Developed Solution Procedure Research Articles

SOLVING PROBLEMS OF UNSTEADY – CONFINED FLOW TO PUMPED WELLS BY COMPUTER

SOLVING PROBLEMS OF UNSTEADY – CONFINED FLOW TO PUMPED WELLS BY COMPUTER

Computational Fluid Dynamics-Based Aeroservoelastic Analysis with Hyper-X Applications

A finite element computational fluids dynamics-based aeroservoelastic analysis methodology is presented in this paper, in which both structural and fluids discretization are achieved by the finite element method, and their interaction is modeled by the transpiration boundary condition technique. In the fluids discipline either inviscid or viscous flow may be accounted for, usually employing unstructured grids.Adescription of a novel viscous flow solver employing unstructured grids is given in detail. Provisions are made for digital as well as analog controllers. These new aeroservoelastic analysis techniques are next applied for the solution of a number of example problems including the novel Hyper-X launch vehicle. Experimental and actual flight test data are also compared with analysis results that signify to the efficacy and accuracy of the newly developed solution procedures.

Calculation of conjugate heat transfer problem with volumetric heat generation using the Galerkin method

A mathematical model of fluid flow across a rod bundle with volumetric heat generation has been built. The rods are heated with volumetric internal heat generation. To construct the model, a volume average technique (VAT) has been applied to momentum and energy transport equations for a fluid and a solid phase to develop a specific form of porous media flow equations. The model equations have been solved with a semi-analytical Galerkin method. The detailed velocity and temperature fields in the fluid flow and the solid structure have been obtained. Using the solution fields, a whole-section drag coefficient C d and a whole-section Nusselt number Nu have also been calculated. To validate the developed solution procedure, the results have been compared to the results of a finite volume method. The comparison shows an excellent agreement. The present results demonstrate that the selected Galerkin approach is capable of performing calculations of heat transfer in a cross-flow where thermal conductivity and internal heat generation in a solid structure has to be taken into account. Although the Galerkin method has limited applicability in complex geometries, its highly accurate solutions are an important benchmark on which other numerical results can be tested.

A mini-line approach for pull production

In high volume manufacturing, the just-in-time (JIT) system using pull production is often successfully applied to achieve good performance in cost, time, and quality. However, its recent application to printed circuit board manufacturing is hampered by three conditions: Product variety proliferation, short product life cycle, and significant machine setup time. The mini-line approach (MLA) proposed in this paper is designed to implement pull production in such manufacturing environments without losing its benefits. MLA is hierarchical in addressing the production planning and control problem, consisting of multiple layers of optimization problems. These problems involve questions such as how many mini-lines should be formed, which product families should be grouped into mini-lines, how many machines should be allocated to each mini-line at each production stage, how much and when each product family should be produced, and how loading and flow of materials should be controlled. We first present the hierarchical framework of MLA, and introduce the static mini-line problem (SMP) that is valid under the condition that the product volume mix does not change. Then, from the SMP, we derive a set of optimization problems that constitute MLA: Similarity index problem, product grouping problem (PGP), and modified line segmentation problem (LSP). Next, we develop solution procedures for these three problems. The overall approach is evaluated by computational experiments where the characteristics of data sets were obtained from a large-scale manufacturer. We demonstrate that MLA performs well under both stable and gradually shifting product volume mix.

Use of student-constructed number stories in a reform-based curriculum

Twelve classes using the reform-based curriculum, Everyday Mathematics (EM), were observed early in first grade. The two lessons observed involved students generating and solving addition and subtraction number stories. In these lessons, teachers were directed to help students link these number stories to representations (pictures or objects) and equations. Because this curriculum emphasizes invented procedures and number sense, the lessons also call for whole-class discussions of students' solutions. Further, the curriculum assumes that teachers will build upon and extend the children's mathematical thinking, highlighting these alternative solution methods and supporting the students' explanations. Results show that students were successful at making up, telling, and solving number stories and used a range of solution methods, including the mathematical representations available in the classrooms. However, only about three-quarters of the teachers established explicit links between the stories and mathematical representations, with fewer than half representing the stories as numbers and equations. Although student-based explanations play an important role in helping children develop solution procedures with understanding, solution methods were only elicited in half of the classes observed, and multiple methods in one-fourth of the classes. Implications for reform curricula, especially how they might clarify new goals for teachers, are discussed.

