机器负荷的优化分配

本文将动态规划方法应用于机器负荷分配问题并给出计算公式。     

具有学习和退化效应的单机干扰管理问题

针对工件同时具有学习和退化效应、机器具有可用性限制这一问题,建立可预见性单机干扰管理模型。在这一模型中,工件的加工时间是既与工件所排的加工位置又与工件开始加工的时间有关的函数。同时,在生产过程中由于机器发生故障或定期维修等扰动事件导致机器在某段时间内不能加工工件。目标是在同时考虑原目标函数和由扰动造成的偏离函数的情况下,构建一个新的最优时间表序列。根据干扰度量函数的不同研究了两个问题,第一个问题的目标函数是极小化总完工时间与总误工时间的加权和;第二个问题的目标函数是极小化总完工时间与总提前时间的加权和。对于所研究的问题,首先证明了最优排序具有的性质,然后建立了相应的拟多项式时间动态规划算法。     

基于退化效应的两台机器流水作业可拒绝排序

考虑了工件具有退化效应的两台机器流水作业可拒绝排序问题,其中工件的加工时间是其开工时间的简单线性增加函数.每个工件或者被接收,依次在两台流水作业机器上被加工,或者被拒绝但需要支付一个确定的费用.考虑的目标是被接收工件的最大完工时间加上被拒绝工件的总拒绝费用之和.证明了问题是NP-难的,并提出了一个动态规划算法.最后对一种特殊情况设计了多项式时间最优算法.     

转包且具有不同费用时间段的排序问题

本文研究制造商可以将工件转包给承包商加工的排序模型,承包商仅有一台机器,转包费用由分配给转包工件的不同时间段费用确定.本文分别研究制造商有一台单机及两台自由作业机器环境情形,需要确定被转包工件集及全部工件的加工顺序,使得工件最大完工时间与转包费用和最小.本文利用归约方法对制造商每个机器环境,证明问题NP困难性,并提出动态规划算法.     

转包且具有不同费用时间段的排序问题（英文）

本文研究制造商可以将工件转包给承包商加工的排序模型,承包商仅有一台机器,转包费用由分配给转包工件的不同时间段费用确定.本文分别研究制造商有一台单机及两台自由作业机器环境情形,需要确定被转包工件集及全部工件的加工顺序,使得工件最大完工时间与转包费用和最小.本文利用归约方法对制造商每个机器环境,证明问题NP困难性,并提出动态规划算法.     

带可分配工期的总误工问题的应急管理

本文考虑了单机排序中带可分配工期的总误工问题的应急管理问题.针对不同情况建立不同的模型,利用交换和动态规划的方法,得到了每个模型的最优解或近似解.     

基于Benders分解算法的反恐应急设施选址-定容-分配问题

反恐应急设施的合理布局和资源配置可缩短救援到达时间并提高应急效率。对已有反恐应急设施选址研究拓展，进一步考虑设施容量有限的情形，并将袭击前后关于应急设施的选址、定容和救援物资分配问题进行集成考虑。将该问题构造为三层规划模型，上中下各层规划分别对应袭击前的选址定容问题、袭击时的袭击点选择问题和袭击后的救援物资分配问题。利用下层规划的对偶变换转化为双层规划，并设计Benders分解算法求解。最后，结合南疆交通网络进行仿真分析，验证了模型和算法的有效性。     

一类复杂约束下的并行机重调度问题研究

研究一类从实际指挥和保障系统提炼的考虑机器多发故障、且具有工件释放时间、机器可用时间、以及机器适用限制等约束的并行同速机重调度问题.首先,建立同时考虑效率、安全和稳定性的混合整数规划重调度模型,该模型利用最大完工时间和总完工时间来度量效率,用重调度前后分配不同机器的工件总数来度量安全性和稳定性;其次,考虑到该问题的NP-hard性和实际调度对机器故障快速响应的要求,提出基于优先规则和右移重调度策略混合的重调度算法框架;最后,将所提重调度算法框架应用于实际案例,分析比较不同优先规则和右移重调度策略组合的求解效果.结果表明,与工件释放时间相关的优先准则与右移重调度策略结合具有较好的优化效果.值得一提的是,文章首次研究具有多重约束的并行机重调度问题(Pm|r_j,a_j,M_j,brkdwn|C_(max),TC,ND).     

