different factors is needed which can be seen as a limitation when the available time is short for the supplier selection process.

VSP which is generally adopted by most of the large organizations is characterized with hierarchical decision making. Moreover, dealing with the real-life concern, the data available for some of the parameters are not complete, representing an uncertainty of parameters. This study is quite helpful for decentralized VSP under uncertain environment to reduce the costs, improve profit margins and to create long-term relationships with selected vendors. The proposed model also provides an avenue to explore the decision making when the leader has control over some of the decision variables.

Reviewing the literature available, this is the first attempt to present a multi-objective VSP where the decision makers are at hierarchical levels considering uncertain parameters such as demand and supply as per the best knowledge of authors. This research further provides an approach to construct scenarios or different cases based on the choice of leader’s choice of controlling factors.

The process approach to multi-level organizational behavior is based on the assumption that multi-level organizational behavior is processual in nature. This article defines group and organizational processes and their representation as process frameworks. Both functional and inclusional classes of levels exist, each of which has at least five categories of levels. All ten categories are special cases of process frameworks. This article provides examples of each category level, which it uses to illustrate new models of organizational work, extended models of interdependence, a new typology of theories based on their levels of processes, and a new tool for survey research called knobby analyses. After explaining the basic idea of knobby analysis, the article briefly describes the processual theory of the organizational hologram, the use of linear programming, and causal-chain analysis to provide multi-level explanations of employee opinion data. These ideas are embodied in conducting a strategic organizational diagnosis, which is the first stage of organizational design. Organizational design encompasses multiple stages, each of which itself involves multiple, multi-level phenomena and analyses. The basic point is that the processual nature of multi-level organizational phenomena gives more hope for improvements in theory building and their application if one uses the process approach rather than a variable approach.

A comprehensive review of the literature for the problem of lot‐size scheduling (serial and assembly) considering the uncapacitated problem and complicated capacitated assembly manufacturing structure. Analyses the different solution techniques and findings for each product set.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

The purpose of this paper is to present an application of a multidisciplinary multi-level design optimization methodology for the optimal design of a complex device from the field of electrical engineering throughout discipline-based decomposition. The considered benchmark is a single-phase low voltage safety isolation transformer.

The multidisciplinary optimization of a safety isolation transformer is addressed within this paper. The bi-level collaborative optimization (CO) strategy is employed to coordinate the optimization of the different disciplinary analytical models of the transformer (no-load and full-load electromagnetic models and thermal model). The results represent the joint decision of the three distinct disciplinary optimizers involved in the design process, under the coordination of the CO's master optimizer. In order to validate the proposed approach, the results are compared to those obtained using a classical single-level optimization method – sequential quadratic programming – carried out using a multidisciplinary feasible formulation for handling the evaluation of the coupling model of the transformer.

Results show a good convergence of the CO process with the analytical modeling of the transformer, with a reduced number of coordination iterations. However, a relatively important number of disciplinary models evaluations were required by the local optimizers.

The CO multi-level methodology represents a new approach in the field of electrical engineering. The advantage of this approach consists in that it integrates decisions from different teams of specialists within the optimal design process of complex systems and all exchanges are managed within a unique coordination process.

This paper presents a multi‐level frontal algorithm and its implementation and applications on parallel computation. A multi‐frontal program is given which may be used for unsymmetric finite element matrix equations. The parallel program is developed on a cluster of workstations. The PVM (parallel virtual machine) system is used to handle communications among networked workstations. The method has advantages such as numbering of the finite element mesh in an arbitrary manner, simple programming organisation, smaller core requirements and computation times. An implementation of this parallel method on workstations is discussed, the speedup and efficiency of this method being demonstrated and compared with general domain decomposition method based on band matrix methods by numerical examples.