Stochastic Demand Model Research Articles

Stochastic measurement-based multi-cloud consolidation for efficient resource distribution

In distributed cloud systems, due to high computational complexity, existing methods cannot infinitely reduce the measurement interval to obtain the mean demand. However, considering both the unpredictability of demand and the diversity of pricing adds significant complexity to the problem. In response, we introduce an efficient algorithm called Stochastic Demand-oriented Resource consolidation based on Meta-heuristics (SDRM). The algorithm introduces the stochastic demand model and formulates a cross-cloud demand consolidation and resource scheduling problem, and tries to solve it efficiently by combining differential evolution algorithm with dynamic programming optimization. The results are provided for experiments utilizing both simulated and real-world data. It demonstrates that compared with traditional algorithms, increasing gain by up to 53%, SDRM just incurs an affordable time expense (i.e., 1.10-2.51 times that of existing algorithms). Therefore, SDRM stands as a compelling solution for resource distribution in heterogeneous cloud environments.

Dynamic pricing strategies for efficient inventory management with auto-correlative stochastic demand forecasting using exponential smoothing method

The research presents a novel approach to inventory modelling, emphasizing stochastic demand and dynamic pricing strategies for a seasonal sales framework. The methodology divides the sales season into intervals, each associated with distinct pricing strategies influenced by stochastic factors. The study employ exponential smoothing for demand forecasting, optimizing inventory replenishment and dynamic pricing strategies through developed algorithms. Notably, the study determine the optimal smoothing parameter for demand forecasting, balancing responsiveness to recent demand patterns with long-term stability. Proposed research achieves a comprehensive framework empowering businesses to enhance competitiveness and profitability by addressing challenges of stochastic demand and dynamic pricing. Dynamic pricing strategies outperformed classical strategies, allowing businesses to respond promptly to demand fluctuations and optimize profit margins during sales seasons. Incorporating stochastic demand models enabled organizations to implement safety stock and buffer inventory levels effectively, mitigating risks associated with uncertain demand patterns. Real-time data analysis was crucial for adjusting price dynamics and making effective management decisions, leading to improved financial performance. The iterative nature of dynamic pricing strategies emphasized the importance of continuous refinement to adapt to evolving market dynamics. This approach enables data-driven decisions, adaptation to market fluctuations, and improved inventory management despite unpredictable demand. Ultimately, this study provides valuable insights and methodologies applicable across industries for efficient and profitable inventory management.

Optimal pricing for dual-channel retailing with stochastic attraction demand model

In dual-channel supply chains, where retailers sell their goods both online and in physical stores, determining the optimal pricing strategy while considering customer behavior is a critical challenge. This study introduces and investigates a dual-channel pricing model that accounts for customer channel choice behavior. Drawing inspiration from market-share models, we incorporate a demand model that reflects the attraction between online and physical stores. Our approach includes stochastic assumptions for potential market demand and price-based interactions between the two channels. In particular, we model the channel’s stochastic demand as a non-linear function of prices and we allow for different customer reactions when the physical store runs out of stock. This paper makes two key contributions. First, we highlight the analytical complexity involved in verifying the joint concavity of the retailer’s expected profit function with respect to selling prices. To address this challenge, we introduce a novel approach to establish the existence of optimal global prices in the context of non-linear demand and a non-linear, non-concave objective function. Secondly, our study offers practical insights by applying the model to various operational scenarios. We provide guidance on the best pricing strategy when physical store capacity is limited. Depending on customer channel preferences, prioritizing the showroom may lead to higher profits. However, optimizing for profit could result in a reduced market share. In a showroom configuration, the retailer’s choice may shift between exclusive physical and exclusive online retailing to maximize profit.

