Stochastic Chain Research Articles

Extending the study on the linear advection equation subject to stochastic velocity field and initial condition

In this paper we extend the study on the linear advection equation with independent stochastic velocity and initial condition performed in Dorini and Cunha (2011). By using both existing and novel results on the stochastic chain rule, we solve the random linear advection equation in the mean square sense. We provide a new expression for the probability density function of the solution stochastic process, which can be computed as accurately as wanted via Monte Carlo simulations, and which does not require the specific probability distribution of the integral of the velocity. This allows us to solve the non-Gaussian velocity case, which was not treated in the aforementioned contribution. Several numerical results illustrate the computations of the probability density function by using our approach. On the other hand, we derive a theoretical partial differential equation for the probability density function of the solution stochastic process. Finally, a shorter and easier derivation of the joint probability density function of the response process at two spatial points is obtained by applying conditional expectations appropriately.

Asymptotic properties of stochastic nutrient-plankton food chain models with nutrient recycling

To investigate the effects of stochasticity and seasonality on the dynamics of aquatic ecosystems, in this paper, we propose two stochastic nutrient-plankton food chain models. For the stochastic model with regime switching, we establish sufficient conditions for the persistence and extinction of plankton. Under mild extra assumptions, the existence of an ergodic stationary distribution is studied. For the stochastic model with seasonal fluctuation, we first perform the survival analysis. Then, based on Khasminskii’s theory for periodic Markov processes, we give sufficient criteria for the existence of a positive stochastic periodic solution. Numerical simulations are carried out to illustrate the analytical results, showing that stochasticity and seasonality may cause the periodic bloom of phytoplankton, which partly explains the formation of algal blooms.

THE RESERVE UNCERTAINTIES IN THE CHAIN LADDER MODEL OF MACK REVISITED

AbstractWe revisit the “full picture” of the claims development uncertainty in Mack’s (1993) distribution-free stochastic chain ladder model. We derive the uncertainty estimators in a new and easily understandable way, which is much simpler than the derivation found so far in the literature, and compare them with the well known estimators of Mack and of Merz–Wüthrich.Our uncertainty estimators of the one-year run-off risks are new and different to the Merz–Wüthrich formulas. But if we approximate our estimators by a first order Taylor expansion, we obtain equivalent but simpler formulas. As regards the ultimate run-off risk, we obtain the same formulas as Mack for single accident years and an equivalent but better interpretable formula for the total over all accident years.

Asymptotic behavior of a food chain model with stochastic perturbation

In this article, asymptotic behavior of a stochastic food chain model is analyzed. First of all, we consider the dynamic of the deterministic system by analyzing the equilibria and their stability conditions. Then by Lyapunov analysis methods, we show that the system has a unique positive solution. After that, the stochastic stability and its long time behavior around the equilibriums of the deterministic system is given. Later, we obtain the stochastic system and its corresponding deterministic system have similar properties when the white noise is small. And then,we show the conditions that there is a stationary distribution of the system which implies that the system is permanent. At last, we make simulations to verify the results of our analysis.

Hierarchical automatic curriculum learning: Converting a sparse reward navigation task into dense reward

Mastering the sparse reward or long-horizon task is critical but challenging in reinforcement learning. To tackle this problem, we propose a hierarchical automatic curriculum learning framework (HACL), which intrinsically motivates the agent to hierarchically and progressively explore environments. The agent is equipped with a target area during training. As the target area progressively grows, the agent learns to explore from near to far, in a curriculum fashion. The pseudo target-achieving reward converts the sparse reward into dense reward, thus the long-horizon difficulty is alleviated. The whole system makes hierarchical decisions, in which a high-level conductor travels through different targets, and a low-level executor operates in the original action space to complete the instructions given by the high-level conductor. Unlike many existing works that manually set curriculum training phases, in HACL, the total curriculum training process is automated and suits the agent’s current exploration capability. Extensive experiments on three sparse reward tasks, long-horizon stochastic chain, grid maze, and the challenging Atari game Montezuma’s Revenge, show that HACL achieves comparable or even better performance but with significantly less training frames.

Refined models of the conductivity distribution at the transition from the Bohemian Massif to the West Carpathians using stochastic MCMC thin sheet inversion of the geomagnetic induction data

Although volume 3D modeling solutions has become widespread in recent time, thin sheet approximation of Earth's conductivity distribution can still serve as a useful tool when quasi-3D conductivity structures in the heterogeneous subsurface are investigated and the available database of observations is limited to long-period electromagnetic induction data from large-scale deep sounding arrays. We present results of stochastic Monte Carlo-Markov Chains MCMC inversion of long-period induction arrows based on the Bayesian statistics strategy. We concentrated on the different methodological aspects of MCMC for Gibbs sampling and for adaptive Metropolis algorithm together with convergence of these methods. The results are presented on a case study from the transition zone between the Bohemian Massif and the West Carpathians where a phantom effect caused by superposition of the prominent SW-NE trending Carpathian Conductivity Anomaly and NW-SE trending anomalous structure related to the fault system at the eastern boundary of the Bohemian Massif appears.

