Dynamic Stochastic Model Research Articles

Optimal and heuristic policies for production and inventory controls in dual supply chains with fluctuating demands

AbstractIn the context of fast‐fashion business, we study the joint control of production, inventory, and unilateral transshipment in dual supply chains in which one supply chain is a responsive supply chain for fashion products and the other is an efficient supply chain for basic products in a fluctuating demand environment (FDE). Our research focuses on: (1) formulating an appropriate model for this complex problem; (2) characterizing the structured optimal policy, which can be used to develop effective heuristic policies; and (3) generalizing our studies for more applications. To address these issues, we formulate a discrete‐time finite‐horizon stochastic dynamic program model in which FDE is represented by a world state evolving in accordance with the discrete‐time Markov chain. The supply chain for the fashion product is modeled by a two‐stage tandem production system with a make‐to‐stock (MTS) stage for the fabric and a subsequent MTS stage for finished fashions. In parallel, the supply chain for the basic products is also modeled by a two‐stage tandem production system with a MTS stage for the fabric and a subsequent make‐to‐order (MTO) stage for finished basics. Further, the two supply chains are coupled via the unilateral transshipment of fabric with random transshipment time. By value iteration, we characterize the optimal policy for the single‐product problem with a set of monotone switching surfaces. The results are extended to the multi‐product multi‐supplier case. Further, based on the structure of the optimal policy, we develop a heuristic policy for the multi‐dimensional dynamic program model. From a practice perspective, we demonstrate the value of transshipment and controlled transshipment, analytically and numerically, and therefore justify the establishment of two separate local manufacturing bases in dual supply chains. Additionally, to achieve both quick response and efficiency, we show that the total cost can be reduced significantly if sufficient fabric is prepared just in time (JIT) for in‐season production at the beginning of a season.

A confidence ellipse analysis for stochastic dynamics model of Alzheimer's disease

The Alzheimer’s disease (AD) is a neurodegenerative disease, which is caused by the aggregation of beta-amyloid peptide ( $$A\beta$$ ) in the patient’s brain and the disorder of $${\text{Ca}}^{2 + }$$ homeostasis in neurons. Caluwé and Dupont (Theor Biol 331:12–18, 2013) proposed a deterministic AD model to explore the effect of $${\text{Ca}}^{2 + }$$ on AD. They demonstrated the positive feedback loop between $$A\beta$$ and $${\text{Ca}}^{2 + }:$$ and the occurrence of bistability. Based on their results, we further discuss the bistable behaviors. We present two periodically feasible drug strategies to alleviate the AD and screen out more effective one. In this paper, we also formulate a stochastic AD model, analyze the existence and uniqueness of global positive solutions and establish sufficient conditions for the existence of ergodic stationary distribution. Furthermore, the confidence ellipses describing the configurational arrangement of stochastic coexistence equilibria are constructed by stochastic sensitivity function technique, and tipping threshold is estimated as well. Noise-induced stochastic switching between two coexistence equilibria is observed in bistability region. Our results provide a new idea to control noise to alleviate AD through physical therapy.

Online parameter estimation for the McKean–Vlasov stochastic differential equation

We analyse the problem of online parameter estimation for a stochastic McKean–Vlasov equation, and the associated system of weakly interacting particles. We propose an online estimator for the parameters of the McKean–Vlasov SDE, or the interacting particle system, which is based on a continuous-time stochastic gradient ascent scheme with respect to the asymptotic log-likelihood of the interacting particle system. We characterise the asymptotic behaviour of this estimator in the limit as t→∞, and also in the joint limit as t→∞ and N→∞. In these two cases, we obtain almost sure or L1 convergence to the stationary points of a limiting contrast function, under suitable conditions which guarantee ergodicity and uniform-in-time propagation of chaos. We also establish, under the additional condition of global strong concavity, L2 convergence to the unique maximiser of the asymptotic log-likelihood of the McKean–Vlasov SDE, with an asymptotic convergence rate which depends on the learning rate, the number of observations, and the dimension of the non-linear process. Our theoretical results are supported by two numerical examples, a linear mean field model and a stochastic opinion dynamics model.

Global Optimization Approach for Parameter Estimation in Stochastic Dynamic Models of Biosystems.

