Joint replenishment and manufacturing activities control in a two stage unreliable supply chain

This paper deals with dynamic stochastic situations faced by supply chains. In this context, various interactions, disparate decisions and random phenomena must be considered. These issues are considered in this paper through a two stage supply chain control problem. The supplier and the transformation stage are both subject to random events such as periods of unavailability due to internal difficulties or market constraints. Our objective is to find information sharing control policies for the supply and production activities that minimises the expected discounted cost of ordering, inventories/backlog and transformation over an infinite horizon. This is an optimal control problem with state constraints and hybrid dynamics of the production and replenishment activities. It is shown that, from a mathematical point of view, the considered problem is difficult to tackle and it calls upon optimal and impulsive control theory notions. A dynamic stochastic model is thus proposed. The existence of an optimal control policy and Hamilton-Jacobi-Bellman optimality condition in terms of the value function of the problem are derived and discussed. A numerical schema is then proposed to solve the obtained optimality conditions equations. A complete control policy is finally developed. The confirmation of such a policy structure is illustrated through sensitivity analysis. Some particular cases are also presented and discussed.     

具分布观测的年龄相关的种群扩散系统生育率控制的非线性问题

本文讨论了具分布观测的年龄相关的种群扩散系统最优生育率控制的非线性问题,证明了系统解的存在唯一性和最优生育率控制的存在性,得到了控制为最优的一阶必要条件及其由偏微分方程组和变分不等式组成的最优性组,并进而建立了最优生育率控制的反馈表达式。这些结果可为种群扩散系统中的最优控制问题的实际研究提供理论基础。     

Cross-country sailplane flight as a dynamic optimization problem

A minimum?time, thermal?to?thermal sailplane trajectory optimization problem is formulated as a non?linear optimal control problem. Numerical solutions are obtained using a gradiaent projection algorithm which incorporates conjugate directions of search. Further insight into the nature of the solutions and the computational process is ontained through an analysis of the linearized sailplane dynamics and the necessary conditions for optimality. Numerical results are presented for two sailplane types and various values of thermal strength and distance between thermals. An additional problem is formulated and solved for the case of bounded control rate.     

Production and set-up control of a failure-prone manufacturing system

The present paper considers a stochastic optimal control problem for a one-machine two-parts manufacturing system, subject to random breakdowns and repairs. The machine under consideration is not completely flexible and hence requires set-up time and cost in order to switch the production from a part type to another. The objective is to find the production plan and sequence of set-ups that minimize the cost function that penalizes inventory/backlog and set-up costs. A continuous dynamic programming formulation of the problem is presented. A numerical scheme is then adopted to solve the obtained optimality conditions equations. The optimal set-up policy. is shown numerically, to be described by a modified hedging corridor strategy. A complete heuristic policy, based on the determination of the boundaries of the corridors that describe the optimal policy in positive and negative areas of the state variables, is developed. The usefulness of such a policy is iJlustrated through experimentation and sensitivity analysis. Extensions to more complex systems are also discussed.     

Optimal control of a non-isothermal tube drawing process

We consider an optimal control problem for a non-isothermal tube drawing process. The goal is to control the circular cross-sectional area of the tube using the drawing speed as the control variable. To achieve this goal, a cost functional of tracking-type is defined, the first-order optimality condition is derived and the Hessian of the reduced cost functional is derived. Numerical simulations based on a steepest descent and a Newton-Conjugate-Gradient algorithm are presented.     

A Review of: “PRACTICAL OPTIMIZATION”

We consider a generalized optimal common due-date assignment problem and derive the optimality conditions for finding the optimal solution in this paper. We show that some versions of the common due-date determination problem can be treated as special cases of this generalized problem. For these special cases, we show that closed-form optimal solutions can be obtained from the optimality conditions. As for the solution of the generalized problem, we suggest an iterative solution procedure to help determine the optimal solution. Finally, we discuss the limiting behaviour of the optimal solution in a special situation and derive the asymptotic result     

ON OPTIMAL ARCHGRIDS

Treated in this work is the optimality of flexureless orthogonal archgrids. Various features of fully stressed arches and archgrids are highlighted and an efficient and simple iterative method for obtaining the optimal solution is proposed. Considering the load proportions carried by arches as independent variables, the optimality of the archgrid is ensured by imposing the conditions of equal elevation at nodal intersections and individual optimality of component arches. Computational effort, is reduced by using a simple updating procedure during repetitive calculations. The convergence of the solution is aptly tested by the convergence of elevations and compressive forces in arches. It is shown that the optimal solutions for some skew archgrid systems can be obtained by solving equivalent orthogonal archgrids.     