Reduction in water consumption in premise plumbing systems: Impacts on lead concentration under different water qualities

Water conservation measures are increasing in response to regulatory requirements addressing the need for lower environmental footprint and in response to water shortages. In households with lead service lines (LSLs), lowering consumption can adversely impact lead release as it will increase stagnation. Using a lead dissolution model and data from extensive pilot studies on excavated LSLs, the impact of adaptation to different water conservation strategies on dissolved lead contamination at the kitchen tap is assessed under three water qualities and three LSL lengths (3, 14 and 30 m) using hydraulic and water quality modelling. Consumers' behavioural variability is also assessed based on integration of EPANET and results of the stochastic water demand model SIMDEUM. Demand reduction increased the dissolved lead concentrations (Pbdiss) at the end of the LSL with mean values ranging from 28.4 to 63.3 μg/L (without corrosion control) and from 4.6 to 9.9 μg/L with corrosion control (addition of orthophosphate and pH adjustment). Adding orthophosphate (1 mg P/L) to the water reduces the mean Pbdiss values at the kitchen tap from 7.1 μg/L to 1.2 μg/L for a high water demand scenario and from 31.2 to 4.9 μg/L for a low water demand scenario. Finally, the Integrated Exposure Uptake Biokinetic (IEUBK) model is used to predict the potential blood lead levels (BLLs) for children aged 0–84 months. Results showed that the orthophosphate addition of only 1 mg P/L can significantly decrease the proportion of children with a BLL >5 μg/dL, from 82 % to 17 %, under the most extreme water conservation scenario studied, using the 90th percentile of Pbdiss concentrations during usage at kitchen tap. Wide variations of Pbdiss concentrations at the kitchen tap were calculated at times of use over a week (up to 155 μg/L in lower demand scenarios, without corrosion control) showing evident limitations of single random daytime sampling.

Aggregate demand response strategies for smart communities with battery-charging/switching electric vehicles

Demand response (DR) plays an important role in the peak shaving and load-shifting of a community, but the avalanche effect creates a huge obstacle in DR with uncoordinated usage of appliances and charging of electric vehicles (EVs). Recognizing the remarkably rising deployment of EVs, there is great potential to coordinate EVs' charging in a charging station or a battery switching station for providing DR. However, the potential benefits of the battery-switching EVs for providing DR and their impacts on the aggregate load of the community have not been fully studied. In this regard, the present study proposes two novel aggregate community-level DR strategies, i.e., a strategy employing battery-charging EVs and a strategy employing battery-switching EVs. The proposed strategies are compared with the conventional strategy that only incorporates community battery energy storage for enabling peak shaving. The cost optimization is conducted with optimization parameters including demand limits during different periods and the power and energy capacity of the battery energy storage system. A stochastic bottom-up demand model for households, a probabilistic model for predicting loads of EVs, and a redistribution time-of-use tariff are implemented in the optimization. A group with 20 households and 20 EVs in New York, USA is used in the case study. The results in the case study show that the total annual costs (electricity tariff cost and battery energy storage cost if any) are reduced by 63.3 %, 54.0 %, and 14.7 % under the battery-switching EV strategy, the battery-charging EV strategy, and the battery energy storage strategy compared to the base case (i.e., DR-free strategy), respectively. Additionally, the battery-switching EV strategy enables DR throughout the day with the maximum temporal flexibility. Last, the developed two EV strategies can provide a good stability of the household loads on the grid and avoid the avalanche effect.

A MODEL TO DEVELOP HOTEL MANAGEMENT SYSTEM TO OPTIMIZE REVENUE

Hotel provides facilities for customers and earns revenue. In this sector of business, many challenges might be faced by the hotel management since there arise price competition between hotels. Hotel management has to follow some strategies to earn maximum revenue. Though it is difficult to estimate actual profit in any epidemic situations, we showed the optimal revenue is possible even within this kind of epidemic situations. And to do this, a revenue management model was developed in terms of pricing and room allocation capacity. Price is the sole factor in this model. Two types of demand models are used, one is deterministic demand model and another is stochastic demand model and both are used for pricing model and capacity model formulation. This work showed how hotels can gain more revenue by using proposed capacity and pricing model, even in the time of global crisis situation like COVID-19 epidemic.