Mechanistic dynamic models have become an essential tool for understanding biomolecular networks and other biological systems. Biochemical stochasticity can be extremely important in some situations, e.g., at the single-cell level where there is a low copy number of the species involved. In these scenarios, deterministic models are not suitable to characterize the dynamics, so stochastic dynamic models should be considered. Here, we address the challenging problem of parameter estimation in stochastic dynamic models. Despite recent advances, this area is considerably less mature than its deterministic counterpart. We present a novel strategy based on two components: (i) global optimization via a hybrid stochastic-deterministic approach, and (ii) stochastic simulation techniques tailored to the sparsity of the available experimental data. Regarding the latter, for cases of dense population data we make use of a novel approach using a Partial Integro-Differential Equation (PIDE) model solved using a semilagrangian method. In order to further speed up the simulations, we also present efficient parallel implementations for multi-core CPUs and also for graphical processing units (GPUs). Importantly, whereas SDE and Fokker Planck approximations of the Chemical Master Equation (CME) apply when the reactant populations are sufficiently large, the PIDE approximation to the CME is valid for very low copy numbers, and therefore they enable us to tackle parameter estimation for systems with large intrinsic molecular noise, (highly stochastic regimes far from the thermodynamic limit). We test our strategy with four challenging problems: a Lotka-Volterra system, a polarization system in S. cerevisiae, a genetic toggle switch, and a genetic circadian oscillator. Our method could successfully solve these problems in very reasonable computation times (often a few minutes for the first two problems) using standard low-cost hardware, showing very significant speedups with respect to recent alternative methods. The code used to obtain the results reported here is available at https://doi.org/10.5281/zenodo.5195408.

On stochastic dynamic modeling of incidence data.

In this paper, a Markov Regime Switching Model of Conditional Mean with covariates, is proposed and investigated for the analysis of incidence rate data. The components of the model are selected by both penalized likelihood techniques in conjunction with the Expectation Maximization algorithm, with the goal of achieving a high level of robustness regarding the modeling of dynamic behaviors of epidemiological data. In addition to statistical inference, Changepoint Detection Analysis is performed for the selection of the number of regimes, which reduces the complexity associated with Likelihood Ratio Tests. Within this framework, a three-phase procedure for modeling incidence data is proposed and tested via real and simulated data.

Pollution and labor market search externalities over the business cycle

We study the relationship between unemployment, environmental policy, and business cycles. We develop a dynamic stochastic general equilibrium real business cycle model that includes both a pollution externality and congestion externalities from labor market search frictions. These frictions generate unemployment on the extensive margin and affect hours worked on the intensive margin. We consider two policies to address the market failures: an emissions tax and a tax or subsidy on job creation. With both policies present, the efficient outcome can be achieved. When one policy is constrained or absent, we solve for the second best. The absence of a vacancy policy to address the congestion externalities substantially affects the value of the emissions tax, both in steady state and over the business cycle.

A computational stochastic dynamic model to assess the risk of breakup in a romantic relationship

We introduce an algorithm to find feedback Nash equilibria of a stochastic differential game. Our computational approach is applied to analyze optimal policies to nurture a romantic relationship in the long term. This is a fundamental problem for the applied sciences, which is naturally formulated in this work as a stochastic differential game with nonlinearities. We use our computational model to analyze the risk of marital breakdown. In particular, we introduce the concept of “love at risk,” which allows us to estimate the probability of a couple breaking up in the face of possible unfavorable scenarios.

Learning Robust Point-to-Point Motions Adversarially: A Stochastic Differential Equation Approach

This letter proposes a robust stochastic differential equation approach for learning point-to-point motions in an adversarial way. The proposed stochastic dynamical model combines the advantages of the stochastic differential equation and the transformer-like function together to achieve both robustness and accuracy of the learning. The adversarial training method is proposed to simplify the way of updating the parameters of the model. The state of the proposed stochastic dynamical system is mathematically proved to converge asymptotically in the mean square sense, and it has been experimentally validated on the LASA dataset and by the trajectory-programming task of the Franka Emika robot. The experimental results show that: (1) the adversarial training method helps the model to achieve higher reproduction accuracy; (2) the trajectories generated by the proposed model achieve higher accuracy in both the noise-free condition (by approximately 14.9%) and the noisy condition (by approximately 17.8%) compared with the state-of-the-art methods in terms of the similarity to the demonstration; and (3) the proposed approach can learn smoother trajectories even if the observations are contaminated by noises.

