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Problem Parameters (problem + parameter)
Selected AbstractsApproximation methods for reliability-based design optimization problemsGAMM - MITTEILUNGEN, Issue 2 2007Irfan Kaymaz Abstract Deterministic optimum designs are obtained without considering of uncertainties related to the problem parameters such as material parameters (yield stress, allowable stresses, moment capacities, etc.), external loadings, manufacturing errors, tolerances, cost functions, which could lead to unreliable designs, therefore several methods have been developed to treat uncertainties in engineering analysis and, more recently, to carry out design optimization with the additional requirement of reliability, which referred to as reliability-based design optimization. In this paper, two most common approaches for reliability-based design optimization are reviewed, one of which is reliability-index based approach and the other performancemeasure approach. Although both approaches can be used to evaluate the probabilistic constraint, their use can be prohibitive when the associated function evaluation required by the probabilistic constraint is expensive, especially for real engineering problems. Therefore, an adaptive response surface method is proposed by which the probabilistic constraint is replaced with a simple polynomial function, thus the computational time can be reduced significantly as presented in the example given in this paper. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Counter-current gas-liquid wavy film flow between the vertical plates analyzed using the Navier-Stokes equationsAICHE JOURNAL, Issue 8 2010Yu. Ya. Abstract The article is devoted to a theoretical analysis of counter-current gas-liquid wavy film flow between vertical plates. We consider two-dimensional nonlinear waves on the interface over a wide variation of parameters. The main interest is to analyse the wave structure at the parameter values corresponding to the onset of flooding observed in experiments. We use the Navier-Stokes equations in their full statement to describe the liquid phase hydrodynamics. For the gas phase equations, we use two models: (1) the Navier-Stokes system and (2) the simplified Benjamin-Miles approach where the liquid phase is a small disturbance for the laminar or turbulent gas flow. With the superficial gas velocity increasing and starting from some value of the velocity, the waves demonstrate a rapid decreasing of both the minimal film thickness and the phase wave velocity. We obtain a region of the gas velocity where we have two solutions at one set of the problem parameters and where the flooding takes place. Both the phase wave velocity and the minimal film thickness are positive numbers at such values of the velocity. We calculate the flooding point dependences on the liquid Reynolds number for two different liquids. The wave regime corresponding to the flooding point demonstrates negative u- velocities in the neighbourhood of the interface near the film thickness maximum. At smaller values of the superficial gas velocity, the negative u- velocities take place in the neighbourhood of the film thickness minimum. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] Design of flexible reduced kinetic mechanismsAICHE JOURNAL, Issue 11 2001Avinash R. Sirdeshpande Reduced mechanisms are often used in place of detailed chemistry because the computational burden of including all the species continuity equations in the reactor model is unreasonably high. Contemporary reduction techniques produce mechanisms that depend strongly on the nominal set of problem parameters for which the reduction is carried out. Effects of variability in these parameters on the reduced mechanism are the focus of this work. The range of validity of a reduced mechanism is determined for variations in initial conditions. Both sampling approaches and quantitative measures of feasibility, such as the flexibility index and the convex hull formulation, are employed. The inverse problem of designing a reduced mechanism that covers the desired range of initial conditions is addressed using a multiperiod approach. The effect of the value of a user-defined tolerance parameter, which determines whether the predictions made by the reduced mechanism are acceptable, is also assessed. The analytical techniques are illustrated with examples from the literature. [source] Nash bargaining over allocations in inventory pooling contractsNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 6 2008Eran Hanany Abstract When facing uncertain demand, several firms may consider pooling their inventories leading to the emergence of two key contractual issues. How much should each produce or purchase for inventory purposes? How should inventory be allocated when shortages occur to some of the firms? Previously, if the allocations issue was considered, it was undertaken through evaluation of the consequences of an arbitrary priority scheme. We consider both these issues within a Nash bargaining solution (NBS) cooperative framework. The firms may not be risk neutral, hence a nontransferable utility bargaining game is defined. Thus the physical pooling mechanism itself must benefit the firms, even without any monetary transfers. The firms may be asymmetric in the sense of having different unit production costs and unit revenues. Our assumption with respect to shortage allocation is that a firm not suffering from a shortfall, will not be affected by any of the other firms' shortages. For two risk neutral firms, the NBS is shown to award priority on all inventory produced to the firm with higher ratio of unit revenue to unit production cost. Nevertheless, the arrangement is also beneficial for the other firm contributing to the total production. We provide examples of Uniform and Bernoulli demand distributions, for which the problem can be solved analytically. For firms with constant absolute risk aversion, the agreement may not award priority to any firm. Analytically solvable examples allow additional insights, e.g. that higher risk aversion can, for some problem parameters, cause an increase in the sum of quantities produced, which is not the case in a single newsvendor setting. