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Highlights • A dynamic equilibrium model is constructed for the closed-loop supply chain network. • The demands and returns are uncertain and time-dependent. • Dynamic equilibrium condition is constructed by evolutionary variational inequality. • The equilibrium decisions are strongly affected by the time-dependent demands. Abstract In this paper, we develop a dynamic equilibrium model of oligopolistic closed-loop supply chain network to account for the seasonality of demand. In this model, demands and returns are uncertain and time-dependent. The dynamic Cournot-Nash equilibrium of the oligopolistic network is constructed by evolutionary variational inequality and projected dynamical systems. The existence and monotonicity results are established and a computational method is developed for finding the dynamic Cournot-Nash equilibrium. Numerical examples are solved to illustrate the performance of our model. The results show that the firms' optimal production and transaction quantities are strongly affected by the time-dependent demands. [ABSTRACT FROM AUTHOR]

Highlights • This paper constructs an equilibrium model of a multi-period supply chain network. • This paper incorporates retailers' dynamic loss-averse behaviors into the model. • This paper studies the effect of dynamic loss-averse behaviors on the decisions. • The decisions include production quantities, transaction quantities, and prices. Abstract This study constructs an equilibrium model of a multi-period supply chain network with uncertain demand. In the multi-period equilibrium model, we consider not only retailers' static loss-averse behaviors, but also their dynamic loss-averse behaviors, in which retailers dynamically adjust their loss-averse parameters according to their gains or losses over the production periods. The equilibrium conditions of the various decision makers and the network are established by the finite-dimensional variational inequality. Finally, numerical examples are solved to show how retailers' loss-averse behaviors would affect decisions, profits of manufacturers and utilities of retailers at equilibrium when compared with their loss-neutral behaviors. [ABSTRACT FROM AUTHOR]

This paper considers a production model involving a manufacturer that uses two different technologies, the green technology and the standard technology. The green product produced by the green technology can be used as a substitute for the traditional product produced by the standard technology, but not vice versa. Three models are considered. The first model concerns with product substitution only and serves as a benchmark model for the next two models, the carbon emission allowance model and the carbon emission trading model. The second model extends the product substitution model by imposing an upper limit on the total carbon emission allowance for each firm. The third model extends the second model to cater for carbon emission trading. For the carbon emission allowance model, analytical result shows that the optimal production quantity of any product depends on both its total carbon emission allowance quota and its unit carbon emission profit, and the effect of substitution improves the service level, the expected profit of the manufacturer, and the green of product mix. For the carbon emission trading model, analytical result shows that whenever the production quantity of any product is optimal, the marginal profit of production (i.e. the additional profit obtained by producing an extra item) should be equal to the unit price of carbon emission trading within the market. Moreover, the optimal policy of either model reduces the total amount of carbon emission, thus producing less pollution to the environment. Lastly, the optimal profits obtained by using the carbon emission trading model are larger than the corresponding optimal profits obtained by using the carbon emission allowance model. [ABSTRACT FROM AUTHOR]