Inventory control under speculation: Myopic heuristics and exact procedures

We consider a periodic review inventory problem in which the purchasing cost exhibits a noticeable increase (deterministic or stochastic) in the second period and remains at the higher value for the remainder of the problem. (This simplification clarifies the nature of the myopic heuristic, but is not necessary for use of the heuristic in practice.) This results in a strategy that holds inventories due to speculation. We develop solution procedures to find the optimal inventory levels for both stationary and non-stationary demands. We establish that the problem with stochastic speculation behaves exactly like a problem with deterministic speculation with the same mean increase in price. We propose, based on the case of deterministic demands, simple myopic heuristics and study their effectiveness. We observe that these heuristics perform very well for exponential demands. However, for the case of uniform demands these heuristics are most effective when the increase in price is large compared to the holding cost.

Managing a Customer Following a Target Reverting Policy

We consider a stochastic, capacitated production-inventory model in which the customer provides information about the expected timing of future orders to the supplier. We allow for randomness in customer order arrivals as well as the quantity demanded, but work under the assumption that the customer is making every effort to follow the schedule provided. We term this as a target reverting policy. This gives rise to an interesting nonstationary inventory control model at the supplier. After characterizing the optimal policy, we develop solution procedures to compute the optimal parameters. An extensive computational study provides insights into the behavior of this model at optimality. Further, comparing the cost of the optimal policy to the cost of simple policies that either ignore the customer's information or the capacity constraint, we are able to provide insights as to when these simplifications could be costly.

Periodic Response of Blades Having Three-Dimensional Nonlinear Shroud Constraints

In this paper, a three-dimensional shroud contact model is employed to predict the periodic response of blades having three-dimensional nonlinear shroud constraint. When subjected to periodic excitation, the resulting relative motion at the shroud contact is assumed to be periodic in three-dimensional space. Based on the three-dimensional shroud contact model, analytical criteria are used to determine the transitions between stick, slip, and separation of the contact interface and are used to simulate hysteresis loops of the induced constrained force, when experiencing periodic relative motion. The constrained force can be considered as a feedback force that influences the response of the shrouded blade. By using the multiharmonic balance method along with Fast Fourier Transform, the constrained force can be approximated by a series of harmonic functions so as to predict the periodic response of a shrouded blade. This approach results in a set of nonlinear algebraic equations, which can be solved iteratively to yield the periodic response of blades having three-dimensional nonlinear shroud constraint. In order to validate the proposed approach, the predicted results are compared with those of the direct-time integration method. The resonant frequency shift, the damping effect, and the jump phenomenon due to nonlinear shroud constraint are examined. The implications of the developed solution procedure to the design of shroud contact are also discussed.

SOLUTION PROCEDURES WITH LIMITED SAMPLE DATA FOR THE OPTIMAL REPLACEMENT PROBLEM

Recently we have developed solution procedures for the optimal replacement problem when the distribution of the time‐to‐failure (ttf) is partially specified by the first two moments, partial and complete. However, we have later learned, using Monte‐Carlo simulation, that when moments are unknown and have to be estimated from sample data, the most accurate procedure developed therein is in practice extremely sensitive to sampling fluctuations.In this paper we modify the procedure to render it less susceptible to sampling variation. In addition, we introduce a new solution procedure that requires specification of only the median and the partial means of the ttf distribution. For both procedures, it is demonstrated that when the moments required for the distribution fitting are known, highly accurate optimal solutions are obtained. Conversely, when the moments are unknown and sample estimates based on small samples are used, both procedures result in stable solutions (low mean‐squared‐errors).

A new technique for optimal time-dynamic distribution substation and feeder planning

This paper presents a new model for optimally sizing and locating distribution substations and feeders in a time-dynamic power distribution system. Recognizing that both linear and nonlinear loads are present within the system, the model's objective is to minimize the combined costs of the construction of substations and feeders with that of losses occurring at fundamental and harmonic frequencies. System specifications include power demand, power capacity, and logical restrictions. Two main contributions of this paper are: (1) the model captures the nonlinear costs due to power flow, as opposed to simplifying linear assumptions found in the literature; and (2) the effects of harmonics are considered. The model is a mixed 0-1 quadratic program, whose mathematical structure permits the application of generalized Benders' decomposition as a solution methodology. The effectiveness of the developed model and solution procedure is illustrated by application of a test example from the literature. The effects of nonlinear power losses and harmonic distortion are shown to influence the planning strategy.

