General Solution Methodology Research Articles

An equilibrium approach for compensating public–private partnership concessionaires for reduced tolls during roadway maintenance

This study considers the possibility of exploiting excess capacity along concurrent tolled roadway facilities operating in a public–private partnership for the purpose of alleviating traffic congestion during improvement action execution on a public roadway facility. Increased access to the tolled facility is enabled by reducing or suspending tolls during periods of roadway improvement action and appropriately compensating the tolled facility concessionaire for expected losses. The problem of determining an optimal reduced toll pricing strategy and compensation level is referred to as the Maintenance Timing and Price Discovery (MTPD) problem. A multi-level optimization model and iterative solution method are proposed to solve this problem. As toll prices often depend on traffic levels, the model also determines the optimal timing and time-of-day and day-of-week for executing the set of required improvement actions over the planning horizon to ensure a lowest total cost. The multi-level model consists of two bilevel models. Solution of the greater model is attained at a Stackelberg equilibrium between these two bilevel models. An additional Stackelberg equilibrium is sought between upper and lower levels of each of these two bilevel models individually. The MTPD formulation and general solution methodology are applied on an illustrative example from which computational results are obtained. Insights from the results show that this strategy for alleviating traffic congestion during roadway maintenance or other improvement activities can lead to substantial savings in total agency and user costs.

Applying Simulation Technique of Vapor-Compression Refrigeration

Calculation intensive courses lead to the need to integrate computer technology into the classroom, especially in courses such as The Refrigeration and air conditioning at then Dronacharya College of Engineering Gurugram (Haryana). Therefore the opportunity arises for the implementation of interactive tools for ease of calculations. Once the students have mastered the concepts and ability to perform the necessary manual calculations, computer programs can be used to allow the students to study more advanced topics in the material without being bogged down in the calculations. To ease the considerable calculations involved in solving vapor-compression refrigeration (VCR) cycle. This program has recently been revised to be compatible with the Microsoft Windows operating environment prevalent today in engineering software. In addition, a fourth refrigerant, R-134a, was added to account for the addition of new refrigerants in use today. Another modification made to the program was the addition of a tutorial for the thermal system analysis of a VCR cycle. This tutorial emulates the general solution methodology used in the course and reinforces the concepts with the students. The program is available via current web pages for the described course.

On the Design of Sparse but Efficient Structures in Operations

It is widely believed that a little flexibility added at the right place can reap significant benefits for operations. Unfortunately, despite the extensive literature on this topic, we are not aware of any general methodology that can be used to guide managers in designing sparse (i.e., slightly flexible) and yet efficient operations. We address this issue using a distributionally robust approach to model the performance of a stochastic system under different process structures. We use the dual prices obtained from a related conic program to guide managers in the design process. This leads to a general solution methodology for the construction of efficient sparse structures for several classes of operational problems. Our approach can be used to design simple yet efficient structures for workforce deployment and for any level of sparsity requirement, to respond to deviations and disruptions in the operational environment. Furthermore, in the case of the classical process flexibility problem, our methodology can recover the k-chain structures that are known to be extremely efficient for this type of problem when the system is balanced and symmetric. We can also obtain the analog of 2-chain for nonsymmetrical system using this methodology. This paper was accepted by Yinyu Ye, optimization.

On the Design of Sparse But Efficient Structures in Operations

It is widely believed that little flexibility added at the right place can reap significant benefits for operations. Unfortunately, despite the extensive literature on this topic, we are not aware of any general methodology that can be used to guide managers to design sparse (i.e., slightly flexible) and yet efficient operations.We address this issue using a distributionally robust approach to model the performance of a stochastic system under different process structures. We use the dual prices obtained from a related conic program to guide managers in the design process. This leads to a general solution methodology for the construction of efficient sparse structures for several classes of operational problems.Our approach can be used to design simple yet efficient structures for workforce deployment and for any level of sparsity requirement, to respond to deviations and disruptions in the operational environment. Furthermore, in the case of the classical process flexibility problem, our methodology can recover the k-chain structures that are known to be extremely efficient for this type of problem when the system is balanced and symmetric. We can also obtain the analog of 2-chain for non-symmetrical system using this methodology.