An optimization model for traceable closed-loop supply chain networks

• A closed-loop supply chain (CLSC) network comprises forward and reverse logistics. • A stochastic multi-product traceable CLSC using a radio frequency identification system is modelled. • Customer acquisition behavior when choosing internet over conventional sales is considered. • A greedy randomized adaptive search procedure (GRASP) is used to solve the problem. • A real-life case study of network marketing shows the applicability of the proposed model. In this paper, a new non-linear mixed-integer mathematical programming problem is proposed to model a stochastic multi-product closed-loop supply chain (CLSC). The radio frequency identification (RFID) system is implemented in the supply chain to decrease product losses and the overall lead time of transportation while computing the profit derived from internet and conventional sales. The resulting traceable CLSC improves upon the existing literature by allowing us to: (1) boost the incorporation of traceability assumptions in mathematical programming problems so as to enhance the efficiency and visibility of a supply chain, (2) analyze the strategic effects that different internet sale formats have on customers’ evaluations and acquisition choices, and (3) account for the environmental and socio-economical dimension by explicitly formalizing employment-based incomes as part of the profit function. Two meta-heuristic algorithms are introduced to solve the proposed optimization problem, namely, the greedy randomized adaptive search procedure (GRASP) and particle swarm optimization (PSO). Twelve test problems of different sizes are generated and solved using these algorithms. The computational results show that GRASP outperforms PSO in terms of both profit and CPU time values. Finally, a case study in the network marketing industry is presented and managerial implications outlined to show the validity of the proposed model and shed more light on its practical implications.

A stochastic risk-averse sustainable supply chain network design problem with quantity discount considering multiple sources of uncertainty

Sustainability in supply chain management is an inescapable and controversial issue due to government legislation and social responsibilities of the organizations. For that reason, a sustainable supply chain network design (SSND) has been recently developed as a means of dealing with environmental and social issues along with the economic aspect of a supply chain. On the other hand, considering uncertainty and risk aversion in the supply chain network design due to the volatility of the markets and the unavailability of sufficient information is inevitable. Thus, in this paper, a risk-averse sustainable multi-objective mathematical model is proposed in order to design and plan a network of the supply chain under uncertainty by incorporating Conditional Value at Risk (CVaR) into the basic configuration of the two-stage stochastic programming. In some other cases, many organizations offer some sort of discount to their customers so that they can compete with their rivals and enhance their accounts receivable. So, it seems ineluctable for companies to contemplate considering discount policies while making such strategic decisions for sustainability. Therefore, in this paper, we propose a mixed integer non-linear programming (MINLP) problem in order to consider discounts in the proposed model. Sensitivity analyses are also conducted on some important risk-aversion parameters in order to evaluate how these parameters affect the proposed mathematical model and the obtained Pareto solutions.

Distribution-Free Stochastic Closed-Loop Supply Chain Design Problem with Financial Management

Financial flow is an important part of supply chain management (SCM) and increasingly playing a crucial role as the amount of global trade increases. Reasonable and scientific financial operation is necessary in closed-loop supply chain management, especially when customer demand is uncertain. However, financial flow, which may lead to an increase in effectiveness, has rarely been considered in the literature. In this paper, we present a closed-loop supply chain design with financial management problem, which is tackled as a stochastic programming model with ambiguity demand set. The main contributions of this work include: (i) A joint chance constrained programming model is proposed to maximize the total profit, and (ii) financial flow and uncertain demand are both taken into consideration. According to the characteristic of the problem, we chose four approaches, namely sample average approximation (SAA), enhanced sample average approximation (ESAA), Markov approximation (MA), and mixed integer second-order conic program (MI-SOCP). Computational experiments were conducted to compare the adopted methods, and 10,000 scenarios were generated to examine the reliability of the methods. Numerical results revealed that the Markov approximation approach can achieve more reliable solutions.

