A stochastic model for operating room planning with elective and emergency demand for surgery

This paper describes a stochastic model for Operating Room (OR) planning with two types of demand for surgery: elective surgery and emergency surgery. Elective cases can be planned ahead and have a patient-related cost depending on the surgery date. Emergency cases arrive randomly and have to be performed on the day of arrival. The planning problem consists in assigning elective cases to different periods over a planning horizon in order to minimize the sum of elective patient related costs and overtime costs of operating rooms. A new stochastic mathematical programming model is first proposed. We then propose a Monte Carlo optimization method combining Monte Carlo simulation and Mixed Integer Programming. The solution of this method is proved to converge to a real optimum as the computation budget increases. Numerical results show that important gains can be realized by using a stochastic OR planning model.     

SOS: A Quantile Estimation Procedure for Dynamic Lot-sizing Problems

This paper reviews some of the current approaches available for computing the demand quantiles required to plan the procurement of items with stochastic non-stationary demands. The paper first describes the stochastic single-item lot-sizing problem considered and then presents a practical solution approach based on a dynamic lot-sizing model. Three methods available to compute demand quantiles are then reviewed and a new procedure based on smoothed order statistics (SOS) is proposed. Finally, the behaviour of these estimation methods, when used to solve single-item lot-sizing problems with non-stationary stochastic demands, is studied by simulation.     

基于随机规划的建筑集群冷热电联供系统优化研究

面向建筑集群的冷热电联供系统的设计和优化是实现建筑楼宇能源成本节约的重要途径。随机因素对该联供系统的优化决策,具有显著的影响。考虑建筑楼宇的能源需求为随机变量,构建随机混合整数规划模型,解决以最小化建筑楼宇总费用为目标时建筑集群冷热电联供系统的优化问题;其次,提出采用Benders多割平面方法求解多目标规划问题,从而寻找冷热电联供系统的设备配置和系统运行的Pareto最优决策;最后,通过实验验证了模型和算法的有效性。实验结果表明建筑集群在协作模式下,相比于非协作模式,具有更低的总费用。     

Application of a Fuzzy Programming Through Stochastic Particle Swarm Optimization to Assessment of Filter Management Strategies in Fluid Power System Under Uncertainty

A fuzzy programming through stochastic particle swarm optimization is developed for the assessment of filter allocation and replacement strategies in fluid power system (FPS) under uncertainty. It can not only handle uncertainties expressed as L-R fuzzy numbers but also enhance the system robustness by transforming the fuzzy inequalities into inclusive constraints. As the simulation results indicate, the developed model can successfully decrease the total cost and enhanced the safety of system. Generally, it is believed that the model can help identify excellent filter allocation and replacement strategy with minimized operation cost and system failure risk while protecting the system.     

Optimal Design of Plane Frames under Uncertainty: A Comparison of Two Approaches

Using the first collapse theorem, the necessary and sufficient survival conditions of an elasto-plastic structure consist of the yield condition and the equilibrium condition. In practical applications several random model parameters have to be taken into account. This leads to a stochastic optimization problem which cannot be solved using the traditional methods. Instead of that, appropriate (deterministic) substitute problems must be formulated. Here, the design of plane frames is considered, where the applied load is supposed to be stochastic. In the first approach the recourse problem will be formulated in the standard form of stochastic linear programming (SLP). In order to apply efficient numerical solution procedures (LP-solvers), approximate recourse problems based on discretization (RPD) and the expected value problem (EVP) are introduced. In the second approach – based on the yield condition – a quadratic cost function will be introduced. After the formulation of the stochastic optimization problem, the expected cost based optimization problem (ECBOP) and the minimum expected cost problem (MECP) are formulated as representatives of appropriate substitute problems. Subsequently, comparative numerical results using these methods are presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal PID control in case of random initial conditions

