Showing papers in "International Journal of Systems Science in 2014"
TL;DR: A robust version of PLS to deal with outliers and missing values, simultaneously is introduced and the effectiveness of the proposed method is finally demonstrated by the application results of the KPI-related prediction and diagnosis on an industrial benchmark of Tennessee Eastman process.
Abstract: In practical industrial applications, the key performance indicator (KPI)-related prediction and diagnosis are quite important for the product quality and economic benefits. To meet these requirements, many advanced prediction and monitoring approaches have been developed which can be classified into model-based or data-driven techniques. Among these approaches, partial least squares (PLS) is one of the most popular data-driven methods due to its simplicity and easy implementation in large-scale industrial process. As PLS is totally based on the measured process data, the characteristics of the process data are critical for the success of PLS. Outliers and missing values are two common characteristics of the measured data which can severely affect the effectiveness of PLS. To ensure the applicability of PLS in practical industrial applications, this paper introduces a robust version of PLS to deal with outliers and missing values, simultaneously. The effectiveness of the proposed method is finally demonst...
145 citations
TL;DR: It is shown that the desired reduced-order models can be obtained by solving a set of strict linear matrix inequalities (LMIs) or a sequential minimisation problem subject to LMI constraints, which are numerically efficient with commercially available software.
Abstract: This paper investigates the problem of model reduction for a class of continuous-time Markovian jump linear systems with incomplete statistics of mode information, which simultaneously considers the exactly known, partially unknown and uncertain transition rates. By fully utilising the properties of transition rate matrices, together with the convexification of uncertain domains, a new sufficient condition for performance analysis is first derived, and then two approaches, namely, the convex linearisation approach and the iterative approach, are developed to solve the model reduction problem. It is shown that the desired reduced-order models can be obtained by solving a set of strict linear matrix inequalities (LMIs) or a sequential minimisation problem subject to LMI constraints, which are numerically efficient with commercially available software. Finally, an illustrative example is given to show the effectiveness of the proposed design methods.
121 citations
TL;DR: An efficient and comprehensive risk assessment methodology using intuitionistic fuzzy hybrid weighted Euclidean distance (IFHWED) operator to overcome the limitations and improve the effectiveness of the traditional FMEA is developed.
Abstract: Failure mode and effects analysis (FMEA) has shown its effectiveness in examining potential failures in products, process, designs or services and has been extensively used for safety and reliability analysis in a wide range of industries. However, its approach to prioritise failure modes through a crisp risk priority number (RPN) has been criticised as having several shortcomings. The aim of this paper is to develop an efficient and comprehensive risk assessment methodology using intuitionistic fuzzy hybrid weighted Euclidean distance (IFHWED) operator to overcome the limitations and improve the effectiveness of the traditional FMEA. The diversified and uncertain assessments given by FMEA team members are treated as linguistic terms expressed in intuitionistic fuzzy numbers (IFNs). Intuitionistic fuzzy weighted averaging (IFWA) operator is used to aggregate the FMEA team members’ individual assessments into a group assessment. IFHWED operator is applied thereafter to the prioritisation and selection of f...
116 citations
TL;DR: In this article, iterative linear matrix inequality algorithms with initial optimisation are developed to solve the state feedback H ∞ suboptimal control problem for fractional-order systems.
Abstract: This article focuses on the state feedback H∞ control problem for commensurate fractional-order systems with a prescribed H∞ performance. For linear time-invariant fractional-order systems, a sufficient condition to guarantee stability with H∞ performance is firstly presented. Then, by introducing a new flexible real matrix variable, the feedback gain is decoupled with complex matrix variables and further parametrised by the new flexible matrix. Moreover, iterative linear matrix inequality algorithms with initial optimisation are developed to solve the state feedback H∞ suboptimal control problem for fractional-order systems. Finally, illustrative examples are given to show the effectiveness of the proposed approaches.
90 citations
TL;DR: Two distributed control protocols are proposed under fixed undirected communication topology and fixed directed communicationTopology for leader-following consensus problem for second-order multi-agent systems with nonlinear inherent dynamics.
