同类机下的供应链排序及转包策略

研究了一类工件排序与转包关联的模型,即工件既可以在制造商的同类机上加工,也可以较高费用转包给某个承包商加工.需要确定被转包的工件集,以及未转包工件的加工顺序,使得工件加工与转包费用在工件最大完工时间满足限制条件下达到极小.证明了该问题的NP困难性,用数学规划方法构造多项式时间近似算法,并分析算法性能比.     

The design of simple subcontracting rules for make-to-order shops: An assessment by simulation

Subcontracting can be an important means of overcoming capacity shortages and of workload balancing, especially in make-to-order companies characterized by high variety, high demand variation and a job shop configuration. But there is a lack of simple, yet powerful subcontracting rules suitable for such contexts. The few existing rules were developed for single work center shops and neglect the actual subcontracting lead time, meaning some subcontracted jobs are destined to become tardy. This study uses Workload Control theory on matching required and available capacity over time to propose four new rules that address these shortcomings. The new rules are compared against four existing rules using an assembly job shop simulation model where the final, assembled product consists of several sub-assemblies that either flow through an internal job shop or are subcontracted. The best new rules stabilize the direct load queuing in front of a work center and significantly improve performance compared to the existing rules. For example, when the workload exceeds capacity by 10%, a 50% reduction in percentage tardy can be achieved. By examining how the workload behaves over time, we reveal that improvements come from selectively subcontracting the sub-assemblies that would otherwise cause overloads, thereby cutting off peaks in the workload.     

Locally averaged risk

Summary A heuristic method of reducing a class of admissible or Bayes decision rules is given. A new risk function is defined which is called the locally averaged risk. Bayes and admissible rules with respect to the new risk function are calledG-Bayes andG-admissible, respectively. It is shown under general assumptions that the class ofG-Bayes decision rules is a subset of the class of Bayes decision rules and the class ofG-admissible decision rules is a subset of the class of admissible decision rules. Some examples are considered, showing that the usual estimates of the parameter of a distribution with squared error as loss function, which are known to be admissible, are alsoG-admissible. This work was supported in part by NASA Grant-NGR 15-003-064 and NSF Grant-GP 7496 at Indiana University.     

Dynamic pricing of inventory with cancellation demand

When an inventory item has such a limited selling period that only a single supply order can be placed to satisfy future demand, a decision-maker must determine the quantity of the order to meet future demand and how to price this stock. Although this problem has received considerable attention, related investigations typically view the demand and selling price as exogenous parameters and assume that customers cannot cancel an order or return the product after purchasing the item. Pricing is, however, an important pervasive marketing vehicle that affects demand, and customers indeed cancel or return their orders after placing them. The newsboy problem is extended here so that demand is price-dependent and customers may cancel their orders. This paper seeks to develop decision rules to maximize the total expected profit over a given planning period. Analysis results demonstrate the feasibility of applying the order-up-to structure to yield the order quantity.     

Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for semisingularly perturbed reaction–diffusion problems

The numerical approximation by a lower‐order anisotropic nonconforming finite element on appropriately graded meshes are considered for solving semisingular perturbation problems. The quasi‐optimal‐order error estimates are proved in the ε‐weighted H¹‐norm valid uniformly, up to a logarithmic factor, in the singular perturbation parameter. By using the interpolation postprocessing technique, the global superconvergent error estimates in ε‐weighted H¹‐norm are obtained. Numerical experiments are given to demonstrate validity of our theoretical analysis. Copyright © 2007 John Wiley & Sons, Ltd.     

Admission policies for the customized stochastic lot scheduling problem with strict due-dates

This papers considers admission control and scheduling of customer orders in a production system that produces different items on a single machine. Customer orders drive the production and belong to product families, and have family dependent due-date, size, and reward. When production changes from one family to another a setup time is incurred. Moreover, if an order cannot be accepted, it is considered lost upon arrival. The problem is to find a policy that accepts/rejects and schedules orders such that long run profit is maximized. This problem finds its motivation in batch industries in which suppliers have to realize high machine utilization while delivery times should be short and reliable and the production environment is subject to long setup times.We model the joint admission control/scheduling problem as a Markov decision process (MDP) to gain insight into the optimal control of the production system and use the MDP to benchmark the performance of a simple heuristic acceptance/scheduling policy. Numerical results show that the heuristic performs very well compared with the optimal policy for a wide range of parameter settings, including product family asymmetries in arrival rate, order size, and order reward.     

