Use Of Stochastic Programming Research Articles

Probabilistic modeling of hardware and software interactions for system reliability assessment

An important aspect of complex hardware-software systems reliability is the interaction between hardware and software. Most of the existing work has assumed either independence between hardware (HW) and software (SW) or a fixed proportion of hardware reported failures to represent HW/SW interactions. These assumptions do not necessarily reflect reality. In this paper, probabilistic HW/SW interactions, in conjunction with hardware and software reliability, are considered to model and assessment overall hardware-software systems reliability. However, incorporating uncertainty demands the use of stochastic programming to estimate the parameters of the hardware reliability model. To capture the HW/SW interactions, a Markov Stochastic process model with uncertainty in transition rates is proposed and solved using Monte Carlo sampling. By combining hardware, software, and probabilistic HW/SW interactions, the overall system reliability can be predicted not only as a point estimator but as quantiles or confidence intervals. The proposed methodology was demonstrated with data from a real computer system provided by Los Alamos National Laboratory. Reliability predictions for a 1,095-day horizon were carried out with an R script in approximately 1.5 s running on a laptop, which demonstrates the feasibility and convenience of the approach. In the four cases analyzed, the 97.5% lower bound of system reliability estimation was above the reliability calculated assuming independent hardware and software reliability.

Lot-Size Models with Uncertain Demand Considering Its Skewness/Kurtosis and Stochastic Programming Applied to Hospital Pharmacy with Sensor-Related COVID-19 Data.

Governments have been challenged to provide timely medical care to face the COVID-19 pandemic. Under this pandemic, the demand for pharmaceutical products has changed significantly. Some of these products are in high demand, while, for others, their demand falls sharply. These changes in the random demand patterns are connected with changes in the skewness (asymmetry) and kurtosis of their data distribution. Such changes are critical to determining optimal lots and inventory costs. The lot-size model helps to make decisions based on probabilistic demand when calculating the optimal costs of supply using two-stage stochastic programming. The objective of this study is to evaluate how the skewness and kurtosis of the distribution of demand data, collected through sensors, affect the modeling of inventories of hospital pharmacy products helpful to treat COVID-19. The use of stochastic programming allows us to obtain results under demand uncertainty that are closer to reality. We carry out a simulation study to evaluate the performance of our methodology under different demand scenarios with diverse degrees of skewness and kurtosis. A case study in the field of hospital pharmacy with sensor-related COVID-19 data is also provided. An algorithm that permits us to use sensors when submitting requests for supplying pharmaceutical products in the hospital treatment of COVID-19 is designed. We show that the coefficients of skewness and kurtosis impact the total costs of inventory that involve order, purchase, holding, and shortage. We conclude that the asymmetry and kurtosis of the demand statistical distribution do not seem to affect the first-stage lot-size decisions. However, demand patterns with high positive skewness are related to significant increases in expected inventories on hand and shortage, increasing the costs of second-stage decisions. Thus, demand distributions that are highly asymmetrical to the right and leptokurtic favor high total costs in probabilistic lot-size systems.

Enabling market participation of distributed energy resources through a coupled market design

In this study, a new market model is proposed to enable the smooth integration of distributed energy resources (DERs) in day-ahead (DA) and balancing (BL) markets. The DA market is a joint energy and reserve market. DERs participate in the local market operated by the distribution market operator (DMO) which is coordinated with the wholesale market. During local market clearing, the DMO considers the technical constraints of the distribution grid to keep the operation of the distribution grid within limits. Moreover, the DMO, through preliminary scheduling, estimates preliminary prices for energy, reserve and balancing services. These can be seen as offer prices by which the DMO will bid into the TMO DA and BL market. The uncertainty of renewable-based DERs is considered through the use of stochastic programming. The proposed market model is compared with a centralised market model. Results show that adding the distribution network constraints to the proposed market model is capable of alleviating overloading and appropriately accounting this effect in terms of increasing the operational cost. Moreover, it has been shown that the scalability of the proposed market model is higher compared to the currently applied centralised market models.

Evaluating the required scenario set size for stochastic programming in forest management planning: incorporating inventory and growth model uncertainty

Developing a plan of action for the future use of forest resources requires a way to predict the development of the forest through time. These predictions require the use of inventory data and growth models that contain a large number of uncertainties. These uncertainties impact the quality of the predictions, and if not accounted for, they can lead to the selection of a suboptimal management plan. To account for and manage the uncertainties and associated risk, we have explored the use of stochastic programming. Stochastic programming can integrate uncertainty into the optimization process by solving the problem for a large number of potential scenarios of the forests future development. The selection of an appropriately sized set of scenarios involves a trade-off between tractability issues and problem representation issues. In this paper, an analysis of the trade-offs is conducted. Two cases are studied, one in which only the uncertainty of the inventory data is included and a second in which both growth model and inventory data uncertainties are included. The impact of increasing the number of scenarios on the problem representation is examined through a simple even-flow problem.

