Sensitivity analysis on the priority of the objective functions in lexicographic multiple objective linear programs

This paper deals with a class of multiple objective linear programs (MOLP) called lexicographic multiple objective linear programs (LMOLP). In this paper, by providing an efficient algorithm which employs the preceding computations as well, it is shown how we can solve the LMOLP problem if the priority of the objective functions is changed. In fact, the proposed algorithm is a kind of sensitivity analysis on the priority of the objective functions in the LMOLP problems.     

Generalized linear fractional programming under interval uncertainty

Data in many real-life engineering and economical problems suffer from inexactness. Herein we assume that we are given some intervals in which the data can simultaneously and independently perturb. We consider a generalized linear fractional programming problem with interval data and present an efficient method for computing the range of optimal values. The method reduces the problem to solving from two to four real-valued generalized linear fractional programs, which can be computed in polynomial time using an appropriate interior point method solver.     

Transition to turbulence, small disturbances, and sensitivity analysis I: A motivating problem

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new “mostly linear” theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence. In this part, we study a highly sensitive one-dimensional Burgers' equation as a motivating problem. Sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance. Also, sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem. In the second part of this work, this analysis will be extended to the three-dimensional Navier-Stokes equations to show that small disturbances have great potential to trigger transition to turbulence.     

Optimal batch sizing in a multi-stage production system with rework consideration

In a production system, rework process plays an important role in eliminating waste and effectively controlling the cost of manufacturing. Determining the optimal batch size in a system that allows for rework is, therefore, a worthwhile objective to minimize the inventory cost of work-in-processes and the finished goods. In this paper, models for the optimum batch quantity in a multi-stage system with rework process have been developed for two different operational policies. Policy 1 deals with the rework within the same cycle with no shortage and policy 2 deals with the rework done after N cycles, incurring shortages in each cycle. The major components that play a role in minimizing this cost of the system are manufacturing setups, work-in-processes, storage of finished goods, rework processing, waiting-time, and penalty costs to discourage the generation of defectives. The mathematical structure of this rework processing model falls under a nonlinear convex programming problems for which a closed-form solution has been proposed and results are demonstrated through numerical examples, followed by sensitivity analyses of different important parameters. It is concluded that the total cost in policy 2 tends to be smaller than that in policy 1 at lower proportion of defectives if the in-process carrying cost is low. Policy 2 may be preferred when the work-in-process carrying cost is low and the penalty cost is negligible.     

Solution continuity in variational conditions

We present some results about Lipschitzian behavior of solutions to variational conditions when the sets over which the conditions are posed, as well as the functions appearing in them, may vary. These results rely on calmness and inner semicontinuity, and we describe some conditions under which those conditions hold, especially when the sets involved in the variational conditions are convex and polyhedral. We then apply the results to find error bounds for solutions of a strongly monotone variational inequality in which both the constraining polyhedral multifunction and the monotone operator are perturbed.      

Parameter uncertainty, sensitivity analysis and prediction error in a water-balance hydrological model

Analysis of uncertainty is often neglected in the evaluation of complex systems models, such as computational models used in hydrology or ecology. Prediction uncertainty arises from a variety of sources, such as input error, calibration accuracy, parameter sensitivity and parameter uncertainty. In this study, various computational approaches were investigated for analysing the impact of parameter uncertainty on predictions of streamflow for a water-balance hydrological model used in eastern Australia. The parameters and associated equations which had greatest impact on model output were determined by combining differential error analysis and Monte Carlo simulation with stochastic and deterministic sensitivity analysis. This integrated approach aids in the identification of insignificant or redundant parameters and provides support for further simplifications in the mathematical structure underlying the model. Parameter uncertainty was represented by a probability distribution and simulation experiments revealed that the shape (skewness) of the distribution had a significant effect on model output uncertainty. More specifically, increasing negative skewness of the parameter distribution correlated with decreasing width of the model output confidence interval (i.e. resulting in less uncertainty). For skewed distributions, characterisation of uncertainty is more accurate using the confidence interval from the cumulative distribution rather than using variance. The analytic approach also identified the key parameters and the non-linear flux equation most influential in affecting model output uncertainty.     

减压氩气环境下激光显微光谱分析再现性和灵敏度的研究

以金属合金光谱分析标样为样品，采用激光显微发射光谱分析系统在减压氩气环境下，实验研究了光谱分析再现性和灵敏度。以原子线作为分析线的RSD减压氩气环境好于常压空气环境，以离子线作为分析线的RSD基本相同，样品的组成和元素的浓度对分析线的RSD有较大的影响。测定的铝合金样品Cu,Zn,Mg浓度曲线斜率是空气环境下的1．5－2倍，表明分析灵敏度得到明显改善，有利于激光显微光谱分析范围的扩展。     

Sensitivity analysis for variational inequalities

Sensitivity analysis results for variational inequalities are presented which give conditions for existence and equations for calculating the derivatives of solution variables with respect to perturbation parameters. The perturbations are of both the variational inequality function and the feasible region. Results for the special case of nonlinear complementarity are also presented. A numerical example demonstrates the results for variational inequalities.The author is indebted to A. V. Fiacco for many valuable suggestions and comments. This work was supported in part by funding from the Economic Regulatory Administration, US Department of Energy, under Contract No. W31109ENG38.     

Unsteady oblique shock waves

A spatially and temporally local analysis is provided for unsteady, oblique shock waves, in which the flow is assumed to be two-dimensional or axisymmetric. Three unsteady parameters, in a laboratory frame, are viewed as the known independent variables. These are the upstream Mach number, the shock Mach number, and the angle of the shock relative to the instantaneous upstream velocity. Other steady and unsteady parameters, such as the velocity turn angles and downstream Mach numbers, are evaluated in closed form, in terms of these three quantities. Trends are assessed, and a sensitivity analysis is provided. It is suggested that the theory may find application in converting a shock capturing algorithm, at an early time during the computational process, into a shock fitting algorithm. Received 30 April 1999 / Accepted 29 November 1999     

Uncertainties in Solubility Calculations

Summary.  When considering the possible migration of hazardous elements in groundwater, one has to take into account several phenomena, e.g. solubility, ion exchange, adsorption, matrix diffusion, and transport paths. Here, we focus upon the solubility which in turn depends on several more or less uncertain chemical properties. Uncertainties in the data during laboratory experiments aiming at measurements of thermodynamic constants may cause uncertainties in the amount of some species of several tenths of the relative mass fraction. The thermodynamic data may then be used for solubility calculations under different conditions and water compositions. Clearly, there are several uncertainties associated with solubility calculations in the rock-water system. First, there is the effect of uncertainties in thermodynamic data such as stability and solubility constants, and also enthalpies of reaction if the water is not at room temperature. Furthermore, there are the rock-water interactions which will change the water composition as different minerals come in contact with the water flowing through a system of fractures. Studies in mineralogy to an accuracy good enough for modeling of water evolution are difficult to perform, and therefore the mineral composition of the rock and thus the water composition should be treated as parameters subjected to uncertainties. In addition, there are also conceptual uncertainties with respect to input data. The calculation of a solubility should be an easy task for every chemist, but in fact results differing by orders of magnitude are found even when the modelers have used the same computer program and the same data. In this paper, uncertainties associated with solubility calculations are discussed. The results are exemplified on the calculated solubilities of some actinides in groundwater from crystalline rock. Received August 21, 2000. Accepted (revised) May 18, 2001