A finite element model for the frequency spectrum estimation of a resonating microplate in a microfluidic chamber

Resonating microplates appear as ideal candidates for microcantilever-based real-time biosensing, because their low planar aspect ratio allows for effectively large Q factors, even in highly viscous fluids like water and other biological liquids. Since, a complete analytical treatment of a plate vibrating in liquid is missing; a fully numerical approach is needed for an effective design of a microcantilever-based Lab-On-Chip, as well as for its correct operation. We here report on a three-dimensional finite element model for an accurate and general solution methodology of the Fluid–Structure interaction for a plate vibrating in a transverse flexural mode within a viscous fluid environment. The model directly allows extracting vibration mode shapes, frequencies and Q factors through an eigenfrequency analysis, thus avoiding time-consuming and time-dependent simulations. A benchmark with the available analytical results (that rely on the classical beam theory) and a comparison with experimental data on a fabricated microcantilever-based Lab-On-Chip confirm the accuracy and the reliability of our numerical calculations. The here proposed model works in a very general context, without limitations about the cantilever planar geometry and material, as well as about the shape of the fluid domain.

On the Derivation of a Closed-Form Expression for the Solutions of a Subclass of Generalized Abel Differential Equations

We investigate the properties of a general class of differential equations described bydy(t)/dt=fk+1(t)y(t)k+1+fk(t)y(t)k+⋯+f2(t)y(t)2+f1(t)y(t)+f0(t),withk>1a positive integer andfi(t), 0≤i≤k+1, withfi(t), real functions oft. Fork=2, these equations reduce to the class ofAbel differential equations of the first kind,for which a standard solution procedure is available. However, fork>2no general solution methodology exists, to the best of our knowledge, that can lead to their solution. We develop a general solution methodology that for odd values ofkconnects the closed form solution of the differential equations with the existence of closed-form expressions for the roots of the polynomial that appears on the right-hand side of the differential equation. Moreover, the closed-form expression (when it exists) for the polynomial roots enables the expression of the solution of the differential equation in closed form, based on the class of Hyper-Lambert functions. However, for certain even values ofk, we prove that such closed form does not exist in general, and consequently there is no closed-form expression for the solution of the differential equation through this methodology.

Optimal Modeling and Filtering of Stochastic Time Series for Geoscience Applications

Sequences of observations or measurements are often modeled as realizations of stochastic processes with some stationary properties in the first and second moments. However in practice, the noise biases and variances are likely to be different for different epochs in time or regions in space, and hence such stationarity assumptions are often questionable. In the case of strict stationarity with equally spaced data, the Wiener-Hopf equations can readily be solved with fast Fourier transforms (FFTs) with optimal computational efficiency. In more general contexts, covariance matrices can also be diagonalized using the Karhunen-Loève transforms (KLTs), or more generally using empirical orthogonal and biorthogonal expansions, which are unfortunately much more demanding in terms of computational efforts. In cases with increment stationarity, the mathematical modeling can be modified and generalized covariances can be used with some computational advantages. The general nonlinear solution methodology is also briefly overviewed with the practical limitations. These different formulations are discussed with special emphasis on the spectral properties of covariance matrices and illustrated with some numerical examples. General recommendations are included for practical geoscience applications.

A symbolic-interval inference approach for constraint satisfaction: implementation on kinematics applications

In this study, a general solution methodology is presented for continuous constraint satisfaction problems. The performance of the method is demonstrated on challenging kinematics problems where the goal is to identify all real solutions. The developed approach assumes a collaborative methodology that integrates interval partitioning (IP), symbolic-interval inference (SII, a novel subdivision direction selection method) and local search. The resulting methodology aims at reducing the search space and discarding infeasible subspaces effectively and reliably during the early stages of the search so that exact solutions can be identified faster by local methods. SII conducts parallel multi-variable bisection with the aim of achieving immediate reduction in total box infeasibility of the majority of sibling boxes generated in every partitioning iteration. Empirical results are obtained on seven kinematics applications and compared with results obtained by other symbolic-interval methods.