Parametric optimal control of uncertain systems under an optimistic value criterion

It is well known that the optimal control of a linear quadratic model is characterized by the solution of a Riccati differential equation. In many cases, the corresponding Riccati differential equation cannot be solved exactly such that the optimal feedback control may be a complex time-oriented function. In this article, a parametric optimal control problem of an uncertain linear quadratic model under an optimistic value criterion is considered for simplifying the expression of optimal control. Based on the equation of optimality for the uncertain optimal control problem, an approximation method is presented to solve it. As an application, a two-spool turbofan engine optimal control problem is given to show the utility of the proposed model and the efficiency of the presented approximation method.     

A Bayesian Approach to Controlling Percent Defective A Model and Application

The purpose of this paper is to develop a general model for controlling the percent defective of an ongoing production process. The model is developed in a Bayesian decision theory framework so that, using dynamic programming, optimal (least cost) control decisions can be found. An application of the model to a real world production process is described in detail. The problems of estimating the model parameters are discussed along with some approaches to overcoming the estimation problems. Finally, the optimal control policies for the real world process are presented and are shown to be straightforward and easily implemented.     

Decomposition method for solving optimal material orientation problems

The strain energy density is considered as a measure of the stiffness/flexibility of the composite structure. A methodology for determining the stationary points of the strain energy density in anisotropic solids is developed. The methodology proposed is based on new problem formulation, derivation and analysis of optimality conditions, and decomposition method. The optimal material orientation problem is formulated in terms of strains. The optimality conditions derived cover different material symmetries, linear and also some non-linear material models. The complexity analysis of the optimality conditions has been performed. The proposed approach allows to divide the solution of the optimal material orientation problem into less complicated subtasks.     

Verification of three‐dimensional anisotropic adaptive processes

A verification methodology for adaptive processes is devised. The mathematical claims made during the process are identified and measures are presented in order to verify that the mathematical equations are solved correctly. The analysis is based on a formal definition of the optimality of the adaptive process in the case of the control of the L^∞‐norm of the interpolation error. The process requires a reconstruction that is verified using a proper norm. The process also depends on mesh adaptation toolkits in order to generate adapted meshes. In this case, the non‐conformity measure is used to evaluate how well the adapted meshes conform to the size specification map at each iteration. Finally, the adaptive process should converge toward an optimal mesh. The optimality of the mesh is measured using the standard deviation of the element‐wise value of the L^∞‐norm of the interpolation error. The results compare the optimality of an anisotropic process to an isotropic process and to uniform refinement on highly anisotropic 2D and 3D test cases. Copyright © 2011 John Wiley & Sons, Ltd.     

Determining the optimum cyclic operation of adsorption chillers by a direct method for periodic optimal control

Adsorption refrigeration systems provide a sustainable possibility to reduce the environmental impact of refrigeration and air-conditioning as they allow for sources of otherwise unused excess waste heat to be reused for cooling purposes. Adsorptive cooling is a discontinuously operated cycling process, and it is well known that the determination of an optimal cycling time yielding maximum cooling power is a key to the design of an efficient mode of operation. The optimal cycle time however strongly depends on operating conditions such as ambient air temperature, available heat source temperature, desired target cooling temperature, and achievable volume flow rates of the secondary heat transfer circuits. In this contribution, we apply a direct method for periodic optimal control to optimize two-bed adsorption chillers. We present a first principles dynamic model of the underlying thermal process. We show that direct methods for periodic optimal control allow for quick and reliable computation of optimal cycle times for a given set of parameters. Contrary to pre-existing methods, fast computation times and guaranteed optimality of the solutions computed by our approach makes it viable to extensively study the simulated optimal cyclic operation of two-bed adsorption chillers under a wide range of varying conditions.     

Multiparameter shape optimization of elastic bars in torsion

The problem of optimal design of the shape of an internal or external boundry of an elastic bar in torsion is formulated by assuming the boundary shape is described by a set of prescribed shape functions and a set of shape parameters. The optimization procedure is reduced to determination of these parameters. For constant volume or material cost constraint, the optimality conditions are derived for the case of maximizing of torsional rigidity of elastic bars of linear material. The optimal shape problem is next formulated by means of the finite element method and the interative solution algorithm is discussed by using the optimality crieria. Several simple numerical examples are included.     

