In this paper we consider stochastic programming problems where the objective function is given as an expected value of a convex piecewise linear random function. With an optimal solution of such a problem we associat...
详细信息
In this paper we consider stochastic programming problems where the objective function is given as an expected value of a convex piecewise linear random function. With an optimal solution of such a problem we associate a condition number which characterizes well or ill conditioning of the problem. Using theory of Large Deviations we show that the sample size needed to calculate the optimal solution of such problem with a given probability is approximately proportional to the condition number.
The aim of this paper is to demonstrate that CP could be abetter candidate than MIP for solving the master problem within a Benders decomposition approach. Our demonstration is based on a case study of a workforce sch...
详细信息
In recent years we have observed an increasing interest in the job mobility patterns of employed persons. A new issue in this context is the mutual dependence of job mobility choice of workers who belong to the same h...
详细信息
In recent years we have observed an increasing interest in the job mobility patterns of employed persons. A new issue in this context is the mutual dependence of job mobility choice of workers who belong to the same household. In the present paper, we focus on bivariate duration models of stock sampled data in which dependence is induced through mixing. We apply the estimation method on the basis of an empirical study on the mutual dependence of job mobility of workers belonging to a two-earner household in the Netherlands, An interesting empirical result is that the marginal willingness to pay for a reduction in commuting time in a two-wage earner household is higher than that usually found for single-earner workers. (C) 2002 Elsevier Science B.V. All rights reserved.
In practical applications of stochastic programming the involved probability distributions are never known exactly. One can try to hedge against the worst expected value resulting from a considered set of permissible ...
详细信息
In practical applications of stochastic programming the involved probability distributions are never known exactly. One can try to hedge against the worst expected value resulting from a considered set of permissible distributions. This leads to a min-max formulation of the corresponding stochastic programming problem. We show that, under mild regularity conditions, such a min-max problem generates a probability distribution on the set of permissible distributions with the min-max problem being equivalent to the expected value problem with respect to the corresponding weighted distribution. We consider examples of the news vendor problem, the problem of moments and problems involving unimodal distributions. Finally, we discuss the Monte Carlo sample average approach to solving such min-max problems.
This paper presents hierarchical improvements to combinatorial stochastic annealing algorithms using a new and efficient sampling technique. The Hammersley Sequence Sampling (HSS) technique is used for updating discre...
详细信息
This paper presents hierarchical improvements to combinatorial stochastic annealing algorithms using a new and efficient sampling technique. The Hammersley Sequence Sampling (HSS) technique is used for updating discrete combinations, reducing the Markov chain length, determining the number of samples automatically, and embedding better confidence intervals of the samples. The improved algorithm, Hammersley stochastic annealing, can significantly improve computational efficiency over traditional stochastic programming methods. This new method can be a useful tool for large-scale combinatorial stochastic programming problems. A real-world case study involving solvent selection under uncertainty illustrates the usefulness of this new algorithm.
Semiconductor capacity planning is a cross-functional decision that requires coordination between the marketing and manufacturing divisions. We examine the main issues of a decentralized coordination scheme in a setti...
详细信息
Semiconductor capacity planning is a cross-functional decision that requires coordination between the marketing and manufacturing divisions. We examine the main issues of a decentralized coordination scheme in a setting observed at a major US semiconductor manufacturer: marketing managers reserve capacity from manufacturing based on product demands, while attempting to maximize profit;manufacturing managers allocate capacity to competing marketing managers so as to minimize operating costs while ensuring efficient resource utilization. This cross-functional planning problem has two important characteristics: (i) both demands and capacity are subject to uncertainty;and (ii) all decision entities own private information while being self-interested. To study the issues of coordination we first formulate the local marketing and the manufacturing decision problem as separate stochastic programs. We then formulate a centralized stochastic programming model (JCA), which maximizes the firm's overall profit. JCA establishes a theoretical benchmark for performance, but is only achievable when all planning information is public. If local decision entities are to keep their planning information private, we submit that the best achievable coordination corresponds to an alternative stochastic model (DCA). We analyze the relationship and the theoretical gap between (JCA) and (DCA), thereby establishing the price of decentralization. Next, we examine two mechanisms that coordinate the marketing and manufacturing decisions to achieve (DCA) using different degrees of information exchange. Using insights from the Auxiliary Problem Principle (APP), we show that under both coordination mechanisms the divisional proposals converge to the global optimal solution of (DCA). We illustrate the theoretic insights using numerical examples as well as a real world case.