Analytic Features of Consumer Free Riding on Carbon Emission and Impact of Dual-Channel Clsc on Environment

Consumer free riding and the environmental impact of Dual-Channel Closed Loop Supply Chain (CLSC) were explored in this article. There was an extensive examination of the literature and a statistical explanation of various conditions in which people either free ride or do not ride. Electronic commerce (EC) generates revenue for manufacturers. However, the production retailer’s overall fossil fuels (SCE) increase, suggesting that is a government tax (GT) on EC could help reduce both client FR and overall carbon emissions (CE). E-tailers must also receive subsidies from the government, which will help ensure social security. Many intriguing research avenues have emerged from the findings. In an effort to address a need in the literature, this study examines CE in a CLSC system where a producer allocates products via traditional and e-tailer channels and purchases recyclable materials from customers for remanufacturing. A retailer, an e-tailer, or a third-party or multi-party that collects old products might be the focus of future research. A new stochastic demand or lead time model may be a potential field for further investigation.

Accelerating Benders decomposition for stochastic incomplete multimodal hub location problem in many-to-many transportation and distribution systems

To customize the hub location model for application in many-to-many transportation and distribution systems, this study introduces a stochastic incomplete multimodal hub location problem with multiple assignments and delivery-time restrictions. This problem explicitly considers the mode-specific hub and link, incomplete inter-hub connectivity, multiple-assignment pattern of demand nodes to hubs and two types of uncertainties in an expected cost-minimization context with delivery-time restrictions. Using a filtering technique, this study first presents a sophisticated path-based formulation for the problem with uncertain demand embedded in a two-stage stochastic programming framework. More importantly, the stochastic demand model is proven to be equivalent to the corresponding deterministic expected value problem (EVP), which can be solved to optimality using Gurobi. By considering the uncertainty in transportation cost, this study further proposes an associated two-stage stochastic program, in which the EVP equivalence does not hold. To solve the stochastic transportation cost version efficiently, the study implements an improved Benders decomposition algorithm by adopting a sample average approximation approach and a dualization strategy. To accelerate the convergence of the proposed Benders decomposition algorithm, this study also presents a multi-cut reformulation and a cut-loop stabilization strategy for Benders acceleration. Numerical experiments based on the well-studied Turkish network and AP dataset corroborate the advantages of the proposed models and the effectiveness of the developed approaches. Some key managerial insights are summarized to effectively guide incomplete, multimodal hub network designs against uncertainty in many-to-many transportation and distribution practices.

Assessing the ability of regions to attract foreign tourists: The case of Italy

This study examines the ability of Italian regions to attract foreign tourists and the factors influencing the choice of regional destinations using a novel Stochastic Frontier Demand Model. The results show that several factors including climate, seasonality, cultural heritage and infrastructures influence tourism performance. Easy accessibility to World Heritage Sites drives international tourism demand too. On average, Southern regions lie below the stochastic frontier and are inefficient, while Northern regions tend to be efficient. Calabria, Sardinia and Molise have a low ability to entice foreign tourists, while Veneto maximizes the number of tourist arrivals, overnight stays and expenditures. JEL Classification: C51; R11; Z32.

Short‐Term Variability Effect on Peak Demand: Assessment Based on a Microcomponent Stochastic Demand Model

AbstractPeak demand plays a major role in water distribution system design. Peak demand assessment is currently facing a double challenge: shifting toward a probabilistic approach, and considering the effect of different spatial and temporal resolutions. Most probabilistic approaches so far have focused on inferring scaling laws by analyzing measurement time series for different spatial and temporal resolutions. The aim of this paper is two‐fold: (a) to present a novel analytical approach that enables to assess the short‐term variability effect on probabilistic peak demands for different spatial and temporal scales, and (b) to ease the understanding of peak demand factors thanks to a physically based (rather than an empirical) approach. This is possible by combining the principles of peak demand analysis with a microcomponent‐based (i.e., end‐use oriented) demand model that enables assessment of short‐term variability. The methodology here proposed is applied to two case studies with the purpose of validating the approach and showing its full potential. Results prove that stochastic demand models can be a powerful tool for peak demand assessment.

