Stochastic Demand Model Research Articles

Optimization of satellite constellation deployment strategy considering uncertain areas of interest

This paper presents an integrated framework to design a flexible multi-stage telecommunication satellite configuration deployment strategy considering the uncertainties in the evolution of the areas of interest over time. The constructed stochastic demand model considers multiple possible scenarios for the evolution of the areas of interest with probabilities based on the market share growth in each area. The optimization aims to find each stage's design with minimum expected lifecycle cost considering all possible scenarios. Each stage of the constellation, assumed to be Flower constellation with circular orbits, provides a regional coverage of the current area of interest as well as additional coverage for the potential future areas of interest. The proposed multi-stage satellite constellation enables the constellation designer to react flexibly and efficiently to the uncertain future expansion of the areas of interest. A case study reveals a reduction in the expected lifecycle cost for an optimized system compared with the all-in-single-stage system and global coverage constellation.

Review of applications for SIMDEUM, a stochastic drinking water demand model with a small temporal and spatial scale

Abstract. Many researchers have developed drinking water demand models with various temporal and spatial scales. A limited number of models is available at a temporal scale of 1 s and a spatial scale of a single home. The reasons for building these models were described in the papers in which the models were introduced, along with a discussion on their potential applications. However, the predicted applications are seldom re-examined. SIMDEUM, a stochastic end-use model for drinking water demand, has often been applied in research and practice since it was developed. We are therefore re-examining its applications in this paper. SIMDEUM's original purpose was to calculate maximum demands in order to design self-cleaning networks. Yet, the model has been useful in many more applications. This paper gives an overview of the many fields of application for SIMDEUM and shows where this type of demand model is indispensable and where it has limited practical value. This overview also leads to an understanding of the requirements for demand models in various applications.

A new stochastic demand model for dual-sourcing supply chain considering disruption risk

In this paper, we propose a single period-product model with two supply channels when disruption is feasible in wholesaler-retailer channels considering back-orders and lost sales. Here we define a maximisation model regarding disruptions in dual channels and sensitivity analysis on the parameters has been done based on it. We test our proposed model by several numerical examples and finally used contour curves to show disruption effects on order quantity and ordering channel selection.

Two echelon supply chain model of agricultural products based on stochastic fuzzy process of cost demand

Stochastic fuzziness existed in supply chain process has important influence on inventory maintenance and decision processing of normal system operation, especially under the situation of coupling existed in two echelon supply chain, this influence will be amplified to some extent. First, for the studied two echelon supply chain objects, joint cost has been taken as target to make optimal model design; second, considering about the stochastic fuzziness existed in two echelon supply chain, the demand rate of market for products as well as supply and distribution time have been selected as main research parameters, two echelon supply stochastic demand model based on triangular fuzzy number has been constructed and then model solving process has been deduced according to the characteristics of design model; last, verification for the performance of proposed model has been made based on parameter influence experiment and horizontal contrast.

A new stochastic demand model for dual-sourcing supply chain considering disruption risk

In this paper, we propose a single period-product model with two supply channels when disruption is feasible in wholesaler-retailer channels considering back-orders and lost sales. Here we define a maximisation model regarding disruptions in dual channels and sensitivity analysis on the parameters has been done based on it. We test our proposed model by several numerical examples and finally used contour curves to show disruption effects on order quantity and ordering channel selection.

Insights into carsharing demand dynamics: Outputs of an agent-based model application to Lisbon, Portugal

ABSTRACTTwo important claims for carsharing systems are their increased flexibility and potential contribution to reducing transport externalities such as pollution. Carsharing typically involves a fleet of vehicles in stations around a city that clients may use on an hourly-payment basis. Classical round-trip systems address a niche market of shopping and errand trips. However, a growing market is now arising providing one-way trips to clients. Great uncertainty remains on the economic viability of this type of carsharing given the complex relation between supply and demand, and how this may influence the level of service provided. Realistic modeling tools that include both supply and demand characterization and allow testing several carsharing operational parameters are scarce. In this sense, a detailed agent-based model was developed to simulate one-way carsharing systems. The simulation incorporates a stochastic demand model discretized in time and space and a detailed environment characterization with realistic travel times. The operation includes maintenance operations, relocations and reservations. The model was applied to the case-study city of Lisbon. Our results show that comparing to other modes, carsharing performs worse than private cars both in terms of time and cost. Nevertheless, it clearly outperforms taxis in terms of cost, and outperforms buses, metro and walking in terms of travel time. The competitiveness of carsharing is highly determined by trip length, becoming more competitive than other modes (travel-time wise) as trips become longer. The operational policies as car-fleet relocation and car reservation showed significant effects in enhancing profit while preserving good customers' satisfaction.

