A General Model and Efficient Algorithms for Reliable Facility Location Problem Under Uncertain Disruptions

This paper studies the reliable uncapacitated facility location problem in which facilities are subject to uncertain disruptions. A two-stage distributionally robust model is formulated, which optimizes the facility location decisions so as to minimize the fixed facility location cost and the expected transportation cost of serving customers under the worst-case disruption distribution. The model is formulated in a general form, where the uncertain joint distribution of disruptions is partially characterized and is allowed to have any prespecified dependency structure. This model extends several related models in the literature, including the stochastic one with explicitly given disruption distribution and the robust one with moment information on disruptions. An efficient cutting plane algorithm is proposed to solve this model, where the separation problem is solved respectively by a polynomial-time algorithm in the stochastic case and by a column generation approach in the robust case. Extensive numerical study shows that the proposed cutting plane algorithm not only outperforms the best-known algorithm in the literature for the stochastic problem under independent disruptions but also efficiently solves the robust problem under correlated disruptions. The practical performance of the robust models is verified in a simulation based on historical typhoon data in China. The numerical results further indicate that the robust model with even a small amount of information on disruption correlation can mitigate the conservativeness and improve the location decision significantly. Summary of Contribution: In this paper, we study the reliable uncapacitated facility location problem under uncertain facility disruptions. The problem is formulated as a two-stage distributionally robust model, which generalizes several related models in the literature, including the stochastic one with explicitly given disruption distribution and the robust one with moment information on disruptions. To solve this generalized model, we propose a cutting plane algorithm, where the separation problem is solved respectively by a polynomial-time algorithm in the stochastic case and by a column generation approach in the robust case. The efficiency and effectiveness of the proposed algorithm are validated through extensive numerical experiments. We also conduct a data-driven simulation based on historical typhoon data in China to verify the practical performance of the proposed robust model. The numerical results further reveal insights into the value of information on disruption correlation in improving the robust location decisions.

The Role of Harvesting in Population Control in Presence of Multiple Stochastic Noise Sources

In this paper, we compare the role of constant and Michaelis-Menten type harvesting in single species population control in presence of stochastic noises sources. Steady state probability distributions and stationary potentials of the population for the two types of harvesting are determined by Fokker-Planck equations. Stochastic bifurcation analysis and mean first passage times have been computed. Noise induced critical transitions are observed depending on the strength of the noises. The extinction possibility of population in stochastic control with Michaelis-Menten type harvesting is higher than the constant rate of harvesting. One of the findings is the transition of the population from bistable to tristable for weak noise and Michaelis-Menten type harvesting. Another finding is noise enhanced stability phenomenon for negatively correlated noises. In case of population control, constant rate of harvesting is better in deterministic case whereas Michaelis-Menten type harvesting is better in stochastic case. The stochastic control is more efficient than deterministic control as average population size in stochastic case is lower than the deterministic case. The results obtained in this study can throw light on toxic phytoplankton blooms and its control in marine ecosystem. Moreover, the study can be useful to explain wild prey population outbreak and its control in deep forest.

A study on stochastic maximal regularity for rough time-dependent problems

We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only progressively measurable in the time variable. For 2m-th order systems with VMO regularity in space, we obtain Lp(Lq) estimates for all p > 2 and q ≥ 2, leading to optimal space-time regularity results. For second order systems with continuous coefficients in space, we also include a first order linear term, under a stochastic parabolicity condition, and obtain Lp(Lp) estimates together with optimal space-time regularity. For linear second order equations in divergence form with random coefficients that are merely measurable in both space and time, we obtain estimates in the tent spaces Tp,2 of Coifman-Meyer-Stein. This is done in the deterministic case under no extra assumption, and in the stochastic case under the assumption that the coefficients are divergence free.

Role of Diurnal Cycle in the Maritime Continent Barrier Effect on MJO Propagation in an AGCM

The barrier effect of the Maritime Continent (MC) in stalling or modifying the propagation characteristics of the MJO is widely accepted. The strong diurnal cycle of convection over the MC is believed to play a dominant role in this regard. This hypothesis is studied here, with the help of a coarse-resolution atmospheric general circulation model (AGCM). The dry dynamical core of the AGCM is coupled to the multicloud parameterization piggybacked with a dynamical bulk boundary layer model. A set of sensitivity experiments is carried out by systematically varying the strength of the MC diurnal flux to assess the impact of the diurnal convective variability on the MJO propagation. The effects of deterministic and stochastic diurnal forcings on MJO characteristics are compared. It is found that the precipitation and zonal wind variance, on the intraseasonal time scales, over the western Pacific region decreases with the increase in diurnal forcing, indicating the blocking of MC precipitation. An increase in precipitation variance over the MC associated with the weakening of precipitation variance over the west Pacific is evident in all experiments. The striking difference between deterministic and stochastic diurnal forcing experiments is that the strength needed for the deterministic case to achieve the same degree of blocking is almost double that of stochastic case. The stochastic diurnal flux over the MC seems to be more detrimental in blocking the MJO propagation. This hints at the notion that the models with inadequate representation of organized convection tend to suffer from the MC-barrier effect.

