可变抽样区间几何EWMA控制图的经济设计

为了降低生产过程周期成本,本文对单位缺陷数服从几何分布时,可变抽样区间的指数加权移动平均(EWMA)控制图进行经济设计。首先建立可变抽样区间几何EWMA控制图的经济模型,使单位时间期望费用最小来确定参数的最优值;其次用遗传算法来寻找经济模型的最优解;最后对可变抽样区间几何EWMA控制图的经济模型进行灵敏度分析和最优性分析。研究结果表明单位时间期望费用分别随着异常原因发生的频率、过程失控时单位时间的质量费用、发现异常原因的时间期望值和纠正过程的时间期望值的增大而增大。     

Optimal inventory policies for an economic order quantity model with decreasing cost functions

In this paper, three total cost minimization EOQ based inventory problems are modeled and analyzed using geometric programming (GP) techniques. Through GP, optimal solutions for these models are found and sensitivity analysis is performed to investigate the effects of percentage changes in the primal objective function coefficients. The effects on the changes in the optimal order quantity and total cost when different parameters of the problems are changed is also investigated. In addition, a comparative analysis between the total cost minimization models and the basic EOQ model is conducted. By investigating the error in the optimal order quantity and total cost of these models, several interesting economic implications and managerial insights can be observed.     

Designing a mixed-model,open-station assembly line using mixed-integer programming

An open-station assembly line that manufactures mixed models of sheet metal cabinets is considered in this research. The problem minimizes the total cost of the idle and utility times incurred in an assembly line with different line parameters (such as launch interval, station length, starting point of work, upstream walk, locus of the operator's movement, etc.) and operation sequences of the mixed models. An open-station system plays a significant controlling role in determining the optimal line parameters that minimize the total cost of idle and utility times in a mixed-model assembly line. Thus, a mixed-integer programming model for an open-station system is developed here to determine line parameters optimally. The model is tested on a three-station mixed-model line, which is a partial representation of a complete long assembly line. This research obtained a set of line parameters that minimize the total cost of idle and utility times optimally. Results indicate that the minimum total cost of idle and utility times in an open-station system decreases with line length. Other results pertinent to the line design are also demonstrated.     

Optimal inventory policies under decreasing cost functions via geometric programming

In this paper, we establish and analyze two economic order quantity (EOQ) based inventory models under total cost minimization and profit maximization via geometric programming (GP) techniques. Through GP, optimal solutions for both models are found and managerial implications on the optimal policy are determined through bounding and sensitivity analysis. We investigate the effects on the changes in the optimal order quantity and the demand per unit time according to varied parameters by studying optimality conditions. In addition, a comparative analysis between the total cost minimization model and the profit maximization model is conducted. By investigating the error in the optimal order quantity of these two models, several interesting economic implications and managerial insights can be observed.     

A simple method to compute economic order quantities: Some observations

Teng [2] presents an arithmetic–geometric mean method to be applied to determine the optimal lot size for the EOQ/EPQ models, taking into account backorders. Although the arithmetic–geometric mean method is correct, arguments as to when (not) to use the arithmetic–geometric mean inequality as optimization method are not complete. Moreover, this optimization method does not focus on the method for deriving the optimal backorders level. The main purpose of this work is to overcome these shortcomings, presents a discussion of when (not) to use the cost minimization method and derives the optimal backorders level.     

Multi-server system with single working vacation

We consider an M/M/R queue with vacations, in which the server works with different service rates rather than completely terminates service during his vacation period. Service times during vacation period, service times during service period and vacation times are all exponentially distributed. Neuts’ matrix–geometric approach is utilized to develop the computable explicit formula for the probability distributions of queue length and other system characteristics. A cost model is derived to determine the optimal values of the number of servers and the working vacation rate simultaneously, in order to minimize the total expected cost per unit time. Under the optimal operating conditions, numerical results are provided in which several system characteristics are calculated based on assumed numerical values given to the system parameters.     

Asymptotic behavior of the optimal cost functional for a rapidly stabilizing indirect control in the singular case

The optimal control problem for a linear system with fast and slow variables in the form of indirect control with a convex terminal cost functional and a smooth geometric constraint on the control is studied. An asymptotic expansion of the cost functional up to any power of a small parameter is constructed.     