This paper develops an integrated single-vendor multi-buyer inventory-transportation synchronized supply chain model. In this paper, the decisions of truck assignment and routing are also considered and as a result, a series of vehicle routing problems (VRP) are required to be solved. Due to the highly complicated objective function and the NP -hard VRP problems, the problem cannot be solved analytically. Hence, meta-heuristics are proposed. By means of the numerical examples and a case study, the meta-heuristics developed are shown to be very effective in solving such comprehensive supply chain models, and the results so obtained are promising. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this article is first to introduce the concept of total quasi-ϕ-asymptotically nonexpansive semigroups which contains many kinds of semi-groups as its special cases, and then to modify the Halpern–Mann-type iteration algorithm for this kind of semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding recent results announced by many authors. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to propose a modified block iterative algorithm for find a common element of the set of common fixed points of an infinite family of quasi-ϕ-asymptotically nonexpansive mappings and the set of an equilibrium problem. Under suitable conditions, some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with the Kadec–Klee property. As an application, at the end of the paper a numerical example is given. The results presented in the paper improve and extend the corresponding results in Qin et al. [Convergence theorems of common elements for equilibrium problems and fixed point problem in Banach spaces, J. Comput. Appl. Math., 225, 2009, 20–30], Zhou et al. [Convergence theorems of a modified hybrid algorithm for a family of quasi-ϕ-asymptotically nonexpansive mappings, J. Appl. Math. Compt., 17 March, 2009, doi:10.1007/s12190-009-0263-4], Takahashi and Zembayshi [Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal., 70, 2009, 45–57], Wattanawitoon and Kumam [Strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Anal. Hybrid Syst., 3, 2009, 11–20] and Matsushita and Takahashi [A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theory, 134, 2005, 257–266] and others. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for an infinite family of strictly pseudo-contractive mappings and the set of common fixed points for nonexpansive semi-groups in Hilbert space. Under suitable conditions some strong convergence theorem are proved. The results presented in the paper extend and improve some recent results. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence of an optimal control problem for a quasi-linear elliptic obstacle variational inequality in which the obstacle is taken as the control. Firstly, we get some existence results under the assumption of the leading operator of the variational inequality with a monotone type mapping in Section . In Section , as an application, without the assumption of the monotone type mapping for the leading operator of the variational inequality, we prove that the leading operator of the variational inequality is a monotone type mapping. Existence of the optimal obstacle is proved. The method used here is different from [Y.Y. Zhou, X.Q. Yang, K.L. Teo, The existence results for optimal control problems governed by a variational inequality, J. Math. Anal. Appl. 321 (2006) 595–608]. [Copyright &y& Elsevier]

Abstract: This paper is concerned with an obstacle optimal control problem for a quasilinear elliptic variational inequality with a source term. The pth power of Laplacian of the obstacle appears in the cost functional. This feature leads that it is hard to derive the optimality system for the underlying problem. The existence for the optimal control is proved and we also show how to obtain optimality system using a passage to the limit in the approximation process. [Copyright &y& Elsevier]

Abstract: In this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality with a source term and the control functions are the upper and the lower obstacles. We assume that the obstacles and are in , but this causes difficulty for deriving the optimality condition. By applying the weak convergence method, we establish existence and incomplete necessary conditions for the optimal control. [Copyright &y& Elsevier]

Abstract: This paper proposes a coordinated single-vendor multi-buyer supply chain model by synchronizing delivery and production cycles. The synchronization is achieved by scheduling the actual delivery days of the buyers and coordinating them with the vendor’s production cycle whilst allowing the buyers to choose their own lot sizes and order cycles. A mathematical model for our proposed coordination is developed and analyzed. The results of our three numerical examples show that the synchronized cycles policy works better than independent optimization as well as restricting buyers to adopt a common order cycle. [Copyright &y& Elsevier]

The joint replenishment problem (JRP) is a multi-item inventory problem. The objective is to develop inventory policies that minimize the total costs (comprised of holding cost and setup cost) over the planning horizon. In this paper, we look at the multi-buyer, multi-item version of the JRP. We propose a new modified genetic algorithm which is very efficient. Tests are conducted on problems from a leading bank in Hong Kong and from the literature. [Copyright &y& Elsevier]

