A mathematical model for a capacity reservation contract

It is common practice in many industries to use a replenishment contract with a mechanism of capacity reservation. In this paper, we focus on a multi-period capacity reservation contract practiced between a buyer, who buys a single type of product and sells it to end-customers, and two or more heterogeneous suppliers, who produce and replenish the product as agreed upon contractually.In this paper, a mathematical model including several key features of a real contract is developed for a single supplier situation from the buyer’s perspective. It is then extended to a multiple supplier model for a system in which there are several heterogeneous suppliers with different capacities and prices. A rolling-horizon implementation strategy is suggested for the efficient application of the models. Extensive computational experiments demonstrate that the model and strategy can produce cost effective contractual terms for the buyer within a few seconds.     

电子市场与期权合约市场并存下的供应链优化

在电子市场与期权合约市场并存条件下,构建供应商的生产成本函数模型,找出供应商的最优产能决策,分销商的最优期权订货量决策,集成化供应链的最优产能决策等.然后借助数值分析,找出供应商的最优期权合约参数,及各最优解的变化规律.分析得到,电子市场准入程度的增大、电子市场价格的增大都会促使供应商提高产能;电子市场价格的增大、供应商期权预订价格的降低、期权执行价格的降低、终端市场需求的增大都会促使分销商增大期权订货量和期权执行量,供应商应选择(期权预定价格较小,期权执行价格较大)的优化决策,并针对不同的市场风险选择不同的期权合约参数组合.     

Integrating link-based discrete credit charging scheme into discrete network design problem

In this paper, we present an optimization model for integrating link-based discrete credit charging scheme into the discrete network design problem, to improve the transport performance from the perspectives of both transport network planning and travel demand management. The proposed model is a mixed-integer nonlinear bilevel programming problem, which includes an upper level problem for the transport authority and a lower level problem for the network users. The lower level sub-model is the traffic network user equilibrium (UE) formulation for a given network design strategy determined by the upper level problem. The network user at the lower level tries to minimize his/her own generalized travel cost (including both the travel time and the value of the credit charged for using the link) by choosing his/her route. While the transport authority at the upper level tries to find the optimal number of lanes and credit charging level with their locations to minimize the total system travel time (or maximize the transportation system performance). A genetic algorithm is used to solve the proposed mixed-integer nonlinear bilevel programming problem. Numerical experiments show the efficiency of the proposed model for traffic congestion mitigation, reveal that interaction effects across the tradable credit scheme and the discrete network design problem which amplify their individual effects. Moreover, the integrated model can achieve better performance than the sequential decision problems.     

Performance analysis and optimization of cognitive radio networks with retransmission control

In usual cognitive radio networks with buffer settings, secondary user packets that are interrupted by primary user packets will return to the SU buffer for later retransmission. But this may increase the average delay of the SU packets. In this paper, we propose a novel spectrum sharing strategy (SSS) to dynamically control the retransmission of the SU packets by introducing a returning threshold and a returning probability. This will simultaneously guarantee the Quality of Service for the SUs. In this SSS, when the transmission of an SU packet is interrupted, if the number of SU packets already in SU buffer reaches a returning threshold that is set in advance as a system parameter, an interrupted SU packet is admitted to return to the SU buffer with a dynamic returning probability. This returning probability is inversely proportional to the total number of packets in the system. Based on the SSS with retransmission control proposed in this paper, we build a discrete-time preemptive priority queueing model to comply with digital nature of modern networks. Accordingly, by presenting and analyzing a two-dimensional discrete-time Markov chain that represents the system state transition, we obtain the steady-state distribution of the system and then provide the formulas for several system performance measures. Moreover, with numerical results, we show the influence of the returning threshold on different performance measures. Finally, by building a net benefit function, we optimize the system performance for the returning threshold to balance different system performance measures.     