Optimal gains for active vibration control by the beam analogy

A numerical approach to determine optimal gains for active optimal vibration control of continuous structures by the finite element method is presented. The approach uses an analogy between the optimality equations for control in the time domain and the governing equations for a set of static beams in the spatial domain. The finite element model of control is generated and analyzed in a fictitious spatial domain. The results are then transferred to the time domain to describe the optimal dynamic response of the system. The analogy (referred to as the beam analogy) allows for an efficient application of the finite element method to solve two-point-boundary-value problems for the finite time control cases. Here it is applied to the infinite time control cases. An algorithm for a direct calculation of optimal gains for closed loop control of time-invariant problems without using Riccatis equation is discussed in detail.     

SAS Software Roadmaps

In this article we compute the expected Fisher information and the asymptotic variance–covariance matrix of the maximum likelihood estimates based on a progressively type II censored sample from a Weibull distribution by direct calculation as well as the missing-information principle. We then use these values to determine the optimal progressive censoring plans. Three optimality criteria are considered, and some selected optimal progressive censoring plans are presented according to these optimality criteria. We also discuss the construction of progressively censored reliability sampling plans for the Weibull distribution. Three illustrative examples are provided with discussion.     

Fractional Optimal Control of Navier-Stokes Equations

In this paper, the non-stationary incompressible fluid flows governed by the Navier-Stokes equations are studied in a bounded domain. This study focuses on the timefractional Navier-Stokes equations in the optimal control subject, where the control is distributed within the domain and the time-fractional derivative is proposed as RiemannLiouville sort. In addition, the control object is to minimize the quadratic cost functional. By using the Lax-Milgram lemma with the assistance of the fixed-point theorem, we demonstrate the existence and uniqueness of the weak solution to this system. Moreover, for a quadratic cost functional subject to the time-fractional Navier-Stokes equations, we prove the existence and uniqueness of optimal control. Also, via the variational inequality upon introducing the adjoint linearized system, some inequalities and identities are given to guarantee the first-order necessary optimality conditions. A direct consequence of the results obtained here is that when α → 1, the obtained results are valid for the classical optimal control of systems governed by the Navier-Stokes equations.     

空间桁架结构动力学形状优化设计

在多阶固有频率约束条件下,采用“渐进结点移动法”,对空间桁架结构的形状进行优化设计,使结构重量达到最小。首先分析固有频率相对结点位置的一阶导数,确定结点移动的效率,即灵敏度数。根据灵敏度分析结果,优先移动效率较高的结点。然后,利用库恩-塔克优化条件检验所得结果,保证优化过程收敛于最小重量设计。最后,用二个典型数值算例验证本文算法的有效性和可靠性。     

Optimal control of melt-spinning processes

An optimal-control problem for a mathematical model of a melt-spinning process is considered. Newtonian models with constant viscosity and temperature-dependent viscosity are used to describe the rheology of the polymeric material, the fiber is made of. The extrusion velocity of the polymer at the spinneret, as well as the velocity and temperature of the quench air serve as control variables. A constrained-optimization problem is derived and a first-order optimality system is set up to obtain the adjoint equations. Numerical solutions are carried out using a steepest-descent algorithm.     

GT cell formation for minimizing the intercell parts flow

A methodology is proposed to design a GT cell by considering the intercell parts flow in GT cellular manufacturing systems. The problem of GT cell formation is described in a graph using the quantities to be produced in the specified time period and the process routes for producing the products. The objective of this paper is to minimize the total number of parts produced in more than one cell. The problem, formulated as a quadratic assignment problem (QAP), is solved using both Lagrangean relaxation technique and the optimality conditions of quadratic program. Furthermore, in order to obtain the giobal optimal solution rather than the local optimal solution, a branch-and-bound algorithm is employed. Finally, numerical examples are used to show the effectiveness of the solution techniques and GT cell formation procedure. Moreover, a computer simulation is presented, showing the effectiveness of cellular manufacturing systems     

微生物连续培养非线性动力系统的性质及最优性条件

本文针对微生物连续发酵生产1,3-丙二醇非线性动力系统,以产物1,3-丙二醇的生产强度最大为目标泛函,建立最优控制模型。用不可微优化理论与方法证明了模型最优解的存在性与一阶最优性条件。论述了最优性函数与一阶最优性条件的等价性。