Dynamic stochastic modeling for adaptive sampling of environmental variables using an AUV

Discharge of mine tailings significantly impacts the ecological status of the sea. Methods to efficiently monitor the extent of dispersion is essential to protect sensitive areas. By combining underwater robotic sampling with ocean models, we can choose informative sampling sites and adaptively change the robot’s path based on in situ measurements to optimally map the tailings distribution near a seafill. This paper creates a stochastic spatio-temporal proxy model of dispersal dynamics using training data from complex numerical models. The proxy model consists of a spatio-temporal Gaussian process model based on an advection–diffusion stochastic partial differential equation. Informative sampling sites are chosen based on predictions from the proxy model using an objective function favoring areas with high uncertainty and high expected tailings concentrations. A simulation study and data from real-life experiments are presented.

Data driven approach for stochastic DEA in machine learning and artificial intelligence to improve the accuracy, stability, and interpretability of the model

The novelty of this research lies in the integration of machine learning and artificial intelligence techniques into stochastic DEA models. While traditional DEA models have been widely used to measure the efficiency of decision-making units, they may not be able to capture complex and nonlinear relationships between inputs and outputs. By integrating advanced machine learning and AI techniques, this research aims to improve the accuracy, stability, and interpretability of stochastic DEA models, providing decision-makers with more reliable and actionable insights. Moreover, this research explores several novel approaches, including the integration of deep learning techniques, ensemble learning, dynamic stochastic DEA models, and explainable AI, to improve the performance of stochastic DEA models. These approaches have the potential to enhance the accuracy of efficiency scores, increase the stability of the model, provide more actionable insights, and improve the model's interpretability. By integrating these approaches into stochastic DEA models, this research aims to provide a comprehensive and effective solution to the problem of measuring the efficiency of decision-making units. This approach has not been explored extensively in the literature, and thus represents a novel and innovative approach to addressing this important research problem.

Vibration response analysis of footbridge based on pedestrian perception

This article aims to study the influence of random crowd loading on the perceived vibration response of pedestrians. Firstly, a vertical vibration response analysis method considering pedestrian perception was established based on the random crowd walking model. Secondly, change rules of maximum vibration response of pedestrians, occurrence time and position interval under different random walk models were compared and analyzed. Finally, the vibration response reduction factor was defined by studying the correlation between the maximum vibration response of pedestrians and the peak acceleration of the structure, and the approximate calculation method of the maximum vibration response of pedestrians was proposed. The results show that the maximum acceleration perceived by pedestrians obeys the normal distribution under the four crowd walking models, the response distribution of ordered arrangement model (OAM) is larger than that of the other three models; The location and occurrence time of the maximum response depend on the distribution of pedestrian locations on the footbridge, and there is no significant change with the increase of population density. In addition, the distribution of OAM and stochastic arrival model (SAM) are consistent, which is concentrated in the middle of the total time-history. In contrast, the distribution of stochastic distribution model (SDM) and dynamic equilibrium model (DEM) are relatively uniform. The maximum error between the calculated acceleration maximum value and the actual acceleration value felt by the pedestrian is less than 5%. These results can provide reference for quantitative evaluation of pedestrian-induced vibration comfort.

Modeling the Effects of Chemotherapeutic Dose Response on a Stochastic Tumor-Immune Model of Prostate Cancer with Androgen Deprivation Therapy

The periodical application of androgen deprivation therapy, immunotherapy, or chemotherapy is an effective method for cancer treatment, but few studies combine them. To explore such comprehensive treatment mechanisms, this paper establishes a pulsed stochastic hybrid dynamics model considering tumor antigenicity and density-dependent mortality. In addition to analyzing the basic properties of solutions such as the tumor-free periodic solution and global attraction of the model, the threshold conditions for the persistence and extinction of prostate cancer cells and effector cells are obtained by using stochastic differential equation theory. Besides, sufficient conditions for the existence of stationary distribution of the system are established. The results reveal that comprehensive therapy or white noise can determine tumor dynamics and suggest that the treatment of prostate cancer should be individualized according to the state of tumor development. Finally, biological significance is discussed and conclusions are given.