A Model for Prepositioning Emergency Relief Items Before a Typhoon with an Uncertain Trajectory

Problem definition: We study the problem faced by the Philippine Department of Social Welfare (DSWD) in prepositioning relief items before landfall of an oncoming typhoon whose future outcome (trajectory and wind speed) is uncertain. Academic/practical relevance: The importance of prepositioning was a hard lesson learned from Super Typhoon Haiyan that devastated the Philippines in 2013, when many affected by the typhoon did not have immediate access to food and water. In a typhoon-prone country, it is important to build resilience through an effective prepositioning model. Methodology: By engaging with DSWD, we developed a practically relevant stochastic prepositioning model. The probability models of municipality-level demand and of supply damage are both dependent on the typhoon outcome. A linear mixed effects model is used to estimate the dependence of demand on the typhoon outcome using a large data set that includes the municipality-level impact of West Pacific typhoons during 2008–2019. The model has two objectives motivated from the practical realities of the Philippine network: prioritizing regions with high demand and prepositioning in all affected regions proportional to their total demand. Results: We find that the choice of the demand model significantly impacts the distributed relief items in the Philippine setting where it is challenging to adjust region-level supply after a typhoon. By using the historical data on past typhoons, we show that in this setting, our stochastic demand model provides the best distribution to date of any existing demand models. Managerial implications: There currently exists a gap between theory and practice in the management of relief inventories. We contribute toward bridging this gap by engaging with DSWD to develop a practically relevant relief distribution model. Our work is an effective example of collaboration with government and nongovernment agencies in developing a relief distribution model.

Dynamic Time Warping Clustering to Discover Socioeconomic Characteristics in Smart Water Meter Data

Socio-economic characteristics are influencing the temporal and spatial variability of water demand - the biggest source of uncertainties within water distribution system modeling. Improving our knowledge on these influences can be utilized to decrease demand uncertainties. This paper aims to link smart water meter data to socio-economic user characteristics by applying a novel clustering algorithm that uses dynamic time warping on daily demand patterns. The approach is tested on simulated and measured single family home datasets. We show that the novel algorithm performs better compared to commonly used clustering methods, both, in finding the right number of clusters as well as assigning patterns correctly. Additionally, the methodology can be used to identify outliers within clusters of demand patterns. Furthermore, this study investigates which socio-economic characteristics (e.g. employment status, number of residents) are prevalent within single clusters and, consequently, can be linked to the shape of the cluster's barycenters. In future, the proposed methods in combination with stochastic demand models can be used to fill data-gaps in hydraulic models.

Staff scheduling in blood collection problems

To improve the blood collection volume and reduce the staff costs, this study investigates the staff scheduling problem faced by blood donation center under variant situations derived from reality. Staff scheduling for blood donation center is a complex task due to the stochastic arriving of blood donors. In this study, we propose the deterministic demand model and stochastic demand model of blood donors according to the number of donors arriving at donation sites. Then, based on the deterministic demand and the stochastic demand models, we consider the number of staff in the blood donation center and group blood donation. Five blood collection scenarios are proposed using the combination of donors and staff. To solve the proposed models, linear transformation and lexicographic order optimal method are applied. To verify the effectiveness of the proposed models, both large-scale and small-scale numerical experiments are conducted and its the stability is also validated using the 10 times of random numerical experiments. All of the experimental results show that the proposed models need few staff when facing adequate staff scenarios, and reduce the number of donors when facing inadequate staff scenarios.

