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Optimal decision making for empty container management at seaport yard

Vinh Ngo Quang, You Sam-Sang You, Long Le Ngoc Bao, Kim Hwan-Seong

LogForum

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2023

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Vol. 19, no. 1

75--89

EN

Background: In global trade, shipping companies are forced to manage empty containers due to imbalances in international trade activities. For decision-makers, the problems require considering restrictions and an uncertain environment and repositioning or leasing the containers to satisfy the rapidly changing global demands regardless of the epidemic outbreak's impact on the seaport. The proposed approach can help decision-makers manage the empty container in port yards more effectively under market uncertainty by employing the Bellman optimality principle for the stochastic dynamic system. Methods: A stochastic production planning model is employed to cope with uncertainty and unexpected events to ensure a robust management strategy. Ito's formula describes the dynamic model for solving a stochastic differential equation. This paper uses stochastic optimal control theory to deal with efficient empty container management at the port yard. The findings have revealed the effectiveness of the proposed framework, which will provide a decision-making support scheme for efficient port operations. Results: The presented algorithm is realized by a novel approach, employing the Hamilton-Jacobi-Bellman (HJB) equation for optimal stochastic control problems. When comparing the model with and without uncertainty events, the gap is just about 0.04 %, proving the robustness of the proposed model. The results provide a decision support system for port managers when managing the empty container in the seaport yard. Conclusions: The proposed model not only figures out the optimal ordering of empty containers for each cycle but also points out the optimal safety stock level. Using a stochastic optimization approach, decision-makers can implement a strategic management policy to optimize seaport operational costs under market disruptions.

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L ∞-error estimates of a finite element method for Hamilton-Jacobi-Bellman equations with nonlinear source terms with mixed boundary condition

Miloudi Madjda, Saadi Samira, Haiour Mohamed

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

452--461

EN

In this paper, we introduce a new method to analyze the convergence of the standard finite element method for Hamilton-Jacobi-Bellman equation with noncoercive operators with nonlinear source terms with the mixed boundary conditions. The method consists of combining Bensoussan-Lions algorithm with the characterization of the solution, in both the continuous and discrete contexts, as fixed point of contraction. Optimal error estimates are then derived, first between the continuous algorithm and its finite element counterpart and then between the continuous solution and the approximate solution.

3

Discrete approximations of the Hamiltonian-Jacobi equation for an optimal control problem of a differential-algebraic system

Bonnans J. F., Chartier P., Zidani H.

Control and Cybernetics

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2003

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Vol. 32, no 1

33-56

EN

This paper discusses the numerical resolution of the Hamilton-Jacobi-Bellman equation associated with optimal control problem when the state equation is of algebraic differential type. We discuss two numerical schemes. The first reduces to the standard framework, while the second does not suppose any knowledge of the Jacobian of the data. We obtain some error estimates, and display numerical results obtained on a simple test problem.

PL

Artykuł rozpatruje rozwiązanie numeryczne równania Hamiltona-Jacobiego-Bellmana, związanego z zagadnieniem sterowania optymalnego w przypadku, gdy równanie stanu jest algebraiczno-różniczkowe. Rozważane są dwie procedury numeryczne. Pierwsza z nich sprowadza się do postępowania standardowego, podczas gdy druga nie zakłada znajomości Jakobianu danych. Otrzymano pewne oceny błędu, a na końcu artykułu pokazano wyniki numeryczne dla prostego zadania testowego.