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The purpose of this paper is to propose a fuel‐optimal virtual centre selection method for formation flying maintenance in the J2 perturbed environment.

Based on the relative orbital elements (ROE) theory, the J2 perturbed relative motions between different satellites in the formation are analyzed, and then the fuel‐optimal virtual centre selection issue for formation flying maintenance are parameterized in terms of ROE. In order to determine the optimal virtual centre, two theories are proposed in terms of ROE.

Numerical simulations demonstrate that the fuel‐optimal virtual centre selection method is valid, and the control of the ROE of each satellite with respect to a virtual optimal centre of the formation is more efficient regarding the fuel consumption than the control of all satellites with respect to a satellite belonging to the formation.

The fuel‐optimal virtual centre selection method is valid for formation flying mission whose member satellite in circular or near circular orbit.

The fuel‐optimal virtual centre selection approach can be used to solve formation flying maintenance problem which involves multiple satellites in the formation.

The paper proposes a fuel‐optimal virtual centre selection method in terms of ROE, and shows that keeping the formation with respect the optimal virtual centre is more fuel efficient.

The purpose of this paper is to propose a new fuel-balanced formation keeping reference trajectories planning method based on selecting the virtual reference center(VRC) in a fuel-balanced sense in terms of relative eccentricity and inclination vectors (E/I vectors).

By using the geometrical intuitive relative E/I vectors theory, the fuel-balanced VRC selection problem is reformulated as the geometrical problem to find the optimal point to equalize the distances between the VRC and the points determined by the relative E/I vectors of satellites in relative E/I vectors plane, which is solved by nonlinear programming method.

Numerical simulations demonstrate that the new proposed fuel-balanced formation keeping strategy is valid, and the new method achieves better fuel-balanced performance than the traditional method, which keeps formation with respect to geometrical formation center.

The new fuel-balanced formation keeping reference trajectories planning method is valid for formation flying mission whose member satellite is in circular or near circular orbit in J2 perturbed orbit environment.

The new fuel-balanced formation keeping reference trajectories planning method can be used to solve formation flying keeping problem, which involves multiple satellites in the formation.

The fuel-balanced reference trajectories planning problem is reformulated as a geometrical problem, which can provide insightful way to understand the dynamic nature of the fuel-balanced reference trajectories planning issue.

The purpose of this paper is to propose a modified fuel-balanced formation keeping strategy based on actively rotating satellites in the formation in the J2 perturbed environment.

Based on the relative orbital elements theory, the J2 perturbed relative motions between different satellites in the formation are analyzed, and then, the method to estimate fuel required to keep the in-plane and out-of-plane relative motions is presented, based on which a modified fuel-balanced formation keeping strategy is derived by considering both in-plane and out-of-plane J2 perturbations.

Numerical simulations demonstrate that the modified fuel-balanced formation keeping strategy is valid, and the modified fuel-balanced formation keeping strategy requires less total fuel consumption than original Vadali and Alfriend’s method.

The modified fuel-balanced formation keeping strategy is valid for formation flying mission whose member satellite is in circular or near-circular orbit.

The modified fuel-balanced formation keeping strategy can be used to solve formation flying keeping problem, which involves multiple satellites in the formation.

The modified fuel-balanced formation keeping strategy is proposed by considering both in-plane and out-of-plane J2 perturbations, which further reduce the fuel consumption than the original Vadali and Alfriend’s method.

The purpose of this paper is to present a method to conduct small satellite rendezvous mission by using the differential aerodynamic forces under J2 perturbation in low earth orbit (LEO).

Each spacecraft is assumed to be equipped with two large flat plates, which can be controlled for generating differential accelerations in all three directions. Based on the kinetic theory, the aerodynamic lift and drag generated by a flat plate are calculated. To describe the relative dynamics under J2 perturbation, a modified model is derived from the high-fidelity linearized J2 equations proposed by Schweighart and Sedwick.

Simulation results demonstrate that the proposed method is valid and efficient to solve satellite rendezvous problem, and the modified model considering J2 effect shows better accuracy than the Horsley’s Clohessy–Wiltshire-based model.

Because aerodynamic force will reduce drastically as orbital altitude rises, the rendezvous control strategy for small satellites presented in this paper should be limited to the scenarios when satellites are in LEO.

The rendezvous control method in this paper can be applied to solve satellite rendezvous maneuver problem for small satellites in LEO.

This paper proposes a modified differential aerodynamic control model by considering J2 perturbation, and simulation results show that it can achieve higher rendezvous control accuracy.

Compiled by K.G.B. Bakewell covering the following journals published by MCB University Press: Facilities Volumes 8‐18; Journal of Property Investment & Finance Volumes 8‐18; Property Management Volumes 8‐18; Structural Survey Volumes 8‐18.

Index by subjects, compiled by K.G.B. Bakewell covering the following journals: Facilities Volumes 8‐18; Journal of Property Investment & Finance Volumes 8‐18; Property Management Volumes 8‐18; Structural Survey Volumes 8‐18.