The aim of this presentation is to construct a robust optimal PID feedback controller, taking into account stochastic uncertainties in the initial conditions. Usually, a precomputed feedback control is based on exactly known model parameters. However, in practice, often exact information about model parameters and initial values is not given. Hence, having an inital point, which differs from the nominal values, a standard precomputed controller may produce bad results. Supposing now that the probability distribution of the random parameter variations is known, in the following stochastic optimisation methods will be applied in order to obtain robust optimal feedback controls. Taking into account stochastic parameter variations at the initial point, the method works with expected total costs arising from the primary control expenses and the tracking error. Furthermore, the free regulator parameters are selected then such that the expected total costs are minimized. After Taylor expansion to calculate expected cost functions and a few transformations an approximate deterministic substitute control problem follows. Here, retaining only linear terms, approximation of expectations and variances of the expected cost functions can be calculated explicitly. By means of splines, numerical approximations of the objective function and the differential equations are obtained then. Using stochastic optimization methods, random parameter variations are incorporated into the optimal control process. Hence, robust optimal feedback controls are obtained. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A robust data envelopment analysis model with different scenarios

Input and output data, under uncertainty, must be taken into account as an essential part of data envelopment analysis (DEA) models in practice. Many researchers have dealt with this kind of problem using fuzzy approaches, DEA models with interval data or probabilistic models. This paper presents an approach to scenario-based robust optimization for conventional DEA models. To consider the uncertainty in DEA models, different scenarios are formulated with a specified probability for input and output data instead of using point estimates. The robust DEA model proposed is aimed at ranking decision-making units (DMUs) based on their sensitivity analysis within the given set of scenarios, considering both feasibility and optimality factors in the objective function. The model is based on the technique proposed by Mulvey et al. (1995) for solving stochastic optimization problems. The effect of DMUs on the product possibility set is calculated using the Monte Carlo method in order to extract weights for feasibility and optimality factors in the goal programming model. The approach proposed is illustrated and verified by a case study of an engineering company.     

Stochastic optimization of an urban rail timetable under time‐dependent and uncertain demand

Urban rail planning is extremely complex, mainly because it is a decision problem under different uncertainties. In practice, travel demand is generally uncertain, and therefore, the timetabling decisions must be based on accurate estimation. This research addresses the optimization of train timetable at public transit terminals of an urban rail in a stochastic setting. To cope with stochastic fluctuation of arrival rates, a two‐stage stochastic programming model is developed. The objective is to construct a daily train schedule that minimizes the expected waiting time of passengers. Due to the high computational cost of evaluating the expected value objective, the sample average approximation method is applied. The method provided statistical estimations of the optimality gap as well as lower and upper bounds and the associated confidence intervals. Numerical experiments are performed to evaluate the performance of the proposed model and the solution method.     

An iterative numerical algorithm for modeling a class of Wiener nonlinear systems

This letter presents an iterative estimation algorithm for modeling a class of output nonlinear systems. The basic idea is to derive an estimation model and to solve an optimization problem using the gradient search. The proposed iterative numerical algorithm can estimate the parameters of a class of Wiener nonlinear systems from input–output measurement data. The proposed algorithm has faster convergence rates compared with the stochastic gradient algorithm. The numerical simulation results indicate that the proposed algorithm works well.     

Using genetic algorithm to solve a new multi-period stochastic optimization model

This paper presents a new asset allocation model based on the CVaR risk measure and transaction costs. Institutional investors manage their strategic asset mix over time to achieve favorable returns subject to various uncertainties, policy and legal constraints, and other requirements. One may use a multi-period portfolio optimization model in order to determine an optimal asset mix. Recently, an alternative stochastic programming model with simulated paths was proposed by Hibiki [N. Hibiki, A hybrid simulation/tree multi-period stochastic programming model for optimal asset allocation, in: H. Takahashi, (Ed.) The Japanese Association of Financial Econometrics and Engineering, JAFFE Journal (2001) 89-119 (in Japanese); N. Hibiki A hybrid simulation/tree stochastic optimization model for dynamic asset allocation, in: B. Scherer (Ed.), Asset and Liability Management Tools: A Handbook for Best Practice, Risk Books, 2003, pp. 269-294], which was called a hybrid model. However, the transaction costs weren’t considered in that paper. In this paper, we improve Hibiki’s model in the following aspects: (1) The risk measure CVaR is introduced to control the wealth loss risk while maximizing the expected utility; (2) Typical market imperfections such as short sale constraints, proportional transaction costs are considered simultaneously. (3) Applying a genetic algorithm to solve the resulting model is discussed in detail. Numerical results show the suitability and feasibility of our methodology.     