Reliability and cost analysis of series system models using fuzzy parametric geometric programming

In this paper, we have discussed series system models with system reliability and cost. We have considered two types of the model; the former focuses on a problem of optimal reliability for series system with cost constraint and the latter is a center system cost model with reliability goal. It is necessary to improve the reliability of the system under limited available cost of system and also to minimize the systems cost subject to target goal of the reliability. Practically, cost of components has always been imprecise with vague in nature. So they are taken as fuzzy in nature and the reliability models are formulated as a fuzzy parametric geometric programming problem. Numerical examples are given to illustrate the model through fuzzy parametric geometric programming technique.     

Fault-Tolerant Geometric Spanners

We present two new results about vertex and edge fault-tolerant spanners in Euclidean spaces. We describe the first construction of vertex and edge fault-tolerant spanners having optimal bounds for maximum degree and total cost. We present a greedy algorithm that for any t > 1 and any non-negative integer k, constructs a k-fault-tolerant t-spanner in which every vertex is of degree O(k) and whose total cost is O(k²) times the cost of the minimum spanning tree; these bounds are asymptotically optimal. Our next contribution is an efficient algorithm for constructing good fault-tolerant spanners. We present a new, sufficient condition for a graph to be a k-fault-tolerant spanner. Using this condition, we design an efficient algorithm that finds fault-tolerant spanners with asymptotically optimal bound for the maximum degree and almost optimal bound for the total cost.     

Optimal geometric process replacement model

In this paper, we study the geometric process replacement model as follows: the successive survival times of the system form a nonincreasing geometric process while the consecutive repair times of the system constitute a non-decreasing geometric process, and the system is replaced at the time of theNth failure after its installation or last replacement. Based on the long-run average cost per unit time, we determine the optimal replacement policyN* show the uniquess of the policyN* and discuss its monotonicity.     

Geometry Optimization of Branched Sheet Metal Products

Geometry Optimization plays an important role concerning to design tasks in mechanical engineering. For those we are studying sheet metal products like cable conduits. We formulate a nonlinear, continuous optimization problem to find an optimal geometry for such a sheet metal product. The goal is to find from a given topology the optimal geometry parameters concerning to the minimal bending of a cable conduit, spanning a huge distance. Hereby a lot of constraints, like given sizes of cross-section areas of the chambers, given quantity of sheet metal, and so on have to be fullfilled. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

交通网络建设序列的动态规划方法

交通网络建设序列优化是交通规划中一个重要问题。文章对交通网络设计及其建设序列问题的研究现状进行了分析。按照网络建设中规划者和用户间的关系,以交通网络建设序列下的各阶段系统总费用作为上层规划,以各阶段的交通流用户平衡模型作为下层规划,建立了双层规划模型。并依照问题的特点,采用动态规划的求解方法进行探讨,而下层模型则采用了基于路径搜索的GP算法进行求解。并针对网络规划算例进行了计算,针对固定和变动客流OD两种情况下的结果进行了分析。计算的结果表明,问题的双层规划模型和动态规划求解算法能够为路网规划决策提供支持。     

Heuristic procedures for a stochastic batch service problem

This paper considers a multi-class batch service problem that involves a class-dependent waiting cost and a service cost in determining customer batch sizes. Unlike a fixed service cost used widely in standard models, the service cost considered in this work is incurred only if the total service time is over the capacity. We formulate this problem as an infinite horizon Markov decision process, and exploit its structural properties to establish theoretical results, including bounds on the optimal action space. We use the results to improve the value iteration procedure. Furthermore, we design heuristic algorithms for large problems. The numerical experiments demonstrate that the class-dependent waiting cost has a considerable influence on the optimal customer batch size. Finally, we evaluate the efficiency of the proposed value iteration procedure and the quality of the heuristic solutions.     

Optimal testing strategies in overlapped design process

Testing is an important activity in product development. Past studies, which are developed to determine the optimal scheduling of tests, often focused on single-stage testing of sequential design process. This paper presents an analytical model for the scheduling of tests in overlapped design process, where a downstream stage starts before the completion of upstream testing. We derive optimal stopping rules for upstream and downstream stages’ testing, together with the optimal time elapsed between beginning the upstream tests and beginning the downstream development. We find that the cost function is first convex then concave increasing with respect to upstream testing duration. A one-dimensional search algorithm is then proposed for finding the unique optimum that minimizes the overall cost. Moreover, the impact of different model parameters, such as the problem-solving capacity and opportunity cost, on the optimal solution is discussed. Finally, we compare the testing strategies in overlapped process with those in sequential process, and get some additional results. The methodology is illustrated with a case study at a handset design company.     

