Topic
Piecewise linear function
About: Piecewise linear function is a research topic. Over the lifetime, 8133 publications have been published within this topic receiving 161444 citations.
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TL;DR: A linear approach using the lexicographic method enables the decision-maker to establish the limit for defective components and late deliveries as constraints in the model and can be effectively used in JIT/Lean supply environments by fixing the number of vendors.
Abstract: The multi-objective problem pertaining to vendor selection becomes complicated with the inclusion of a discount pricing schedule due to its nature of piecewise linearity. To overcome the difficulty of solving such a piecewise linear multi-objective problem, a linear approach is described in this paper. The use of the lexicographic method enables the decision-maker to establish the limit for defective components and late deliveries as constraints in the model. Demand can be exactly met considering the defective components present in the supply. Applying this approach to a manufacturing firm has proved its practicality. Also, the proposed methodology can be effectively used in JIT/Lean supply environments by fixing the number of vendors .
47 citations
TL;DR: A new piecewise linear upper bound is presented on this function, called the network recourse function, which is compared to the standard Madansky bound, and is shown computationally to be a little weaker, but much faster to find.
Abstract: We consider the optimal value of a pure minimum cost network flow problem as a function of supply, demand and arc capacities. We present a new piecewise linear upper bound on this function, which is called the network recourse function. The bound is compared to the standard Madansky bound, and is shown computationally to be a little weaker, but much faster to find. The amount of work is linear in the number of stochastic variables, not exponential as is the case for the Madansky bound. Therefore, the reduction in work increases as the number of stochastic variables increases. Computational results are presented.
47 citations
TL;DR: In this paper, the authors derived a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable.
Abstract: We derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the diffusive flux in the lowest-order Raviart- Thomas-Nedelec space linked with mesh dual to the original simplicial one, previously introduced by the last author in the pure diffusion case. They also rely on elaborated Poincare, Friedrichs, and trace inequalities-based auxiliary estimates designed to cope optimally with the reaction dominance. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideas of local minimizations of the estimators by local modifications of the reconstructed diffusive flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimates.
47 citations
TL;DR: In this paper, the bifurcations of bounded solutions from homoclinic orbits for time-perturbed discontinuous systems were studied and a functional analytic method was used.
Abstract: We study bifurcations of bounded solutions from homoclinic orbits for time-perturbed discontinuous systems. Functional analytic method is used. An illustrative example of a periodically perturbed piecewise linear differential equation in $$\mathbb{R}^3$$
is presented.
47 citations
TL;DR: The semilinear Duhem model is considered and an identification method for rate-independent and rate-dependent hysteresis is developed, which has the form of a switching linear time-invariant system with ramp-plus-step forcing.
Abstract: We consider the semilinear Duhem model and develop an identification method for rate-independent and rate-dependent hysteresis. For rate-independent hysteresis, we reparameterize the system in terms of the input signal, so that the system has the form of a switching linear time-invariant system with ramp-plus-step forcing. For rate-dependent hysteresis, the system can be viewed as a switching linear time-invariant system for triangle wave inputs. Least-squares-based methods are developed to identify the rate-independent and rate-dependent semilinear Duhem models
47 citations