Exact Input Data Research Articles

A fuzzy modeling for single machine scheduling problem with deteriorating jobs

Article history: Received 1 January 2010 Received in revised form 10 May 2010 Accepted 1 June 2010 Available online 2 June 2010 This paper addresses a bi-criteria scheduling problem with deteriorating jobs on a single machine. We develop a model for a single machine bi-criteria scheduling problem (SMBSP) with the aim of minimizing total tardiness and work in process (WIP) costs. WIP cost increases as a job passes through a series of stages in the production process. Due to the uncertainty involved in real-world scheduling problems, it is sometimes unrealistic or even impossible to acquire exact input data. Hence, we consider the SMBSP under the hypothesis of fuzzy L-R processing time's knowledge and fuzzy L-R due date. The effectiveness of the proposed model and the denoted methodology is demonstrated through a test problem. © 2010 Growing Science Ltd. All rights reserved.

Duality, efficiency computations and interpretations in imprecise DEA

Data envelopment analysis (DEA) has proven to be a useful tool for assessing efficiency or productivity of organizations which is of vital practical importance in managerial decision making. While DEA assumes exact input and output data, the development of imprecise DEA (IDEA) broadens the scope of applications to efficiency evaluations involving imprecise information which implies various forms of ordinal and bounded data possibly or often occurring in practice. The primary purpose of this article is to characterize the variable efficiency in IDEA. Since DEA describes a pair of primal and dual models, also called envelopment and multiplier models, we can basically consider two IDEA models: One incorporates imprecise data into envelopment model and the other includes the same imprecise data in multiplier model. The issues of rising importance are thus the relationships between the two models and how to solve them. The groundwork we will make includes a duality study, which makes it possible to characterize the efficiency solutions from the two models and link with the efficiency bounds and classifications that some of the published IDEA studies have done. The other purposes are to present computational aspects of the efficiency bounds and how to interpret the efficiency solutions. The computational method developed here extends the previous IDEA method to effectively incorporate a more general form of strict ordinal data and partial orders in its framework, which in turn overcomes some drawbacks of the previous approaches. The interpretation of the resulting efficiency is also important but we have never seen it before.

The method of fundamental solutions for detection of cavities in EIT

In this paper, the method of fundamental solutions (MFS) is used to solve numerically an inverse problem which consists of finding an unknown cavity within a region of interest based on given boundary Cauchy data. A range of examples are used to demonstrate that the technique is very effective at locating cavities in both two- and three-dimensional geometries for exact input data. The technique is then developed to include a regularisation parameter that enables cavities to be located accurately and stably even for noisy input data.

A fuzzy-mixed-integer goal programming model for a parallel-machine scheduling problem with sequence-dependent setup times and release dates

This paper presents a new mixed-integer goal programming (MIGP) model for a parallel-machine scheduling problem with sequence-dependent setup times and release dates. Two objectives are considered in the model to minimize the total weighted flow time and the total weighted tardiness simultaneously. Due to the complexity of the above model and uncertainty involved in real-world scheduling problems, it is sometimes unrealistic or even impossible to acquire exact input data. Hence, we consider the parallel-machine scheduling problem with sequence-dependent set-up times under the hypothesis of fuzzy processing time's knowledge and two fuzzy objectives as the MIGP model. In addition, a quite effective and applicable methodology for solving the above fuzzy model are presented. At the end, the effectiveness of the proposed model and the denoted methodology is demonstrated through some test problems.

Uncertainty quantification and apportionment in air quality models using the polynomial chaos method

Current air quality models generate deterministic forecasts by assuming perfect model, perfectly known parameters, and exact input data. However, our knowledge of the physics is imperfect. It is of interest to extend the deterministic simulation results with “error bars” that quantify the degree of uncertainty, and analyze the impact of the uncertainty input on the simulation results. This added information provides a confidence level for the forecast results. Monte Carlo (MC) method is a popular approach for air quality model uncertainty analysis, but it converges slowly. This work discusses the polynomial chaos (PC) method that is more suitable for uncertainty quantification (UQ) in large-scale models. We propose a new approach for uncertainty apportionment (UA), i.e., we develop a PC approach to attribute the uncertainties in model results to different uncertainty inputs. The UQ and UA techniques are implemented in the Sulfur Transport Eulerian Model (STEM-III). A typical scenario of air pollution in the northeast region of the USA is considered. The UQ and UA results allow us to assess the combined effects of different input uncertainties on the forecast uncertainty. They also enable to quantify the contribution of input uncertainties to the uncertainty in the predicted ozone and PAN concentrations.

The inverse source problem for the variable coefficients convection-diffusion equation

This article is concerned with the numerical solution of an inverse source problem associated with the variable coefficients convection-diffusion equation. The Dual Reciprocity Boundary Element Method (DRBEM) is combined with an iterative Sequential Quadratic Programming (SQP) procedure in order to identify the locations and strengths of several point sources. As the number of sources needs to be estimated a priori, there are three possible cases, namely correct, over and under estimation of this number. All the three situations are investigated and a study of stability of the proposed numerical technique is performed by adding random noise into the exact input data.