Abstract: In this paper, the leader-following consensus problem for second-order multi-agent systems with nonlinear inherent dynamics is investigated. Two distributed control protocols are proposed under fixed undirected communication topology and fixed directed communication topology. Some sufficient conditions are obtained for the states of followers converging to the state of virtual leader globally exponentially. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Simulations are also given to verify the effectiveness of the theoretical results.
87 citations
TL;DR: The JSMAA software as mentioned in this paper is an open source and divided in separate graphical user interface and library components, enabling its use in systems with a model generation subsystem, such as SMAA-2, SMAA O and SMAA TRI.
Abstract: Most software for multi-criteria decision analysis MCDA implement a small set of compatible methods as a closed monolithic program. With such software tools, the decision models have to be input by hand. In some applications, however, the model can be generated using external information sources, and thus it would be beneficial if the MCDA software could integrate in the comprehensive information infrastructure. This article motivates for the need of model generation in the methodological context of stochastic multicriteria acceptability analysis SMAA, and describes the JSMAA software that implements SMAA-2, SMAA-O and SMAA-TRI methods. JSMAA is an open source and divided in separate graphical user interface and library components, enabling its use in systems with a model generation subsystem.
70 citations
TL;DR: A new approach based on direct search and features ranking technology is proposed to optimise features selection and parameter setting for 1-norm and least-squares SVM models for bankruptcy prediction.
Abstract: Due to the economic significance of bankruptcy prediction of companies for financial institutions, investors and governments, many quantitative methods have been used to develop effective prediction models. Support vector machine SVM, a powerful classification method, has been used for this task; however, the performance of SVM is sensitive to model form, parameter setting and features selection. In this study, a new approach based on direct search and features ranking technology is proposed to optimise features selection and parameter setting for 1-norm and least-squares SVM models for bankruptcy prediction. This approach is also compared to the SVM models with parameter optimisation and features selection by the popular genetic algorithm technique. The experimental results on a data set with 2010 instances show that the proposed models are good alternatives for bankruptcy prediction.
69 citations
TL;DR: Fuzzy programming technique and a gradient based optimisation - generalised reduced gradient method are applied to beget the optimal solutions of multi-objective solid transportation problems (MOSTP) under various uncertain environments.
Abstract: This paper investigates multi-objective solid transportation problems (MOSTP) under various uncertain environments. The unit transportation penalties/costs are taken as random, fuzzy and hybrid variables respectively, in three different uncertain multi-objective solid transportation models and in each case, the supplies, demands and conveyance capacities are fuzzy. Also, apart from source, demand and capacity constraints, an extra constraint on the total budget at each destination is imposed. Chance-constrained programming technique has been used for the first two models to obtain crisp equivalent forms, whereas expected value model is formulated for the last. We provide an another approach using the interval approximation of fuzzy numbers for the first model to obtain its crisp form and compare numerically two approaches for this model. Fuzzy programming technique and a gradient based optimisation - generalised reduced gradient (GRG) method are applied to beget the optimal solutions. Three numerical exam...
68 citations
TL;DR: This paper focuses on modelling the network flow equilibrium problem on a multimodal transport network with bus-based park-and-ride (P&R) system and congestion pricing charges, and proposes a fixed-point model with unique solution for the equilibrium flows.
Abstract: This paper focuses on modelling the network flow equilibrium problem on a multimodal transport network with bus-based park-and-ride P&R system and congestion pricing charges. The multimodal network has three travel modes: auto mode, transit mode and P&R mode. A continuously distributed value-of-time is assumed to convert toll charges and transit fares to time unit, and the users’ route choice behaviour is assumed to follow the probit-based stochastic user equilibrium principle with elastic demand. These two assumptions have caused randomness to the users’ generalised travel times on the multimodal network. A comprehensive network framework is first defined for the flow equilibrium problem with consideration of interactions between auto flows and transit bus flows. Then, a fixed-point model with unique solution is proposed for the equilibrium flows, which can be solved by a convergent cost averaging method. Finally, the proposed methodology is tested by a network example.
66 citations
TL;DR: An actuator fault estimation approach for a class of nonlinear descriptor systems is proposed and the design of the proposed observer is reformulated as a set of linear matrix inequalities (LMIs), which can be conveniently solved by standard LMI tools.
