scholarly journals Two-Stage Robust Counterpart Model for Humanitarian Logistics Management

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Feng Yang
Keyword(s):  
Optimization Theory ◽  
Transportation Cost ◽  
Service Level ◽  
Humanitarian Logistics ◽  
Logistics Management ◽  
Actual Situation ◽  
Two Stage ◽  
Worst Case ◽  
Robust Counterpart ◽  
Emergency Decision

In the early stages of a major public emergency, decision-makers were troubled by the timely distribution of a large number of donations. In order to distribute caring materials reasonably and efficiently, considering the transportation cost and time delay cost, this paper takes the humanitarian logistics management as an example to study the scheduling problem. Based on the actual situation of insufficient supply during the humanitarian logistics management, this paper using optimization theory establishes a two-stage stochastic chance constrained (TS-SCC) model. In addition, due to the randomness of emergency occurrence and uncertainty of demand, the TS-SCC model is further transformed into the two-stage robust counterpart (TS-RC) model. At the same time, the validity of the model and the efficiency of the algorithm are verified by simulations. The result shows that the model and algorithm constructed are capable to obtain the distribution scheme of caring materials even in worst case. In the TS-BRC (with box set) model, the logistics service level increased from 89.83% to 93.21%, while in the TS-BPRC (with mixed box and polyhedron set) model, it increases from 90.32% to 94.96%. Besides, the model built in this paper can provide a more reasonable dispatching plan according to the actual situation of caring material supply.

Linearized Robust Counterparts of Two-Stage Robust Optimization Problems with Applications in Operations Management

2020 ◽  
Author(s):  
Amir Ardestani-Jaafari ◽  
Erick Delage
Keyword(s):  
Robust Optimization ◽  
Operations Management ◽  
Optimization Problems ◽  
Close Relation ◽  
Bilinear Programming ◽  
Two Stage ◽  
Bilinear Models ◽  
Robust Counterpart ◽  
Adjustable Robust Counterpart ◽  
Affinely Adjustable Robust Counterpart

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method mainly relies on a linearization scheme employed in bilinear programming; therefore, we will say that it gives rise to the linearized robust counterpart models. We identify a close relation between this linearized robust counterpart model and the popular affinely adjustable robust counterpart model. We also describe methods of modifying both types of models to make these approximations less conservative. These methods are heavily inspired by the use of valid linear and conic inequalities in the linearization process for bilinear models. We finally demonstrate how to employ this new scheme in location-transportation and multi-item newsvendor problems to improve the numerical efficiency and performance guarantees of robust optimization.

scholarly journals Aircraft Inertial Measurement Unit Fault Diagnosis Based on Adaptive Two-Stage UKF

2020 ◽  
Vol 38 (4) ◽  
pp. 806-813
Author(s):  
Qizhi He ◽  
Weiguo Zhang ◽  
Xiaoxiong Liu ◽  
Weinan Li
Keyword(s):  
Kalman Filter ◽  
Random Walk ◽  
Fault Diagnosis ◽  
Inertial Measurement Unit ◽  
Unscented Kalman Filter ◽  
Random Walk Model ◽  
Measurement Unit ◽  
Actual Situation ◽  
Two Stage ◽  
Inertial Measurement

In the case of nonlinear systems with random bias, the Optimal Two-Stage Unscented Kalman Filter (OTSUKF) can obtain the optimal estimation of system state and bias. But it requires random bias to be accurately modeled, while it is always very difficult in actual situation because the aircraft is a typical nonlinear system. In this paper, the faults of the Inertial Measurement Unit (IMU) are treated as a random bias, and the random walk model is used to describe the fault. The accuracy of the random walk model depends on the degree of matching between the covariance of the random walk model and the actual situation. For the IMU fault diagnosis method based on OTSUKF, the covariance of the random walk model is assigned with a constant matrix, and the value of the matrix is initialized empirically. It is very difficult to select a matching matrix in practical applications. For this problem, in this paper, the covariance matrix of the random walk model is adaptively adjusted online based on the innovation covariance matching technique, and an adaptive Two-Stage Unscented Kalman Filter (ATSUKF) is proposed to solve the fault diagnosis problem of the IMU. The simulation experiment compares the IMU fault diagnosis performance of OTSUKF and ATSUKF, and verifies the effectiveness of the proposed adaptive method.