Reinforcement learning and stochastic dynamic programming for jointly scheduling jobs and preventive maintenance on a single machine to minimise earliness-tardiness

This paper addresses the problem of stochastic jointly scheduling of resumable jobs and preventive maintenance on a single machine, subject to random breakdowns, to minimise the earliness-tardiness cost. The main objective is to investigate using trending machine learning-based methods compared to stochastic optimisation approaches. We propose two different methods from both fields as we solve the same problem firstly with a stochastic dynamic programming model in an approximation way, then with an attention-based deep reinforcement learning model. We conduct a detailed experimental study according to solution quality, run time, and robustness to analyse their performances compared to those of an existing approach in the literature as a baseline. Both algorithms outperform the baseline. Moreover, the machine learning-based algorithm outperforms the stochastic dynamic programming-based heuristic as we report up to 30.5% saving in total cost, a reduction of computational time from 67 min to less than 1 s on big instances, and a better robustness. These facts highlight clearly its potential for solving such problems.

Is It Possible to Predict COVID-19? Stochastic System Dynamic Model of Infection Spread in Kazakhstan.

Since the start of the COVID-19 pandemic, scientists have begun to actively use models to determine the epidemiological characteristics of the pathogen. The transmission rate, recovery rate and loss of immunity to the COVID-19 virus change over time and depend on many factors, such as the seasonality of pneumonia, mobility, testing frequency, the use of masks, the weather, social behavior, stress, public health measures, etc. Therefore, the aim of our study was to predict COVID-19 using a stochastic model based on the system dynamics approach. We developed a modified SIR model in AnyLogic software. The key stochastic component of the model is the transmission rate, which we consider as an implementation of Gaussian random walks with unknown variance, which was learned from real data. The real data of total cases turned out to be outside the predicted minimum-maximum interval. The minimum predicted values of total cases were closest to the real data. Thus, the stochastic model we propose gives satisfactory results for predicting COVID-19 from 25 to 100 days. The information we currently have about this infection does not allow us to make predictions with high accuracy in the medium and long term. In our opinion, the problem of the long-term forecasting of COVID-19 is associated with the absence of any educated guess regarding the dynamics of β(t) in the future. The proposed model requires improvement with the elimination of limitations and the inclusion of more stochastic parameters.

Closing the gaps in the continuum of depression care for persons with HIV: modeling the impact on viral suppression in the United States.

Depression is prevalent among persons with HIV (PWH) and is associated with poorer adherence and lack of viral load suppression (VLS). When treated for depression, PWH are more likely to stay in HIV care and adhere to medications; however, for many PWH, depression is not adequately diagnosed or treated. We adapted Progression and Transmission of HIV (PATH 3.0), a U.S. agent-based dynamic stochastic simulation model, by incorporating a continuum of depression care and estimating the impact on VLS of an enhanced depression diagnosis and care scenario (EDC). We compared EDC - whereby every PWH is assessed for depression, gets treatment if diagnosed, and of those, half achieve remission - to a status quo scenario (SQ) on VLS. Based on published findings, assumptions for SQ were: 34.7% depressed, 45% diagnosed, 55.3% treated and 33% of treated achieving remission. Compared to PWH without depression, we assumed the probability of being non-virally suppressed increased by 1.57 times for PWH with depression (PWH-D), and by 0.95 times for PWH with remitted depression. There was an average increase of 14.6% (11.5-18.5) in the proportion of PWH-D who achieved VLS in EDC compared to SQ. Among all PWH, there was a 4.7% (3.4-6.0) increase in the proportion who achieved VLS in EDC compared to SQ. Fully diagnosing and adequately treating depression would improve health and quality of life for a substantial proportion of PWH-D and result in a nearly 5% increase in expected rates of VLS in the United States, supporting national prevention goals.

Dynamic-stochastic modeling of the Northern Dvina runoff long-term fluctuations

Dynamic-stochastic modeling of the Northern Dvina runoff long-term fluctuations

Stochastic Dynamic Response and Long-Term Settlement Performance of Superstructure–Underground Tunnel–Soil Systems Subjected to Subway-Traffic Excitation

The vibration impact force from the long-term operation of a subway affects the comfort of the residents living above the superstructure and the long-term settlement deformation of the tunnel foundation. A method for evaluating the dynamic responses of superstructure–tunnel systems is important, especially because of the randomness of vibration impact force. The coupling effect of the randomness of train-vibration excitation and the nonlinearity of the geotechnical properties that are subjected to dynamic action leads to challenges in the evaluation of the performance of superstructure–underground tunnel–soil systems under train vibration. In this study, a stochastic dynamic model of subway vibration-load excitation was established; then, the time histories of samples with rich probability characteristics in the same set system were generated. According to the nonlinear dynamic finite element analysis, several nonlinear dynamic responses of the deterministic superstructure–tunnel soil-foundation system were obtained. Finally, the probabilistic performance evolution of the superstructure–tunnel soil-foundation system was obtained by integrating the first-passage and probability density evolution theories, and the long-term deformation performance of the tunnel foundation was evaluated using time-varying reliability. This study presents a novel probabilistic method and a more objective performance index for the dynamic performance assessment of superstructure–underground tunnel–soil systems that are subjected to subway-traffic excitation.

