Economic design of screening procedures when the rejected items are reprocessed

In a screening inspection, all of the items are subject to acceptance inspection. If an item fails to meet the predetermined specifications, it is rejected. In this paper, economic screening procedures are considered when the rejected items are reprocessed. It is assumed that the reprocessed and nonreprocessed items are produced by the same manufacturing process and therefore their quality characteristics are identically and independently distributed. Screening procedures based on the performance variable of interest and a variable which is correlated with the performance variable are considered. Cost models are constructed which involve the cost incurred by imperfect quality, reprocessing cost, and inspection cost. Methods of finding the optimal screening procedures are presented and an example is given.     

Integral approximation of the characteristic function of a spherical cap by algebraic polynomials

A problem of optimal boundary control of thermal sources for a stationary model of natural thermal convection of a high-viscosity inhomogeneous incompressible fluid in the Boussinesq approximation is investigated. Conditions for the solvability of the problem, as well as necessary and sufficient optimality conditions, are specified. Optimality conditions and the corresponding adjoint problems defining the gradient of the quality functional are written for several special cases of the functional. Computational procedures for finding an optimal control based on gradient methods are described. The results of numerical experiments are given.     

Optimal and near-optimal policies for lost sales inventory models with at most one replenishment order outstanding

In this paper we use policy-iteration to explore the behaviour of optimal control policies for lost sales inventory models with the constraint that not more than one replenishment order may be outstanding at any time. Continuous and periodic review, fixed and variable lead times, replenishment order sizes which are constrained to be an integral multiple of some fixed unit of transfer and service level constraint models are all considered. Demand is discrete and, for continuous review, assumed to derive from a compound Poisson process. It is demonstrated that, in general, neither the best (s, S) nor the best (r, Q) policy is optimal but that the best policy from within those classes will have a cost which is generally close to that of the optimal policy obtained by policy iteration. Finally, near-optimal computationally-efficient control procedures for finding (s, S) and (r, Q) policies are proposed and their performance illustrated.     

Algorithms for solving discrete optimal control problems with infinite time horizon and determining minimal mean cost cycles in a directed graph as decision support tool

Time-discrete systems with a finite set of states are considered. Discrete optimal control problems with infinite time horizon for such systems are formulated. We introduce a certain graph-theoretic structure to model the transitions of the dynamical system. Algorithms for finding the optimal stationary control parameters are presented. Furthermore, we determine the optimal mean cost cycles. This approach can be used as a decision support strategy within such a class of problems; especially so-called multilayered decision problems which occur within environmental emission trading procedures can be modelled by such an approach.     

Economic off-line quality control strategy with two types of inspection errors

A commonly used quality control method is to inspect products to identify their quality and to perform the related disposition of acceptance, salvage or rejection based on the findings. While the issue of finding the most economical inspection/disposition policy has been studied for a batch of units produced from an unreliable system, previous studies assumed the inspections to be perfect. In this study, we further extend the inspection/disposition model to consider two types of inspection errors in order to facilitate the adaptation of this economic inspection/disposition model to real world applications. We first describe an inspection/disposition policy for the two types of inspection errors and then obtain the related mathematical formulae. An algorithm is presented for determining the optimal inspection/disposition policy. Finally, numerical examples are given to illustrate the effect of inspection errors on the optimal inspection/disposition policy under the following three quality control policies: cost minimizing, zero-defects and perfect information policy.     

On the Numerical Solution of Differential Games for Neutral-Type Linear Systems

The paper deals with a zero-sum differential game, in which the dynamics of a conflict-controlled system is described by linear functional differential equations of neutral type and the quality index is the sum of two terms: the first term evaluates the history of motion of the system realized up to the terminal time, and the second term is an integral–quadratic evaluation of the corresponding control realizations of the players. To calculate the value and construct optimal control laws in this differential game, we propose an approach based on solving a suitable auxiliary differential game, in which the motion of a conflict-controlled system is described by ordinary differential equations and the quality index evaluates the motion at the terminal time only. To find the value and the saddle point in the auxiliary differential game, we apply the so-called method of upper convex hulls, which leads to an effective solution in the case under consideration due to the specific structure of the quality index and the geometric constraints on the control actions of the players. The efficiency of the approach is illustrated by an example, and the results of numerical simulations are presented. The constructed optimal control laws are compared with the optimal control procedures with finitedimensional approximating guides, which were developed by the authors earlier.     

