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Time Problem (time + problem)
Selected AbstractsVolume determination for bulk materials in bunkersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2004S. A. Ahmed Abstract A simple model for the determination of the shape of large granular piles in complicated geometries is discussed. An eikonal formulation of the problem is proposed. Two distinct cases arise. In cylindrical geometries, i.e., if both container and possible obstacles have vertical walls, the problem is equivalent to a two-dimensional travel time problem with obstacles, while in general geometries, this analogy breaks down. In the first case, classical one-sided discretizations are generalized to handle obstacles without loss in accuracy. In the second case, a fast and efficient numerical method is proposed, implemented and tested. The discrete problems are solved through fast marching. Copyright © 2004 John Wiley & Sons, Ltd. [source] The effectiveness of the longest delivery time rule for the flow shop delivery time problemNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2003Philip Kaminsky Abstract In the flow shop delivery time problem, a set of jobs has to be processed on m machines. Every machine has to process each one of the jobs, and every job has the same routing through the machines. The objective is to determine a sequence of the jobs on the machines so as to minimize maximum delivery completion time over all the jobs, where the delivery completion time of a job is the sum of its completion time, and the delivery time associated with that job. In this paper, we prove the asymptotic optimality of the Longest Delivery Time algorithm for the static version of this problem, and the Longest Delivery Time among Available Jobs (LDTA) algorithm for the dynamic version of this problem. In addition, we present the result of computational testing of the effectiveness of these algorithms. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003 [source] Optimal auditing in the banking industryOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 2 2008T. Bosch Abstract As a result of the new regulatory prescripts for banks, known as the Basel II Capital Accord, there has been a heightened interest in the auditing process. Our paper considers this issue with a particular emphasis on the auditing of reserves, assets and capital in both a random and non-random framework. The analysis relies on the stochastic dynamic modeling of banking items such as loans, reserves, Treasuries, outstanding debts, bank capital and government subsidies. In this regard, one of the main novelties of our contribution is the establishment of optimal bank reserves and a rate of depository consumption that is of importance during an (random) audit of the reserve requirements. Here the specific choice of a power utility function is made in order to obtain an analytic solution in a Lévy process setting. Furthermore, we provide explicit formulas for the shareholder default and regulator closure rules, for the case of a Poisson-distributed random audit. A property of these rules is that they define the standard for minimum capital adequacy in an implicit way. In addition, we solve an optimal auditing time problem for the Basel II capital adequacy requirement by making use of Lévy process-based models. This result provides information about the optimal timing of an internal audit when the ambient value of the capital adequacy ratio is taken into account and the bank is able to choose the time at which the audit takes place. Finally, we discuss some of the economic issues arising from the analysis of the stochastic dynamic models of banking items and the optimization procedure related to the auditing process. Copyright © 2007 John Wiley & Sons, Ltd. [source] Computational optimal control of the terminal bunt manoeuvre,Part 2: minimum-time caseOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2007S. Subchan Abstract This is the second part of a paper studies trajectory shaping of a generic cruise missile attacking a fixed target from above. The problem is reinterpreted using optimal control theory resulting in a minimum flight time problem; in the first part the performance index was time-integrated altitude. The formulation entails non-linear, two-dimensional (vertical plane) missile flight dynamics, boundary conditions and path constraints, including pure state constraints. The focus here is on informed use of the tools of computational optimal control, rather than their development. The formulation is solved using a three-stage approach. In stage 1, the problem is discretized, effectively transforming it into a non-linear programming problem, and hence suitable for approximate solution with DIRCOL and NUDOCCCS. The results are used to discern the structure of the optimal solution, i.e. type of constraints active, time of their activation, switching and jump points. This qualitative analysis, employing the results of stage 1 and optimal control theory, constitutes stage 2. Finally, in stage 3, the insights of stage 2 are made precise by rigorous mathematical formulation of the relevant two-point boundary value problems (TPBVPs), using the appropriate theorems of optimal control theory. The TPBVPs obtained from this indirect approach are then solved using BNDSCO and the results compared with the appropriate solutions of stage 1. The influence of boundary conditions on the structure of the optimal solution and the performance index is investigated. The results are then interpreted from the operational and computational perspectives. Copyright © 2007 John Wiley & Sons, Ltd. [source] STEERING A MOBILE ROBOT: SELECTION OF A VELOCITY PROFILE SATISFYING DYNAMICAL CONSTRAINTSASIAN JOURNAL OF CONTROL, Issue 4 2000M.A. Benayad ABSTRACT We present an open loop control design allowing to steer a wheeled mobile robot along a prespecified smooth geometric path, minimizing a given cost index and satisfying a set of dynamical constraints. Using the concept of "differential flatness," the problem is equivalent to the selection of the optimal time parametrization of the geometric path. This parametrization is characterized by a differential equation involving a function of the curvilinear coordinate along the path. For the minimum time problem, as well as for another index (such as the maximum value of the centripetal acceleration) to be minimized over a given time interval, the problem then reduces to the optimal choice of this function of the curvilinear coordinate. Using spline functions interpolation, the problem can be recast as a finite parameter optimization problem. Numerical simulation results illustrate the procedure. [source] Numerical analysis of boundary-value problems for singularly perturbed differential-difference equations: small shifts of mixed type with rapid oscillationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2004M. K. Kadalbajoo Abstract We study the boundary-value problems for singularly perturbed differential-difference equations with small shifts. Similar boundary-value problems are associated with expected first-exit time problems of the membrane potential in models for activity of neurons (SIAM J. Appl. Math. 1994; 54: 249,283; 1982; 42: 502,531; 1985; 45: 687,734) and in variational problems in control theory. In this paper, we present a numerical method to solve boundary-value problems for a singularly perturbed differential-difference equation of mixed type, i.e. which contains both type of terms having negative shifts as well as positive shifts, and consider the case in which the solution of the problem exhibits rapid oscillations. The stability and convergence analysis of the method is given. The effect of small shift on the oscillatory solution is shown by considering the numerical experiments. The numerical results for several test examples demonstrate the efficiency of the method. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||