Stochastic Context Research Articles

A kernel mixing strategy for use in adaptive Markov chain Monte Carlo and stochastic optimization contexts

Performing Markov chain Monte Carlo parameter estimation on complex mathematical models can quickly lead to endless searching through highly multimodal parameter spaces. For computationally complex models, one rarely has prior knowledge of the optimal proposal distribution. In such cases, the Markov chain can become trapped near a suboptimal mode, lowering the computational efficiency of the method. With these challenges in mind, we present a novel MCMC kernel which incorporates both mixing and adaptation. The method is flexible and robust enough to handle parameter spaces that are highly multimodal. Other advantages include not having to locate a near-optimal mode with a different method beforehand, as well as requiring minimal computational and storage overhead from standard Metropolis. Additionally, it can be applied in any stochastic optimization context which uses a Gaussian kernel. We provide results from several benchmark problems, comparing the kernel's performance in both optimization and MCMC cases. For the former, we incorporate the kernel into a simulated annealing method and real-coded genetic algorithm. For the latter, we incorporate it into the standard Metropolis and adaptive Metropolis methods.

A Novel Virtual Power Plant Uncertainty Modeling Framework Using Unscented Transform

This paper proposes a new strategy for modeling predictability uncertainty in a stochastic context for decision making within a Virtual Power Plant (VPP). Modeling variable renewable energy generation is an essential step for effective VPP planning and operation. However, it is also a challenging task due to the uncertain nature of its sources. Therefore, developing tools to effectively predict these uncertainties is essential for the optimal participation of VPPs in the electricity market. The purpose of this paper is to present a novel method to model the uncertainties associated with energy dispatching in a VPP using the Unscented Transform (UT) method. The proposed algorithm minimizes the risks associated with the VPP operation in a computationally efficient and simple manner, and can be used in real-time on a power system. The proposed framework was evaluated based on an Electric Power System (EPS) model with historical data. Case studies have been performed to demonstrate the effectiveness of the proposed framework in minimizing power demand and renewable-energy-forecasting uncertainty for a VPP.

Risk-Averse Bargaining in a Stochastic Optimization Context

Problem definition: Bargaining situations are ubiquitous in economics and management. We consider the problem of bargaining for a fair ex ante distribution of random profits arising from a cooperative effort of a fixed set of risk-averse agents. Our approach integrates optimal managerial decision making into bargaining situations with random outcomes and explicitly models the impact of risk aversion. The proposed solution rests on a firm axiomatic foundation and yet allows to compute concrete bargaining solutions for a wide range of practically relevant problems. Methodology/results: We model risk preferences using coherent acceptability functionals and base our bargaining solution on a set of axioms that can be considered a natural extension of Nash bargaining to our setting. We show that the proposed axioms fully characterize a bargaining solution, which can be efficiently computed by solving a stochastic optimization problem. We characterize special cases where random payoffs of players are simple functions of overall project profit. In particular, we show that, for players with distortion risk functionals, the optimal bargaining solution can be represented by an exchange of standard options contracts with the project profit as the underlying asset. We illustrate the concepts in the paper with a detailed example of risk-averse households that jointly invest into a solar plant. Managerial implications: We demonstrate that there is no conflict of interest between players about management decisions and that risk aversion facilitates cooperation. Furthermore, our results on the structure of optimal contracts as a basket of option contracts provides valuable guidance for negotiators. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.1076 .

Distributed Stochastic Dual Subgradient for Constraint-Coupled Optimization

In this letter we consider a distributed stochastic optimization framework in which agents in a network aim to cooperatively learn an optimal network-wide policy. The goal is to compute local functions to minimize the expected value of a given cost, subject to individual constraints and average coupling constraints. In order to handle the challenges of the distributed stochastic context, we resort to a Lagrangian duality approach that allows us to derive an associated stochastic dual problem with a separable structure. Thus, we propose a distributed algorithm, without a central coordinator, that exploits consensus iterations and stochastic approximation to find an optimal solution to the problem, with attractive scalability properties. We demonstrate convergence of the proposed scheme and validate its behavior through simulations.

