This research examines how a Constrained nonlinear programming model for ERP implementation (CNL_ERP) can facilitate Small and medium sized enterprises (SMEs) to deploy resources to address the Critical Success Factor...
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This research examines how a Constrained nonlinear programming model for ERP implementation (CNL_ERP) can facilitate Small and medium sized enterprises (SMEs) to deploy resources to address the Critical Success Factors (CSFs) in the pre-implementation phase, and to invest in them during implementation to increase the probability that the implementation will be successful. Applications of CNL_ERP in three case studies demonstrate that the average ERP implementation outcomes outperform the observed results. Using the Generalised Reduced Gradient Method, we developed an ERP implementation strategy realising resource allocation to CSFs. The strategy provides a rich picture of where to concentrate effort in the initial, intermediate and final phases, and is very helpful in enabling an SME to understand the progress of an ERP project and the resources needed. In case there are changes in resources (such as budget, team performance), the model enables SMEs to rank CSFs, and to adjust resources allocations accordingly to achieve the best ERP implementation performance.
The COVID-19 pandemic has caused huge impacts to human health and world's econ-omy. Finding out the balance between social productions and pandemic control becomes crucial. In this paper, we first extend the SIR m...
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The COVID-19 pandemic has caused huge impacts to human health and world's econ-omy. Finding out the balance between social productions and pandemic control becomes crucial. In this paper, we first extend the SIR model by introducing two new status. We calibrate the model by 2022 Shanghai COVID-19 outbreak. The results shows compared to zero-constraint policy, under our control policy, 50 % more life can be saved at the cost of 2.13 % loss of consumptions. Our results also emphasize the importance of the dynamic nature and the timing of control policy, either a static pandemic control or a lagged pandemic control damages badly to people's livelihood and social productions. Counter factual experiments show that compared to the baseline, when a persistent high-strength control is applied, aggregate productions decreases by 57 %;when pandemic control ends too early, the death would rise by 15 %, when pandemic control starts too late, the death rises by 23 % and aggregate productions decreases by 13 %.
A brief history of integer and continuous nonlinear programming is presented as well as the current obstacles to practical use of these mathematical programming techniques It is forecast that the useful contributions ...
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A brief history of integer and continuous nonlinear programming is presented as well as the current obstacles to practical use of these mathematical programming techniques It is forecast that the useful contributions to nonlinear programming actualls made in the next few years are more likely to he consolidations than theoretical breakthroughs These contributions are likely to be the documentation of standard test problems, construction of user oriented software, and comparisons of currently known algorithms to demonstrate which techniques are best for specific problems. [ABSTRACT FROM AUTHOR]
A kind of generalized convex set, called as local star-shaped E-invex set with respect to., is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named...
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A kind of generalized convex set, called as local star-shaped E-invex set with respect to., is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal E-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocal E-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.
The effectiveness of four active-set logics, Kelley's dual-violator rule, Sargent's worst-violator rule, Goldfarb's rule and Das' logic has been studied for three optimization processes of Newton, quas...
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The effectiveness of four active-set logics, Kelley's dual-violator rule, Sargent's worst-violator rule, Goldfarb's rule and Das' logic has been studied for three optimization processes of Newton, quasi-Newton and steepestdcoccnt typco. The dual-violator and worot-violator rulcc attempt to chooco the active set as small as possible at some risk of infeasibility, while the other two logics drop constraints in a delicate and quite conservative manner which guarantees feasibility, to alleviate the cycling phenomenon often met with least-constrained strategies. An enumerative combinational logic, inefficient for large numbers of constraints, is also evaluated as a yardstick. In calculations for 24 quadratic test problems with linear constraints used in the present study, it is found that where relatively few constraints are active at the solution, the dual-violator and worst-violator rules performed better than or as well as the Goldfarb and Das logic, and in other cases where many constraints are active at the solution the Goldfarb and Das logics tend to perform comparatively better.