Estimating the Operating Reserve Demand Curve for Efficient Adoption of Renewable Sources in Korea

As the proportions of variable renewable sources (VRSs) such as solar and wind energy increase rapidly in the power system, their uncertainties inevitably undermine power supply reliability and increase the amount of operating reserve resources required to manage the system. However, because operating reserves have the characteristics of a public good and their value is related to the social cost of blackouts, it is difficult to determine their market price efficiently, which leads to inefficiencies in procuring operating reserves. This study estimates the operating reserve demand curve (ORDC) of the Korean power system to provide an effective basis for measuring the proper value and quantity of operating reserves needed to meet the reliability standard. A stochastic dynamic optimization model is applied to incorporate the probabilistic characteristics of VRS and the inter-hour constraint, which is necessary for analyzing load-following reserves. An econometric model and the Monte Carlo simulation method are used to generate the forecast profiles of solar and wind generation. The results indicate that the proper amount of hourly operating reserves needed in 2034 is approximately 4.4 times higher than that in 2020 at the current reserve offer price. The ORDC of 2020 has a price-inelastic shape, whereas the ORDC of 2034 has a price-elastic shape because the reserve requirement varies considerably with its offer price level in the high-VRS penetration case. This variability is due to alternatives, such as VRS curtailment or load shedding, which can replace the reserve requirement. This study also showed that VRS curtailment is an effective balancing resource as an alternative to reserves.

Nonlinear random vibration of the slender deep-water pier under seismic excitation

The present study investigates the nonlinear random vibration of the deep-water pier exposed to horizontal seismic excitation. First of all, the stochastic dynamic model of the pier is formulated. During the process, the pier is simplified as a cantilever beam fixed on the rock foundation, the seismic excitation is treated as Gaussian white noise, the hydrodynamic pressure is described with the radiation wave theory, and the equation for the nonlinear kinematic of the pier is deduced by the means of Kane’s method. Then, with the application of the stochastic averaging (SA) technique, the Fokker–Plank–Kolmogorov (FPK) equation governing the transient probability density function (PDF) of the amplitude envelope and the backward Kolmogorov (BK) equation for the conditional reliability function (CRF) are derived, respectively. The closed-form stationary PDF can be yielded directly from the reduced FPK equation, while the CRF and the conditional PDF of first-passage time are given after solving the BK equation numerically. Numerical discussions are performed to illustrate the trend of excitation intensity, mass ratio, immersion ratio, and inner and outer hydrodynamic effect on the stationary response and first-passage failure are examined, respectively. It has been shown that increases in the excitation intensity, mass ratio, and immersion ratio can amplify the response and reduce the reliability of the deep-water pier system. The hydrodynamic effect also leads to an amplification of the system response and a reduction in the reliability of the system. Similarly, the presence of inner water can also exacerbate these effects, and this phenomenon becomes more pronounced with increasing immersed ratios. Additionally, the analytical solution is validated by the result obtained by pertained Monte Carlo simulations (MCS). It is noted that this work will be helpful for the optimal seismic design of deep-water piers.

A dynamical stochastic model of yeast translation across the cell cycle

Translation is a central step in gene expression, however its quantitative and time-resolved regulation is poorly understood. We developed a discrete, stochastic model for protein translation in S. cerevisiae in a whole-transcriptome, single-cell context. A “base case” scenario representing an average cell highlights translation initiation rates as the main co-translational regulatory parameters. Codon usage bias emerges as a secondary regulatory mechanism through ribosome stalling. Demand for anticodons with low abundancy is shown to cause above-average ribosome dwelling times. Codon usage bias correlates strongly both with protein synthesis rates and elongation rates. Applying the model to a time-resolved transcriptome estimated by combining data from FISH and RNA-Seq experiments, it could be shown that increased total transcript abundance during the cell cycle decreases translation efficiency at single transcript level. Translation efficiency grouped by gene function shows highest values for ribosomal and glycolytic genes. Ribosomal proteins peak in S phase while glycolytic proteins rank highest in later cell cycle phases.