Impact of product mix flexibility and allocation policies on technology

In this article we present two contrasting models-(i) a static allocation model (SAM) that does not capture benefits of operational flexibility and (ii) a dynamic allocation model (DAM) that recognizes explicitly the impact of operational policies. Since the resulting optimization models are intractable, we develop solution procedures suitable for practical problems. In addition, we report results of a simulation study to examine the impact of alternative allocation policies and to verify the solutions provided by the procedures developed in this article. Our results suggest that explicit inclusion of the effect of operating policies in making technology and capacity choices can make a significant difference. The results also indicate that service levels are not overly sensitive to the alternate operating policies. Together these results imply that capacity strategies generated by our dynamic allocation model are robust with respect to the alternate operating policies considered in our experiments.

OPTIMUM SCHEDULE FOR PREVENTIVE MAINTENANCE: A GENERAL SOLUTION FOR A PARTIALLY SPECIFIED TIME‐TO‐FAILURE DISTRIBUTION

The classic problem of determining an optimum schedule for preventive maintenance when the time‐to‐failure (TTF) is random has been previously addressed in the literature under various distributional assumptions. However, no general solution that requires only partial distributional information (in the form of the first few moments) has been suggested. In this paper we develop solution procedures characterized by four features: (1) The solutions are general in the sense that only the first few moments of the TTF distribution need to be specified. (2) The optimal solution is given explicitly in terms of the decision variables, thus allowing simple sensitivity analysis. (3) When the TTF moments are unknown, a new two‐moment (partial and complete) distributional fitting procedure, used in the solution routine, ensures a better representation for the underlying TTF distribution relative to three‐moment or four‐moment distributional fitting. (4) When the TTF observations are truncated, simple routines to calculate maximum likelihood estimates are developed. We demonstrate that the partiál distributional specification, required for the new solution procedures, does not detract meaningfully from the optimality of the solution.

Heuristic solution approaches to operational forest planning problems

Operational forest planning problems are typically very difficult problems to solve due to problem size and constraint structure. This paper presents three heuristic solution approaches to operational forest planning problems. We develop solution procedures based on Interchange, Simulated Annealing and Tabu search. These approaches represent new and unique solution strategies to this problem. Results are provided for applications to two actual forest planning problems and indicate that these approaches provide near optimal solutions in relatively short amounts of computer time.

New results for aggregating integer-valued equations

A variety of results have been given for aggregating integer-valued (diophantine) equations whose variables are restricted to nonnegative integers. In each, integer weights are identified for the equations so that their linear combination yields a single equation with the same solution set of the original system of equations. Because the coefficients of the aggregated equation tend to achieve unwieldy sizes as the number of original equations increases, the goal is to identify weights so these coefficients will lie in a range as limited as possible. We give theorems which separately and in combination provide new methods for aggregating general integer-valued equations. Our results include formulations that do not require linearity of the original system, or nonnegativity of component variables. We also demonstrate that our theorems yield as special cases earlier results (analytical formulae) conjectured to yield the smallest possible weights for less general domains. As another application, the presented results were used to develop a highly efficient approach for the integer knapsack problem. Empirical outcomes show that the developed solution procedure is significantly superior to advanced branch and bound methods (previously established to be the most efficient knapsack solution procedures).

An Integrated Systems Approach for Design of Aerospace Structures

This paper is primarily concerned with the analysis and design of structural systems relating to aeronautical and aerospace engineering. Some numerical formulations are presented that deal with the synthesis of these systems integrating such disciplines as structures, unsteady aero-dynamics and control engineering. A general-purpose finite element computer program developed for associated large-scale computations is also described in some detail. Finally, results of relevant numerical analyses pertaining to some representative aircraft and spacecraft, obtained by utilizing the program, are presented that testify to the efficacy of the currently developed solution procedures.

Approximate steady-state distribution for a large repairable item inventory system

This paper examines a model for a repairable inventory system where some items are condemned upon failure. These condemnations require an ordering policy which we take to be an ( s, S) policy. We model this system as a version of the classical machine repair problem using continuous time Markov processes. We develop solution procedures based on approximations to the steady state probability distribution, which enable us to obtain the operating characteristics of ( s, S) policies very easily, with or without an ordering leadtime. The approximate models are found to be very accurate and computationally very efficient.

Determining the optimal scheme of zoned effluent charges for the control of air pollution

A minimum costly zoned effluent charge program for the control of air pollution is considered paying attention to the general situation where polluters' cost functions of treating pollutant are unknown to the policy authority, and an iterative procedure by which the authority can attain a set of optimal charges is presented. The algorithm consists of steps of estimating the unknown treatment cost functions by observing polluter behavior and steps of revising charges based on the estimated cost functions. In the latter steps, a newly developed solution procedure for the zoned charge programming problem is involved. Simulated use of the algorithm indicates that the iterative charge revision procedure proposed in this paper can effectively provide the optimal scheme of zoned effluent charges.