Abstract: The purpose of this article is to modify the Halpern-type iteration algorithm for total quasi-ϕ-asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results of [X.L. Qin, Y.J. Cho, S.M. Kang, H. Y. Zhou, Convergence of a modified Halpern-type iterative algorithm for quasi-ϕ-nonexpansive mappings, Appl. Math. Lett. 22 (2009) 1051–1055], [Z.M. Wang, Y.F. Su, D.X. Wang, Y.C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011) 2364–2371], [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890–3906], [C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400–2411] and others. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is by using the hybrid iterative method to prove some strong convergence theorems for approximating a common element of the set of solutions to a system of generalized mixed equilibrium problems and the set of common fixed points for two countable families of closed and asymptotically relatively nonexpansive mappings in Banach space. The results presented in the paper improve and extend the corresponding results of Su et al. [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890–3906], Li and Su [H.Y. Li, Y.F. Su, Strong convergence theorems by a new hybrid for equilibrium problems and variational inequality problems, Nonlinear Anal. 72 (2) (2010) 847–855], Chang et al. [S.S. Chang, H.W. Joseph Lee, Chi Kin Chan, A new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in Banach spaces with applications, Nonlinear Anal. TMA 73 (2010) 2260–2270], Kang et al. [J. Kang, Y. Su, X. Zhang, Hybrid algorithm for fixed points of weak relatively nonexpansive mappings and applications, Nonlinear Anal. HS 4 (4) (2010) 755–765], Matsushita and Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theory 134 (2005) 257–266], Tan et al. [J.F. Tan, S.S. Chang, M. Liu, J.I. Liu, Strong convergence theorems of a hybrid projection algorithm for a family of quasi-ϕ-asymptotically nonexpansive mappings, Opuscula Math. 30 (3) (2010) 341–348], Takahashia and Zembayashi [W. Takahashi, K. Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal. 70 (2009) 45–57] and Wattanawitoon and Kumam [K. Wattanawitoon, P. Kumam, Strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Anal. Hybrid Systems 3 (2009) 11–20] and others. [Copyright &y& Elsevier]

Abstract: The purpose of this article is to prove some approximation theorems of common fixed points for countable families of total quasi-ϕ-asymptotically nonexpansive mappings which contain several kinds of mappings as its special cases in Banach spaces. In order to get the approximation theorems, the hybrid algorithms are presented and are used to approximate the common fixed points. Using this result, we also discuss the problem of strong convergence concerning the maximal monotone operators in a Banach space. The results of this article extend and improve the results of Matsushita and Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theor. 134 (2005) 257–266], Plubtieng and Ungchittrakool [S. Plubtieng, K. Ungchittrakool, Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in Banach spaces, J. Approx. Theor. 149 (2007) 103–115], Li, Su [H. Y. Li, Y. F. Su, Strong convergence theorems by a new hybrid for equilibrium problems and variational inequality problems, Nonlinear Anal. 72(2) (2010) 847-855], Su, Xu and Zhang [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890–3960], Wang et al. [Z.M. Wang, Y.F. Su, D.X. Wang, Y.C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011) 2364–2371], Chang et al. [S.S. Chang, H.W. Joseph Lee, Chi Kin Chan, A new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in Banach spaces with applications, Nonlinear Anal. 73 (2010) 2260–2270], Chang et al. [S.S. Chang, C.K. Chan, H.W. Joseph Lee, Modified block iterative algorithm for quasi-ϕ-asymptotically nonexpansive mappings and equilibrium problem in Banach spaces, Appl. Math. Comput. 217 (2011) 7520–7530], Ofoedu and Malonza [E.U. Ofoedu, D.M. Malonza, Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type, Appl. Math. Comput. 217 (2011) 6019–6030] and Yao et al. [Y.H. Yao, Y.C. Liou, S.M. Kang, Strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings, Appl. Math. Comput. 208 (2009) 211–218]. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is by using the generalized projection approach to introduce an iterative scheme for finding a solution to a system of generalized nonlinear variational inequality problem. Under suitable conditions, some existence and strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces. The results presented in the paper improve and extend some recent results. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to prove by using a new hybrid method a strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem, the set of solutions for a variational inequality problem and the set of common fixed points for a pair of relatively nonexpansive mappings in a Banach space. As applications, we utilize our results to obtain some new results for finding a solution of an equilibrium problem, a fixed point problem and a common zero-point problem for maximal monotone mappings in Banach spaces. [Copyright &y& Elsevier]