Integrating risk preferences in forest harvest scheduling

Through a stochastic programming framework, risk preferences can be included in forest planning. The value of utilizing stochastic programming is always positive; however, the value depends on the information quality and risk preferences of the decision maker. Harvest scheduling requires decisions be taken based on imperfect information and assumptions regarding the future state of the forest and markets. The aim of this study is to incorporate elements of risk management into forest management, so that the decision maker can understand the risks associated with utilizing the imperfect data. Incorporation of uncertainty is done through stochastic programming. This allows for the decision maker’s attitude towards risk to be incorporated into the development of a solution. By means of a simple even-flow problem formulation, a method of using stochastic programming to incorporate explicit trade-off between objective function value and risk of not meeting the constraints has been developed. The different models highlight the importance of including uncertainty in management of forest resources. In general, as the decision maker becomes more risk averse, the incorporation of uncertainty into the model becomes more important. The use of stochastic programming allows for additional information to be included in the formulation, and this allows for the decision maker to account for downside risk.

Renewable Energies in Medium-Term Power Planning

The medium-term generation planning over a yearly horizon for generation portfolios including hydro generation and non-dispatchable renewables such as wind power and solar photovoltaic generation reveals how the penetration of these technologies reduces the share of other technologies and how it changes the profits and the profit spread in liberalized electricity markets. The matching of the load duration curves in different periods and the forced outages of generation units are here addressed through probabilistic methods and a heuristic is employed to guess which of the load-matching constraints may be active at the solution. There are well-established models for hydro generation in medium-term planning, but specific models are necessary to account for wind power and photovoltaic generation. A proposal for these is made in this work, which is suitable for use in the load duration curve matching through probabilistic methods. Moreover the stochasticity of the renewable sources requires the use of stochastic programming employing scenario trees, here developed using quasi-Monte Carlo techniques. Medium-term pumping schemes are also considered. Several realistic cases will be solved for two behavioral principles of a pure pool market: endogenous cartel and equilibrium.

A Stochastic Programming Optimization Model of Container Shipping of Sea-Carriage

The paper dose research about the optimization of container shipping of sea carriage for meeting the goods transport requirement by use of stochastic programming. Both laden and empty containers are combined into a system. In particular, the effect of special laden container shipping capacity on the shipping plan is investigated. In the model, the objective function is to maximize the total profit of container shipping. The profit caused by laden container shipping minus the cost caused by both laden and empty container shipping equal to the total profit. The constraints to the model include meeting the need of both laden and empty containers, shipping limit to both common and special laden containers, the number of empty container supported. The number of empty containers is stochastic and the model is transmitted to an integer programming. Lingo9.0 is used to solve the model and shipping methods in varied parameters are shown by simulation. The aim of the paper is to provide a reasonable plan of container shipping of sea-carriage, so the container shipping cost of a shipping company can be reduced and the its profit made by container shipping are maximized.

Use of Stochastic Programming in Least-cost Feed Formulation for African Catfish (Clarias gariepinus) in Semi-intensive Culture System in Nigeria

Use of Stochastic Programming in Least-cost Feed Formulation for African Catfish (Clarias gariepinus) in Semi-intensive Culture System in Nigeria

Two aspects of optimal diet determination for pig production: efficiency of solution and incorporation of cost variation

For many decades linear programming has been used to find minimum cost diets, notably in the chicken and pig meat industries. More recently, animal growth models together with nonlinear optimisation methods have been used to find feeding schedules which simultaneously minimise feed costs and maximise market return, so maximising gross margin. Genetic algorithms can handle these problems, albeit slowly. In this paper we study the particular nature of the objective function (for pig meat production) and develop a global optimisation algorithm tailored to its discontinuous structure. We also demonstrate the use of stochastic programming to cope with changing feed costs and changing price at slaughter.

5.3. Markov models

This paper introduces the use of Markov models for engineering-economic planning. Markov models capture the uncertainty and dynamics in the engineering- economic decision environment. The paper describes how, when, and why to use Markov models. It describes the steps of model formulation, parameter estimation and solution. It discusses the use of stochastic programming to optimize decisions. Software are identified which perform the required calculations. An application for system expansion planning, reported in a previous paper, is summarized.