Abstract: This article proposes an actuator fault estimation approach for a class of nonlinear descriptor systems. The radial basis function RBF neural networks are utilised to model the actuator faults. The adaptive fault estimation observer is designed by exploiting the on-line learning ability of RBF neural networks to approximate the actuator fault. The adaptive algorithm of the RBF networks is established by the Lyapunov theory, and the design of the proposed observer is reformulated as a set of linear matrix inequalities LMIs, which can be conveniently solved by standard LMI tools. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed fault diagnosis method.
61 citations
TL;DR: The specific problem of falls of old adults is addressed by devising a technological solution for monitoring these users by combining video cameras, accelerometers and GPS sensors in a multi-modal approach to monitor humans inside and outside the domestic environment.
Abstract: The society is changing towards a new paradigm in which an increasing number of old adults live alone. In parallel, the incidence of conditions that affect mobility and independence is also rising as a consequence of a longer life expectancy. In this paper, the specific problem of falls of old adults is addressed by devising a technological solution for monitoring these users. Video cameras, accelerometers and GPS sensors are combined in a multi-modal approach to monitor humans inside and outside the domestic environment. Machine learning techniques are used to detect falls and classify activities from accelerometer data. Video feeds and GPS are used to provide location inside and outside the domestic environment. It results in a monitoring solution that does not imply the confinement of the users to a closed environment.
TL;DR: A unified approximate method is derived for general fractional order linear or nonlinear dynamic systems via combining the proposed new method with the distributed frequency model approach.
Abstract: Approximations for general fractional order dynamic systems are of much theoretical and practical interest. In this paper, a new approximate method for fractional order integrator is proposed. The poles of the approximate model are unrelated to the order of integrator. This feature shows benefits on extending the algorithm to the systems containing various fractional orders. Then a unified approximate method is derived for general fractional order linear or nonlinear dynamic systems via combining the proposed new method with the distributed frequency model approach. Numerical examples are given to show the wide applicability of our method and to illustrate the acceptable accuracy for approximations as well.
TL;DR: This paper addresses the robust H∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs) by utilising Takagi–Sugeno (T–S) fuzzy set approach and develops a fuzzy model, which can approach theNon-linear dynamics of FAHVs more exactly.
Abstract: By utilising Takagi–Sugeno (T–S) fuzzy set approach, this paper addresses the robust H∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics’ enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T–S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is desi...
TL;DR: In this paper, the issue of H∞ iterative learning controller design is considered for a class of discrete-time systems with data dropouts and a sufficient condition guaranteeing both stability of the ILC process and the desired H ∞ performance in the iteration domain is presented.
Abstract: In this paper, the issue of H∞ iterative learning controller design is considered for a class of discrete-time systems with data dropouts. With the super-vector formulation of iterative learning control (ILC), such a system can be formulated as a linear discrete-time stochastic system in the iteration domain, and then a sufficient condition guaranteeing both stability of the ILC process and the desired H∞ performance in the iteration domain is presented. The condition can be derived in terms of linear matrix inequalities that can be solved by using existing numerical techniques. A numerical simulation example is also included to validate the theoretical results.
TL;DR: This article first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities, and applies the homogeneous domination approach to design a scaled homogeneous observer and controller.
Abstract: This article addresses the problem of global finite-time output feedback stabilisation for a class of nonlinear systems in nontriangular form with an unknown output function. Since the output function is not precisely known, traditional observers based on the output is not implementable. We first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities. Then, we apply the homogeneous domination approach to design a scaled homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally finite-time stable.
TL;DR: Using the graph theory, Lyapunov theory and the homogeneous domination method, some sufficient conditions for finite-time consensus of second-order multi-agent systems are established under the different kinds of communication topologies.
Abstract: This article considers the finite-time consensus of multiple second-order dynamic agents without velocity measurements. A feasible protocol under which each agent can only obtain the measurements of its position relative to its neighbours is proposed. By applying the graph theory, Lyapunov theory and the homogeneous domination method, some sufficient conditions for finite-time consensus of second-order multi-agent systems are established under the different kinds of communication topologies. Some examples are presented to illustrate the effectiveness of the theoretical results.