scholarly journals Robust Day-Ahead Dispatch for Integrated Power-Heat-Gas Microgrid considering Wind Power Uncertainty

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Yang Liu ◽  
Yanli Ye ◽  
Xianbang Chen ◽  
Huaqiang Li ◽  
Yuan Huang
Keyword(s):  
Wind Power ◽  
Deterministic Model ◽  
Economic Dispatch ◽  
Two Stage ◽  
Worst Case ◽  
Constraint Generation ◽  
Second Stage ◽  
Robust Model ◽  
Operation Cost ◽  
Made In

Wind power generation has been widely deployed in the modern power system due to the issues of energy crisis and environment pollution. Meanwhile, the microgrid is gradually regarded as a feasible way to connect and accommodate the distributed wind power generations. Recently, more research studies also focus on incorporating various energy systems, for example, heat and gas into the microgrid in terms of satisfying different types of load demands. However, the uncertainty of wind power significantly impacts the economy of the integrated power-heat-gas microgrid. To deal with this issue, this paper presents a two-stage robust model to achieve the optimal day-ahead economic dispatch strategy considering the worst-case wind power scenarios. The first stage makes the initial day-ahead dispatch decision before the observation of uncertain wind power. The additional adjustment action is made in the second stage once the wind power uncertainty is observed. Based on the duality theory and Big-M approach, the original second-stage problem can be dualized and linearized. Therefore, the column-and-constraint generation algorithm can be further implemented to achieve the optimal day-ahead economic dispatch strategy for the integrated power-heat-gas microgrid. The experimental results indicate the effectiveness of the presented approach for achieving operation cost reduction and promoting wind power utilization. The robustness and the economy of the two-stage robust model can be balanced, of which the performances significantly outperform those of the single-stage robust model and the deterministic model.

A Second Order Approximation Technique for Robust Shape Optimization

2011 ◽  
Vol 104 ◽  
pp. 13-22 ◽  
Author(s):  
Adrian Sichau ◽  
Stefan Ulbrich
Keyword(s):  
Shape Optimization ◽  
Order Approximation ◽  
Trust Region ◽  
State Equation ◽  
Second Order ◽  
Approximation Technique ◽  
Worst Case ◽  
Second Order Approximation ◽  
Robust Counterpart ◽  
Adjoint Approach

We present a second order approximation for the robust counterpart of general uncertain nonlinear programs with state equation given by a partial di erential equation.We show how the approximated worst-case functions, which are the essential part of the approximated robust counterpart, can be formulated as trust-region problems that can be solved effciently using adjoint techniques. Further, we describe how the gradients of the worst-case functions can be computed analytically combining a sensitivity and an adjoint approach. This methodis applied to shape optimization in structural mechanics in order to obtain optimal solutions that are robust with respect to uncertainty in acting forces. Numerical results are presented.

scholarly journals Robust Optimization Model for Bi-objective Emergency Medical Service Design Problem with Demand Uncertainty

2019 ◽  
Vol 20 (2) ◽  
pp. 95
Author(s):  
Diah Chaerani ◽  
Siti Rabiatul Adawiyah ◽  
Eman Lesmana
Keyword(s):  
Robust Optimization ◽  
Emergency Medical Service ◽  
Design Problem ◽  
Medical Service ◽  
Optimal Solution ◽  
Service Design ◽  
Mixed Integer ◽  
Worst Case ◽  
Robust Counterpart ◽  
Emergency Medical

Bi-objective Emergency Medical Service Design Problem is a problem to determining the location of the station Emergency Medical Service among all candidate station location, the determination of the number of emergency vehicles allocated to stations being built so as to serve medical demand. This problem is a multi-objective problem that has two objective functions that minimize cost and maximize service. In real case there is often uncertainty in the model such as the number of demand. To deal the uncertainty on the bi-objective emergency medical service problem is using Robust Optimization which gave optimal solution even in the worst case. Model Bi-objective Emergency Medical Service Design Problem is formulated using Mixed Integer Programming. In this research, Robust Optimization is formulated for Bi-objective Emergency Medical Service Design Problem through Robust Counterpart formulation by assuming uncertainty in demand is box uncertainty and ellipsoidal uncertainty set. We show that in the case of bi-objective optimization problem, the robust counterpart remains computationally tractable. The example is performed using Lexicographic Method and Branch and Bound Method to obtain optimal solution. 

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