군용항공기 소음예측시 오차저감에 관한 연구

Aircraft noise is a serious problem to inhabitants near airports. INM is one of programs for determining the predicted noise impact in the vicinity of airports. It has been widely used for engineers to evaluate aircraft noise. However it is difficult to predict aircraft noise in case of lack of exact INM input data. The exact informations about a fighter plane are not known well for a security problem. This study presents methods of reducing errors between measurement and simulation when the exact INM input data is not known. Especially we adjusted the thrust force of aircraft engine and reduced the error.

F.A.L.C.A.D.E.: a fuzzy software for the energy and environmental balances of products

It is generally well known that the reliability of Life Cycle Analysis (LCA) studies depends upon exact, complete and sharp input data that, unfortunately, are not always available. Furthermore, when available, the input data are affected by uncertainty whose importance is not always adequately taken into consideration. This paper describes the software F.A.L.C.A.D.E. (Fuzzy Approach to Life Cycle Analysis and Decision Environment): a tool designed for the calculation of the eco-profile of products, based on a fuzzy logic approach. The originality of the method already treated in other papers is to use the fuzzy representation to manage the complex relationships that arise in compiling an eco-balance. In particular, the model allows to give further attributes to the numerical data of the inventory based to the expert knowledge. The uncertainty of data is clearly defined by means of four fuzzy linguistic variables: the age of the data, the kind of technology to which data are referred to, the statistical and geographic representativeness of the data. The main model’s strength is transparency. Many LCA tools appear, unfortunately, as “black boxes” leaving the actual influence of the algorithms upon the final results unclear. On the other hand, with F.A.L.C.A.D.E. the user is able to observe and control all the calculation steps from the input of data to the final results. For instance, F.A.L.C.A.D.E. uses a linear sub-model that, starting from the inventory matrixes, allows to calculate an eco-profile together with a conditioning number “ CN”, which describes how sensitive is the linear model to errors when solving the system of equations. Finally, the software present a set of tables summarising the results obtained with the fuzzy model. These results can be compared with those obtained with other methods. The software represents therefore a tool to evaluate the quality of Life Cycle Inventory (LCI) study. F.A.L.C.A.D.E. has been developed using an object-oriented programming. The result is a flexible tool whose structure can be easily changed by the user (variables, linguistic rules, domains of the fuzzy groups, etc.). As case study, the software has been applied to the LCA of a plaster material commonly used in building construction.

Inverse determination of surface temperature in thin-film/substrate systems with interface thermal resistance

This work examines the effect of interface thermal resistance on the estimation of surface temperatures in thin-film/substrate systems. A radiation-boundary-condition model based on the acoustic mismatch model (AMM) is employed to consider the interface thermal resistance between thin-film and substrate. The inverse heat conduction problem is solved using the space-marching technique. The influences of interface thermal resistance, measurement locations, and measurement errors on this method are studied in detail. Numerical results show that the inverse method accurately estimates surface conditions and temperature distributions in a two-layer system even with an abrupt temperature drop at the interface. Sensor locations and interface thermal resistance only slightly affect the accuracy of the inverse estimation during the transient process when the exact input data (without measurement errors) are applied. However, the inaccuracy might be amplified by the interface thermal resistance and sensor locations if measurement errors exist.

Inverse radiation problem of axisymmetric turbulent sooting free flame

An iteration method is extended to reconstruct the time-averaged temperature distribution in turbulent axisymmetric sooting free flame by the multi-wavelength measured data of low time-resolution outgoing emission and transmission radiation intensities. A Gaussian probability density function is used to simulate the turbulent fluctuation of temperature. The reconstruction of time-averaged temperature profile consists of three steps. First, the time-averaged spectral absorption coefficient is retrieved from the time-averaged transmissivity data by iteration method. Then the time-averaged blackbody spectral radiation intensity is estimated from the low time-resolution outgoing spectral emission radiation intensities. Finally, the time-averaged temperature and its standard deviation are approximately reconstructed from the multi-wavelength time-averaged spectral emission radiation data by the least-square method. Both exact and noisy input data have been used to test the performance of the proposed inversion method. The results show that the time-averaged temperature profiles can be estimated with good accuracy by the presented inversion method, even with noisy input data, and the standard deviation of temperature is more sensitive to the measurement errors. In the case of large temperature fluctuation, the errors of estimation for time-averaged temperature profile are large if the turbulent fluctuation is not taken into account.

Rigorous solution of linear programming problems with uncertain data

This note gives a synopsis of new methods for solving linear systems and linear programming problems with uncertain data. All input data can vary between given lower and upper bounds. The methods calculate very sharp and guaranteed error bounds for the solution set of those problems and permit a rigorous sensitivity analysis. For problems with exact input data in general the calculated bounds differ only in the last bit in the mantissa, i.e. they are of maximum accuracy.

Analysis of the surface-probe equation

An integrating surface-probe is a tool for the determination of local fluxes from surface-integrated measurements. For an axisymmetric system, the data analysis involves the numerical solution of a severely ill-conditioned Volterra integral equation of the first kind. This study establishes the existence of a unique solution under certain conditions and considers solution techniques based on product integration and also evaluation of the inversion integral. The methods are tested for convergence against exact input data, and the performance of the best methods against simulated experimental data is studied.