Investigating optimal aggregation interval sizes of loop detector data for freeway travel-time estimation and prediction

With recent increases in the deployment of intelligent transportation system (ITS) technologies, traffic management centers have the ability to obtain and archive large amounts of data regarding the traffic system. These data can then be employed in estimations of current conditions and the prediction of future conditions on the roadway network. In this paper, we propose a general solution methodology for the identification of the optimal aggregation interval sizes of loop detector data for four scenarios (i) link travel-time estimation, (ii) corridor / route travel-time estimation, (iii) link travel-time forecasting, and (iv) corridor / route travel-time forecasting. This study applied cross validated mean square error (CVMSE) model for the link and route travel-time estimations, and a forecasting mean square error (FMSE) model for the link and corridor / route travel-time forecasting. These models were applied to loop detector data obtained from the Kyeongbu expressway in Korea. It was found that the optimal aggregation sizes for the travel-time estimation and forecasting were 3 to 5 min and 10 to 20 min, respectively.

Identifying optimal data aggregation interval sizes for link and corridor travel time estimation and forecasting

With the recent increase in the deployment of ITS technologies in urban areas throughout the world, traffic management centers have the ability to obtain and archive large amounts of data on the traffic system. These data can be used to estimate current conditions and predict future conditions on the roadway network. A general solution methodology for identifying the optimal aggregation interval sizes for four scenarios is proposed in this article: (1) link travel time estimation, (2) corridor/route travel time estimation, (3) link travel time forecasting, and (4) corridor/route travel time forecasting. The methodology explicitly considers traffic dynamics and frequency of observations. A formulation based on mean square error (MSE) is developed for each of the scenarios and interpreted from a traffic flow perspective. The methodology for estimating the optimal aggregation size is based on (1) the tradeoff between the estimated mean square error of prediction and the variance of the predictor, (2) the differences between estimation and forecasting, and (3) the direct consideration of the correlation between link travel time for corridor/route estimation and forecasting. The proposed methods are demonstrated using travel time data from Houston, Texas, that were collected as part of the automatic vehicle identification (AVI) system of the Houston Transtar system. It was found that the optimal aggregation size is a function of the application and traffic condition.

The long-term mine production scheduling problem

Recognizing the complexity of coal mining management, e.g., the scarcity of financial resources and a variation in the quality of coal found in different sections of a mine, in this paper, we develop a mixed-binary programming model as an aid for generating mine production schedules in order to obtain coal of the desired quality and maximize the associated net present value. The model is based on the definition of the mine layout as a precedence network, with the nodes representing mining sections. A general solution methodology based on the Benders' decomposition of the model is developed. It exploits the special nature of the resulting subproblems in order to develop an effective solution procedure. Computational experience of this procedure, along with the results of its application to a mining case, are presented.

Natural convection in three-dimensional porous cavities: integral transform method

A transient three-dimensional Darcy model of natural convection in porous medium filled cavities is studied, using a vorticity-vector potential formulation and the generalized integral transform technique (GITT). A general formulation and solution methodology for vertical cavities (insulated vertical walls with differential horizontal wall temperatures) is developed. Results for cubic cavities are presented while evaluating the Rayleigh number effects for stable situations, observing the transient evolution of the heat transfer process. The convergence behavior of the proposed eigenfunction expansion solution is investigated and comparisons with previously reported steady-state solutions are critically performed.

INTEGRAL TRANSFORMS FOR HEAT AND FLUID FLOW IN TWO- AND THREE-DIMENSIONAL POROUS MEDIA

Hybrid numerical-analytical algorithms, based on the generalized integral transform technique, are developed and reviewed to handle transient two- and three-dimensional heat and fluid flow in cavities filled with a porous material. A general formulation and solution methodology for horizontal and vertical cavities is developed. To illustrate the algorithm computational behavior, specific situations are more closely considered, under the Darcy model for natural convection in porous medium filled cavities. The problem is analyzed with and without the time derivative term in the flow equations, using a vorticity-vector potential formulation, which automatically reduces to the streamfunction-only formulation for two-dimensional situations. Results for rectangular (2D) and parallelepiped (3D) vertical cavities are presented to demonstrate the convergence behavior of the proposed eigenfunction expansion solutions and comparisons with previously reported numerical solutions are critically performed.