A solution algorithm for multi-period bi-level channel optimization with dynamic price-dependent stochastic demand

We extend the single-period decentralized channel optimization problem with stochastic demand into a multi-period, non-autonomous one and propose an efficient general solution algorithm for it. A supply channel composed of two price-setting agents in a bi-level (Stackelberg) framework has to address an uncertain dynamic demand for a perishable good at different times. The stochastic demand model is general (additive-multiplicative). A class of price-dependent memory functions is embedded in the proposed representation of uncertain demand such that they carry the effect of demand level at present over to the demand in the future. Due to this dependence of the current demand to the pricing history, the state space of the ensuing games becomes highly nested. The proposed iterative algorithm decouples the nested equilibria into separate yet interdependent sub-problems and provides explicit solutions. All the model variables and parameters are considered explicitly time-dependent enabling the model to cover cases with finite and infinite time-horizons. Flexibility and generality of our solution scheme make it applicable to a wide variety of economic contexts. In a series of examples we demonstrate how, fed by different market specifications and memory functions, the solution algorithm can find equilibrium results for a diverse set of scenarios at different times.

Value of Point-of-Load Voltage Control for Enhanced Frequency Response in Future GB Power System

The need for Enhanced Frequency Response (EFR) is expected to increase significantly in future low-carbon Great Britain (GB) power system. One way to provide EFR is to use power electronic compensators (PECs) for point-of-load voltage control (PVC) to exploit the voltage dependence of loads. This paper investigates the techno-economic feasibility of such technology in future GB power system by quantifying the total EFR obtainable through deploying PVC in the urban domestic sector, the investment cost of the installment and the economic and environmental benefits of using PVC. The quantification is based on a stochastic domestic demand model and generic medium and low-voltage distribution networks for the urban areas of GB and a stochastic unit commitment (SUC) model with constraints for secure post-fault frequency evolution is used for the value assessment. Two future energy scenarios in the backdrop of 2030 with `smart' and `non-smart' control of electric vehicles and heat pumps, under different levels of penetration of battery energy storage system (BESS) are considered to assess the value of PEC, as well as the associated payback period. It is demonstrated that PVC could effectively complement BESS towards EFR provision in future GB power system.

A Comparative Study of Optimal Energy Management Strategies for Energy Storage with Stochastic Loads

This paper aims to present the significance of predicting stochastic loads to improve the performance of a low voltage (LV) network with an energy storage system (ESS) by employing several optimal energy controllers. Considering the highly stochastic behaviour that rubber tyre gantry (RTG) cranes demand, this study develops and compares optimal energy controllers based on a model predictive controller (MPC) with a rolling point forecast model and a stochastic model predictive controller (SMPC) based on a stochastic prediction demand model as potentially suitable approaches to minimise the impact of the demand uncertainty. The proposed MPC and SMPC control models are compared to an optimal energy controller with perfect and fixed load forecast profiles and a standard set-point controller. The results show that the optimal controllers, which utilise a load forecast, improve peak reduction and cost savings of the storage device compared to the traditional control algorithm. Further improvements are presented for the receding horizon controllers, MPC and SMPC, which better handle the volatility of the crane demand. Furthermore, a computational cost analysis for optimal controllers is presented to evaluate the complexity for a practical implementation of the predictive optimal control systems.

Rainwater harvesting for urban flood management – An integrated modelling framework

It is well known that rainwater harvesting (RWH) can augment water supply and reduce stormwater pollutant discharges. Due to the lack of continuous 2D modelling of urban flood coverage and its associated damage, the ability of RWH to reduce urban flood risks has not been fully evaluated. Literature suggests that small distributed storage spaces using RWH tanks will reduce flood damage only during small to medium flooding events and therefore cumulative assessment of their benefits is needed. In this study we developed a new integrated modelling framework that implements a semi-continuous simulation approach to investigate flood prevention and water supply benefits of RWH tanks. The framework includes a continuous mass balance simulation model that considers antecedent rainfall conditions and water demand/usage of tanks and predicts the available storage prior to each storm event. To do so, this model couples a rainfall-runoff tank storage model with a detailed stochastic end-use water demand model. The available storage capacity of tanks is then used as a boundary condition for the novel rapid flood simulation model. This flood model was developed by coupling the U.S. EPA Storm Water Management Model (SWMM) to the Cellular-Automata Fast Flood Evaluation (CA-ffé) model to predict the inundation depth caused by surcharges over the capacity of the drainage network. The stage-depth damage curves method was used to calculate time series of flood damage, which are then directly used for flood risk and cost-benefit analysis. The model was tested through a case study in Melbourne, using a recorded rainfall time series of 85 years (after validating the flood model against 1D-2D MIKE-FLOOD). Results showed that extensive implementation of RWH tanks in the study area is economically feasible and can reduce expected annual damage in the catchment by up to approximately 30 percent. Availability of storage space and temporal distribution of rainfall within an event were important factors affecting tank performance for flood reduction.

