Bayesian forecasting models provide distributional estimates for random parameters, and relative to classical schemes, have the advantage that they can rapidly capture changes in nonstationary systems using limited hi...
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Bayesian forecasting models provide distributional estimates for random parameters, and relative to classical schemes, have the advantage that they can rapidly capture changes in nonstationary systems using limited historical data. Unlike deterministic optimization, stochastic programs explicitly incorporate distributions for random parameters in the model formulation, and thus have the advantage that the resulting solutions more fully hedge against future contingencies. In this paper, we exploit the strengths of Bayesian prediction and stochastic programming in a rolling-horizon approach that can be applied to solve real-world problems. We illustrate the methodology on an employee production scheduling problem with uncertain up-times of manufacturing equipment and uncertain production rates. Computational results indicate the value of our approach.
The emphasis of this paper is to introduce a novel concept of birandom variable and to exhibit the framework of birandom programming. The so-called birandorn variable is a measurable mapping from a probability space t...
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The emphasis of this paper is to introduce a novel concept of birandom variable and to exhibit the framework of birandom programming. The so-called birandorn variable is a measurable mapping from a probability space to a collection of random variables. Based on this definition, the expected value operator of birandom variable and chance measures of birandom event are further introduced. As a generalized scenario of stochastic programming, a spectrum of birandont programming models are developed to deal with birandom systems. To solve the proposed models, birandom simulations are presented and then a hybrid intelligent algorithm is designed by embedding neural networks into genetic algorithm. Finally, some numerical experiments are provided to illustrate the effectiveness of the algorithm. (c) 2007 Elsevier Ltd. All rights reserved.
Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when se...
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Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible to define multi-level programs with any number of levels. In most of the real life problems in mathematical programming, the parameters are considered as random variables. The branch of mathematical programming which deals with the theory and methods for the solution of conditional extremum problems under incomplete information about the random parameters is called "stochastic programming". Supply chain planning problems are concerned with synchronizing and optimizing multiple activities involved in the enterprise, from the start of the process, such as procurement of the raw materials, through a series of process operations, to the end, such as distribution of the final product to customers. Enterprise-wide supply chain planning problems naturally exhibit a multi-level decision network structure, where for example, one level may correspond to a local plant control/scheduling/planning problem and another level to a corresponding plant-wide planning/network problem. Such a multi-level decision network structure can be mathematically represented by using "multi-level programming" principles. In this paper, we consider a "probabilistic bi-level linear multi-objective programming problem" and its application in enterprise-wide supply chain planning problem where (1) market demand, (2) production capacity of each plant and (3) resource available to all plants for each product are random variables and the constraints may consist of joint probability distributions or not. This probabilistic model is first converted into an equivalent deterministic model in each level, to which fuzzy programming technique is applied to solve the multi-objective nonlinear programming problem to ob
Innovative prevention, adaptation, and mitigation approaches as well as policies for sustainable flood management continue to be challenges faced by decision-makers. In this study, a mixed interval-fuzzy two-stage int...
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Innovative prevention, adaptation, and mitigation approaches as well as policies for sustainable flood management continue to be challenges faced by decision-makers. In this study, a mixed interval-fuzzy two-stage integer programming (IFTIP) method is developed for flood-diversion planning under uncertainty. This method improves upon the existing interval, fuzzy, and two-stage programming approaches by allowing uncertainties expressed as probability distributions, fuzzy sets, and discrete intervals to be directly incorporated within the optimization framework. In its modelling formulation, economic penalties as corrective measures against any infeasibilities arising because of a particular realization of the uncertainties are taken into account. The method can also be used for analysing a variety of policy scenarios that are associated with different levels of economic penalties. A management problem in terms of flood control is studied to illustrate the applicability of the proposed approach. The results indicate that reasonable solutions have been generated. They can provide desired flood-diversion alternatives and capacity-expansion schemes with a minimized system cost and a maximized safety level. The developed IFTIP is also applicable to other management problems that involve uncertainties presented in multiple formats as well as complexities in policy dynamics.
We consider a network design problem arising in mobile communications. At the core of the network is a number of mobile switching centers (MSCs), each serving a number of base station controllers (BSCs). The network d...