TL;DR: The comparison between the convergence rate of second-order neighbour protocol and the one of general protocol is developed and when multi-agent system achieves maximum speed consensus, the relation between the parameter in general protocol and that in second- order neighbour protocol is analysed.
Abstract: This paper mainly investigates the consensus of second-order multi-agent systems by using the second-order neighbours’ information. The comparison between the convergence rate of second-order neighbour protocol and the one of general protocol is developed. When multi-agent system achieves maximum speed consensus, the relation between the parameter in general protocol and that in second-order neighbour protocol is analysed. If there exists delay in communication, the delay margins of general protocol and second-order neighbour protocol are derived. Numerical examples are given to illustrate the effectiveness of the proposed methods.
TL;DR: The Takagi–Sugeno fuzzy model approach is extended to the stability analysis and controller design for interval type-2 (IT2) fuzzy systems with time-varying delay to show the merits of the proposed method and illustrate the design processes of IT2 fuzzy controller for a nonlinear system with parameter uncertainties.
Abstract: The type-2 fuzzy models can handle the system uncertainties directly based on the type-2 fuzzy sets. In this paper, the Takagi–Sugeno fuzzy model approach is extended to the stability analysis and controller design for interval type-2 IT2 fuzzy systems with time-varying delay. Delay-dependent robust stability criteria are developed in terms of linear matrix inequalities by using the improvement technique of free-weighting matrices. Less conservative results are obtained by considering the information contained in the footprint of uncertainty. Finally, two simulation examples are presented to illustrate the effectiveness of the theoretical results. One is provided to show the merits of the proposed method, the other based on the continuous stirred tank reactor model is given to illustrate the design processes of IT2 fuzzy controller for a nonlinear system with parameter uncertainties.
TL;DR: A robust adaptive integrated finite-time control scheme is proposed to enable the spacecraft track command position and attitude in a pre-determined time, despite of external disturbance, unknown mass property and thruster misalignment.
Abstract: This paper tackles the problem of integrated translation and rotation finite-time control of a rigid spacecraft with actuator misalignment and unknown mass property. Due to the system natural couplings, the coupled translational and rotational dynamics of the spacecraft is developed, where a thruster configuration with installation misalignment and unknown mass property are taken into account. By solving an equivalent designated trajectory tracking problem via backstepping philosophy, a robust adaptive integrated finite-time control scheme is proposed to enable the spacecraft track command position and attitude in a pre-determined time, despite of external disturbance, unknown mass property and thruster misalignment. The finite-time closed-loop stability is guaranteed within the Lyapunov framework. Two scenario numerical simulations demonstrate the effect of the designed controller.
TL;DR: The acceptance of m-commerce is influenced by factors including performance expectancy, social influence, facilitating conditions and privacy concern; while effort expectancy is insignificant in this case.
Abstract: This study aims to examine the positive and negative factors that can significantly explain user acceptance of mobile commerce m-commerce in Macau. A technology acceptance model for m-commerce with five factors is constructed. The proposed model is tested using data collected from 219 respondents. Confirmatory factor analysis is performed to examine the reliability and validity of the model, and structural equation modelling is performed to access the relationship between behaviour intention and each factor. The acceptance of m-commerce is influenced by factors including performance expectancy, social influence, facilitating conditions and privacy concern; while effort expectancy is insignificant in this case. The results of the study are useful for m-commerce service providers to adjust their strategies for promoting m-commerce services. This study contributes to the practice by providing a user technology acceptance model for m-commerce that can be used as a foundation for future research.
TL;DR: An enhanced prediction accuracy of diagnosis of Parkinson's disease (PD) is presented to prevent the delay and misdiagnosis of patients using the proposed robust inference system and experimentally shows best results with supportive statistical inference.
