Regularized Methods for a Two-Stage Robust Production Planning Problem and its Sample Average Approximation

In this paper,we consider a two-stage robust production planning model where the first stage problem determines the optimal production quantity upon considering the worst-case revenue generated by the uncertain future demand,and the second stage problem determines the possible demand of consumers by using a utility-based model given the production quantity and a realization of the random variable.We derive an equivalent single-stage reformulation of the two-stage problem.However,it fails the convergence analysis of the sample average approximation(SAA)approach for the reformulation directly.Thus we develop a regularized approximation of the second stage problem and derive its closed-form solution.We then present conditions under which the optimal value and the optimal solution set of the proposed SAA regularized approximation problem converge to those of the single-stage reformulation problem as the regularization parameter shrinks to zero and the sample size tends to infinity.Finally,some preliminary numerical examples are presented to illustrate our theoretical results.

Effect of weld reinforcement on axial plastic buckling of welded steel cylindrical shells

The effect of weld reinforcement on axial plastic buckling of welded steel cylindrical shells is investigated through experimental and numerical buckling analysis using six welded steel cylindrical shell specimens. The relationship between the amplitude of weld reinforcement and the axial plastic buckling critical load is explored. The effect of the material yield strength and the number of circumferential welds on the axial plastic buckling is studied. Results show that circumferential weld reinforcement represents a severe imperfect form of axially compressed welded steel cylindrical shells and the axial plastic buckling critical load decreases with the increment of the mean amplitude of circumferential weld reinforcement. The material yield strength and the number of circumferential welds are found to have no significant effect on buckling waveforms; however, the axial plastic buckling critical load can be decreased to some extent with the increase of the number of circumferential welds.

Time Consistent Multi-period Worst-Case Risk Measure in Robust Portfolio Selection

In this paper,we first construct a time consistent multi-period worst-case risk measure,which measures the dynamic investment risk period-wise from a distributionally robust perspective.Under the usually adopted uncertainty set,we derive the explicit optimal investment strategy for the multi-period robust portfolio selection problem under the multi-period worst-case risk measure.Empirical results demonstrate that the portfolio selection model under the proposed risk measure is a good complement to existing multi-period robust portfolio selection models using the adjustable robust approach.

Development on test equipment of coal slurry mixing tank

A coal slurry mixing tank is a key piece of equipment in the preparation of coal slurry for direct coal liquefaction.It is a gas-liquid-solid three-phase mixing device.Based on the performance of the existing coal slurry mixing equipment,a type of test equipment for horizontal continuous coal slurry preparation was developed,but to this point has limited research results.The test equipment consists of a mixing cylinder,mixer,stirring impeller and other components.Slurry mixing experiments were undertaken using the prototype,testing the performance of the device.A mathematical model was proposed specifically for the operation of a coal slurry mixing tank that is horizontally operated with high slurry concentration and rotary flow.The flow field in the horizontal coal mixing tank was simulated with the computational fluid dynamic (CFD) method.The experimental results match well with the CFD simulation results.Results show that the test device of a coal slurry mixing tank can be used to model the mixing of pulverized coal and the solvent oil.A strong correlation was obtained.

Data-driven Stochastic Programming with Distributionally Robust Constraints Under Wasserstein Distance:Asymptotic Properties

Distributionally robust optimization is a dominant paradigm for decision-making problems where the distribution of random variables is unknown.We investigate a distributionally robust optimization problem with ambiguities in the objective function and countably infinite constraints.The ambiguity set is defined as a Wasserstein ball centered at the empirical distribution.Based on the concentration inequality of Wasserstein distance,we establish the asymptotic convergence property of the datadriven distributionally robust optimization problem when the sample size goes to infinity.We show that with probability 1,the optimal value and the optimal solution set of the data-driven distributionally robust problem converge to those of the stochastic optimization problem with true distribution.Finally,we provide numerical evidences for the established theoretical results.