Flexible Demand Through Point-of-Load Voltage Control in Domestic Sector

Demand reduction through voltage control at substations (VCSs) is commonly used. However, during high loading conditions the allowable depth of voltage reduction could be limited by the large voltage drop across the feeders. Distributed voltage control at the points of connection of individual loads (e.g., supply point of a cluster of domestic customers) allows larger flexibility in demand, especially during high loading as demonstrated in this paper. A high-resolution stochastic demand model and the aggregate power-voltage sensitivity of individual domestic customers are used to compare the demand reduction capability of point-of-load voltage control (PVC) against VCS. The rating of the voltage compensators required for PVC is evaluated to weigh the benefits against the required investment. First, the results are shown on a generic low voltage network with random distribution of clusters of domestic customers at various buses and random length of feeder segments to draw general conclusions. Then, the Cigre benchmark medium- and low-voltage networks are used to substantiate the findings. A case study on an islanded microgrid is presented to show that PVC reduces frequency variations caused by fluctuating wind power generation.

Developing a stochastic sewer model to support sewer design under water conservation measures

Population growth and climate change place a strain on water resources; hence, there are growing initiatives to reduce household water use. UKWIR (2016) have a stated aim to halve water abstraction by 2050. This will significantly reduce inflow to sewer systems and increase wastewater concentration. This work presents a new stochastic sewer model that can be used to predict both hydraulic and pollutant loading for various water saving scenarios. The stochastic sewer model is based on integration of the stochastic water demand model SIMDEUM® with the InfoWorks ICM® (Sewer Edition) hydraulic model and software. This model has been developed using foul sewer networks, i.e. where household discharges are the dominant inflow; however, it could also be used in combined sewage systems where rainwater flows would add to the stochastic dry weather flow (DWF). The stochastic sewer model was tested and validated on several real catchments in the Wessex Water area of the UK. Calibration was carried out using metered consumption data. The stochastic sewer model gives an accurate prediction of the diurnal patterns of sewage discharge at a household level and was validated using real flow measurements within the catchment. The results obtained indicate that this model can be used to accurately predict changes in flow due to water conservation. A preliminary study for the impact of low water use on this validated network model has been conducted and it was found that overnight and daytime flow was reduced by up to 80% whereas evening flows remained largely similar. Extended stagnation times were observed in the street scale pipes (150 mm) in the low water use scenario.

Designing near-optimal policies for energy management in a stochastic environment

With the rapid growth in renewable energy and battery storage technologies, there exists significant opportunity to improve energy efficiency and reduce costs through optimization. However, optimization algorithms must take into account the underlying dynamics and uncertainties of the various interconnected subsystems in order to fully realize this potential. To this end, we formulate and solve an energy management optimization problem as a Markov Decision Process (MDP) consisting of battery storage dynamics, a stochastic demand model, a stochastic solar generation model, and an electricity pricing scheme. The stochastic model for predicting solar generation is constructed based on weather forecast data from the National Oceanic and Atmospheric Administration. A near-optimal policy design is proposed via stochastic dynamic programming. Simulation results are presented in the context of storage and solar-integrated residential and commercial building environments. Results indicate that the near-optimal policy significantly reduces the operating costs compared to several heuristic alternatives. The proposed framework facilitates the design and evaluation of energy management policies with configurable demand-supply-storage parameters in the presence of weather-induced uncertainties.