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We consider a network design problem arising in mobile communications. At the core of the network is a number of mobile switching centers (MSCs), each serving a number of base station controllers (BSCs). The network design problem involves three major groups of decisions - deployment of a number of new MSCs, allocation of BSCs to new and existing MSCs, and capacity expansion of transmission links interconnecting the MSCs. These decisions must be made so as to minimize the incurred costs while meeting customer demand and observing the capacity restrictions. We formulate the problem as a two-stage stochastic program with mixed-integer recourse. To solve the problem we apply a dual decomposition procedure, solving scenario subproblems by means of branch and cut. The solution procedure has been tested on a real life problem instance provided by SONOFON, a Danish mobile communication network operator, and we report results of our computational experiments.
This paper studies the optimal allocation of transmit power in a wireless communication network. First, a stochastic programming formulation is introduced, based on penalizing violations of quality-of-service constrai...
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This paper studies the optimal allocation of transmit power in a wireless communication network. First, a stochastic programming formulation is introduced, based on penalizing violations of quality-of-service constraints. The maximization of the certainty equivalent signal-to-interference ratio under Rayleigh fading corresponds to a penalty model where (max-min) fairness is explicitly taken into consideration. Second, optimum dynamic power allocation is discussed. Efficient dynamic resource allocation under both linear and logarithmic utility functions is addressed. The dynamic model studies the optimal trade-off between instantaneous quality-of-service and a delay-penalized reliable quality-of-service. Related work on optimal stochastic power control is summarized.
In this paper, we consider a stochastic programming approach to multistage post-tax portfolio optimization. Asset performance information is specified as a scenario tree generated by two alternative methods based on s...
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In this paper, we consider a stochastic programming approach to multistage post-tax portfolio optimization. Asset performance information is specified as a scenario tree generated by two alternative methods based on simulation and optimization. We assume three tax wrappers involving the same instruments for an efficient investment strategy and determine optimal allocations to different instruments and wrappers. The tax rules are integrated with the linear and mixed integer stochastic models to yield air overall tax and return-efficient multistage portfolio. The computational performance of these models is tested using a case study with different scenario trees. Our experiments show that optimal portfolios obtained by both linear programming and mixed integer stochastic models diversify over wrappers and the original capital is distributed among assets within each wrapper. (C) 2003 Elsevier B.V. All rights reserved.
Consideration was given to the problem of stochastic programming with the quantile (VaR) criterion. Conditions related with the characteristics of probabilistic distributions under which the quantile function is conve...
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Consideration was given to the problem of stochastic programming with the quantile (VaR) criterion. Conditions related with the characteristics of probabilistic distributions under which the quantile function is convex in strategy were presented. Relationship between convexity of the quantile function and convexity of the function of integral (CVaR) quantile criterion was shown.
作者：
Sahin, KHDiwekar, UMUniv Illinois
Ctr Uncertain Syst Tools Optimizat & Management Dept Bioind Chicago IL 60514 USA Univ Illinois
Dept Chem Engn Inst Environm Sci & Technol Chicago IL 60514 USA
A new nonlinear programming algorithm is proposed for stochastic programming problems. This method relies on sampling to estimate the probabilistic objective function and constraints. The computational burden of exces...
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A new nonlinear programming algorithm is proposed for stochastic programming problems. This method relies on sampling to estimate the probabilistic objective function and constraints. The computational burden of excessive model calculations for determining the search direction is bypassed through a reweighting method using Kernel Density Estimation. The improvements accomplished by this algorithm called Better Optimization of Nonlinear Uncertain Systems (BONUS) are presented through two real world case studies involving parameter design for off-line quality control of a chemical reactor, and optimal capacity expansion for electric utilities in uncertain markets.
A price determination mode for large consumers is proposed under the present environments with large consumers purchasing electric power from the electricity supply utility in some area in Yunnan. With abundant waterp...
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A price determination mode for large consumers is proposed under the present environments with large consumers purchasing electric power from the electricity supply utility in some area in Yunnan. With abundant waterpower in Yunnan, most of consumed electric power of large consumers is signed in the form of contracts. The contract price is determined by optimizing resources and maximizing profits of the supply utility. The different price is in accordance with different demand-price elasticity of large consumers. The difference between planned and actual consumption power is balanced in two spot markets. Because of the randomicity of spot price and trading power, the sale price of the supply utility in spot market is calculated based on stochastic programming. At last, simulation verifies the rationality of the models, which solves a part of problems faced by the supply utility in selling electricity to large consumers.
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