The spatio-temporal trends of urban growth and surface urban heat islands over two decades in the Semarang Metropolitan Region

This paper conveys the findings of a study of the development of Semarang Metropolitan Region (SMR) over two decades. The developments seen were urbanisation and its impact on Surface Urban Heat Islands (SUHI). This research used remote sensing data satellite imagery of Landsat 5 T M and Landsat 8 OLI to see land cover change from 1998 to 2018. Furthermore, to predict the land cover change, this research used a Stochastic Cellular Automata-Markov Chain (SCA-MC) algorithm. Measurements of the LST and SUHI used Landsat products with Thermal Infra-Red Sensors (TIRS) Band 10 (2018) and TIRS Band 6 (1998). The classification of the results from 1998 to 2018 indicates a widespread change in the built-up area of about 74.62%, revealing urban expansion in the SMR. Moreover, there has been a decline in the vegetation canopy of 36.14%, resulting in an increase in average surface temperature of 2–5 °C. Areas with increased surface temperatures reached more than 30 °C, which is an increase of 245.57 km2 from 1998 to 2018. Furthermore, the SCA-MC prediction suggests the scenario to mitigate the SUHI through Spatial planning instruments. Thus, control of development is essential to the sustainability of the SMR, through land use planning scenarios.

Residential activity pattern modelling through stochastic chains of variable memory length

Residential activity modelling has attracted considerable attention over the last years. This is particularly due to the fact that residential energy demand loads are highly dependent on the activity patterns of the household. Therefore, activity models are being increasingly used to underpin high-resolution energy demand models. This paper details the implementation of a new methodology for the analysis of empirical activity data that allows for the identification of characteristic behavioural patterns within them. The identified patterns are then used as the basis for the construction of a high-resolution residential user activity model. The model attempts to capture the statistical characteristics of the empirical data in the form of a stochastic process with memory of variable length. The proposed model is compared to a model based on the predominant first-order Markov chain approach. In addition to the modelling approach, a new metric for assessing the quality of activity sequences simulations is proposed. Given the amount of empirical data contained in any of the individual time-use datasets currently available, it would appear that the performance improvement over the predominant first-order Markov chain approach is modest. However, the validation results show that the proposed approach has the potential for broadening our understanding of the scheduling of activities in people’s day-to-day lives and how this relates to the observed variability in both activity and energy consumption patterns.

Brownian motion on a stochastic harmonic oscillator chain: limitations of the Langevin equation

Diffusion of a Brownian particle along a linear chain of coupled stochastic harmonic oscillators is investigated using molecular dynamics (MD) and stochastic modeling. The latter technique is based on the Langevin equation (LE) derived by applying linear response theory to the chain degrees of freedom. When the coupling strength between the particle and the chain oscillators is comparable to or exceeds the chain coupling strength, the LE becomes inaccurate in its predictions of the diffusion coefficient value; however, it does reproduce qualitatively correctly the non-monotonic dependence of the diffusion coefficient on the particle-chain coupling strength, also found in MD simulations. The diffusion coefficient versus temperature curves determined from MD and Langevin simulations agree very well with each other at low temperatures. At high temperatures, the diffusion coefficient obtained from Langevin simulations is proportional to temperature, as predicted by Einstein’s relation. In contrast, the diffusion coefficient from MD is a non-linear function of temperature and is significantly greater than in Langevin simulations. Next, it is shown that Langevin description breaks down when the coupling between the chain oscillators is too strong. Finally, when an external constant force is applied to the particle, the Langevin description becomes qualitatively wrong. Namely, MD shows that the particle quickly detaches itself from the chain and moves at a constant acceleration due to the external force, whereas Langevin simulations predict constant terminal velocity of the particle.

Stationary distribution of a stochastic food chain chemostat model with general response functions

In this paper, we focus on a food chain chemostat model with general response functions, perturbed by white noise. Under appropriate assumptions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution by using stochastic Lyapunov analysis method. Our main effort is to construct the suitable Lyapunov function.

A supply chain member should set its margin later if another member's cost is highly uncertain

Recently, there have been several cases in which a large-scale retailer has demanded a margin for a consumer product from a supplier before the supplier has determined the margin or the wholesale price, reflecting a power shift from upstream suppliers to downstream retailers in supply chains. Given the recent change of power structures in supply chains, we investigate a practical decision-making problem of when a supply chain member should set its margin in the presence of uncertainty based on a stochastic game-theoretic supply chain model. We assume a typical two-echelon supply chain that consists of a manufacturer and a retailer, each of which determines the margin of a product based on private information of its marginal cost. Hence, the cost structure of a firm is uncertain and is known only to the firm. We construct an incomplete information game model with this setting, drawing the following clear-cut managerial implication: a supply chain member should set its margin later if the other member's cost is highly uncertain. By delaying decision-making, the late-moving member can make a more precise inference on the cost of the early-moving member by observing the margin demanded by the early-mover, thereby choosing a more desirable margin. Despite the current power shift from manufacturers to large-scale retailers in various consumer product categories, our result warns a retailer that if it assumes leadership to demand a margin from a manufacturer in an uncertain environment simply because it has power, it may cut its own throat.