When expansion stalls: an extension to the concept of range pinning in ecology

Identifying the factors modulating range expansion is essential to accurately predict changes in the spatial distribution of populations. By preventing population growth after dispersal, Allee effects can lead to front stops in discrete space, called 'pinning' if permanent. However, other mechanisms, such as positive density‐dependent dispersal, have also been shown to affect the rate of range expansion and generate discrete‐space front stops, albeit temporarily. In this study, we investigated the stability of the front stops generated by such mechanisms in relation to the carrying capacity of the environment. To this end, we performed artificial range expansions in discrete space using stochastic simulations and microcosm experiments. Simulation results confirmed that density‐dependent dispersal alone can generate sustained front stops, albeit for a limited range of carrying capacities. We also highlighted the synergy between Allee effects and density‐dependent dispersal on pinning emergence. Experimental results, obtained using a model species known to exhibit density‐dependent dispersal, but without Allee effects, confirmed the model results. Furthermore, our study raises the issue of carefully considering the conditions for pinning stability, in a stochastic context and depending on the time‐scale considered.

Stochastic EM methods with variance reduction for penalised PET reconstructions

Expectation-maximisation (EM) is a popular and well-established method for image reconstruction in positron emission tomography (PET) but it often suffers from slow convergence. Ordered subset EM (OSEM) is an effective reconstruction algorithm that provides significant acceleration during initial iterations, but it has been observed to enter a limit cycle. In this work, we investigate two classes of algorithms for accelerating OSEM based on variance reduction for penalised PET reconstructions. The first is a stochastic variance reduced EM algorithm, termed as SVREM, an extension of the classical EM to the stochastic context that combines classical OSEM with variance reduction techniques for gradient descent. The second views OSEM as a preconditioned stochastic gradient ascent, and applies variance reduction techniques, i.e., SAGA and SVRG, to estimate the update direction. We present several numerical experiments to illustrate the efficiency and accuracy of the approaches. The numerical results show that these approaches significantly outperform existing OSEM type methods for penalised PET reconstructions, and hold great potential.

The strong trace property and the Neumann problem for stochastic conservation laws

We establish the well-posedness of the Neumann problem for stochastic conservation laws with multiplicative noise. As a crucial point in order to prove the uniqueness of the kinetic solution to the referred problem we establish a new strong trace theorem for stochastic conservation laws, which extends to the stochastic context the pioneering theorem by Vasseur. Existence of kinetic solutions is proved through the vanishing viscosity method and the detailed analysis of the corresponding stochastic parabolic problem is also made here for the first time, as far as the authors know.

Analyzing accessibility to fire stations: A floating catchment area model for stochastic transportation networks with travel time correlation

AbstractImproving the spatial accessibility of fire stations is a key factor in minimizing property loss and reducing injuries and deaths. Most existing studies neglect the effect of travel time correlation and uncertainty on the level of accessibility in non‐normally distributed networks. In this article, a two‐step floating catchment area (2SFCA) model is introduced to measure accessibility in correlated non‐normal uncertain transportation networks. The model extends the conventional 2SFCA measures by considering the catchment area of supply and demand locations in stochastic contexts. The proposed measure is applied to a study area to investigate the impacts of travel time correlation, travel time uncertainty, and non‐normal distributions on the accessibility value. It is further used to analyze access inequality between different areas of the case study and to identify segregated places in terms of accessibility to the fire stations. In addition, the conventional 2SFCA measure is executed to provide an evaluation of the outputs of the proposed model. Results highlight significant difference between the introduced model and the other existing measure. They also show inequality of accessibility in the study area and the way that the model parameters affect the accessibility level. Furthermore, results offer several methodological implications for accessibility analysis in time‐dependent networks.

Formulation and probabilistic assessment of reversible biodegradation pathway of Diclofenac in groundwater