自由作业环境下的供应链排序

本文研究了一类集成工件加工和发送的供应链排序模型.利用排序理论和动态规划方法,获得了两机器情形下的供应链排序问题的多项式时间近似算法,并证明算法的性能比为2.     

具有机器故障的单机随机JIT排序问题

对中断－继续和中断－重复两种模型研究具有机器故障的单机随机JIT排序问题, 目标函数是期望完工时间 与工期方差和. 对中断－继续模型证明SSDE问题的最优排序具有关于期望加工时间的V-形性质, 并给出了一个拟多项式 的动态规划算法. 同时对SSDE问题和ESSD问题 进行了比较, 证明了SSDE问题的最优解是一个非常好的ESSD问题的近似最优解. 在一定的条件下, SSDE问题 的最优解就是ESSD问题的最优解. 对中断－重复模型, 由于完工时间的方差无法求出, JIT排序问题至今没得到解决, 故从实际 应用角度用SSDE问题替代ESSD问题, 证明了SSDE问题最优解具有关于期望占用机器时间的V-形性质, 并给出了 一个拟多项式的动态规划算法, 提出了一个研究JIT问题的中断－重复模型的新思路.     

CIR利率模型中基于对数效用的投资组合最优化问题

本文研究了CIR 利率模型中基于对数效用的最优长期投资问题和无限时间域上的最优折算消费问题. 通过求解相关的动态规划方程, 获得了这两个最优化问题的最优策略及值函数的明确表现形式.     

Merton problem in a discrete market with frictions

We study the classical optimal investment and consumption problem of Merton in a discrete time model with frictions. Market friction causes the investor to lose wealth due to trading. This loss is modeled through a nonlinear penalty function of the portfolio adjustment. The classical transaction cost and the liquidity models are included in this abstract formulation. The investor maximizes her utility derived from consumption and the final portfolio position. The utility is modeled as the expected value of the discounted sum of the utilities from each step. At the final time, the stock positions are liquidated and a utility is obtained from the resulting cash value. The controls are the investment and the consumption decisions at each time. The utility function is maximized over all controls that keep the after liquidation value of the portfolio non-negative. A dynamic programming principle is proved and the value function is characterized as its unique solution with appropriate initial data. Optimal investment and consumption strategies are constructed as well.     

基于动态VaR约束与随机波动率模型的最优投资策略

研究Stein-Stein随机波动率模型下带动态VaR约束的最优投资组合选择问题. 假设投资者的目标是最大化终端财富的期望幂效用,可投资于无风险资产和一种风险资产, 风险资产的价格过程由Stein-Stein随机波动率模型刻画. 同时, 投资者期望能在投资过程中利用动态VaR约束控制所面对的风险.运用Bellman动态规划方法和Lagrange乘子法, 得到了该约束问题最优策略的解析式及特殊情形下最优值函数的解析式; 并通过理论分析和数值算例, 阐述了动态VaR约束与随机波动率对最优投资策略的影响.     

Portfolio selection in discrete time with transaction costs and power utility function: a perturbation analysis

In this article, we study a multi-period portfolio selection model in which a generic class of probability distributions is assumed for the returns of the risky asset. An investor with a power utility function rebalances a portfolio comprising a risk-free and risky asset at the beginning of each time period in order to maximize expected utility of terminal wealth. Trading the risky asset incurs a cost that is proportional to the value of the transaction. At each time period, the optimal investment strategy involves buying or selling the risky asset to reach the boundaries of a certain no-transaction region. In the limit of small transaction costs, dynamic programming and perturbation analysis are applied to obtain explicit approximations to the optimal boundaries and optimal value function of the portfolio at each stage of a multi-period investment process of any length.     

Utility maximization in an illiquid market

We consider a stochastic optimization problem of maximizing the expected utility from terminal wealth in an illiquid market. A discrete time model is constructed with few additional state variables. The dynamic programming approach is then developed and used for numerical studies. No-arbitrage conditions were also discussed.     