Abstract: This article presents an enhanced prediction accuracy of diagnosis of Parkinson's disease PD to prevent the delay and misdiagnosis of patients using the proposed robust inference system. New machine-learning methods are proposed and performance comparisons are based on specificity, sensitivity, accuracy and other measurable parameters. The robust methods of treating Parkinson's disease PD includes sparse multinomial logistic regression, rotation forest ensemble with support vector machines and principal components analysis, artificial neural networks, boosting methods. A new ensemble method comprising of the Bayesian network optimised by Tabu search algorithm as classifier and Haar wavelets as projection filter is used for relevant feature selection and ranking. The highest accuracy obtained by linear logistic regression and sparse multinomial logistic regression is 100% and sensitivity, specificity of 0.983 and 0.996, respectively. All the experiments are conducted over 95% and 99% confidence levels and establish the results with corrected t-tests. This work shows a high degree of advancement in software reliability and quality of the computer-aided diagnosis system and experimentally shows best results with supportive statistical inference.
TL;DR: Using a multiple linear copositive Lyapunov function, and by using the average dwell time approach, some sufficient stability criteria of global uniform exponential stability are established in both the continuous-time and the discrete-time cases, respectively.
Abstract: This paper addresses the stability problem of switched positive linear systems with stable and unstable subsystems. Based on a multiple linear copositive Lyapunov function, and by using the average dwell time approach, some sufficient stability criteria of global uniform exponential stability are established in both the continuous-time and the discrete-time cases, respectively. Finally, some numerical examples are given to show the effectiveness of the proposed results.
TL;DR: This paper addresses the optimal least-squares linear estimation problem for a class of discrete-time stochastic systems with random parameter matrices and correlated additive noises and proposes a recursive algorithm with a simple computational procedure derived for the optimal linear filter.
Abstract: This paper addresses the optimal least-squares linear estimation problem for a class of discrete-time stochastic systems with random parameter matrices and correlated additive noises. The system presents the following main features: (1) one-step correlated and cross-correlated random parameter matrices in the observation equation are assumed; (2) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. Using an innovation approach and these correlation assumptions, a recursive algorithm with a simple computational procedure is derived for the optimal linear filter. As a significant application of the proposed results, the optimal recursive filtering problem in multi-sensor systems with missing measurements and random delays can be addressed. Numerical simulation examples are used to demonstrate the feasibility of the proposed filtering algorithm, which is also compared with other filters that have been proposed.
TL;DR: The issue of exponential stability of a class of continuous-time switched nonlinear singular systems consisting of a family of stable and unstable subsystems with time-varying delay, and the average dwell-time and switching signal conditions are considered.
Abstract: The issue of exponential stability of a class of continuous-time switched nonlinear singular systems consisting of a family of stable and unstable subsystems with time-varying delay is considered in this paper. Based on the free-weighting matrix approach, the average dwell-time approach and by constructing a Lyapunov-like Krasovskii functional, delay-dependent sufficient conditions are derived and formulated to check the exponential stability of such systems in terms of linear matrix inequalities LMIs. By checking the corresponding LMI conditions, the average dwell-time and switching signal conditions are obtained. This paper also highlights the relationship between the average dwell-time of the switched nonlinear singular time-delay system, its stability and the exponential convergence rate of differential and algebraic states. A numerical example shows the effectiveness of the proposed method.
TL;DR: The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighbourhood of the desired reference signal in the sense of mean quartic value.
Abstract: This paper is concerned with the problem of adaptive fuzzy output tracking control for a class of nonlinear pure-feedback stochastic systems with unknown dead-zone. Fuzzy logic systems in Mamdani type are used to approximate the unknown nonlinearities, then a novel adaptive fuzzy tracking controller is designed by using backstepping technique. The control scheme is systematically derived without requiring any information on the boundedness of dead-zone parameters (slopes and break-points) and the repeated differentiation of the virtual control signals. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighbourhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.
TL;DR: A new position synchronised control algorithm is developed for multiple robotic manipulator systems that can stabilise position tracking of each robotic manipulators while coordinating its motion with the other manipulators.
Abstract: In this study, a new position synchronised control algorithm is developed for multiple robotic manipulator systems. In the merit of system synchronisation and integral sliding mode control, the proposed approach can stabilise position tracking of each robotic manipulator while coordinating its motion with the other manipulators. With the integral sliding mode, the proposed approach has insensitiveness against the lumped system uncertainty within the entire process of operation. Further, a perturbation estimator is proposed to reduce chattering effect. The corresponding stability analysis is presented to lay a foundation for theoretical understanding to the underlying issues as well as safely operating real systems. An illustrative example is bench tested to validate the effectiveness of the proposed approach.