Transitional dynamics in network game with heterogeneous agents: stochastic case

In this paper, stochastic parameters are introduced into the network games model with production and knowledges externalities. This model was formulated by V. Matveenko and A. Korolev and generalized two-period Romer model. Agents' productivities have deterministic and Wiener components. The research represents the dynamics of a single agent and the dynamics in a triangle which occurs in the process of unifying agents. Explicit expressions of the dynamics of a single agent and dyad agents in the form of Brownian random processes were obtained. A qualitative analysis of the solutions of stochastic equations and systems was carried out.

Digital platforms and modeling.

This work continues to publish authors at the VIII All-Russian Conference (with international participation) Theory and Practice of System Dynamics 2019. Various definitions and examples of digital platforms are provided. The network model and solution of the problem of decentralization of management in stochastic case is described.

Dynamic Load Vectors for Localization of Mass and Stiffness Perturbations

The well-established Dynamic Damage Locating Vector (DDLV) method offers localization of structural damage through a linear transformation of the null vectors of the transfer matrix change or, in the stochastic case of unknown input, a surrogate hereof. The null vectors are referred to as DDLVs, and it has been previously shown how applying these as loads to the structural domain will result in zero steady-state strain in any subdomain containing stiffness perturbations. The present paper explores the use of DDLVs for localization of mass-related damage and proves that any mass perturbation will, upon application of the DDLVs, be confined to the subdomain exhibiting zero steady-state motion. Since the strain field is realized from a surjective linear transformation of the displacement field, the DDLVs allow for localization of both mass- and stiffness-related damage without adding computational complexity to the existing procedures. The paper outlines the interrogation scheme for both damage types and demonstrates the basic principles through numerical and experimental examples.

Local Impact of Stochastic Shallow Convection on Clouds and Precipitation in the Tropical Atlantic

The local impact of stochastic shallow convection on clouds and precipitation is tested in a case study over the tropical Atlantic on 20 December 2013 using the Icosahedral Nonhydrostatic Model (ICON). ICON is used at a grid resolution of 2.5 km and is tested in several configurations that differ in their treatment of shallow convection. A stochastic shallow convection scheme is compared to the operational deterministic scheme and a case with no representation of shallow convection. The model is evaluated by comparing synthetically generated irradiance data for both visible and infrared wavelengths against actual satellite observations. The experimental approach is designed to distinguish the local effects of parameterized shallow convection (or lack thereof) within the trades versus the ITCZ. The stochastic cases prove to be superior in reproducing low-level cloud cover, deep convection, and its organization, as well as the distribution of precipitation in the tropical Atlantic ITCZ. In these cases, convective heating in the subcloud layer is substantial, and boundary layer depth is increased as a result of the heating, while evaporation is enhanced at the expense of sensible heat flux at the ocean’s surface. The stochastic case where subgrid shallow convection is deactivated below the resolved deep updrafts indicates that local boundary layer convection is crucial for a better representation of deep convection. Based on these results, our study points to a necessity to further develop parameterizations of shallow convection for use at the convection-permitting resolutions and to assuredly include them in weather and climate models even as their imperfect versions.

Space-time Poisson Flow Intensity Density with Zero Occurrence Probability on Stochastic Subsets of Its Spatial Definition Domain

Object of research: space-time Poisson flows.Subject of research: influence patterns of the stochastic subset characteristics of the spatial definition domain of the space-time Poisson flow on its intensity density.Work objective: to determine a relationship between the space-time Poisson flow intensity density and the characteristics of the inhomogeneity subdomains of the spatial definition domain where this flow is specified.A problem to be solved: to determine the space-time Poisson flow intensity density to meet a selected criterion, i.e. a conditional intensity density, where the condition is that the points in the flow state space belong to the stochastic inhomogeneity subdomains.We consider a space-time Poisson flow whose spatial domain contains stochastic subdomains of inhomogeneity. An equality criterion to zero occurrence probability generated by this flow in the inhomogeneity subdomains is used to derive an expression for the flow intensity density.The case has been considered when positions of inhomogeneity subdomain centers are random, and their angular positions relative to these centers and their shapes are defined and unchanged at analysis interval.To describe them, we used the probability densities of the inhomogeneity subdomain centers, which are time variant. A theorem is proved that substantiates the structure of the intensity density of the space-time Poisson flow with a stochastic inhomogeneous spatial domain of definition. The relationship of this characteristic with the probabilistic characteristics of inhomogeneity subdomain parameters is shown.Examples are given to illustrate a procedure for determining the intensity densities of space-time Poisson flows for both stochastic and deterministic structures of inhomogeneity subdomains. It is shown that for the stochastic case, taking into account the random nature of their location leads to a solution significantly different from the singular case.The scope of possible practical use of the results obtained for tasks related to the search for objects of observation is determined.