A Collaborative Stochastic Closed-loop Supply Chain Network Design for Tire Industry

Recent papers in the concept of Supply Chain Network Design (SCND) have seen a rapid development in applying the stochastic models to get closer to real-world applications. Regaring the special characteristics of each product, the stracture of SCND varies. In tire industry, the recycling and remanufacturing of scraped tires lead to design a closed-loop supply chain. This paper proposes a two-stage stochastic model for a closed-loop SCND in the application of tire industry. The first stage of model optimizes the expected total cost. Then, financial risk has been considered as the second stage of model to control the uncertainty variables leading to a robust solution. To solve the developed problem, Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) have been used. To enhace the efficiency of metaheuristic algorithms, Response Surface Method (RSM) has been applied. Finally, the proposed model is evaluated by different test problem with different complexity and a set of metrics in terms of Pareto optimal solutions.

A two-stage multi-echelon stochastic blood supply chain problem

This paper presents a two-stage stochastic programming problem for red blood cells that simultaneously considers production, inventory and location decisions. In the first stage, the problem determines the number of mobile blood collection facilities to deploy, while the second stage determines inventory and production decisions. The problem aims to minimize three objective functions: the number of outdated units, system costs, and blood delivery time. Using the epsilon-constraint method, the tri-objective problem is converted to a single-objective mixed integer programming (MIP) problem which is solved using CPLEX for a real case study from The Hashemite Kingdom of Jordan. Finally, managerial insights are drawn from computational experiments.

Propagation of current waves along a transmission line with randomly located non-uniformities inside a rectangular resonator

Abstract. In this paper, we investigate the propagation of high-frequency current waves along a stochastic transmission line inside a rectangular cavity using as basis the model of a transmission line with the symmetry of the resonator. The stochastization of the line is created by a stochastically arranged chain of loads. Using similar models one also can take into account stochastic geometry of the line. Research has shown a significant difference between the propagation of the current wave along the transmission line with stochastic loads in free space and in the resonator. In the first case, the average square of the absolute value of the transmission coefficient exponentially tends to zero with increasing length of the line due to interference phenomena for current waves. In the second case, in the average, the current can penetrate through the stochastic chain of the loads due to the re-reflection of the signal from the walls of the resonator.

Stochastic multi-site supply chain planning in textile and apparel industry under demand and price uncertainties with risk aversion

A multi-product, multi-period, multi-site supply chain production and transportation planning problem, in the textile and apparel industry, under demand and price uncertainties is considered in this paper. The problem is formulated using a two-stage stochastic programming model taking into account the production amount, the inventory and backorder levels as well as the amounts of products to be transported between the different plants and customers in each period. Risk management is addressed by incorporating a risk measure into the stochastic programming model as a second objective function, which leads to a multi-objective optimization model. The objectives aim to simultaneously maximize the expected net profit and minimize the financial risk measured. Two risk measures are compared: the conditional-value-at-risk and the downside risk. As the considered objective functions conflict with each other’s, the problem solution is a front of Pareto optimal robust alternatives, which represents the trade-off among the different objective functions. A case study using real data from textile and apparel industry in Tunisia is presented to illustrate the effectiveness of the proposed model and the robustness of the obtained solutions.

Multi-objective stochastic closed-loop supply chain network design with social considerations

Nowadays, operation managers usually need efficient supply chain networks including important design factors such as economic and social considerations. The recent decade has seen a rapid development of controlling the uncertainty in supply chain configurations along with proposing novel solution approaches. By investigating the related studies, this paper shows that most of the current studies consider the economic aspects and just a few works present the two-stage stochastic programming as well as social considerations to design a closed-loop supply chain network. This motivated our attempts to consider economic and social aspects simultaneously by using the mentioned suppositions among the first studies. Another main contribution of this paper is the hybridization and tuning of a number of recent algorithms to address the problem. The results show that the proposed hybrid metaheuristic algorithms outperform the best existing techniques on the majority of case studies.

Writing, Proofreading and Editing in Information Theory

Information is a physical entity amenable to be described by an abstract theory. The concepts associated with the creation and post-processing of the information have not, however, been mathematically established, despite being broadly used in many fields of knowledge. Here, inspired by how information is managed in biomolecular systems, we introduce writing, entailing any bit string generation, and revision, as comprising proofreading and editing, in information chains. Our formalism expands the thermodynamic analysis of stochastic chains made up of material subunits to abstract strings of symbols. We introduce a non-Markovian treatment of operational rules over the symbols of the chain that parallels the physical interactions responsible for memory effects in material chains. Our theory underlies any communication system, ranging from human languages and computer science to gene evolution.