Stochastic integer programming problems under probabilistic constraints are considered. Deterministic equivalent formulations of the original problem are obtained by using p -efficient points of the distribution funct...
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Stochastic integer programming problems under probabilistic constraints are considered. Deterministic equivalent formulations of the original problem are obtained by using p -efficient points of the distribution function of the right hand side vector. A branch and bound solution method is proposed based on a partial enumeration of the set of these points. The numerical experience with the probabilistic lot-sizing problem shows the potential of the solution approach and the efficiency of the algorithms implemented.
A method is presented for solving the "practical" problem of moments to produce probability density functions (PDFs) using non-classical orthogonal polynomials. PDFs are determined from given sets of moments...
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A method is presented for solving the "practical" problem of moments to produce probability density functions (PDFs) using non-classical orthogonal polynomials. PDFs are determined from given sets of moments by applying the Gram-Schmidt process with the aid of computer algebra. By selecting weighting functions of similar shape to desired PDFs, orthogonal polynomial series are obtained that are stable at high order and allow accurate approximation of tail probabilities. The method is first demonstrated by approximating a chi(2) PDF with an orthogonal series based on a lognormal weighting function. More general orthogonal expansions, based on Pearson type I and Johnson transform distributions, are then demonstrated. These expansions are used to produce PDFs for maximum daily river discharge, concrete strength, and maximum seasonal snow depths, using Limited data sets. In all three cases the moments of the high order series are found to closely match those of the data. (C) 2000 Elsevier Science Ltd. All rights reserved.
作者：
Khan, WAKhan, MAHayhurst, DRGIK
Inst Engn Sci & Technol Fac Mech Engn Topi 23460 District Swabi Pakistan GIK
Inst Engn Sci & Technol Fac Comp Sci & Engn Topi Pakistan Univ Manchester
Inst Sci & Technol Dept Mech Engn Manchester M60 1QD Lancs England
The routing of tools, dies, torches, electric area, ray beams and jets to produce features on a workpiece is a travelling salesman problem (TSP) of variable size and unpredictable node distribution. The orientation of...
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The routing of tools, dies, torches, electric area, ray beams and jets to produce features on a workpiece is a travelling salesman problem (TSP) of variable size and unpredictable node distribution. The orientation of the nodes may be in two-dimensional planes or three-dimensional spaces. An optimal path for the TSP can be found using tour construction, subtour elimination and tour-to-tour improvement procedures. Exact solution of the TSP for large numbers of nodes incurs a high computing cost. Enumeration of the problem domain can lead to a globally optimal solution at reduced computing cost. Technological constraints can be used to reduce the problem size for formulation as a TSP under multiple constraints. The solution of a TSP with constraints results in large savings in non-productive movement with no changes in productive movement. The savings in non-productive movement in repetitive batch-type manufacturing lead to reduced machine tool residence time and lower power consumption.
To economize machining process used in component manufacturing number of procedures an used. Typical parameters which are optimized are feed rate, spindle speed, depth of cut, machining time etc. Almost no considerati...
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To economize machining process used in component manufacturing number of procedures an used. Typical parameters which are optimized are feed rate, spindle speed, depth of cut, machining time etc. Almost no consideration is given to non-productive machining time, which is an important parameter on modern computer numerical control machine tools. Its importance is further augmented in the area of numerically controlled cutting where surface area to thickness ratio is high. The problem is formulated as a large scale traveling salesman problem. The cases of symmetric, asymmetric and symmetric asymmetric TSP in two dimensions are presented. The stochastic search procedure simulated annealing algorithm is used to solve these instances of TSP. The perturbation scheme is modified for asymmetric graph and mixed symmetric asymmetric graph TSPs. An investigation is also carried out for empirically finding a suitable value of acceptance probability for random topology of nodes. Effect of problem size and node distribution on the convergence is also monitored. Solution of symmetric, asymmetric and mixed symmetric asymmetric TSPs are provided. This solution allows the optimization of non-productive movement thus reducing the machine tool resident time and the power consumption. The solution is also applicable to a number of other areas such as multi axes production machinery, pick and place technology, and quality control machines. (C) 1999 Elsevier Science B.V. All rights reserved.
Decision makers faced with uncertain information often experience regret upon learning that an alternative action would have been preferable to the one actually selected. Models that minimize the maximum regret can be...