Research on estimation model of the battery state of charge in a hybrid electric vehicle based on the classification and regression tree

ABSTRACT

In order to achieve the accurate estimation of state of charge (SOC) of the battery in a hybrid electric vehicle (HEV), this paper proposed a new estimation model based on the classification and regression tree (CART) which belongs to a kind of decision tree. The basic principle and modelling process of the CART decision tree were introduced in detail in this paper, and we used the voltage, current, and temperature of the battery in an HEV to estimate the value of SOC under the driving cycle. Meanwhile, we took the energy feedback of the HEV under the regenerative braking into consideration. The simulation data and experimental data were used to test the effectiveness of the estimation model of CART, and the results indicate that the proposed estimation model has high accuracy, the relative error of simulation is within 0.035, while the relative error of experiment is less than 0.05.     

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

The operation of a stand‐alone photovoltaic (PV) system ultimately aims for the optimization of its energy storage. We present a mathematical model for cost‐effective control of a stand‐alone system based on a PV panel equipped with an angle adjustment device. The model is based on viscosity solutions to partial differential equations, which serve as a new and mathematically rigorous tool for modeling, analyzing, and controlling PV systems. We formulate a stochastic optimal switching problem of the panel angle, which is here a binary variable to be dynamically controlled under stochastic weather condition. The stochasticity comes from cloud cover dynamics, which is modeled with a nonlinear stochastic differential equation. In finding the optimal control policy of the panel angle, switching the angle is subject to impulsive cost and reduces to solving a system of Hamilton‐Jacobi‐Bellman quasi‐variational inequalities (HJBQVIs). We show that the stochastic differential equation is well posed and that the HJBQVIs admit a unique viscosity solution. In addition, a finite‐difference scheme is proposed for the numerical discretization of HJBQVIs. A demonstrative computational example of the HJBQVIs, with emphasis on a stand‐alone experimental system, is finally presented with practical implications for its cost‐effective operation.     

An analytical method for cost analysis in multi-stage supply chains: A stochastic network model approach

This paper studies the cost distribution characteristics in multi-stage supply chain networks. Based on the graphical evaluation and review technique, we propose a novel stochastic network mathematical model for cost distribution analysis in multi-stage supply chain networks. Further, to investigate the effects of cost components, including the procurement costs, inventory costs, shortage costs, production costs and transportation costs of supply chain members, on the total supply chain operation cost, we propose the concept of cost sensitivity and provide corresponding algorithms based on the proposed stochastic network model. Then the model is extended to analyze the cost performance of supply chain robustness under different order compensation ability scenarios and the corresponding algorithms are developed. Simulation experiment shows the effectiveness and flexibility of the proposed model, and also promotes a better understanding of the model approach and its managerial implications in cost management of supply chains.     

收益管理中单产品动态定价的稳健模型研究

在收益管理的动态定价模型的研究中,由传统的确定性模型和随机模型所得到的定价策略常常受限制于需求估计的准确性,当对需求的估计出现偏差时定价策略可能达不到最大化收益的目的,因此定价策略即最优解的稳健性越来越受到研究者的重视。针对需求函数系数的不确定性,在未知需求分布的条件下,应用稳健最优化思想,提出了一种稳健的动态定价模型,并对模型的最优解和最大收益进行了数值模拟分析。     

生产和运输成本问题的机会约束规划方法

当供应商的生产能力和销售商的需求量是随机参数时,建立了一类产品生产和运输成本问题的数学模型,它是一种随机优化模型.利用机会约束规划方法研究了在给定置信水平和其它相关约束条件时,此类随机优化问题的确定型等价式.给出了每个供应商给每个销售商的送货量,且达到了总运输成本最低.实际案例研究表明所建立的模型和求解方法有效,且分析了不同置信水平下最优值的变化,提供了选择最佳置信水平的方法.     