We present a conceptual and mathematical framework leading to the development of a biodegradation model capable to interpret the observed reversibility of the Pharmaceutical Sodium Diclofenac along its biological degradation pathway in groundwater. Diclofenac occurrence in water bodies poses major concerns due to its persistent (and bioactive) nature and its detection in surface waters and aquifer systems. Despite some evidences of its biodegradability at given reducing conditions, Diclofenac attenuation is often interpreted with models which are too streamlined, thus potentially hampering appropriate quantification of its fate. In this context, we propose a modeling framework based on the conceptualization of the molecular mechanisms of Diclofenac biodegradation which we then embed in a stochastic context, thus enabling one to quantify predictive uncertainty. We consider reference environmental conditions (biotic and denitrifying) associated with a set of batch experiments that evidence the occurrence of a reversible biotransformation pathway, a feature that is fully captured by our model. The latter is then calibrated in the context of a Bayesian modeling framework through an Acceptance-Rejection Sampling approach. By doing so, we quantify the uncertainty associated with model parameters and predicted Diclofenac concentrations. We discuss the probabilistic nature of uncertain model parameters and the challenges posed by their calibration with the available data. Our results are consistent with the recalcitrant behavior exhibited by Diclofenac in groundwater and documented through experimental data and support the observation that unbiased estimates of the hazard posed by Diclofenac to water resources should be assessed through a modeling strategy which fully embeds uncertainty quantification.

Simultaneous Planning of Production, Setup and Maintenance for an Unreliable Multiple Products Manufacturing System

The work presented in this paper addresses the problem of joint optimization of the production, setup and corrective maintenance activities of a manufacturing system. This system consists of a machine subject to breakdowns and repairs and producing two types of parts. A corrective maintenance strategy whose repair rate depends on the number of setup operations already performed on the production system is considered in this work. The objective of this research is to propose a policy that controls production, setup, and corrective maintenance. The contribution of this paper is through the control of the repair rate, combined with the planning of production and setup in a dynamic and stochastic context. Optimality conditions in the form of Hamilton-Jacoby-Bellman (HJB) equations are obtained and a numerical approach is proposed in order to deal with the joint optimization issues. Extensive simulations are performed to address many scenarios that illustrate the interactions between production, setup and maintenance activities.

Simultaneous Planning of Production, Setup and Maintenance for an Unreliable Multiple Products Manufacturing System

The work presented in this paper addresses the problem of joint optimization of the production, setup and corrective maintenance activities of a manufacturing system. This system consists of a machine subject to breakdowns and repairs and producing two types of parts. A corrective maintenance strategy whose repair rate depends on the number of setup operations already performed on the production system is considered in this work. The objective of this research is to propose a policy that controls production, setup, and corrective maintenance. The contribution of this paper is through the control of the repair rate, combined with the planning of production and setup in a dynamic and stochastic context. Optimality conditions in the form of Hamilton-Jacoby-Bellman (HJB) equations are obtained and a numerical approach is proposed in order to deal with the joint optimization issues. Extensive simulations are performed to address many scenarios that illustrate the interactions between production, setup and maintenance activities.

Analysis of Knocking Characteristic in Dual Fuel Engine - the Effects on Diethyl Ether

In Diesel engines, where fuel is pumped into highly compressed air towards the end of the compression cycle, knocking is more or less unavoidable. By this time there is already a quantity of fuel in the combustion chamber which will first burn in areas of higher oxygen density before the full charge is combusted. The sudden rise in pressure and temperature produces the distinctive 'knock' or 'clatter' diesel, some of which must be allowed in engine design. The aim of knock control strategies is to try to maximize the trade-off between protecting the engine from damaging knock incidents, and optimizing the output torque of the engine. Knock events are a random process and independent. Knock controllers can't be programmed in a deterministic model. Due to the random nature of arriving knock events, a single time history simulation or experiment of knock control methods cannot provide a repeatable measurement of the controller efficiency. The desired trade-off must therefore be achieved in a stochastic context that could provide an appropriate environment for designing and evaluating the output of various knock control strategies with rigorous statistical properties. Clutching characteristics of a dual fuel diesel engine with direct injection of diesel and a liquid petroleum product in dual fuel mode. The engine is tested for knock reduction by adding Diethyl ether in to the diesel along with Liquid petroleum product. Variation of knocking was plotted with respect to different parameters and the result booted as knocking is minimized by the addition of diethyl ether.