阶、时滞及系数都未知的系统的辨识和适应控制

假设对一个客观的物理系统我们一无所知,唯一可以获得的信息是给了系统的输入后可以量测到系统的输出、对这种“一无所知”的系统的辨识和适应控制并不是容易的事情,下面我们假定客观的系统是由随机差分方程描述的,即输入、输出和噪声之间的关系如下:     

Parameters estimation,mixed synchronization,and antisynchronization in chaotic systems

Mixed synchronization between two Hindmarsh–Rose neuron models is realized by optimizing the scheme of Lyapunov function with two selectable gain coefficients. Based on the Lyapunov stability theory, the distribution of synchronization region and the nonsynchronization region in the two‐parameter phase space is calculated, respectively. And then the optimized parameter observers and controllers are approached analytically. All unknown parameters with different orders of magnitude are identified accurately, and the error function for corresponding variables decreases to stable value when the two gain coefficients are given values in the synchronization region. Otherwise, only the four larger unknown parameters are estimated exactly and the error function of corresponding variables decreases stably to certain minimal value with an order about 1 × 10^?6, whereas the smallest unknown parameter is approached greatly although the error of corresponding variables are stabilized within certain transient period. © 2014 Wiley Periodicals, Inc. Complexity 20: 64–73, 2014     

Global Error Estimators for Order 7, 8 Runge–Kutta Pairs

Dormand, Prince and their colleagues [3–5] showed in a sequence of papers that the approximation of an initial value differential system propagated by a Runge–Kutta pair, together with a continuous approximation obtained using additional derivative values could be utilized to obtain estimates of the global error. They illustrated the results using pairs of orders p–1 and p for several values of p. The current authors [13] have developed a more direct representation of the order conditions, characterized families of global error estimators for Runge–Kutta pairs of arbitrary values of p, and showed that efficient global error estimating Runge–Kutta methods are based on the nodes of a Lobatto quadrature formula. Here, formulas for a good 7, 8 pair, interpolants of each of orders 7 and 8, and global error estimators of orders 10 and 12 illustrate how to obtain global error estimates of orders 9, 10, or 11, for arbitrary initial value systems. One set of graphs indicates that the stated order of the global error estimators is achieved numerically, and a second set illustrates the relative efficiency for several global error estimators when the approximation is propagated with a variable stepsize.     

Minimizing Labor Requirements in a Periodic Vehicle Loading Problem

In this paper, we address a logistics problem that a manufacturer of auto parts in the north of Spain described to the authors. The manufacturer stores products in its warehouse until customers retrieve them. The customers and the manufacturer agree upon an order pickup frequency. The problem is to find the best pickup schedule, which consists of the days and times during the day that each customer is expected to retrieve his/her order. For a given planning horizon, the optimization problem is to minimize the labor requirements to load the vehicles that the customers use to pick up their orders. Heuristically, we approach this situation as a decision problem in two levels. At the first level, customers are assigned to a calendar, consisting of a set of days with the required frequency during the planning horizon. Then, for each day, the decision at the second level is to assign each customer to a time slot. The busiest time slot determines the labor requirement for a given day. Therefore, once customers have been assigned to particular days in the planning horizon, the second-level decision is a multiprocessor scheduling problem, where each time slot is the equivalent of a processor, and where the objective is to minimize the makespan. A metaheuristic procedure is developed for the problem of minimizing labor requirements in this periodic vehicle-loading problem and artificial as well as real data are used to assess its performance.     

Optimal admission and pricing control problems in service industries with multiple servers and sideline profit

This paper deals with the problem of selecting profitable customer orders sequentially arriving at a company operating in service industries with multiple servers in which two classes of services are provided. The first class of service is designed to meet the particular needs of customers; and the company (1) makes a decision on whether to accept or to reject the order for this service (admission control) and (2) decides a price of the order and offers it to an arriving customer (pricing control). The second class of service is provided as a sideline, which prevents servers from being idle when the number of customer orders for the first class is less than the number of servers. This yields the sideline profit. A cost is paid to search for customer orders, which is called the search cost. In the context of search cost, the company has an option whether to conduct the search or not. In this paper, we discuss both admission control and pricing control problems within an identical framework as well as examine the structure of the optimal policies to maximize the total expected net profit gained over an infinite planning horizon. We show that when the sideline profit is large, the optimal policies may not be monotone in the number of customer orders in the system. Copyright © 2008 John Wiley & Sons, Ltd.     

Refined mixed finite element method for the elasticity problem in a polygonal domain

The purpose of this article is to study a mixed formulation of the elasticity problem in plane polygonal domains and its numerical approximation. In this mixed formulation the strain tensor is introduced as a new unknown and its symmetry is relaxed by a Lagrange multiplier, which is nothing else than the rotation. Because of the corner points, the displacement field is not regular in general in the vicinity of the vertices but belongs to some weighted Sobolev space. Using this information, appropriate refinement rules are imposed on the family of triangulations in order to recapture optimal error estimates. Moreover, uniform error estimates in the Lamé coefficient λ are obtained for λ large. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 323–339, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10009     

Global Approximation of Solutions of Time-Dependent Variational Inequalities

We consider a class of parametric variational inequalities where both the operator and the convex set depend on time. This kind of variational inequalities are useful to model many time dependent equilibrium problems. We study the Lipschitz continuity of the solutions with respect to the time parameter and construct approximations for them which minimize the average worst case error. Some improved estimates of the Lipschitz constant for this class of problems are given. In order to illustrate our procedure, we study a classical network equilibrium problem.     

