Optimizing the pricing and replenishment policy for non-instantaneous deteriorating items with stochastic demand and promotional efforts

Retailer promotional activity has become prevalent in the business world. Promotional efforts impact the replenishment policy and the sale price of goods. In this paper, the problem of replenishment policy and pricing for non-instantaneous deteriorating items subject to promotional effort is considered. We adopt a price dependent stochastic demand function in which shortages are allowed and partially backlogged. The major objective is to simultaneously determine the optimal selling price, the optimal replenishment schedule, and the optimal order quantity to maximize the total profit. First, we prove that a unique optimal replenishment schedule exists for any given selling price. Second, we prove that the total profit is a concave function of price. Third, we present an algorithm to obtain the optimal solution and solve a numerical example. Last, we extend the numerical example by performing a sensitivity analysis of the model parameters and discuss specific managerial insights.     

Data-driven policy iteration algorithm for continuous-time stochastic linear-quadratic optimal control problems

This paper studies a continuous-time stochastic linear-quadratic (SLQ) optimal control problem on infinite-horizon. Combining the Kronecker product theory with an existing policy iteration algorithm, a data-driven policy iteration algorithm is proposed to solve the problem. In contrast to most existing methods that need all information of system coefficients, the proposed algorithm eliminates the requirement of three system matrices by utilizing data of a stochastic system. More specifically, this algorithm uses the collected data to iteratively approximate the optimal control and a solution of the stochastic algebraic Riccati equation (SARE) corresponding to the SLQ optimal control problem. The convergence analysis of the obtained algorithm is given rigorously, and a simulation example is provided to illustrate the effectiveness and applicability of the algorithm.     

带技术投资的保险公司最优策略

本文站在保险公司的角度,假定1)保险公司采用连续比例再保险的方式将自身的部分风险转移到再保险公司,2)保险公司可以选择在某一时刻进行项目投资,该投资不直接产生收益,但可以降低公司所面临的风险.本文的目标是通过选择最佳投资时刻和最优再保险比例来最小化破产概率.运用混合随机决策–最优停时方法,本文求解出破产概率和最优再保险策略的显式表达式以及最佳投资时刻的半显式解.作为本文结果的一个应用,本文以数值模拟的方式揭示了投资效果,投资金额和最佳投资时刻3者之间的关系:1)投资总是可以降低破产概率;2)投资效果越明显,投资所需金额越小,则应该选择尽早投资;反之则应该推迟投资时间,等积累到足够的资金再进行投资.     

The active learning hypothesis of the job–demand–control model: an experimental examination

The active learning hypothesis of the job–demand–control model [Karasek, R. A. 1979. “Job Demands, Job Decision Latitude, and Mental Strain: Implications for Job Redesign.” Administration Science Quarterly 24: 285–307] proposes positive effects of high job demands and high job control on performance. We conducted a 2 (demands: high vs. low) × 2 (control: high vs. low) experimental office workplace simulation to examine this hypothesis. Since performance during a work simulation is confounded by the boundaries of the demands and control manipulations (e.g. time limits), we used a post-test, in which participants continued working at their task, but without any manipulation of demands and control. This post-test allowed for examining active learning (transfer) effects in an unconfounded fashion. Our results revealed that high demands had a positive effect on quantitative performance, without affecting task accuracy. In contrast, high control resulted in a speed–accuracy tradeoff, that is participants in the high control conditions worked slower but with greater accuracy than participants in the low control conditions.     

Personal impressions of the dawn of modern control

For many, the dawn of modern control was the dramatic appearance at the first IFAC world congress of the papers by Boltyanski, Gamkrelidze, Mischenko and Pontryagin on the maximum principle, by Bellman on dynamic programming and feedback control and by Kalman on the general theory of control systems. These, and related papers by the same authors, triggered a revolution in our subject that continues to this day. I joined Imperial College London in 1959 and was soon swept up into the excitement of this revolution. This essay traces my personal impressions of the dawn of modern control and its evolution, in a few selected areas with which I am familiar, into a mature and comprehensive subject; these impressions are personal and restricted, inevitably, by my ability to appreciate the whole picture. They hopefully give some idea of how the new ideas were received and developed but do not provide a complete picture and certainly fall far short of constituting, as the editors have emphasized, a history of this development. They should be regarded as the impressions of one participant in this exciting revolution.     

On the stability of receding horizon control for continuous-time stochastic systems

We study the stability of receding horizon control for continuous-time non-linear stochastic differential equations. We illustrate the results with a simulation example in which we employ receding horizon control to design an investment strategy to repay a debt.     

Operations Research and public policy for Africa: harnessing the revolution in management science instruction

Operations Research (OR) has made major contributions in the developed world to public policy domains that are of great relevance to Africa. Inasmuch as OR has failed to live up to its potential for addressing such issues in Africa, a principal barrier may have been distance between OR analysts and decision makers. However, the revolution in management science instruction and potential to train end‐user modelers has democratized OR. This makes training for policy makers and managers in the public and non‐profit sectors in Africa both feasible and highly beneficial. Existing management science courses for public and non‐profit leaders, such as those taught at Carnegie Mellon's Heinz School, could be adapted to fit the needs of educators and policy makers in Africa and disseminated via a “train the trainers” approach. A plan is sketched whereby 800,000 end‐user modelers might be trained in Africa (one for every 1000 people) at an annual cost of about $5 million/year. Such budgets are well within the range of investments in human capital formation currently being made in Africa.     