一种加入创新粒子的粒子群

粒子群算法是一种基于群体智能的随机并行算法,它在很多优化问题中都得到了比较好的应用。本文针对粒子群容易陷入局部最优解,提出了一种加入创新粒子的粒子群,实验模拟结果表明加入创新粒子的粒子群有更好的结果和收敛速度。     

Scenario tree generation for multiperiod financial optimization by optimal discretization

Multiperiod financial optimization is usually based on a stochastic model for the possible market situations. There is a rich literature about modeling and estimation of continuous-state financial processes, but little attention has been paid how to approximate such a process by a discrete-state scenario process and how to measure the pertaining approximation error.?In this paper we show how a scenario tree may be constructed in an optimal manner on the basis of a simulation model of the underlying financial process by using a stochastic approximation technique. Consistency relations for the tree may also be taken into account. Received: December 15, 1998 / Accepted: October 1, 2000?Published online December 15, 2000     

Rare Event Probability Estimation in the Presence of Epistemic Uncertainty on Input Probability Distribution Parameters

The accurate estimation of rare event probabilities is a crucial problem in engineering to characterize the reliability of complex systems. Several methods such as Importance Sampling or Importance Splitting have been proposed to perform the estimation of such events more accurately (i.e., with a lower variance) than crude Monte Carlo method. However, these methods assume that the probability distributions of the input variables are exactly defined (e.g., mean and covariance matrix perfectly known if the input variables are defined through Gaussian laws) and are not able to determine the impact of a change in the input distribution parameters on the probability of interest. The problem considered in this paper is the propagation of the input distribution parameter uncertainty defined by intervals to the rare event probability. This problem induces intricate optimization and numerous probability estimations in order to determine the upper and lower bounds of the probability estimate. The calculation of these bounds is often numerically intractable for rare event probability (say 10^?5), due to the high computational cost required. A new methodology is proposed to solve this problem with a reduced simulation budget, using the adaptive Importance Sampling. To this end, a method for estimating the Importance Sampling optimal auxiliary distribution is proposed, based on preceding Importance Sampling estimations. Furthermore, a Kriging-based adaptive Importance Sampling is used in order to minimize the number of evaluations of the computationally expensive simulation code. To determine the bounds of the probability estimate, an evolutionary algorithm is employed. This algorithm has been selected to deal with noisy problems since the Importance Sampling probability estimate is a random variable. The efficiency of the proposed approach, in terms of accuracy of the found results and computational cost, is assessed on academic and engineering test cases.     

Reliability based assignment in stochastic-flow freight network

Based on the reliability of transportation time, a transportation assignment model of stochastic-flow freight network is designed in this paper. This transportation assignment model is built by mean of stochastic chance-constraint programming and solved with a hybrid intelligent algorithm (HIA) which integrates genetic algorithm (GA), stochastic simulation (SS) and neural network (NN). GA is employed to report the optimal solution as well as the optimal objective function values of the proposed model. SS is used to simulate the value of uncertain system reliability function. The uncertain function approximated via NN is embedded into GA to check the feasibility and to compute the fitness of the chromosomes. These conclusions have been drawn after a test of numerical case using the proposed formulations. System reliability, total system cost and flow on each path would finally reach at their own convergence points. Increase of the system reliability causes increase of the total time cost. The system reliability and the total time cost converge at a possible Nash Equilibrium point.     

Simultaneous kriging-based estimation and optimization of mean response

Robust optimization is typically based on repeated calls to a deterministic simulation program that aim at both propagating uncertainties and finding optimal design variables. Often in practice, the “simulator” is a computationally intensive software which makes the computational cost one of the principal obstacles to optimization in the presence of uncertainties. This article proposes a new efficient method for minimizing the mean of the objective function. The efficiency stems from the sampling criterion which simultaneously optimizes and propagates uncertainty in the model. Without loss of generality, simulation parameters are divided into two sets, the deterministic optimization variables and the random uncertain parameters. A kriging (Gaussian process regression) model of the simulator is built and a mean process is analytically derived from it. The proposed sampling criterion that yields both optimization and uncertain parameters is the one-step ahead minimum variance of the mean process at the maximizer of the expected improvement. The method is compared with Monte Carlo and kriging-based approaches on analytical test functions in two, four and six dimensions.