Production planning and control of unreliable hybrid manufacturing-remanufacturing systems with quality-based categorization of returns

Because of environmental and economic benefits, remanufacturing has become an integral part of a large number of manufacturing companies. This new reality forces them to focus on production planning and control (PPC) to minimize costs and reduce the environmental impact by decreasing waste and resource consumption. This paper deals with a PPC problem within a hybrid manufacturing-remanufacturing system (HMRS), which evolves in a constrained dynamic and stochastic context. The problem considers jointly three central decisions to optimize the long-term total cost. The main objective is to find both remanufacturing and manufacturing production rates as well as the policy used to switch between the remanufacturing modes of returns with different quality conditions. The optimal control policy characterization is performed combining optimal control theory and numerical techniques. Such policies consist of hedging point ones and stock-based switching decisions. Additional relevant control policies adapted from the literature are also considered and compared to the developed policies through a combined simulation-optimization approach, which optimize the policies control parameters. Both illustrative examples and a comparative analysis bring out the practical aspects of the proposed control policies and the interdependence between the quality conditions of returns and the production control settings. They also bring effective solutions to assist decision makers controlling simultaneously remanufacturing, manufacturing and switching operations for proper management of resource utilization, inventories and productivity.

Evaluating Gaussian process metamodels and sequential designs for noisy level set estimation

We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic simulators, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student-t observations; (ii) Student-t processes (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1–6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.

Technical efficiency and its determinants in the Indian textile garments industry

PurposeThis paper aims to examine technical efficiency and its determinants in Indian textile garments industry in post-agreement on textiles and clothing regime and evaluate the technical efficiency among micro, small and medium enterprises (MSMEs) firms.Design/methodology/approachThis study uses unbalanced panel data for the period 2005–2010 to 2015–2016. The stochastic frontier function is used to estimate technical efficiency and its determinants.FindingsThe results show that the overall ecosystem of textile garments’ value chains could be improved to enhance the technical efficiency thereof. The result also reveals that small-scale firms have the highest technical efficiency scores, and medium-scale firms have the least technical efficiency score among all the categories of MSMEs.Research limitations/implicationsThe textile garments industry needs to define its innovation strategies, as these strategies lead to different results that can be achieved only through the management of resources dedicated to the generation and implementation of innovations.Practical implicationsThis study has shown that to offset India’s cost disadvantage in the international markets, there is a need to develop an ecosystem of textile manufacturing and value chains, eliminate the inverted duty structure (where inputs are taxed at a higher rate than the final product) and switch over from shuttle looms toward shuttle-less looms. This would unleash the potential of textile and garments industry and make it globally competitive and technically efficient. Further, there will be an alignment with the ease of doing business with an appropriate mix of policy, technology, institution, infrastructure, information and services.Originality/valueUsing frontier production function takes stochastic context into account for the dynamic character of technical efficiency and its components. Most of the past studies have assessed technical efficiency at the aggregate level using three-digit National Industrial Classification (NIC) or four-digit NIC code. An analysis at higher levels of aggregation masks the variation in technical efficiency. This study used five-digit NIC data to measure the firm-specific technical efficiency of the textile industry. According to the authors’ knowledge, this study is the first of its kind in the Indian textile industry using stochastic frontier approach and panel data. Further, it also looks at the contribution of different determinants in technical efficiency to the firms.

Stochastic attentions and context learning for person re-identification.

The discriminative parts of people’s appearance play a significant role in their re-identification across non overlapping camera views. However, just focusing on the discriminative or attention regions without catering the contextual information does not always help. It is more important to learn the attention with reference to their spatial locations in context of the whole image. Current person re-identification (re-id) approaches either use separate modules or classifiers to learn both of these; the attention and its context, resulting in highly expensive person re-id solutions. In this work, instead of handling attentions and the context separately, we employ a unified attention and context mapping (ACM) block within the convolutional layers of network, without any additional computational resources overhead. The ACM block captures the attention regions as well as the relevant contextual information in a stochastic manner and enriches the final person representations for robust person re-identification. We evaluate the proposed method on 04 public benchmarks of person re-identification i.e., Market1501, DukeMTMC-Reid, CUHK03 and MSMT17 and find that the ACM block consistently improves the performance of person re-identification over the baseline networks.