Approaches for solving the stochastic equilibrium assignment with variable demand: internal vs. external solution algorithms

This paper proposes and compares different approaches within the general fixed-point framework that allows to deal with multi-user (stochastic) equilibrium assignment with variable demand (VD). The aim was threefold: (i) compare the efficiency and the effectiveness of the internal and the external approaches to stochastic equilibrium assignment with VD; (ii) investigate the efficiency and the effectiveness of different algorithms based on the method of successive averages and its extensions; (iii) investigate the effects of different averaging schemes, different convergence criteria and different path choice models, such as Multinomial Logit model, C-Logit model and Multinomial Probit model. Analyses were carried out with respect to a real network and considering different indicators of both efficiency and effectiveness.     

滇池流域可持续发展动态投入产出最优控制模型

根据包含了污染排放及治理、水资源使用等数据的昆明市环境保护投入产出表,建立了一个最优控制模型,该模型可用来求取滇池流域经济的最优发展轨迹及污染的最优治理水平.本研究有助于制订“十五”期间滇池流域可持续发展规划.     

基于因果建模的强化学习控制: 现状及展望

基于因果建模的强化学习技术在智能控制领域越来越受欢迎. 因果技术可以挖掘控制系统中的结构性因果知识, 并提供了一个可解释的框架, 允许人为对系统进行干预并对反馈进行分析. 量化干预的效果使智能体能够在复杂的情况下 (例如存在混杂因子或非平稳环境) 评估策略的性能, 提升算法的泛化性. 本文旨在探讨基于因果建模的强化学习控制技术 (以下简称因果强化学习) 的最新进展, 阐明其与控制系统各个模块的联系. 首先介绍了强化学习的基本概念和经典算法, 并讨论强化学习算法在变量因果关系解释和迁移场景下策略泛化性方面存在的缺陷. 其次, 回顾了因果理论的研究方向, 主要包括因果效应估计和因果关系发现, 这些内容为解决强化学习的缺陷提供了可行方案. 接下来, 阐释了如何利用因果理论改善强化学习系统的控制与决策, 总结了因果强化学习的四类研究方向及进展, 并整理了实际应用场景. 最后, 对全文进行总结, 指出了因果强化学习的缺点和待解决问题, 并展望了未来的研究方向.     

System dynamics modelling for supply-chain management: A case study on a supermarket chain in the UK

This paper presents a system dynamics (SD) approach for the analysis of the demand amplification problem, also known as the bullwhip effect, which has been studied fairly extensively in the literature. The construction of an SD model is reported using a part of a supermarket chain system in the UK as an example. Based on the model, the causes of the dynamic behaviour of the system and the sources of amplification from the downstream to the upstream of the chain are investigated. The impact of information delays, demand forecasting and information sharing on the performance of the multi‐echelon supply chain is analysed. Some implementation issues are also addressed based on the simulation analysis.     

The H2-control for jump linear systems: cluster observations of the Markov state

The H₂-norm control problem of discrete-time Markov jump linear systems is addressed in this paper when part of, or the total of the Markov states is not accessible to the controller. The non-observed part of the Markov states is grouped in a number of clusters of observations; the case with a single cluster retrieves the situation when no Markov state is observed. The control action is provided in linear feedback form, which is invariant on each cluster, and this restricted complexity setting is adopted, aiming at computable solutions. We explore a recent result by de Oliveira, Bernussou, and Geromel (Systems Control Lett. 37 (1999) 261) involving an LMI characterization to establish a H₂ solution that is stabilizing in the mean square sense. The novelty of the method is that it can handle in LMI form the situation ranging from no Markov state observation to complete state observation. In addition, when the state observation is complete, the optimal H₂-norm solution is retrieved.     

The Boltzmann–Hamel equations for the optimal control of mechanical systems with nonholonomic constraints

In this paper, we generalize the Boltzmann–Hamel equations for nonholonomic mechanics to a form suited for the kinematic or dynamic optimal control of mechanical systems subject to nonholonomic constraints. In solving these equations one is able to eliminate the controls and compute the optimal trajectory from a set of coupled first‐order differential equations with boundary values. By using an appropriate choice of quasi‐velocities, one is able to reduce the required number of differential equations by m and 3m for the kinematic and dynamic optimal control problems, respectively, where m is the number of nonholonomic constraints. In particular we derive a set of differential equations that yields the optimal reorientation path of a free rigid body. In the special case of a sphere, we show that the optimal trajectory coincides with the cubic splines on SO(3). Copyright © 2010 John Wiley & Sons, Ltd.     

The Use of the Ritz Method and Laplace Transform for Solving 2D Fractional‐Order Optimal Control Problems Described by the Roesser Model

In this article a numerical solution is presented for a class of two‐dimensional fractional‐order optimal control problems (2D‐FOOCPs) with one input and two outputs. To implement the numerical method, the Legendre polynomial basis is used with the aid of the Ritz method and the Laplace transform. By taking the Ritz method as a basic scheme into account and applying a new constructed fractional operational matrix to estimate the fractional and integer order derivatives of the basis, the given 2D‐FOOCP is reduced to a system of algebraic equations. One of the advantages of the proposed method is that it provides greater flexibility in which the given initial and boundary conditions of the problem are imposed. Moreover, satisfactory results are obtained in just a small number of polynomials order. The convergence of the method is extensively investigated and finally two illustrative examples are included to show the validity and applicability of the novel proposed technique in the current work.     

The importance of the CobiT framework IT processes for effective internal control over financial reporting in organizations: An international survey

This paper presents the results of an international survey of IT professionals exploring the relationships between CobiT's IT processes and financial reporting. Our respondents rated the importance of each of CobiT's 34 processes from the viewpoint of effective internal control over financial reporting. Results revealed five processes that were deemed specially critical. We also find interesting patterns of results as a function of respondents’ employment type and geographic location. This survey of IT professionals shed light on the relevance of a widely used IT governance framework—CobiT—from the perspective of organizations’ internal controls.