基于排队的两类顾客易逝品库存控制策略研究

本文采用排队理论在面向两类顾客需求的环境下讨论易逝品库存排队系统控制策略问题。首先刻画面向两类顾客服务且具有马尔科夫结构的易逝品库存系统排队模型,获得库存水平状态的稳态概率分布以及作为库存成本控制的系统稳态性能指标。接下来,构建库存控制成本函数及考虑服务水平约束的库存控制优化模型,设计了改进的遗传算法。最后,数值算例揭示出系统参数的敏感性和相应的管理启示。     

On the ergodic and the adaptive control of stochastic differential delay systems

Some problems of ergodic control and adaptive control are formulated and solved for stochastic differential delay systems. The existence and the uniqueness of invariant measures that are solutions of the stochastic functional differential equations for these systems are verified. For an ergodic cost criterion, almost optimal controls are constructed. For an unknown system, the invariant measures and the optimal ergodic costs are shown to be continuous functions of the unknown parameters. Almost self-optimizing adaptive controls are feasibly constructed by an approximate certainty equivalence principle.This research was partially supported by NSF Grants ECS-91-02714 and ECS91-13029.     

System modeling and performance analysis of the power saving class type II in BWA networks

For reducing the energy consumption of the Mobile Station in mobile Broadband Wireless Access networks, IEEE 802.16 offers three kinds of sleep mode operations called power saving classes type I, type II and type III. In order to investigate mathematically the inherent relationships between the performance measures and the system parameters, we propose in this paper a novel method for modeling the sleep mode with the power saving class type II in IEEE 802.16 and analyzing the performance of this sleep mode. Considering the attractive feature that some data frames can be transmitted during the listening state, we present a queueing model with two kinds of busy mechanisms to capture the working principle of the sleep mode operations with the power saving class type II. With the first and higher derivatives of the probability generating functions, we can give the averages and the standard deviations for the system performance using the diffusion approximation for the operating process of the system. We also propose methods for measuring the system performance in terms of the switching ratio, the energy saving ratio, and the average response time of data frames, as well as giving the expressions for these performance measures. Numerical results are provided with analysis and simulation to show the average performance measures, standard deviations and the cost function with different system loads. Moreover, we construct a cost function with the aim of determining the optimal time length of the sleep window to minimize the cost function.     

基于排队模型的电动汽车充电桩数量优化设计

通过对电动汽车充电行为的分析,采用顾客带有不耐烦和止步行为的有限容量M/M/C/N排队模型对充电场所充电服务系统进行建模.通过求解模型的平衡方程,获得系统稳态下的队长分布及其它多项性能指标.以系统性能指标为基础,从经济效益与社会效益的角度提出了充电服务系统优化设计的目标函数,并通过数字例子对优化模型进行了说明.分析了模型参数对系统充电桩最优配置数的影响,从中可看出,系统容量、顾客的不耐烦率及顾客的止步概率等参数对充电桩数量的优化设计都会产生不可忽视的影响.     

An efficient step size control for continuation methods

In solving a nonlinear equation by the use of a continuation method one of the crucial problems is the choice of the step sizes. We present a model for the total computational cost of a standard numerical continuation process and solve the problem of optimal step size control for this model. Using the theoretical results as a basis, we develop an adaptive step size algorithm for Newton's method. This procedure is computationally inexpensive and it gives quite satisfactory results compared to some other numerical experiments found in the literature.     

Optimal patient and personnel scheduling policies for care-at-home service facilities

In this paper we study the problem of personnel planning in care-at-home facilities. We model the system as a Markov decision process, which leads to a high-dimensional control problem. We study monotonicity properties of the system and derive structural results for the optimal policy. Based on these insights, we propose a trunk reservation heuristic to control the system. We provide numerical evidence that the heuristic yields close to optimal performance, and scales well for large problem instances.     