We discuss the problem of hedging between the natural gas and electric power markets. Based on multiple forecasts for natural gas prices, natural gas demand, and electricity prices, a stochastic optimization model adv...
详细信息
We discuss the problem of hedging between the natural gas and electric power markets. Based on multiple forecasts for natural gas prices, natural gas demand, and electricity prices, a stochastic optimization model advises a decision maker on when to buy or sell natural gas and when to transform gas into electricity. For relatively small models, branch-and-bound solves the problem to optimality. Larger models are solved using Benders decomposition and Lagrangian relaxation. We apply our approach to the system of an electric utility and succeed in solving problems with 50 000 binary variables in less than 4 min to within 1.16% of the optimal value.
A theoretical and numerical assessment of the validity of Eulerian truncation in stochastic modeling is presented. Specifically, we analyze and compare theoretically various existing Eulerian-based first-order techniq...
详细信息
A theoretical and numerical assessment of the validity of Eulerian truncation in stochastic modeling is presented. Specifically, we analyze and compare theoretically various existing Eulerian-based first-order techniques with and without invoking Eulerian truncation and quantify the terms truncated and retained in the stochastic perturbation equations using high resolution Monte Carlo simulations. We also analyze and compare numerically various existing Eulerian-based first-order techniques and Monte Carlo simulation. The obtained results have demonstrated theoretically and numerically that existing Eulerian-based stochastic perturbation techniques are equivalent. The terms truncated are indeed one order higher than those retained. Therefore, we conclude that Eulerian truncation is mathematically consistent and asymptotic.
In the optimal control of industrial, field or service robots, the standard procedure is to determine first off-line a reference trajectory and a feedforward control, based on some selected nominal values of the unkno...
详细信息
In the optimal control of industrial, field or service robots, the standard procedure is to determine first off-line a reference trajectory and a feedforward control, based on some selected nominal values of the unknown stochastic model parameters, and to correct then the inevitable and increasing deviation of the state or performance of the robot from the prescribed state or performance of the system by online measurement and control actions. Due to the stochastic variations of the model parameters, increasing measurement and correction actions are needed during the process. By optimal stochastic trajectory planning (OSTP), based on stochastic optimization methods, the available a priori and sample information about the robot and its working environment is incorporated into the control process. Consequently, more robust reference trajectories and feedforward controls are obtained which cause much less online control actions. In order to maintain a high quality of the guiding functions, the reference trajectory and the feedforward control can be updated at some later time points such that additional information about the control process is available. After the presentation of the Adaptive Optimal stochastic Trajectory Planning (AOSTP) procedure based on stochastic optimization methods, several numerical techniques for the computation of robust reference trajectories and feedforward controls under real-time conditions are presented. Additionally, numerical examples for a Manutec r3 industrial robot are discussed. The first one demonstrates real-time solutions of (OSTP) based on a sensitivity analysis of a before-hand calculated reference trajectory. The second shows the differences between reference trajectories based on deterministic methods and the stochastic methods introduced in this paper. Based on simulations of the robots behavior, the increased robustness of stochastic reference trajectories is demonstrated.
In this work, we focus on the interaction between optimisation technologies and the management of natural resources. In recent years, the environmental impact of planning decisions has received increasing attention, a...
详细信息
In this work, we focus on the interaction between optimisation technologies and the management of natural resources. In recent years, the environmental impact of planning decisions has received increasing attention, as negative effects on the ecosystem may affect production and consumption. Hence, there is a need to assess and quantify environmental services as well as environmental impacts, so that these can be included in the decision-making process. At the same time, recent trends in optimisation software and Internet technology have spawned a new research area in the field of distributed optimisation applications for several domains, including environmental management. We make use of the platform developed within the OSP CRAFT project, and implement an Internet-based Decision Support System (DSS), which embodies a land management stochastic programming model. The platform takes advantage of an Application Service Provision architecture, whereby decision makers are able to access the optimisation model and analyse its solutions on a subscription basis. In this framework, the remote DSS is easily interfaced with existing local repository of environment data, such as pollution measurements, soil and water resources information, as well as global GIS datasets.
暂无评论