Heterogeneous trading agents

In this article, we present a multiagent system (MAS) simulation of a financial market and investigate the requirements to obtain realistic data. The model consists of autonomous, interactive agents that buy stock on a financial market. Transaction decisions are based on a number of individual and collective elements, the former being risk aversion and a set of decision rules reflecting their anticipation of the future evolution of prices and dividends and the latter the information arriving on the market influencing the decision making process of each trader. We specifically look at this process and the following observations hold: The market behavior is determined by the information arriving at the market and agent heterogeneity is required in order to obtain the right statistical properties of the price and return time series. The observed results are not sensitive to changes in the parameter values. © 2003 Wiley Periodicals, Inc.     

Graded Meshes for Higher Order FEM

A singularly perturbed one-dimensional convection-diffusion problem is solved numerically by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded (based on a mesh generating function) in the fine mesh region. Error estimates in the ε-weighted energy norm are proved. We derive an 'optimal' mesh generating function in order to minimize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving error estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results.     

Averaging of Differential Equations Generating Oscillations and an Application to Control

In this article we consider differential equations which generate oscillating solutions. These oscillations are due to the presence of a small parameter l>0 ; however, they are not present in the coefficients but instead they are caused by a penalty term involving an antisymmetric operator. Our aims are twofold. In the first part we study asymptotics at all orders, for lM 0 , construct approximate solutions, and derive estimates of the error between the exact solution and the approximate ones. One of the motivations of this part is the study to high orders of the geostrophic asymptotics in atmospheric science, but there are many other possible applications involving in particular the wave equation. The actual applications of our results to atmospheric science will be discussed elsewhere [STW], as well as, on the mathematical side, the application to partial differential equations [TW1]. In the second part of this article we study a control problem involving such an equation and study the behavior of the state equation, of the optimal control, and of the optimality equation as lM 0 . For the control part we restrict ourselves to a linear equation and to the first order in the asymptotics lM 0 , leaving nonlinear problems and higher orders to a future work.     

Primal and dual linear decision rules in stochastic and robust optimization

Linear stochastic programming provides a flexible toolbox for analyzing real-life decision situations, but it can become computationally cumbersome when recourse decisions are involved. The latter are usually modeled as decision rules, i.e., functions of the uncertain problem data. It has recently been argued that stochastic programs can quite generally be made tractable by restricting the space of decision rules to those that exhibit a linear data dependence. In this paper, we propose an efficient method to estimate the approximation error introduced by this rather drastic means of complexity reduction: we apply the linear decision rule restriction not only to the primal but also to a dual version of the stochastic program. By employing techniques that are commonly used in modern robust optimization, we show that both arising approximate problems are equivalent to tractable linear or semidefinite programs of moderate sizes. The gap between their optimal values estimates the loss of optimality incurred by the linear decision rule approximation. Our method remains applicable if the stochastic program has random recourse and multiple decision stages. It also extends to cases involving ambiguous probability distributions.     

Development and calibration of a currency trading strategy using global optimization

We have developed a new financial indicator—called the Interest Rate Differentials Adjusted for Volatility (IRDAV) measure—to assist investors in currency markets. On a monthly basis, we rank currency pairs according to this measure and then select a basket of pairs with the highest IRDAV values. Under positive market conditions, an IRDAV based investment strategy (buying a currency with high interest rate and simultaneously selling a currency with low interest rate, after adjusting for volatility of the currency pairs in question) can generate significant returns. However, when the markets turn for the worse and crisis situations evolve, investors exit such money-making strategies suddenly, and—as a result—significant losses can occur. In an effort to minimize these potential losses, we also propose an aggregated Risk Metric that estimates the total risk by looking at various financial indicators across different markets. These risk indicators are used to get timely signals of evolving crises and to flip the strategy from long to short in a timely fashion, to prevent losses and make further gains even during crisis periods. Since our proprietary model is implemented in Excel as a highly nonlinear “black box” computational procedure, we use suitable global optimization methodology and software—the Lipschitz Global Optimizer solver suite linked to Excel—to maximize the performance of the currency basket, based on our selection of key decision variables. After the introduction of the new currency trading model and its implementation, we present numerical results based on actual market data. Our results clearly show the advantages of using global optimization based parameter settings, compared to the typically used “expert estimates” of the key model parameters.     

装备维修器材生产路径双目标问题优化决策方法研究

在装备维修器材供应保障中,针对精确保障背景下部队用户对器材保障精度的要求,构建了最小化总成本和最大化订单精准执行率的双目标优化决策模型。在ε-约束法框架内,开发可生成近似Pareto前沿的两阶迭代启发式算法,并采用模糊逻辑决策法选择符合决策者偏好的折中最优解。随机实例测试结果表明所提出的模型和算法可以很好地应用在双目标优化问题的研究中,并在求解不同规模实例时表现出优异的性能。