Search results

Presents a new approach to working set generation for personnel scheduling problems. In full‐time (FT) and mixed‐workforce (MW) experiments, generates the schedules in the working sets from the use of two‐phase heuristic labour scheduling solution procedures. The solution procedures were implemented on a 386 microcomputer and did not require the specification of the size of the working sets in advance. In the FT experiment, the general set‐covering formulations (GSCFs) associated with the produced working sets were solved with integer programming. The new working set procedure yielded optimal integer solutions for all 36 test problems in the FT experiment. Owing to the size and complexity of the problem data in the MW experiment, the GSCFs associated with the working sets were solved with linear programming, and heuristic rounding procedures were applied to obtain feasible integer solutions. The mean labour costs of these solutions averaged 0.69 per cent less than the mean cost of solutions obtained via the application of heuristic rounding procedures applied to the linear programme solutions for the GSCFs associated with the master sets. Compares solution costs for the new working set method with those associated with other working set generation/refinement procedures. Results indicate that the new method produces lower solution costs in less control processing unit time.

The purpose of this paper is to present outcomes of efforts made over the last 20 years to extend the applicability of the Richardson extrapolation procedure to numerical predictions of multidimensional, steady and unsteady, fluid flow and heat transfer phenomena in regular and irregular calculation domains.

Pattern-preserving grid-refinement strategies are proposed for mathematically rigorous generalizations of the Richardson extrapolation procedure for numerical predictions of steady fluid flow and heat transfer, using finite volume methods and structured multidimensional Cartesian grids; and control-volume finite element methods and unstructured two-dimensional planar grids, consisting of three-node triangular elements. Mathematically sound extrapolation procedures are also proposed for numerical solutions of unsteady and boundary-layer-type problems. The applicability of such procedures to numerical solutions of problems with curved boundaries and internal interfaces, and also those based on unstructured grids of general quadrilateral, tetrahedral, or hexahedral elements, is discussed.

Applications to three demonstration problems, with discretizations in the asymptotic regime, showed the following: the apparent orders of accuracy were the same as those of the numerical methods used; and the extrapolated results, measures of error, and a grid convergence index, could be obtained in a smooth and non-oscillatory manner.

Strict or approximate pattern-preserving grid-refinement strategies are used to propose generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions. Such extrapolation procedures play an indispensable role in the verification and validation techniques that are employed to assess the accuracy of numerical predictions which are used for designing, optimizing, virtual prototyping, and certification of thermofluid systems.

In the inelastic stability analysis of plated structures, incremental‐iterative finite element methods sometimes encounter prohibitive solution difficulties in the vicinity of sharp limit points, branch points and other regions of abrupt non‐linearity. Presents an analysis system that attempts to trace the non‐linear response associated with these types of problems at minor computational cost. Proposes a semi‐heuristic method for automatic load incrementation, termed the adaptive arc‐length procedure. This procedure is capable of detecting abrupt non‐linearities and reducing the increment size prior to encountering iterative convergence difficulties. The adaptive arc‐length method is also capable of increasing the increment size rapidly in regions of near linear response. This strategy, combined with consistent linearization to obtain the updated tangent stiffness matrix in all iterative steps, and with the use of a “minimum residual displacement” constraint on the iterations, is found to be effective in avoiding solution difficulties in many types of severe non‐linear problems. However, additional procedures are necessary to negotiate branch points within the solution path, as well as to ameliorate convergence difficulties in certain situations. Presents a special algorithm, termed the bifurcation processor, which is effective for solving many of these types of problems. Discusses several example solutions to illustrate the performance of the resulting analysis system.

Integrated decision of pricing and inventory control for a deteriorating product is known as a good practice in revenue management discipline. The purpose of this paper is to formulate the problem of joint pricing and inventory decision in a manufacturer–retailer supply chain with deteriorating items and backlogging. Furthermore, the other purpose is to develop an efficient algorithm to obtain the equilibrium solution.

In this study, a manufacturer–retailer supply chain of a deteriorating product is considered. The retailer aims to maximize his profit, for which he jointly determines the retail price and replenishment cycle. In addition, the manufacturer should decide on the wholesale price to maximize her profit. Considering the problem as a manufacturer-Stackelberg game, the equilibrium solution is formulated and analyzed for both the manufacturer and the retailer. Moreover, two different procedures are developed to obtain the equilibrium solution. The first procedure is an exact procedure for the Taylor-approximated model and the second is a simulated annealing (SA)-embedded algorithm for the actual model.

