Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.

Stochastic constraint programming

Abstract: To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number of complete algorithms and approximation procedures. Finally, we discuss a number of extensions of stochastic constraint programming to relax various assumptions like the independence between stochastic variables, and compare with other approaches for decision making under uncertainty.

Operating Room Pooling and Parallel Surgery Processing Under Uncertainty

Abstract: Operating room (OR) scheduling is an important operational problem for most hospitals. In this study, we present a novel two-stage stochastic mixed-integer programming model to minimize total expected operating cost given that scheduling decisions are made before the resolution of uncertainty in surgery durations. We use this model to quantify the benefit of pooling ORs as a shared resource and to illustrate the impact of parallel surgery processing on surgery schedules. Decisions in our model include the number of ORs to open each day, the allocation of surgeries to ORs, the sequence of surgeries within each OR, and the start time for each surgeon. Realistic-sized instances of our model are difficult or impossible to solve with standard stochastic programming techniques. Therefore, we exploit several structural properties of the model to achieve computational advantages. Furthermore, we describe a novel set of widely applicable valid inequalities that make it possible to solve practical instances. Based on our results for different resource usage schemes, we conclude that the impact of parallel surgery processing and the benefit of OR pooling are significant. The latter may lead to total cost reductions between 21% and 59% on average.

Contributions to the theory of stochastic programming

Abstract: Two stochastic programming decision models are presented. In the first one, we use probabilistic constraints, and constraints involving conditional expectations further incorporate penalties into the objective. The probabilistic constraint prescribes a lower bound for the probability of simultaneous occurrence of events, the number of which can be infinite in which case stochastic processes are involved. The second one is a variant of the model: two-stage programming under uncertainty, where we require the solvability of the second stage problem only with a prescribed (high) probability. The theory presented in this paper is based to a large extent on recent results of the author concerning logarithmic concave measures.

Data-Driven Stochastic Unit Commitment for Integrating Wind Generation

Abstract: Considering recent development of deregulated energy markets and the intermittent nature of renewable energy generation, it is important for power system operators to ensure cost effectiveness while maintaining the system reliability To achieve this goal, significant research progress has recently been made to develop stochastic optimization models and solution methods to improve reliability unit commitment run practice, which is used in the day-ahead market for ISOs/RTOs to ensure sufficient generation capacity available in real time to accommodate uncertainties Most stochastic optimization approaches assume the renewable energy generation amounts follow certain distributions However, in practice, the distributions are unknown and instead, a certain amount of historical data are available In this research, we propose a data-driven risk-averse stochastic unit commitment model, where risk aversion stems from the worst-case probability distribution of the renewable energy generation amount, and develop the corresponding solution methods to solve the problem Given a set of historical data, our proposed approach first constructs a confidence set for the distributions of the uncertain parameters using statistical inference and solves the corresponding risk-averse stochastic unit commitment problem Then, we show that the conservativeness of the proposed stochastic program vanishes as the number of historical data increases to infinity Finally, the computational results numerically show how the risk-averse stochastic unit commitment problem converges to the risk-neutral one, which indicates the value of data

Uncertain random programming with applications

Abstract: Uncertain random variable is a tool to deal with a mixture of uncertainty and randomness. This paper presents an operational law of uncertain random variables, and shows an expected value formula by using probability and uncertainty distributions. This paper also provides a framework of uncertain random programming that is a type of mathematical programming involving uncertain random variables. Finally, some applications of uncertain random programming are discussed.