Compiled by K.G.B. Bakewell covering the following journals published by MCB University Press: Facilities Volumes 8‐18; Journal of Property Investment & Finance Volumes 8‐18; Property Management Volumes 8‐18; Structural Survey Volumes 8‐18.

Compiled by K.G.B. Bakewell covering the following journals published by MCB University Press: Facilities Volumes 8‐18; Journal of Property Investment & Finance Volumes 8‐18; Property Management Volumes 8‐18; Structural Survey Volumes 8‐18.

Supply chains (SCs) have been growingly virtualized in response to the market challenges and opportunities that are presented by new and cost-effective internet-based technologies today. This paper designed a virtual closed-loop supply chain (VCLSC) network based on multiperiod, multiproduct and by using the Internet of Things (IoT). The purpose of the paper is the optimization of the VCLSC network.

The proposed model considers the maximization of profit. For this purpose, costs related to virtualization such as security, energy consumption, recall and IoT facilities along with the usual costs of the SC are considered in the model. Due to real-world demand fluctuations, in this model, demand is considered fuzzy. Finally, the problem is solved using the Grey Wolf algorithm and Firefly algorithm. A numerical example and sensitivity analysis on the main parameters of the model are used to describe the importance and applicability of the developed model.

The findings showed that the Firefly algorithm performed better and identified more profit for the SC in each period. Also, the results of the sensitivity analysis using the IoT in a VCLSC showed that the profit of the virtual supply chain (VSC) is higher compared to not using IoT due to tracking defective parts and identifying reversible products. In proposed model, chain members can help improve chain operations by tracking raw materials and products, delivering products faster and with higher quality to customers, bringing a new level of SC efficiency to industries. As a result, VSCs can be controlled, programmed and optimized remotely over the Internet based on virtual objects rather than direct observation.

There are limited researches on designing and optimizing the VCLSC network. This study is one of the first studies that optimize the VSC networks considering minimization of virtual costs and maximization of profits. In most researches, the theory of VSC and its advantages have been described, while in this research, mathematical optimization and modeling of the VSC have been done, and it has been tried to apply SC virtualization using the IoT. Considering virtual costs in VSC optimization is another originality of this research. Also, considering the uncertainty in the SC brings the issue closer to the real world. In this study, virtualization costs including security, recall and energy consumption in SC optimization are considered.

1. Investigates the role of IoT for virtual supply chain profit optimization and mathematical optimization of virtual closed-loop supply chain (VCLSC) based on multiperiod, multiproduct with emphasis on using the IoT under uncertainty.

2. Considering the most important costs of virtualization of supply chain include: cost of IoT information security, cost of IoT energy consumption, cost of recall the production department, cost of IoT facilities.

3. Selection of the optimal suppliers in each period and determination of the price of each returned product in virtual supply chain.

4. Solving and validating the proposed model with two meta-heuristic algorithms (the Grey Wolf algorithm and Firefly algorithm).

Investigates the role of IoT for virtual supply chain profit optimization and mathematical optimization of virtual closed-loop supply chain (VCLSC) based on multiperiod, multiproduct with emphasis on using the IoT under uncertainty.

Considering the most important costs of virtualization of supply chain include: cost of IoT information security, cost of IoT energy consumption, cost of recall the production department, cost of IoT facilities.

Selection of the optimal suppliers in each period and determination of the price of each returned product in virtual supply chain.

Solving and validating the proposed model with two meta-heuristic algorithms (the Grey Wolf algorithm and Firefly algorithm).

Current industrial scenario is largely dependent on cloud computing paradigms. On-demand services provided by cloud data centre are paid as per use. Hence, it is very important to make use of the allocated resources to the maximum. The resource utilization is highly dependent on the allocation of resources to the incoming request. The allocation of requests is done with respect to the physical machines present in the datacenter. While allocating the tasks to these physical machines, it needs to be allocated in such a way that no physical machine is underutilized or over loaded. To make sure of this, optimal load balancing is very important.

The paper proposes an algorithm which makes use of the fitness functions and duopoly game theory to allocate the tasks to the physical machines which can handle the resource requirement of the incoming tasks. The major focus of the proposed work is to optimize the load balancing in a datacenter. When optimization happens, none of the physical machine is neither overloaded nor under-utilized, hence resulting in efficient utilization of the resources.

The performance of the proposed algorithm is compared with different existing load balancing algorithms such as round-robin load (RR) ant colony optimization (ACO), artificial bee colony (ABC) with respect to the selected parameters response time, virtual machine migrations, host shut down and energy consumption. All the four parameters gave a positive result when the algorithm is simulated.

The contribution of this paper is towards the domain of cloud load balancing. The paper is proposing a novel approach to optimize the cloud load balancing process. The results obtained show that response time, virtual machine migrations, host shut down and energy consumption are reduced in comparison to few of the existing algorithms selected for the study. The proposed algorithm based on the duopoly function and fitness function brings in an optimized performance compared to the four algorithms analysed.