TL;DR: A multi-objective optimisation model based on disaster scenario information updates is proposed in an attempt to coordinate efficiency and equity through timely and appropriate decisions regarding issues such as vehicle routing and relief allocation.
Abstract: This paper addresses a multi-supplier, multi-affected area, multi-relief, and multi-vehicle relief allocation problem in disaster relief logistics. A multi-objective optimisation model based on disaster scenario information updates is proposed in an attempt to coordinate efficiency and equity through timely and appropriate decisions regarding issues such as vehicle routing and relief allocation. An optimal stopping rule is also proposed to determine the optimum period of delay before responding to disaster, because decision making requires accurate disaster information. The main contribution of this paper is solving relief allocation problem in a novel way by correlating operational research with statistical decision making and Bayesian sequential analysis. Finally, a case is presented based on the post-disaster rescue in Eastern China after supertyphoon Saomai to test the applicability and show the potential advantages of the proposed model.
TL;DR: Consensus conditions which contain the feedback gain conditions and delay conditions are proposed for systems over fixed and switching topologies, respectively and allowable delay bounds are obtained for both systems by solving the optimal robust stabilisation problems.
Abstract: This paper studies the consensus of a group of linear dynamic agents with a uniform communication delay and focuses on searching an allowable delay bound. As long as the delay is less than this bound, there exist linear feedback consensus protocols driving the multi-agent system to achieve consensus. Both fixed and switching topology cases are investigated. In both cases, the consensus problem is converted to the robust stability problem of corresponding uncertain state-delayed systems. By using Lyapunov–Krasovskii functional analysis, consensus conditions which contain the feedback gain conditions and delay conditions are proposed for systems over fixed and switching topologies, respectively. Furthermore, allowable delay bounds are obtained for both systems by solving the optimal robust stabilisation problems. Numerical examples are given to illustrate the results.
TL;DR: The results demonstrate that the IOLPSOA-based protocol outperforms the other three protocols, which can efficiently repair the routing topology changed by the sink movement, reduce the communication overhead and prolong the lifetime of WSNs with mobile sink.
Abstract: The growth of mobile handheld devices promotes sink mobility in an increasing number of wireless sensor networks WSNs applications. The movement of the sink may lead to the breakage of existing routes of WSNs, thus the routing recovery problem is a critical challenge. In order to maintain the available route from each source node to the sink, we propose an immune orthogonal learning particle swarm optimisation algorithm IOLPSOA to provide fast routing recovery from path failure due to the sink movement, and construct the efficient alternative path to repair the route. Due to its efficient bio-heuristic routing recovery mechanism in the algorithm, the orthogonal learning strategy can guide particles to fly on better directions by constructing a much promising and efficient exemplar, and the immune mechanism can maintain the diversity of the particles. We discuss the implementation of the IOLPSOA-based routing protocol and present the performance evaluation through several simulation experiments. The results demonstrate that the IOLPSOA-based protocol outperforms the other three protocols, which can efficiently repair the routing topology changed by the sink movement, reduce the communication overhead and prolong the lifetime of WSNs with mobile sink.
TL;DR: The main purpose of this paper is to investigate the optimal replenishment lot size of supplier and optimal production rate of manufacturer under three levels of trade credit policy for supplier–manufacturer–retailer supply chain.
Abstract: The main purpose of this paper is to investigate the optimal replenishment lot size of supplier and optimal production rate of manufacturer under three levels of trade credit policy for supplier–manufacturer–retailer supply chain. The supplier provides a fixed credit period to settle the accounts to the manufacturer, while the manufacturer gives a fixed credit period to settle the account to the retailer and the retailer, in turn, also offers a credit period to each of its customers to settle the accounts. We assume that the supplier supplies the raw material to the manufacturer and sends back the defective raw materials to the outside supplier after completion of inspection at one lot with a sales price. The system always produces good items in the model. Also, we consider the idle times of supplier and manufacturer. Finally, numerical examples are provided to illustrate the behaviour and application of the model with graphical simulation.