Multi-objective inventory routing with uncertain demand using population-based metaheuristics

This article studies a tri-objective formulation of the inventory routing problem, extending the recently studied bi-objective formulation. As compared to distance cost and inventory cost, which were discussed in previous work, it also considers stockout cost as a third objective. Demand is modeled as a Poisson random variable. State-of-the-art evolutionary multi-objective optimization algorithms and a new method based on swarm intelligence are used to compute approximation of the 3-D Pareto front. A benchmark previously used in bi-objective inventory routing is extended by incorporating a stochastic demand model with an expected value that equals the average demand of the original benchmark. The results provide insights into the shape of the optimal trade-off surface. Based on this the dependences between different objectives are clarified and discussed. Moreover, the performances of the four different algorithmic methods are compared and due to the consistency in the results, it can be concluded that a near optimal approximation to the Pareto front can be found for problems of practically relevant size.

Stochastic and Statistical Analysis of Utility Revenues and Weather Data Analysis for Consumer Demand Estimation in Smart Grids.

In smart grid paradigm, the consumer demands are random and time-dependent, owning towards stochastic probabilities. The stochastically varying consumer demands have put the policy makers and supplying agencies in a demanding position for optimal generation management. The utility revenue functions are highly dependent on the consumer deterministic stochastic demand models. The sudden drifts in weather parameters effects the living standards of the consumers that in turn influence the power demands. Considering above, we analyzed stochastically and statistically the effect of random consumer demands on the fixed and variable revenues of the electrical utilities. Our work presented the Multi-Variate Gaussian Distribution Function (MVGDF) probabilistic model of the utility revenues with time-dependent consumer random demands. Moreover, the Gaussian probabilities outcome of the utility revenues is based on the varying consumer n demands data-pattern. Furthermore, Standard Monte Carlo (SMC) simulations are performed that validated the factor of accuracy in the aforesaid probabilistic demand-revenue model. We critically analyzed the effect of weather data parameters on consumer demands using correlation and multi-linear regression schemes. The statistical analysis of consumer demands provided a relationship between dependent (demand) and independent variables (weather data) for utility load management, generation control, and network expansion.

Impact of inventory inaccuracies on products with inventory-dependent demand

We explore the impact of inventory inaccuracy on the product whose demand is dependent on inventory level based on a general, stochastic demand model. The shrinkage error and misplacement error are considered simultaneously in our paper. To assess the impact of inventory inaccuracy and the benefits of RFID, we consider the following three approaches of inventory decisions: (1) the retailer is not aware of the inventory inaccuracies; (2) the retailer considers the inventory errors when making inventory decisions; (3) RFID technology is adopted to reduce the inventory errors. The comparison between the first two approaches is used to assess the consequence of ignoring inventory inaccuracies, while the comparison between the second and the third approach reflects the benefits of RFID. We derive the optimal ordering quantity and expected profit analytically, and investigate the variation of available for sales quantity, optimal service level and expected optimal profit with the inventory inaccuracies explicitly. A necessary condition that the tag price should be satisfied to guarantee RFID implementation beneficial is derived. By analyzing the variation of the benefits of integrating error information and adopting RFID with the inventory inaccuracies numerically, our results imply the retailers should pay more attention to inventory inaccuracy errors when the product is characterized with high demand sensitivity.

A method of forecasting wholesale electricity market prices

In this paper, we employ a fundamental principle of classical mechanics known as the least-action principle to model the complex relationship between expected load and expected price in electricity spot markets. We consider markets that feature a centralized electricity dispatch system that optimizes grid parameters to determine the minimum spot nodal prices. Using the example of the Australian National Electricity Market (NEM) and a calibrated stochastic demand model, we develop a mathematical approach that determines the price evolution, including intraday and seasonal features. The proposed model links the concept of a deterministically modeled price with stochastically modeled demand. The demand-price relationship is complex, and it must include not only the level of demand within the constraint of maximum generating capacity, but also the change in demand within the constraints of generator ramping rates. While this paper uses the NEM as an example, the proposed approach is applicable to any energy market that satisfies the above conditions.

Multi-Objective Demand Response Model Considering the Probabilistic Characteristic of Price Elastic Load

Demand response (DR) programs provide an effective approach for dealing with the challenge of wind power output fluctuations. Given that uncertain DR, such as price elastic load (PEL), plays an important role, the uncertainty of demand response behavior must be studied. In this paper, a multi-objective stochastic optimization problem of PEL is proposed on the basis of the analysis of the relationship between price elasticity and probabilistic characteristic, which is about stochastic demand models for consumer loads. The analysis aims to improve the capability of accommodating wind output uncertainty. In our approach, the relationship between the amount of demand response and interaction efficiency is developed by actively participating in power grid interaction. The probabilistic representation and uncertainty range of the PEL demand response amount are formulated differently compared with those of previous research. Based on the aforementioned findings, a stochastic optimization model with the combined uncertainties from the wind power output and the demand response scenario is proposed. The proposed model analyzes the demand response behavior of PEL by maximizing the electricity consumption satisfaction and interaction benefit satisfaction of PEL. Finally, a case simulation on the provincial power grid with a 151-bus system verifies the effectiveness and feasibility of the proposed mechanism and models.