Lead time and response time in a pull production control system

In the late 80s, most manufacturers have shifted their manufacturing strategies from cost and quality to speed. This paper focuses on two performance measures of speed: manufacturing lead time and response time. Manufacturing lead time is the sum of the processing time to convert raw material to finished goods and the waiting time at the buffers. Response time is the time between the customer places an order and the customer receives the order. In this paper we develop a queueing model of a pull-based production control system for a single-stage facility. The intent of the model is two-fold. First, we highlight the trade-off between manufacturing lead time and response time. Second, we develop an optimization model to determine an optimal control system that guarantees certain delivery performance (in terms of response time).     

带有止步和状态相依的M/Ej/1/N排队系统的矩阵解法

研究了带有止步和服务率依赖于状态的M/Ej/1/N排队系统.顾客到达系统时,以一定的概率选择进入系统或止步(不进入系统).顾客接受服务的服务率依赖于系统中的顾客数,当系统中的顾客数不超过临界值k时,服务员慢速服务;否则,服务员快速服务.利用分块矩阵的方法,推出了稳态概率向量所满足的矩阵形式的迭代公式,给出了稳态概率的表达式和计算过程.作为特例,考虑了N=4时系统稳态概率的计算.在此基础上,还求出了系统的一些性能指标,并建立了以临界值k为控制变量的费用模型.通过数值分析,求出了使费用函数最小的最优临界值k*,并进一步研究了模型参数对最优临界值和最优费用的影响.     

顺序相依拆卸线平衡多目标优化模型及算法研究

拆卸是产品回收过程最关键环节之一,拆卸效率直接影响再制造成本。本文在分析现有模型不足基础上,考虑最小化总拆卸时间,建立多目标顺序相依拆卸线平衡问题优化模型,并提出了一种自适应进化变邻域搜索算法。所提算法引入种群进化机制,并采用一种组合策略构建初始种群,通过锦标赛法选择个体进化;在局部搜索时,设计了邻域结构自适应选择策略,并采用基于交叉的全局学习机制加速跳出局部最优,以提高算法寻优能力。对比实验结果,证实了所提模型的合理性以及算法的高效性。     

Demand selection decisions for a multi-echelon inventory distribution system

In this paper, we study an integrated demand selection and multi-echelon inventory control problem that generalizes the classical deterministic single distribution centre (DC) multi-retailer model by incorporating demand selection decisions. In addition to the ordering and holding cost components, a concave operating cost of the DC and a capacity on the total market demand served are also considered. For given revenue and cost parameters, the problem is to determine which sets of demand to fulfill and which multi-echelon inventory control policy to implement so as to maximize the net profit. We show that the problem can be formulated as a nonlinear discrete optimization model. We analyse the structural properties of the model and, based on these, outline an approach to solve the model efficiently. We also present some interesting managerial insights obtained from the numerical experiments.     

MULTISPECIES EXPLOITATION WITH EVOLUTIONARY SWITCHING OF HARVESTING STRATEGIES

In this paper, we propose a bioeconomic model which describes a fishery in which each of two noninteracting species is harvested by a given group of fishers during a defined time period. Then the Fishing Regulatory Authority allows each fisher to reconsider the harvesting decision at fixed (discrete) periods of time. The model derives from an Italian fisheries management experience in the Northern Adriatic Sea, where this kind of “self‐adjusting” fishing policy has been proposed to regulate harvesting of two shellfish species. The proposed dynamic model assumes the form of a hybrid system, as the natural growth functions of the two species (in continuous time) are coupled with a discrete time adaptive system that regulates how agents switch from one harvesting strategy to the other period by period according to an evolutionary mechanism based on profit comparison. In order to obtain some insights into the basic mechanisms of the system, some relevant benchmark cases are analyzed before tackling (mainly numerically) the complete hybrid model. Our results suggest that, for proper sets of parameters, this kind of myopic and adaptive self‐regulation may ensure a virtuous trade‐off between profit maximization and resource conservation, driven by cost externalities and market pressure.     