Portfolio optimization in a Lévy market with intertemporal substitution and transaction costs

We investigate an infinite horizon investment-consumption model in which a single agent consumes and distributes her wealth between a risk-free asset (bank account) and several risky assets (stocks) whose prices are governed by Lévy (jump-diffusion) processes. We suppose that transactions between the assets incur a transaction cost proportional to the size of the transaction. The problem is to maximize the total utility of consumption under Hindy-Huang-Kreps intertemporal preferences. This portfolio optimisation problem is formulated as a singular stochastic control problem and is solved using dynamic programming and the theory of viscosity solutions. The associated dynamic programming equation is a second order degenerate elliptic integro-differential variational inequality subject to a state constraint boundary condition. The main result is a characterization of the value function as the unique constrained viscosity solution of the dynamic programming equation. Emphasis is put on providing a framework that allows for a general class of Lévy processes. Owing to the complexity of our investment-consumption model, it is not possible to derive closed form solutions for the value function. Hence, the optimal policies cannot be obtained in closed form from the first order conditions for the dynamic programming equation. Therefore, we have to resort to numerical methods for computing the value function as well as the associated optimal policies. In view of the viscosity solution theory, the analysis found in this paper will ensure the convergence of a large class of numerical methods for the investment-consumption model in question.     

Efficient frontier of utility and CVaR

We study the efficient frontier problem of maximizing the expected utility of terminal wealth and minimizing the conditional VaR of the utility loss. We establish the existence of the optimal solution with the convex duality analysis. We find the optimal value of the constrained problem with the sequential penalty function and the dynamic programming method.      

No-arbitrage and optimal investment with possibly non-concave utilities: a measure theoretical approach

We consider a discrete-time financial market model with finite time horizon and investors with utility functions defined on the non-negative half-line. We allow these functions to be random, non-concave and non-smooth. We use a dynamic programming framework together with measurable selection arguments to establish both the characterisation of the no-arbitrage property for such markets and the existence of an optimal portfolio strategy for such investors.     

SOLVING DYNAMIC WILDLIFE RESOURCE OPTIMIZATION PROBLEMS USING REINFORCEMENT LEARNING

ABSTRACT. An important technical component of natural resource management, particularly in an adaptive management context, is optimization. This is used to select the most appropriate management strategy, given a model of the system and all relevant available information. For dynamic resource systems, dynamic programming has been the de facto standard for deriving optimal state‐specific management strategies. Though effective for small‐dimension problems, dynamic programming is incapable of providing solutions to larger problems, even with modern microcomputing technology. Reinforcement learning is an alternative, related procedure for deriving optimal management strategies, based on stochastic approximation. It is an iterative process that improves estimates of the value of state‐specific actions based in interactions with a system, or model thereof. Applications of reinforcement learning in the field of artificial intelligence have illustrated its ability to yield near‐optimal strategies for very complex model systems, highlighting the potential utility of this method for ecological and natural resource management problems, which tend to be of high dimension. I describe the concept of reinforcement learning and its approach of estimating optimal strategies by temporal difference learning. I then illustrate the application of this method using a simple, well‐known case study of Anderson [1975], and compare the reinforcement learning results with those of dynamic programming. Though a globally‐optimal strategy is not discovered, it performs very well relative to the dynamic programming strategy, based on simulated cumulative objective return. I suggest that reinforcement learning be applied to relatively complex problems where an approximate solution to a realistic model is preferable to an exact answer to an oversimplified model.     

On optimal investment in a reinsurance context with a point process market model

We study an insurance model where the risk can be controlled by reinsurance and investment in the financial market. We consider a finite planning horizon where the timing of the events, namely the arrivals of a claim and the change of the price of the underlying asset(s), corresponds to a Poisson point process. The objective is the maximization of the expected total utility and this leads to a nonstandard stochastic control problem with a possibly unbounded number of discrete random time points over the given finite planning horizon. Exploiting the contraction property of an appropriate dynamic programming operator, we obtain a value-iteration type algorithm to compute the optimal value and strategy and derive its speed of convergence. Following Schäl (2004) we consider also the specific case of exponential utility functions whereby negative values of the risk process are penalized, thus combining features of ruin minimization and utility maximization. For this case we are able to derive an explicit solution. Results of numerical computations are also reported.