Abstract: By using viscosity approximation methods for asymptotically nonexpansive mappings in Banach spaces, some sufficient and necessary conditions for a new type of iterative sequences to converging to a fixed point which is also the unique solution of some variational inequalities are obtained. The results presented in the paper extend and improve some recent results in [C.E. Chidume, Jinlu Li, A. Udomene, Convergence of paths and approximation of fixed points of asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 138 (2) (2005) 473–480; N. Shahzad, A. Udomene, Fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in Banach spaces, Nonlinear Anal. 64 (2006) 558–567; T.C. Lim, H.K. Xu, Fixed point theories for asymptotically nonexpansive mappings, Nonlinear Anal. TMA, 22 (1994) 1345–1355; H.K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004) 279-291]. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to study the convergence problems of the implicity iteration process for an asymptotically nonexpansive semigroups in general Banach spaces. The results presented in this paper extend and improve the corresponding results announced by many authors. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for -inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. As applications, at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings. The results presented in the paper extend and improve some recent results of Yao and Yao [Y.Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput. 186 (2) (2007) 1551–1558], Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonlinear mappings and monotone mappings, Appl. Math. Comput. (2007) doi:10.1016/j.amc.2007.07.075], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for Equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2006) 506–515], Su, Shang and Qin [Y.F. Su, M.J. Shang, X.L. Qin, An iterative method of solution for equilibrium and optimization problems, Nonlinear Anal. (2007) doi:10.1016/j.na.2007.08.045] and Chang, Cho and Kim [S.S. Chang, Y.J. Cho, J.K. Kim, Approximation methods of solutions for equilibrium problem in Hilbert spaces, Dynam. Systems Appl. (in print)]. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to study Reich’s strongly convergence theorems for asymptotically nonexpansive mappings in Banach spaces. Under some general conditions an affirmative partial answer to Reich’s open question is given and some recent results are improved and generalized. [Copyright &y& Elsevier]

Nowadays, intensified globalization and consequent competitive pressures have reemphasized the importance of third party logistics (3PL) in managing logistics processes as well as customer and supplier relationships within the supply chain management (SCM). However, 3PL providers and their upstream and downstream parties within the whole chain have usually interacted as disconnected entities in the logistics performance management process. Despite the increased interest in using and improving logistics information systems, the number of researchers investigating the design and implementation of this process in close detail is still very small. This paper proposes an intelligent performance measurement system (K-LPMS) for measuring the performance of 3PL providers and their upstream and downstream supply chain partners. With the help of K-LPMS, 3PL providers are capable to fulfil different customer’s supply chain service requirement through accessing the capability of each SC partners and reconfigure SC network. This paper describes the structure of K-LPMS and its features. The results of testing and applying the tool in companies are presented. This paper concludes by discussing the implications of this research for managers, and identifying directions for future research. [Copyright &y& Elsevier]

Abstract: Background: Patient falls have been identified as a significant health problem in the general hospital patient population. The Morse Fall Scale (MFS) is an individualized criterion-referenced assessment tool designed for measuring the likelihood of patient falls in hospitals. Despite the scale has demonstrated high validity and reliability in the previous researches, this study is to provide additional validity tests to determine the applicability in the Chinese hospital population. Objectives: To examine the predictive power of the MFS to predict patient falls. To conduct reliability tests on internal consistency, item analysis, inter-rater and test–retest reliability. Design: The study was a cross-sectional study. Settings: The medical and geriatric units of three rehabilitation hospitals in Hong Kong participated in the study. Participants: A convenience sample of 954 Chinese patients was recruited sequentially upon admission in the hospital ward units. They ranged in age from 17 to 100 years, with a mean of 70.2 years. Methods: The patients were assessed for fall risk using the MFS on admission. Data was collected on the number of patients who fell rather than the number of falls. Results: The scale had a sensitivity of 31% and a specificity of 83% when the cut-off point was determined at 45. The field test demonstrated excellent inter-rater reliability with an ICC value of 0.97 (95%CI 0.94–0.98). Repeatability was high with an ICC of 0.98 (95% CI 0.98–0.99). The evaluation revealed a low Cronbach''s alpha coefficient and a low to moderate item-to-scale correlation. Conclusions: The evidence collected in this study has shown both the positive and negative aspects of using the MFS in assessing the fall risk of Chinese patients during rehabilitation. The discriminative validity and internal consistency reliability provide researchers and clinicians with a major step in further developing or modifying the scale. [Copyright &y& Elsevier]