It is found that Taylor-approximated procedure is more accurate than SA-embedded procedure. However, the latter is more time-efficient. Moreover, it is observed that the obtained solution is highly sensitive to demand parameters, while it is not the case for the cost parameters.

The paper models a real industrial problem, and its results could be used in analyzing any manufacturer–retailer supply chain with deteriorating items. Among others, the fruit and vegetable supply chains are more likely to have a similar setting, and this study’s results are applicable for such chains in food industry.

Considers a multi‐stage multi‐product production, inventory and transportation system including lot production processes and develops a mathematical model for a pull type ordering system. The decision variables of the presented model are initial ordering quantities and the objective is to minimize the sum of the replenishment level at each inventory point. The model is formulated as an integer programming problem, and an approximate procedure is proposed to obtain a near optimal solution in short time using a mathematical programming package. Finally, shows a numerical example of the model applied to an actual manufacturing system of an automobile parts manufacturer in order to verify the effectiveness of the solution procedure and to clarify the applicability of the modelling approach.

Presents an efficiency study of different refinement procedures for the p‐version of the adaptive finite element method in two‐dimensional elasticity problems. The refinement strategy, based on the estimated error in energy norm, attempts an optimal distribution of the nodeless degrees of freedom associated with the basic approximation parameter of the order p of the hierarchical shape functions. This procedure is combined with appropriate matrix‐handling techniques and equation solvers in order to achieve a solution of a given accuracy with the minimum computational resources in terms of computing time and storage. To this extent, convergence studies are performed with constant and variable adaptivity indices, with error estimators based on global and elemental approaches and with domain decomposition matrix‐handling techniques and the preconditioned conjugate gradient solver.

The evaluation of linear dynamic response analysis of large structures by vector superposition requires, in its traditional formulation, the solution of a large and expensive eigenvalue problem. A method of solution based on a Ritz transformation to a reduced system of generalized coordinates using load dependent vectors generated from the spatial distribution of the dynamic loads is shown to maintain the high expected accuracy of modern computer analysis and significantly reduces the execution time over eigensolution procedures. New computational variants to generate load dependent vectors are presented and error norms are developed to control the convergence characteristics of load dependent Ritz solutions. Numerical applications on simple structural systems are used to show the relative efficiency of the proposed solution procedures.

The purpose of this paper is to numerically solve Eikonal and Hamilton‐Jacobi equations using the finite element method; to use both explicit Taylor Galerkin (TG) and implicit methods to obtain shortest wall distances; to demonstrate the implemented methods on some realistic problems; and to use iterative generalized minimal residual method (GMRES) method in the solution of the equations.

The finite element method along with both the explicit and implicit time discretisations is employed. Two different forms of governing equations are also employed in the solution. The Eikonal equation in its original form is used in the explicit Taylor Galerkin discretisation to save computational time. For implicit method, however, the convection‐diffusion form in its conservation form is used to maintain spatial stability.

The finite element solution obtained is both accurate and smooth. As expected the implicit method is much faster than the explicit method. Though the proposed finite element solution procedures in serial is slower than the standard search procedure, they are suitable to be used in a parallel environment.

The finite element procedure for Eikonal and Hamilton‐Jacobi equations are attempted for the first time. Though the finite volume and finite difference‐based computational fluid dynamics (CFD) solvers have started employing differential equations for wall distance calculations, it is not common for finite element solvers to use such wall distance calculations. The results presented here clearly show that the proposed methods are suitable for unstructured meshes and finite element solvers.

Argues that the dynamic‐explicit approach has in recent years been successfully applied to the solution of various quasi‐static, elastic‐plastic problems, especially in the metal forming area. A condition for the success has, however, been that the problems have been displacement‐driven. The solution of similar force‐driven problems, using this approach, has been shown to be much more complicated and computationally time consuming because of the difficulties in controlling the unphysical dynamic forces. Describes a project aiming to develop a methodology by which a force‐driven problem can be analysed with similar computational effort as a corresponding displacement‐driven one. To this end an adaptive loading procedure has been developed, in which the loading rate is controlled by a prescribed velocity norm. Presents several examples in order to exhibit the merits of the proposed procedure.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.