Multi-depot vehicle scheduling problems with time windows and waiting costs

The multi-depot vehicle scheduling problem with time windows (MDVSPTW) consists of scheduling a fleet of vehicles to cover a set of tasks at minimum cost. Each task is restricted to begin within a prescribed time interval and vehicles are supplied by different depots. The problem is formulated as an integer nonlinear multi-commodity network flow model with time variables and is solved using a column generation approach embedded in a branch-and-bound framework. This paper breaks new ground by considering costs on exact waiting times between two consecutive tasks instead of minimal waiting times. This new and more realistic cost structure gives rise to a nonlinear objective function in the model. Optimal and heuristic versions of the algorithm have been extensively tested on randomly generated urban bus scheduling problem (UBSP) and freight transport scheduling problem (FTSP). The results show that such a general solution methodology outperforms specialized algorithms when minimal waiting costs are used, and can efficiently treat the case with exact waiting costs.

A Model for Planning Resource Requirements in Health Care Organizations

ABSTRACTIn this paper we present a general model and solution methodology for planning resource requirements (i.e., capacity) in health care organizations. To illustrate the general model, we consider two specific applications: a blood bank and a health maintenance organization (HMO). The blood bank capacity planning problem involves determining the number of donor beds required and determining the size of the nursing and support staff necessary. Capacity must be sufficient to handle the expected number of blood donors without causing excessive donor waiting times. Similar staff, equipment, and service level decisions arise in the HMO capacity planning problem. To determine resource requirements, we develop an optimization/queueing network model that minimizes capacity costs while controlling customer service by enforcing a set of performance constraints, such as setting an upper limit on the expected time a patient spends in the system. The queueing network model allows us to capture the stochastic behavior of health care systems and to measure customer service levels within the optimization framework.

The efficiency of endoreversible heat engines with heat leak

Finite-time thermodynamics are used for studying the performance of endoreversible heat engines with heat leak. A comprehensive formulation and a general solution methodology, valid for any mode of heat supply or release, are presented. Detailed analyses are conducted for several heat transfer modes and universal analytical and numerical results for the efficiency at maximum power are generated. Many established laws and major conclusions derived in several references are shown to represent very special cases of the new formulations. Furthermore, the nature of the leakage power law is found to deeply affect the efficiency at maximum power. Finally, for no leakage situations, if the heat to the engine is supplied and released via similar heat transfer modes, then the lowest efficiency at maximum power, when the only thermal resistance is between the working fluid and the hot reservoir, is found to be giben by 1/n, n being the power of the heat transfer law.

Generalized non-Newtonian elastohydrodynamic lubrication

Realistic prediction of the behaviour of a lubricant in elastohydrodynamic contact requires consideration of proper rheological model(s) that take the non-Newtonian characteristics of the fluid into account. A general formulation and solution methodology is presented that can treat an elastohydrodynamic lubrication problem with any simple, non-Newtonian constitutive equation.

Graphical and natural language interface with a knowledge-based concurrent engineering environment

Effective on-line communication between cooperating users with the mediation of machines (“virtual team” concept) is a necessity in new-generation concurrent engineering design and manufacture systems. The communication means for solving this problem are natural language and graphics. Managing the graphical and natural language user interfaces is a task full of ill-structured problems for which the knowledge-based approach offers a general solution methodology. Our knowledge-based expert system shell, implemented in Smalltalk, provides support mechanisms for flexible construction of such user interfaces. The natural language knowledge definition and editing is based on the novel percept-calculus knowledge representation scheme used in the system. The graphical module of the interface is capable of presenting diverse kinds of qualitative and quantitative data in various graphical forms which can be made interactive, serving as data input, data navigation, or design variation tools. An appropriate graphical knowledge base contains knowledge about general methods of graphical data presentation.

An ( s, Q) policy with setup reduction in a single-stage batch manufacturing system

In this paper, we analyze an ( s, Q) policy for a single-stage batch manufacturing system where the input items are gradually converted to the end product at a finite rate during the manufacturing period. The effects of setup reduction are considered. We assume that the demand for the end product is a general deterministic function of time horizon and that the input items are procured externally. The problem of minimizing the combined inventory costs of the end product and the input items is formulated as a mathematical programming problem, and a general solution methodology is developed. Using the power-form demand rate function, we present a numerical example.

Deterministic inventory models incorporating marketing decisions

This paper investigates a finite replenishment inventory model in which the demand of an item is a deterministic function of price and advertising expenditures. The formulated models also incorporate learning effects and the possibility of defective items in the production process. A general solution methodology is developed to determine the optimal lot size, price mark-up, and advertising expenditure simultaneously. This method utilizes separable programming resulting in an effective computer technique to find the global optimal solution. Closed-form solutions are found for special cases.