Water–Food–Energy Nexus Tradeoffs in the São Marcos River Basin

Given its potentialities and characteristics, energy generation, food production, and water availability have a strong interdependency and correlation. Water is needed to produce energy and food, while energy is required to produce water and food. This nexus brings several challenges when scarce water resources must be allocated among competing uses, often in the form of unexpected tradeoffs. Addressing those challenges requires knowledge about the water–food–energy nexus and the associated tradeoffs to support water allocation and management decisions. Those tradeoffs are still not properly understood in the uncertain and stochastic context of water availability. When not properly accounted for, the results are conflicts, loss of investments, environmental impacts, and limited effectiveness of sectoral policies, all of which undermine a country’s development model relying on water and energy security. This paper addresses the competitive uses of recent irrigated agriculture expansion and existing hydropower production in a Brazilian watershed with water conflicts, assessing the economic tradeoffs and water values between energy and irrigated agricultural production under uncertainty. An explicitly stochastic hydro-economic model is used to determine water’s economic value and its variation in space and time. Results indicate that the agricultural benefits outweigh the potential energy losses, and the best course of action should explore an economically compensated reallocation strategy, upon negotiation among users, rather than imposing water supply cutbacks to the agriculture sector.

Logic-Based Benders Decomposition and Binary Decision Diagram Based Approaches for Stochastic Distributed Operating Room Scheduling

The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery durations are considered to be uncertain. In order to obtain solutions for the challenging stochastic model, we use sample average approximation and develop two enhanced decomposition frameworks that use logic-based Benders (LBBD) optimality cuts and binary decision diagram based Benders cuts. Specifically, to the best of our knowledge, deriving LBBD optimality cuts in a stochastic programming context is new to the literature. Our computational experiments on a hospital data set illustrate that the stochastic formulation generates robust schedules and that our algorithms improve the computational efficiency. Summary of Contribution: We propose a new model for an important problem in healthcare scheduling, namely, stochastic distributed operating room scheduling, which is inspired by a current practice in Toronto, Ontario, Canada. We develop two decomposition methods that are computationally faster than solving the model directly via a state-of-the-art solver. We present both some theoretical results for our algorithms and numerical results for the evaluation of the model and algorithms. Compared with its deterministic counterpart in the literature, our model shows improvement in relevant evaluation metrics for the underlying scheduling problem. In addition, our algorithms exploit the structure of the model and improve its solvability. Those algorithms also have the potential to be used to tackle other planning and scheduling problems with a similar structure.

A joint production and carbon trading policy for unreliable manufacturing systems under cap-and-trade regulation

Manufacturing systems are one of the largest emitters of carbon emissions. Governments enforce environmental regulations to control and reduce such emissions. Cap-and-trade is one of the most efficient and widely-used regulations in which a tradable initial allowance is given to each emitter to sell or buy in the carbon market. In this study, we address the trading and production planning problem for unreliable manufacturing systems under cap-and-trade regulation. Regarding the carbon price which randomly changes in the market, it is challenging and complex for companies to know how to determine their production rate and trading quantity to take advantage of the carbon market. We aim to develop a new joint production and trading control policy for unreliable manufacturing systems considering the stochastic and dynamic context. Our objective is to guide the managers to jointly determine when to buy/sell allowances or increase/decrease the production rate to minimize the total cost and reduce carbon emissions of the system. The policy is specifically designed for the cap-and-trade regulation to minimize total costs consisting of emission, backlog, inventory, trading, and transaction costs. Simulation modelling, experimental design, and response surface methodology are implemented to optimize parameters of our proposed control policy. Finally, sensitivity analysis as well as comparative study are carried out to show how our proposed joint policy brings significant cost saving and emissions reduction in comparison with existing policies adapted from the literature.

Stochastic nonlinear ground response analysis via a case study site in Shiraz city

This study attempts to investigate the influence of the dynamic soil properties uncertainties on ground response analysis via a case study site. For this purpose, nonlinear time-domain ground response analysis and uncertainties in soil parameters are coupled simultaneously using a coded program in MATLAB. To take full advantage of the real data, two investigation boreholes are drilled in the site. The analysis is performed deterministically and then extended to the stochastic context in order to take into consideration the variability of Plastic Index, shear wave velocity, and unit weight of the soil. In a part of this study, the capability of the three different methods for predicting the stochastic fundamental period of the site including modal analysis, approximate method, and nonlinear method, is investigated. To achieve the advantage of the stochastic analysis, the maximum Coefficient of Variation (COV) of the peak ground motion parameters, fundamental period, response spectrum, and amplification factor are calculated. The results demonstrate that the heterogeneity of the soil parameters has a significant effect on the variation of the surface Peak Ground Displacement (PGD). Among the other stochastic responses, the fundamental period has received the least effect from soil parameters’ uncertainty.