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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.

2

Optimization of stochastic production-inventory model for deteriorating items in a definite cycle using Hamilton-Jacobi-Bellman equation

Hau Bui Minh, Kim Hwan-Seong, Long Le Ngoc Bao, You Sam-Sang

LogForum

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2022

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Vol. 18, no. 4

397--411

EN

Background: Inventory control is essential for a manufacturer to achieve the desired profit in successful supply chain management. This paper deals with the production-inventory system under the decrease in production rate. The model includes three stages: before the decrease in production, after the decrease in production, and after a period of inventory shortage. Throughout the stages, the stochastic inventory model is always affected by random factors and the deterioration of inventory quality. Method: The article uses the economic order quantity (EOQ) framework to evaluate costs in the production-inventory model. To optimize the manufacturer’s profit with the stochastic factor, Hamilton-Jacobi-Bellman (HJB) equation is presented to find the production rate to make the inventory model to guarantee its intended goals in a determined cycle. Result: Analytical solutions are provided for optimization of the stochastic production-inventory model. Numerical experiments show that inventory level, production rate, and profit over time are based on the optimal initial value of the production rate. Conclusion: The manufacturer’s profit comes from the stages of importing raw materials, processing and producing, storing and supplying items. Finding the initial value of the production rate can make the inventory level and production rate to ensure their desired value and get the target profit within a specified time.

3

The LQG homing problem for a Wiener process with random infinitesimal parameters

Lefebvre Mario, Moutassim Abderrazak

Archives of Control Sciences

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2019

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Vol. 29, No. 3

413--422

EN

The problem of optimally controlling a Wiener process until it leaves an interval (a, b) for the first time is considered in the case when the infinitesimal parameters of the process are random. When a = -∞, the exact optimal control is derived by solving the appropriate system of differential equations, whereas a very precise approximate solution in the form of a polynomial is obtained in the two-barrier case.

4

Application of atatistical linearization techniques to design of quqsi-optimal active control of nonlinear system

Socha L.

Journal of Theoretical and Applied Mechanics

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2000

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Vol. 38 nr 3

591-605

EN

A comparison between the applicability of statistical linearizationmethods with moment criteria and criteria in probability density space to the determination of quasi-optimal external control for the nonlinear dynamic system excited by a coloured Gaussian noise and the mean square criterion is discussed in this paper. To determine the quasi-optimal control two modified versions of a standard iterative procedure are proposed, where three versions of statistical linearization with moment criteriaand two versions with criteria in the probability density space were combined with the optimal control method for linear systems with the mean square criterion. The detailed considerations are given for a nonlinear 2-degree-of-freedom system with external control force excited by a coloured Gaussian noise which is treated as an outputof 2D linear filter. The control is assumed as a linear feedback. The obtained results are illustrated by a numerical example.Zastosowanie sta

PL

zastosowanie statystycznej linearyzacji w nieliniowych układach do wyznaczania kwazi-optymalnego aktywnego sterowania. W pracy przedstawiono porównanie zastosowania kilku metod statystycznej linearyzacji z kryteriami momentowymi oraz z przestrzeni gęstości prawdopodobieństw do wyznaczania kwazi-optymalnego, addytywnego sterowaniaw układach nieliniowych z wymuszeniem w postaci kolorowego Gaussowskiego szumu i ze średnio kwadratowym kryterium optymalizacji. W celu wyznaczenia kwazi-optymalnego sterowania zaproponowano dwie zmodyfikowane wersje standardowej procedury iteracyjnej, gdzie trzy wersje statystycznej linearyzacji z momentowymi kryteriami i dwie wersje z kryteriami w przestrzeni gęstości prawdopodobieństw wykorzystano łącznie ze standardowym algorytmem wyznaczania sterowania optymalnego w układach liniowych ze średniokwadratowym wskaźnikiem jakości. Szczegółowa analiza została przedstawiona dla układów o dwu stopniach swobody z zewnętrznym wymuszeniem w postaci Gaussowskiego szumu kolorowego traktowanego jako wyjście z dwuwymiarowego filtru liniowego. Sterowanie przyjęto jako liniowe sprzężenie zwrotne. Otrzymane wyniki zilustrowano na przykładzie numerycznym.

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Infinite horizon reflected backward stochastic differential equations and applications in mixed control and game problems

Hamadène S., Lepeltier J.-P., Wu Z.

Probability and Mathematical Statistics

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1999

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Vol. 19, Fasc. 2

211--234

EN

We prove existence and uniqueness results of the solution for infinite horizon reflected backward stochastic differential equations with one or two barriers. We also apply these results to get the existence of optimal control strategy for the mixed control problem and a saddle-point strategy for the mixed game problem when, in both situations, the horizon is infinite.