Objectives: This study was designed to evaluate the role of cardiac resynchronization therapy (CRT) in heart failure (HF) patients with narrow QRS complexes (<120 ms) and echocardiographic evidence of mechanical asynchrony. Background: Cardiac resynchronization therapy is currently recommended to advanced HF patients with prolonged QRS duration. Echocardiographic assessment of systolic mechanical asynchrony has been proven useful to predict a favorable response after CRT. Methods: A total of 102 HF patients with New York Heart Association (NYHA) functional class III or IV were enrolled. Among them, 51 had wide QRS (>120 ms) and 51 had narrow QRS (<120 ms). Tissue Doppler imaging (TDI) was employed to select patients with systolic asynchrony (increased asynchrony index) in the narrow-QRS group. Clinical and echocardiographic assessments were performed at baseline and 3 months after CRT. Results: There was a significant reduction of left ventricular (LV) end-systolic volume in both narrow (122 +/- 42 cc vs. 103 +/- 47 cc, p < 0.001) and wide (148 +/- 74 cc vs. 112 +/- 64 cc, p < 0.001) QRS groups. Improvement of NYHA functional class (both p < 0.001), maximal exercise capacity (both p < 0.05), 6-min hall-walk distance (both p < 0.01), ejection fraction (both p < 0.001), and mitral regurgitation (both p < 0.005) was also observed. In both groups, the degree of baseline mechanical asynchrony determined LV reverse remodeling to a similar extent, as shown by the superimposed regression lines. Withholding CRT for 4 weeks resulted in loss of echocardiographic benefits. Conclusions: Cardiac resynchronization therapy for HF patients with narrow QRS complexes and coexisting mechanical asynchrony by TDI results in LV reverse remodeling and improvement of clinical status. The amplitude of benefit is similar to the wide-QRS group provided that similar extent of systolic asynchrony is selected. [ABSTRACT FROM AUTHOR]

Objectives: This study was designed to evaluate the role of cardiac resynchronization therapy (CRT) in heart failure (HF) patients with narrow QRS complexes (<120 ms) and echocardiographic evidence of mechanical asynchrony. Background: Cardiac resynchronization therapy is currently recommended to advanced HF patients with prolonged QRS duration. Echocardiographic assessment of systolic mechanical asynchrony has been proven useful to predict a favorable response after CRT. Methods: A total of 102 HF patients with New York Heart Association (NYHA) functional class III or IV were enrolled. Among them, 51 had wide QRS (>120 ms) and 51 had narrow QRS (<120 ms). Tissue Doppler imaging (TDI) was employed to select patients with systolic asynchrony (increased asynchrony index) in the narrow-QRS group. Clinical and echocardiographic assessments were performed at baseline and 3 months after CRT. Results: There was a significant reduction of left ventricular (LV) end-systolic volume in both narrow (122 ± 42 cc vs. 103 ± 47 cc, p < 0.001) and wide (148 ± 74 cc vs. 112 ± 64 cc, p < 0.001) QRS groups. Improvement of NYHA functional class (both p < 0.001), maximal exercise capacity (both p < 0.05), 6-min hall-walk distance (both p < 0.01), ejection fraction (both p < 0.001), and mitral regurgitation (both p < 0.005) was also observed. In both groups, the degree of baseline mechanical asynchrony determined LV reverse remodeling to a similar extent, as shown by the superimposed regression lines. Withholding CRT for 4 weeks resulted in loss of echocardiographic benefits. Conclusions: Cardiac resynchronization therapy for HF patients with narrow QRS complexes and coexisting mechanical asynchrony by TDI results in LV reverse remodeling and improvement of clinical status. The amplitude of benefit is similar to the wide-QRS group provided that similar extent of systolic asynchrony is selected. [Copyright &y& Elsevier]