Optimal software testing in the setting of controlled Markov chains

The controlled Markov chains (CMC) approach to software testing treats software testing as a control problem, where the software under test serves as a controlled object that is modeled as controlled Markov chain, and the software testing strategy serves as the corresponding controller. In this paper we extend the CMC approach to software testing to the case that the number of tests that can be applied to the software under test is limited. The optimal testing strategy is derived if the true values of all the software parameters of concern are known a priori. An adaptive testing strategy is employed if the true values of the software parameters of concern are not known a priori and need to be estimated on-line during software testing by using testing data. A random testing strategy ignores all the related information (true values or estimates) of the software parameters of concern and follows a uniform probability distribution to select a possible test case. Simulation results show that the performance of an adaptive testing strategy cannot compete that of the optimal testing strategy, but should be better than that of a random testing strategy. This paper further justifies the idea of software cybernetics that is aimed to explore the interplay between software theory/engineering and control theory/engineering.     

An extension of Banerjee and Rahim's model for economic design of moving average control chart for a continuous flow process

In this paper, we propose a model of a moving average control chart (MA control chart) with a Weibull failure mechanism from an economic viewpoint. When the process-failure mechanism follows a Weibull model or other models having increasing hazard rates, it is desirable to have the decreasing sampling interval with the age of the system. The MA control chart is used to monitor quality characteristics of raw material or products in a continuous process. A cost model utilizing a variable scheme instead of fixed sampling lengths in a continuous flow process is studied in this research. The variable sampling scheme is used to maintain a constant integrated hazard rate over each sampling interval. Optimal values for the design parameter, the moving subgroup size, the sampling interval, and the control limit coefficient are determined by minimizing the loss-cost model. The performance of the loss cost with various Weibull parameters is studied. A sensitivity analysis shows that the design parameters and loss cost depend on the model parameters and shift amounts.     

Synchronization of different-order chaotic systems: Adaptive active vs. optimal control

In this paper, an adaptive algorithm is proposed for synchronization of chaotic systems with different orders. A modular adaptive control strategy is applied to make states of the slave system track those of the master, despite the unknown parameters. One of the most advantages of the modularity approach, which is applied for the first time in chaos synchronization, is its flexibility in choosing identification and control modules and designing them completely independently. In this paper, a modified recursive least square algorithm is used to identify the unknown parameters of the slave system, and the control module is designed by means of two different algorithms. First it is designed based on active control method, and then, in order to synchronize with a lower energy, we design an optimal controller. The two methods are applied on a practical case study, and the results are compared. Two different dimensional neuron models, the HR neuron model and the cable model of cylindrical cell, are considered as the master and slave systems, respectively. Simulation results confirm the effectiveness of the proposed method.     

电子商务环境下考虑退货的选址库存问题模型与算法

选址库存问题(location inventory problem, LIP)是物流系统集成的经典问题之一,也是企业需要面对的管理决策难题。本文考虑在电子商务环境下无质量缺陷的退货商品可简单再包装后重新进入销售市场这一现实情况,对设施选址和库存控制进行集成优化,构建随机需求下有退货的LIP模型。针对此问题求解的复杂性,设计了改进的自适应混合差分进化算法对模型进行整体求解。最后,通过多组算例验证了模型和算法的实用性和优越性,可为设施选址、库存控制和商品配送回收决策提供重要参考依据。     

An Adaptive Nonmonotone Projected Barzilai-Borwein Gradient Method with Active Set Prediction for Nonnegative Matrix Factorization

In this paper, we first present an adaptive nonmonotone term to improve the efficiency of nonmonotone line search, and then an active set identification technique is suggested to get more efficient descent direction such that it improves the local convergence behavior of algorithm and decreases the computation cost. By means of the adaptive nonmonotone line search and the active set identification technique, we put forward a global convergent gradient-based method to solve the nonnegative matrix factorization (NMF) based on the alternating nonnegative least squares framework, in which we introduce a modified Barzilai-Borwein (BB) step size. The new modified BB step size and the larger step size strategy are exploited to accelerate convergence. Finally, the results of extensive numerical experiments using both synthetic and image datasets show that our proposed method is efficient in terms of computational speed.