Multi-Resource Fairness

Designing efficient and fair algorithms for sharing multiple resources between heterogeneous demands is becoming increasingly important. Applications include compute clusters shared by multi-task jobs and routers equipped with middleboxes shared by flows of different types. We show that the currently preferred objective of Dominant Resource Fairness (DRF) has a significantly less favorable efficiency-fairness tradeoff than alternatives like Proportional Fairness and our proposal, Bottleneck Max Fairness. We propose practical algorithms to realize these sharing objectives and evaluate their performance under a stochastic demand model. It is shown, in particular, that the strategyproofness property that motivated the choice of DRF for an assumed fixed set of jobs or flows, is largely irrelevant when demand is dynamic.

Planning for the unexpected: The value of reserve capacity for public transport network robustness

Public transport networks (PTN) are subject to recurring service disruptions. Most studies of the robustness of PTN have focused on network topology and considered vulnerability in terms of connectivity reliability. While these studies provide insights on general design principles, there is lack of knowledge concerning the effectiveness of different strategies to reduce the impacts of disruptions. This paper proposes and demonstrates a methodology for evaluating the effectiveness of a strategic increase in capacity on alternative PTN links to mitigate the impact of unexpected network disruptions. The evaluation approach consists of two stages: identifying a set of important links and then for each identified important link, a set of capacity enhancement schemes is evaluated. The proposed method integrates stochastic supply and demand models, dynamic route choice and limited operational capacity. This dynamic agent-based modelling of network performance enables to capture cascading network effects as well as the adaptive redistribution of passenger flows. An application for the rapid PTN of Stockholm, Sweden, demonstrates how the proposed method could be applied to sequentially designed scenarios based on their performance indicators. The method presented in this paper could support policy makers and operators in prioritizing measures to increase network robustness by improving system capacity to absorb unexpected disruptions.

A Method of Forecasting Wholesale Electricity Market Prices

In this paper we employ a fundamental principle of classical mechanics known as the Least Action Principle to model the complex relationship between expected load and expected price in electricity spot markets. We consider here markets that feature a centralised electricity dispatch system that optimises grid parameters to determine the minimum spot nodal prices. Using the example of the Australian National Electricity Market (NEM) and a calibrated stochastic demand model, we develop the mathematical approach that determines the price evolution including intra-day and seasonal features. The proposed model links the concept of a deterministically-modelled price with a stochastically-modelled demand. The demand-price relationship is complex, and must include not only the level of demand within the constraint of maximum generating capacity, but also the change in demand within the constraints of generator ramping rates. While this paper uses the NEM as an example, the proposed approach is applicable to any energy market that satisfies the above conditions.

The economic lot-size scheduling problem with equally sized batch shipment policy and stochastic demands

This study investigates economic lot–size scheduling problem (ELSP) comprising stochastic demand and equally sized batch shipment policy in a one–supplier multi–buyer integrated inventory model. All buyers have agreed on a joint replenishment policy with a common replenishment cycle (CRC). Equally sized batch shipment scheduling policy for each product in one CRC is applied to the whole system. The objective is to determine the optimal common replenishment cycle and the numbers of batch–shipment for each product, all of which minimises the integrated total cost. Moreover, a new concept is introduced; namely, critical replenishment cycle. The replenishment cycle division (RCD) and recursive tightening (RT) methods are then developed to obtain the optimal solutions to the subject problem. Two theorems are verified to ensure that the solution of ELSP involving equally sized batch shipment and stochastic demand model with the CRC policy obtained by the RCD and RT methods reaches the global optimum. An example is presented to illustrate the procedures involved in the RCD and RT methods. [Received 5 March 2013; Revised 25 September 2013; Revised 3 December 2013; Accepted 11 December 2013]

A novel relational approach for assembly system supply planning under environmental uncertainty

We propose a new optimisation approach to address a multi-period, inventory control problem for an assembly system under stochastic environment. Significant drawback in a construction of a real-life model for a multi-product, multi-component assembly system is the fact that the shortage cost is typically known for a final product while the optimisation is carried out on assembly components. In the cases when the same type of components assemble different types of finished products, this becomes insuperable obstacle for most of the known approaches. In addition, restrictive assumptions about component demand are common for number of published models. Therefore, we develop a framework, which has the ability to incorporate real shortage costs of the final products within the optimisation process and to incorporate more realistic assumptions about product demand. The aim is to define a completely new optimisation approach in the case of complex component’s interdependencies in assembly systems. The inclusion of the proposed model in the optimisation process is shown by the example of a known simple stochastic demand model. Simple SQL procedures have been presented which benefits from the relational structure of the problem.