在预报更新的环境下具有两种配送方式的供应链模型

本文研究在预报更新环境下具有快、慢两种配送方式和需求预报更新的库存系统，为了得到更多关于费用参数和预报改进对最优定货量以及最优的平均费用的影响，我们考虑两个周期的情形．以动态规划为工具我们得到了系统的最优策略．对于需求预报服从均匀分布情形，本文得到了最优定货量和最优的平均总费用的精确表达式．我们通过一些数值例子来说明库存费用、罚金、需求的预报改进和预报误差对最优定货量和最优的     

Dynamic Programming Algorithms for Generating Optimal Strip Layouts

This paper presents dynamic programming algorithms for generating optimal strip layouts of equal blanks processed by shearing and punching. The shearing and punching process includes two stages. The sheet is cut into strips using orthogonal guillotine cuts at the first stage. The blanks are punched from the strips at the second stage. The algorithms are applicable in solving the unconstrained problem where the blank demand is unconstrained, the constrained problem where the demand is exact, the unconstrained problem with blade length constraint, and the constrained problem with blade length constraint. When the sheet length is longer than the blade length of the guillotine shear used, the dynamic programming algorithm is applied to generate optimal layouts on segments of lengths not longer than the blade length, and the knapsack algorithm is employed to find the optimal layout of the segments on the sheet. Experimental computations show that the algorithms are efficient.     

Existence and approximation of nonlocal optimal design problems driven by parabolic equations

This work is a follow‐up to a series of articles by the authors where the same topic for the elliptic case is analyzed. In this article, a class of nonlocal optimal design problem driven by parabolic equations is examined. After a review of results concerning existence and uniqueness for the state equation, a detailed formulation of the nonlocal optimal design is given. The state equation is of nonlocal parabolic type, and the associated cost functional belongs to a broad class of nonlocal integrals. In the first part of the work, a general result on the existence of nonlocal optimal design is proved. The second part is devoted to analyzing the convergence of nonlocal optimal design problems toward the corresponding classical problem of optimal design. After a slight modification of the problem, either on the cost functional or by considering a new set of admissibility, the G‐convergence for the state equation and, consequently, the convergence of the nonlocal optimal design problem are proved.     

基于随机规划的建筑集群冷热电联供系统优化研究

面向建筑集群的冷热电联供系统的设计和优化是实现建筑楼宇能源成本节约的重要途径。随机因素对该联供系统的优化决策,具有显著的影响。考虑建筑楼宇的能源需求为随机变量,构建随机混合整数规划模型,解决以最小化建筑楼宇总费用为目标时建筑集群冷热电联供系统的优化问题;其次,提出采用Benders多割平面方法求解多目标规划问题,从而寻找冷热电联供系统的设备配置和系统运行的Pareto最优决策;最后,通过实验验证了模型和算法的有效性。实验结果表明建筑集群在协作模式下,相比于非协作模式,具有更低的总费用。     

基于风险偏好和公平偏好的PPP项目政府补偿机制研究

本文在综合考虑社会资本风险偏好和公平偏好的基础上,构建了政府与社会资本之间的Stackelberg博弈模型,分析了社会资本风险偏好和公平偏好影响下PPP项目政府补偿机制的最优设计。研究表明:社会资本的最优投资水平随风险规避度的增高而降低,随公平偏好程度的增高而增高;政府补偿机制的最优设计应是在考虑单期风险及公平溢价成本的基础上,估计单期期望运营收益的高低,进而协调年建设成本补偿及运营期补偿系数两者的相对关系,设计最优的年建设成本补偿和运营期补偿系数。     

Thermodynamic optimization of an irreversible regenerative closed Brayton cycle based on thermoeconomic performance criterion

An irreversible regenerative closed Brayton cycle has been optimized using a thermoeconomic objective criterion which is defined as the ratio of net power output to the total cost rate. The total cost rate includes fuel, investment, environmental and operation & maintenance cost rates. In the considered model pressure drops, heat leakages, irreversibilities due to finite-rate heat transfer and internal dissipations have been included. The effects of design parameters, such as isentropic temperature ratio of compressor and turbine, regenerator effectiveness, pressure loss parameter of the cycle, on the general and optimal thermoeconomic performances have been investigated in detail. The results of the study will be helpful for the performance analysis and optimization of practical Brayton heat engine systems.