允许租用货栈的库存系统的最优进货策略

本文从实际背景出发，提出了允许租用货栈的库存系统的库存模型，在一般时变需求并允许短缺的假定下，得到了寻求该系统最优进货策略的一种交替逼近方法。并给出了数字例子。     

Discrete Lagrangian algorithm for finding geodesics on triangular meshes

The present paper introduces an approximation method for finding open geodesics on triangular surfaces. The algorithm is specifically designed to be able to solve real world problems where geodesic paths are needed. We use the model of geodesic curvature flow for open curves in the Lagrangian formulation. The model is enriched with a tangential term in order to have a control over the quality of the discretization grid during the computation. The governing equation of the flow is solved by a numerical method based on a semi-implicit time discretization and a finite difference space discretization. The paper presents the numerical scheme and various implementation details as well as numerous experiments to demonstrate the performance of the method and to provide comparison with several other well known methods. We also present a Grasshopper component for Rhinoceros for finding optimal paths on surface meshes that we developed and that includes our algorithm.     

Efficient Computation of Bayesian Optimal Discriminating Designs

An efficient algorithm for the determination of Bayesian optimal discriminating designs for competing regression models is developed, where the main focus is on models with general distributional assumptions beyond the “classical” case of normally distributed homoscedastic errors. For this purpose, we consider a Bayesian version of the Kullback–Leibler (KL). Discretizing the prior distribution leads to local KL-optimal discriminating design problems for a large number of competing models. All currently available methods either require a large amount of computation time or fail to calculate the optimal discriminating design, because they can only deal efficiently with a few model comparisons. In this article, we develop a new algorithm for the determination of Bayesian optimal discriminating designs with respect to the Kullback–Leibler criterion. It is demonstrated that the new algorithm is able to calculate the optimal discriminating designs with reasonable accuracy and computational time in situations where all currently available procedures are either slow or fail.     

The multiple-choice multi-period knapsack problem

This paper introduces the multiple-choice multi-period knapsack problem in the interface of multiple-choice programming and knapsack problems. We first examine the properties of the multiple-choice multi-period knapsack problem. A heuristic approach incorporating both primal and dual gradient methods is then developed to obtain a strong lower bound. Two branch-and-bound procedures for special-ordered-sets type 1 variables that incorporate, respectively, a special algorithm and the multiple-choice programming technique are developed to locate the optimal solution using the above lower bound as the initial solution. A computer program written in IBM's APL2 is developed to assess the quality of this lower bound and to evaluate the performance of these two branch-and-bound procedures.     

Multiobjective models in identification of random fields

The paper deals with mathematical models for identification problems of random fields. Two basic classes of random fields are presented and their applicability to real-life problems is emphasized. The problem of optimal identification of the random field is developed by means of kriging theory. Several multiobjective cases are considered and possible procedures for aiding the decision making identification process of random fields are discussed. Some remarks related to the application as well as to possible extension of presented methods are included.     

A two-period supply contract model for a decentralized assembly system

Supply contract helps in coordinating the supply of quantities from different suppliers in order to meet the demand for a product. In this paper, supply contract models are developed by considering an assembly system operated under a centralized and a decentralized control modes. The centralized control mode considers a single decision maker and offers a global optimal solution. However, the decentralized control mode considers each player in the contract as a decision maker and offers local optimal solutions based on the production and cost characteristics of each player. Such local optimal solutions are adjusted through coordinating parameters to obtain global optimal solutions. If a contract developed for a decentralized control mode achieves the global optimal solution, then the supply chain (or channel) is said to be coordinated.     

Stochastic optimization algorithms for barrier dividend strategies

This work focuses on finding optimal barrier policy for an insurance risk model when the dividends are paid to the share holders according to a barrier strategy. A new approach based on stochastic optimization methods is developed. Compared with the existing results in the literature, more general surplus processes are considered. Precise models of the surplus need not be known; only noise-corrupted observations of the dividends are used. Using barrier-type strategies, a class of stochastic optimization algorithms are developed. Convergence of the algorithm is analyzed; rate of convergence is also provided. Numerical results are reported to demonstrate the performance of the algorithm.     