Optimal multi-scale capacity planning for power-intensive continuous processes under time-sensitive electricity prices and demand uncertainty. Part I: Modeling

Time-sensitive electricity prices (as part of so-called demand-side management in the smart grid) offer economical incentives for large industrial customers. In part I of this paper, we propose an MILP formulation that integrates the operational and strategic decision-making for continuous power-intensive processes under time-sensitive electricity prices. We demonstrate the trade-off between capital and operating expenditures with an industrial case study for an air separation plant. Furthermore, we compare the insights obtained from a model that assumes deterministic demand with those obtained from a stochastic demand model. The value of the stochastic solution (VSS) is discussed, which can be significant in cases with an unclear setup, such as medium baseline product demand and growth rate, large variance or skewed demand distributions. While the resulting optimization models are large-scale, they can be solved within three days of computational time. A decomposition algorithm for speeding-up the solution time is described in part II.

Designing Networked Energy Infrastructures with Architectural Flexibility

Development of networked energy infrastructures (like gas pipe networks), generally requires a significant amount of capital investment under resources, market and institutional uncertainties. Several independent suppliers and consumers are to be connected into these networks. However, the actual commitment of these parties and the capacities they require from the network can remain uncertain for a long time. This is a challenging task for development co-owners because decisions, such as network architectures, have to be made while uncertainty exists. In order to effectively explore through the design space and identify architecturally flexible designs addressing a view of capacity uncertainty, a simulation framework based on a combination of Monte Carlo simulation and Graph Theory is proposed. It integrates a stochastic capacity demand model and network design heuristic algorithm. The framework will be able to evaluate architectural design options and show that architectural flexibility can significantly improve the value of the infrastructure project by reducing downside risks and benefiting from upside gains compared to the deterministic design approach.

Simulating Carsharing Operations through Agent-based Modelling: An Application to the City of Lisbon, Portugal

The increasing use of automobiles has had significant negative impacts on urban life: pollution, excessive energy use and time lost in traffic. The quick rise of auto externalities has policy makers facing the hard challenge of balancing demand for mobility on the one hand, and assuring sustainable urban life on the other. One strategy that can aid reducing these externalities is carsharing. Carsharing typically involves a fleet of vehicles in stations around a city, which clients may use on an hourly payment basis. Classical round-trip systems only address a niche market of urban trips such as shopping and errands, and few companies have risked the one-way carsharing option in the past due to vehicle stocks imbalance. Currently these systems are gaining new attention with important car builders investing in providing the one-way market in many cities in Europe and the United States. Nevertheless, there is still great uncertainty on the financial and economic viability of this type of carsharing. This results from a lack of realistic modeling tools that allow testing several operational parameters of this transportation alternative. In this paper we present a very detailed and realistic model to assess the potential of one way carsharing systems done through the use of agent based simulation. The simulation incorporates a stochastic demand model discretized in time and space and a detailed road network. It aims to assess the economic performance of the system both from the users’ perspective and the carsharing operator. The performance is a function of several planning and operational decisions which are included in the model: fleet size; station or free parking areas location decision; pricing policies. Some lower level configurations are also analyzed, such as an information system, vehicle reservation and maintenance operations scheduling. This paper focuses on the analysis of the spatial distribution and fleet size impacts on the demand for this transport option. This model was developed for the city of Lisbon, but its flexible architecture allows it to be adapted to different cities. Therefore this may become a tool that government authorities can use to rigorously estimate carsharing impacts and at the same time help private companies to manage their systems better.

Complex Adaptive Systems Framework to Assess Supply-Side and Demand-Side Management for Urban Water Resources

The availability of water resources in many urbanizing areas is the emergent property of the adaptive interactions among consumers, policy, and the hydrologic cycle. As water availability becomes more stressed, public officials often implement restrictions on water use, such as bans on outdoor watering. Consumers are influenced by policy and the choices of other consumers to select water-conservation technologies and practices, which aggregate as the demand on available water resources. Policy and behavior choices affect the availability of water for future use as reservoirs are depleted or filled. This research posited urban water supply as a complex adaptive system (CAS) by coupling a stochastic consumer demand model and a water supply model within an agent-based modeling (ABM) framework. Public officials were simulated as agents to choose water conservation strategies and interbasin transfer strategies, and consumers were simulated as agents, influenced by various conservation-based programs to select water conservation technologies and behaviors, and correspondingly update their individual demand models. A water supply reservoir was simulated to receive rainfall from the contributing watershed and to supply the demands of consumer agents. The ABM framework was applied to an illustrative urban case study. A set of scenarios was developed to represent moderate and strong water conservation strategies, and was simulated for a long-term precipitation record to evaluate the sustainability of water conservation practices.