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008 [source] Revenue sharing contracts in a supply chain with uncontractible actionsNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 5 2008Albert Y. Ha Abstract We consider a supplier,customer relationship where the customer faces a typical Newsvendor problem of determining perishable capacity to meet uncertain demand. The customer outsources a critical, demand-enhancing service to an outside supplier, who receives a fixed share of the revenue from the customer. Given such a linear sharing contract, the customer chooses capacity and the service supplier chooses service effort level before demand is realized. We consider the two cases when these decisions are made simultaneously (simultaneous game) or sequentially (sequential game). For each game, we analyze how the equilibrium solutions vary with the parameters of the problem. We show that in the equilibrium, it is possible that either the customer's capacity increases or the service supplier's effort level decreases when the supplier receives a larger share of the revenue. We also show that given the same sharing contract, the sequential game always induces a higher capacity and more effort. For the case of additive effort effect and uniform demand distribution, we consider the customer's problem of designing the optimal contract with or without a fixed payment in the contract, and obtain sensitivity results on how the optimal contract depends on the problem parameters. For the case of fixed payment, it is optimal to allocate more revenue to the supplier to induce more service effort when the profit margin is higher, the cost of effort is lower, effort is more effective in stimulating demand, the variability of demand is smaller or the supplier makes the first move in the sequential game. For the case of no fixed payment, however, it is optimal to allocate more revenue to the supplier when the variability of demand is larger or its mean is smaller. Numerical examples are analyzed to validate the sensitivity results for the case of normal demand distribution and to provide more managerial insights. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008 [source] Production to order and off-line inspection when the production process is partially observableNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 8 2007Abraham Grosfeld-Nir Abstract This study combines inspection and lot-sizing decisions. The issue is whether to INSPECT another unit or PRODUCE a new lot. A unit produced is either conforming or defective. Demand need to be satisfied in full, by conforming units only. The production process may switch from a "good" state to a "bad" state, at constant rate. The proportion of conforming units in the good state is higher than in the bad state. The true state is unobservable and can only be inferred from the quality of units inspected. We thus update, after each inspection, the probability that the unit, next candidate for inspection, was produced while the production process was in the good state. That "good-state-probability" is the basis for our decision to INSPECT or PRODUCE. We prove that the optimal policy has a simple form: INSPECT only if the good-state-probability exceeds a control limit. We provide a methodology to calculate the optimal lot size and the expected costs associated with INSPECT and PRODUCE. Surprisingly, we find that the control limit, as a function of the demand (and other problem parameters) is not necessarily monotone. Also, counter to intuition, it is possible that the optimal action is PRODUCE, after revealing a conforming unit. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007 [source] A comparative study of efficient iterative solvers for generalized Stokes equationsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2008Maxim Larin Abstract We consider a generalized Stokes equation with problem parameters ,,0 (size of the reaction term) and ,>0 (size of the diffusion term). We apply a standard finite element method for discretization. The main topic of the paper is a study of efficient iterative solvers for the resulting discrete saddle point problem. We investigate a coupled multigrid method with Braess,Sarazin and Vanka-type smoothers, a preconditioned MINRES method and an inexact Uzawa method. We present a comparative study of these methods. An important issue is the dependence of the rate of convergence of these methods on the mesh size parameter and on the problem parameters , and ,. We give an overview of the main theoretical convergence results known for these methods. For a three-dimensional problem, discretized by the Hood,Taylor ,,2,,,1 pair, we give results of numerical experiments. Copyright © 2007 John Wiley & Sons, Ltd. [source] | ||||||||||