In theory, a scheduling problem can be formulated as a mathematical programming problem. In practice, dispatching rules are considered to be a more practical method of scheduling. However, the combination of mathemati...
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In theory, a scheduling problem can be formulated as a mathematical programming problem. In practice, dispatching rules are considered to be a more practical method of scheduling. However, the combination of mathematical programming and fuzzy dispatching rule has rarely been discussed in the literature. In this study, a fuzzy nonlinear programming (FNLP) approach is proposed for optimizing the scheduling performance of a four-factor fluctuation smoothing rule in a wafer fabrication factory. The proposed methodology considers the uncertainty in the remaining cycle time of a job and optimizes a fuzzy four-factor fluctuation-smoothing rule to sequence the jobs in front of each machine. The fuzzy four-factor fluctuation-smoothing rule has five adjustable parameters, the optimization of which results in an FNLP problem. The FNLP problem can be converted into an equivalent nonlinear programming (NLP) problem to be solved. The performance of the proposed methodology has been evaluated with a series of production simulation experiments;these experiments provide sufficient evidence to support the advantages of the proposed method over some existing scheduling methods.
Distributed control systems have opened avenues for incorporating steady state optimization techniques to achieve business objectives in industry. Use of nonlinear programming techniques in plant optimization has been...
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Distributed control systems have opened avenues for incorporating steady state optimization techniques to achieve business objectives in industry. Use of nonlinear programming techniques in plant optimization has been discussed. Status of nonlinear programming software and integration of various software modules for plant optimization have been included. Implementation in power and process industries have been mentioned.
One weakness of feasible decreasing direction methods for nonlinear programming is that if the current iterative point is close to the boundary of the feasible region and the search direction points toward the boundar...
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One weakness of feasible decreasing direction methods for nonlinear programming is that if the current iterative point is close to the boundary of the feasible region and the search direction points toward the boundary, then only a short step can be taken along this direction to maintain feasibility. The improvement on objective value, therefore, will be little. To overcome such drawbacks, we present a new gradient projection method with affine scaling. We give all the details on the new algorithm as well as some important convergence results.
The aggregate constraint homotopy method uses a single smoothing constraint instead of m-constraints to reduce the dimension of its homotopy map, and hence it is expected to be more efficient than the combined homotop...
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The aggregate constraint homotopy method uses a single smoothing constraint instead of m-constraints to reduce the dimension of its homotopy map, and hence it is expected to be more efficient than the combined homotopy interior point method when the number of constraints is very large. However, the gradient and Hessian of the aggregate constraint function are complicated combinations of gradients and Hessians of all constraint functions, and hence they are expensive to calculate when the number of constraint functions is very large. In order to improve the performance of the aggregate constraint homotopy method for solving nonlinear programming problems, with few variables and many nonlinear constraints, a flattened aggregate constraint homotopy method, that can save much computation of gradients and Hessians of constraint functions, is presented. Under some similar conditions for other homotopy methods, existence and convergence of a smooth homotopy path are proven. A numerical procedure is given to implement the proposed homotopy method, preliminary computational results show its performance, and it is also competitive with the state-of-the-art solver KNITRO for solving large-scale nonlinear optimization.
The present paper is devoted to the application of the space transformation techniques for solving nonlinear programming problems. By using surjective mapping the original constrained optimization problem is transform...
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The present paper is devoted to the application of the space transformation techniques for solving nonlinear programming problems. By using surjective mapping the original constrained optimization problem is transformed to a problem in a new space with only equality constraints. For the numerical solution of the latter problem the stable version of the gradient-projection and Newton's methods are used. After inverse transformation to the original space a family of numerical methods for solving optimization problems with equality and inequality constraints is obtained. The proposed algorithms are based on the numerical integration of the systems of ordinary differential equations. These algorithms do not require feasibility of starting and current points, but they preserve feasibility. As a result of space transformation the vector fields of differential equations are changed and additional terms are introduced which serve as a barrier preventing the trajectories from leaving the feasible set. A proof of convergence is given.
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