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Decision makers faced with uncertain information often experience regret upon learning that an alternative action would have been preferable to the one actually selected. Models that minimize the maximum regret can be useful in such situations, especially when decisions are subject to ex post review. Of particular interest are those decision problems that can be modeled as linear programs with interval objective function coefficients. The minimax regret solution for these formulations can be found using an algorithm that, at each iteration, solves first a linear program to obtain a candidate solution and then a mixed integer program (MIP) to maximize the corresponding regret. The exact solution of the MIP is computationally expensive and becomes impractical as the problem size increases. In this paper, we develop a heuristic for the MTP and investigate its performance both alone and in combination with exact procedures. The heuristic is shown to be effective for problems that are significantly larger than those previously reported in the literature. (C) 1999 Elsevier Science B.V. All rights reserved.
A nested layered network mapping and algorithm is presented for parallel computational solutions of discrete stochastic programming problems with random coefficients. The algorithm is general purpose and efficiently i...
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A nested layered network mapping and algorithm is presented for parallel computational solutions of discrete stochastic programming problems with random coefficients. The algorithm is general purpose and efficiently implementable on multiprocessor systems with associative memory. Details of its implementation on a 64-CPU parallel computer and results are presented for a hard problem arising in antibody-inventory optimization in vitro. Performance is discussed along with scope vis-a-vis other general purpose efficient algorithms for discrete SPPs. Scope and Purpose: Many real world optimization problems require solutions of large scale discrete programming problems with random or uncertain coefficients and inputs. Computational difficulties arise owing to the involvement of multiple summations of large number of nonlinear mathematical terms which may not satisfy any common regularity condition within the range of summations. Parallel and associative memory based algorithms are currently in demand for solving such problems. A general purpose computing network design is presented here which contributes in the above direction. Parallel implementation and results are illustrated on a real-world problem of cost (energy) minimization.
We consider a stochastic knapsack problem that packs multiple classes of random items. The pairs of profit and resource requirement for items of the same class are independent and identically distributed. However, suc...
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We consider a stochastic knapsack problem that packs multiple classes of random items. The pairs of profit and resource requirement for items of the same class are independent and identically distributed. However, such pairs for different classes of items are independent but not necessarily identically distributed. We investigate convergence and the asymptotic value of the ratio of the knapsack value function to the capacity when the capacity increases. We consider two growth models for the multi-class stochastic knapsack problem, one where the number of available items grows proportionally to the capacity and the other one where the available items are sampled until their total resource requirement does not exceed the capacity. By extending the results of Meanti et al. on a single class of random items, we show that for each growth model, the ratio converges almost surely to a computable constant. For special cases where resource requirements or profit coefficients are deterministic, we present simple interpretations on the asymptotic values. Finally, we present an exponential order upperbound on the tail probability of the ratio. (C) 1997 Elsevier Science B.V.
The problem of reducing SO2 emissions in Europe is considered. The costs of reduction are assumed to be uncertain and are modeled by a set of possible scenarios. A mean-variance model of the problem is formulated and ...
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The problem of reducing SO2 emissions in Europe is considered. The costs of reduction are assumed to be uncertain and are modeled by a set of possible scenarios. A mean-variance model of the problem is formulated and a specialized computational procedure is developed. The approach is applied to the trans-boundary air pollution model with real-world data.
Coal blending is one of several options available for reducing sulfur emissions from coal-fired power plants. However, decisions about coal blending must deal with uncertainty and variability in coal properties, and w...
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Coal blending is one of several options available for reducing sulfur emissions from coal-fired power plants. However, decisions about coal blending must deal with uncertainty and variability in coal properties, and with the effect of off-design coal characteristics on power plant performance and cost. To deal with these issues, a multi-objective chance-constrained optimization model is developed for an illustrative coal blending problem. Sulfur content, ash content and heating value are treated as normally distributed random variables. The objectives of the model include minimizing the: 1) expected (mean) costs of coal blending;2) standard deviation of coal blending costs;3) expected sulfur emissions;and 4) standard deviation in sulfur emissions. The cost objective function includes coal purchasing cost, ash disposal cost, sulfur removal cost, and fuel switching costs. Chance constraints include several risk measures, such as the probability of exceeding the sulfur emission standard. Several results are presented to illustrate the model.
This paper discusses practical methods for handling normally distributed random technical (yield) coefficients in linear programs that optimize natural resource allocation and scheduling, These methods are practical i...
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This paper discusses practical methods for handling normally distributed random technical (yield) coefficients in linear programs that optimize natural resource allocation and scheduling, These methods are practical in the sense that they are applicable to large-scale real world models and do not require nonlinear solution methods. The paper begins with a description and demonstration of postoptimization approaches that are applicable to large, linear problems, and then explores methods for reducing overall risk through land allocation diversification, A central theme of the paper is the importance of providing some sort of allowance for uncertainty when presenting optimization results, which promotes a more realistic view of the problem by analysts and decision makers alike.
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