具有优势机器的无空闲同顺序Flow Shop排序问题

本文讨论具有优势机器的无空闲同顺序Flow Shop排序问题的两种特殊情况,第一种情况是具有增减系列优势机器,第二种情况是具有减增系列优势机器．对于目标函数是最大完工时间,加权完工时间和,最大延误和延误工件数等问题,给出了求解最优排序的有效方法．     

The production–inventory problem of a product with time varying demand,production and deterioration rates

In this paper, we consider the production–inventory problem in which the demand, production and deterioration rates of a product are assumed to vary with time. Shortages of a cycle are allowed to be backlogged partially. Two models are developed for the problem by employing different modeling approaches over an infinite planning horizon. Solution procedures are derived for determining the optimal replenishment policies. A procedure to find the near-optimal operating policy of the problem over a finite time horizon is also suggested.     

On the optimal control of integral-functional equations

The problem of the optimal control of stochastic integral-functional equations of neutral type with an intergral quality functional is considered. For the case of a linear quadratic problem an explicit form of the optimal control is presented.

A class of equations which originated in the synthesis of Volterra equations, and stochastic differential equations with after-effects of neutral type are discussed. The problem of the optimal control of such systems is an essential development of the theory of controlled differential equations /1–8/. Examples of real objects whose mathematical models contain equations with an after-effect are discussed in /9/. A study of integral equations of neutral type is essential in controlling the motion of bodies in a continuous medium, /10/. Volterra equations first arose in the theory of creep and form the basis of this theory /11, 12/.     

Modeling calibration functions for the technologies of system analysis of quality and certification of biomaterials

Possibilities are considered of using the modern methods of computer modeling for the technologies of system analysis of quality and certification of biomaterials. The practical methods and algorithms are described to calculate the adequate calibration models from a collection of the standard samples based on the application of the international standard ISO 11095. Applications of numerical simulation methods are investigated for construction of calibration functions under variation of the initial data concerning standard samples within the intervals of their attested values. It is shown that the proposed technology of finding the optimal calibration from a collection of adequate models allows us to improve the precision of the ecoanalytical measurements of the composition of toxic micro-impurities in biomedia.     

An evaluation of semidefinite programming based approaches for discrete lot-sizing problems

The present work is intended as a first step towards applying semidefinite programming models and tools to discrete lot-sizing problems including sequence-dependent changeover costs and times. Such problems can be formulated as quadratically constrained quadratic binary programs. We investigate several semidefinite relaxations by combining known reformulation techniques recently proposed for generic quadratic binary problems with problem-specific strengthening procedures developed for lot-sizing problems. Our computational results show that the semidefinite relaxations consistently provide lower bounds of significantly improved quality as compared with those provided by the best previously published linear relaxations. In particular, the gap between the semidefinite relaxation and the optimal integer solution value can be closed for a significant proportion of the small-size instances, thus avoiding to resort to a tree search procedure. The reported computation times are significant. However improvements in SDP technology can still be expected in the future, making SDP based approaches to discrete lot-sizing more competitive.     

Discrete Adjoint based Sensitivity Analysis for Optimal Active Flow Control of High-Lift Configurations

Blowing and suction type of active flow control techniques can be used to delay the flow separation on the flap and to enhance the aerodynamic performance of high-lift configurations. Effective separation control and maximum enhancement in the mean lift coefficient are achieved by finding the optimal actuation parameters. The optimal set of actuation parameters can be obtained by combining the gradient based algorithms with discrete adjoints. In the present work, an unsteady discrete adjoint incompressible RANS solver is developed for the optimal active separation control. The adjoint solver is applied to the test case of active flow control on the flap of a 2D high-lift configuration. Sensitivity gradients are presented to demonstrate the accuracy of unsteady adjoint RANS solver. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

最小树的一般算法

本文根据设计并行算法的基本原则,给出了最小树的两个对偶定理.在此基础上,建立了两种对偶的同步并行算法的雏型.这两种算法恰恰在对偶的意义下,概括了以往的最小树算法.