Stochastic regret minimization for revenue management problems with nonstationary demands

We study an admission control model in revenue management with nonstationary and correlated demands over a finite discrete time horizon. The arrival probabilities are updated by current available information, that is, past customer arrivals and some other exogenous information. We develop a regret‐based framework, which measures the difference in revenue between a clairvoyant optimal policy that has access to all realizations of randomness a priori and a given feasible policy which does not have access to this future information. This regret minimization framework better spells out the trade‐offs of each accept/reject decision. We proceed using the lens of approximation algorithms to devise a conceptually simple regret‐parity policy. We show the proposed policy achieves 2‐approximation of the optimal policy in terms of total regret for a two‐class problem, and then extend our results to a multiclass problem with a fairness constraint. Our goal in this article is to make progress toward understanding the marriage between stochastic regret minimization and approximation algorithms in the realm of revenue management and dynamic resource allocation. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 433–448, 2016     

A branch-and-bound algorithm to minimize total flow time with unequal release dates

This article examines the single-machine scheduling problem to minimize total flow time with unequal release dates. This problem has been proven to be NP-hard. We present a necessary and sufficient condition for local optimality which can also be considered as a priority rule. On the basis of this condition, we then define a class of schedules which contains all optimal solutions. We present some efficient heuristic algorithms using the previous condition to build a schedule belonging to this subset. We also prove some new dominance theorems, discuss the results found in the literature for this problem, and propose a branch-and-bound algorithm in which the heuristics are used to provide good upper bounds. We compare this new algorithm with existing algorithms found in the literature. Computational results on problems with up to 100 jobs indicate that the proposed branch-and-bound algorithm is superior to previously published algorithms. © 1992 John Wiley & Sons. Inc.     

有限马氏链最优停止的线性规划解

离散时间的有限状态马尔可夫链最优停止的值函数存在的一个充分条件是所对应的线性规划有解,且其最优解等于值函数,本文证明这个条件还是必要的。     

基于全维PI观测器的混沌系统鲁棒故障检测设计

研究了在干扰存在情况下基于全维PI观测器的混沌系统鲁棒故障检测设计问题。基于一类Sylvester矩阵方程的参数化解,给出了干扰和残差信号解耦的充要条件,并建立了具有鲁棒故障检测功能的全维PI观测器设计的参数化方法。Lorenz混沌系统的数值算例及其计算结果表明：在干扰存在的情况下,基于全维PI观测器的混沌系统鲁棒故障检测设计方法简单有效。     

A cumulative damage shock model with imperfect preventive maintenance

In this article we consider a cumulative damage shock model under a periodic preventive maintenance (PM) policy. The PM is imperfect in the sense that each PM reduces the damage level by 100(1 – b)%, 0 < b < 1. A system suffers damage due to shocks and fails when the damage level exceeds some threshold. We derive a sufficient condition for the time to failure to have an IFR distribution. We also discuss the associated problem of finding the number of PM's that minimizes the expected cost rate.     

Optimal control of continuous-time terminal-value birth-and-death processes and airline overbooking

Consider a continuous-time airline overbooking problem that relates to a single-leg flight and a single service class with a stationary fare. Passengers may cancel their reservations at any time and receive a full refund. Therefore fares can be thought of as being paid at flight time. At that time, the airline bumps passengers in excess of flight capacity and pays a penalty for so doing. The wflight-time revenue, that is, fares received less bumping penalties paid, is quasiconcave in the number of reservations at that time. We model the reservations process as a continuous-time terminal-value birth-and-death process. A more general model than is necessary for an airline reservations system is considered, in which the airline controls both the reservation acceptance (birth) and the cancellation (death) rates. In current practice airlines do not control cancellation rates (though other industries do exercise such control, e.g., hotels) and control reservation acceptance rates by declining reservation requests. The more general model might be applied to other targeting applications, such as steering a vehicle through space toward a target location. For the general model a piecewise-constant booking-limit policy is optimal; that is, at all times the airline accepts reservation requests up to a booking limit if the current number of reservations is less than that booking limit, and declines reservation requests otherwise. When the airline is allowed to decline all reservation requests, as is the case in practice, the booking-limit optimal policy defined by using the greatest optimal booking limit at all times is piecewise constant. Moreover, these booking limits fall toward flight time. © 1996 John Wiley & Sons, Inc.     

一类非线性时滞系统的时滞相关稳定性分析

针对一类非线性时变时滞系统,基于T-S模糊模型,采用自由权矩阵的方法,研究了该系统的稳定性问题。设计了一个与系统状态变量的导数有关的模糊控制器,推导出该控制器使闭环系统渐近稳定的充分条件,该条件等价于一类线性矩阵不等式（LMI）的可解性,并以仿真算例证明了控制器的有效性。     

On efficient algorithms for finding efficient salvo policies

We consider the salvo policy problem, in which there are k moments, called salvos, at which we can fire multiple missiles simultaneously at an incoming object. Each salvo is characterized by a probability p_i: the hit probability of a single missile. After each salvo, we can assess whether the incoming object is still active. If it is, we fire the missiles assigned to the next salvo. In the salvo policy problem, the goal is to assign at most n missiles to salvos in order to minimize the expected number of missiles used. We consider three problem versions. In Gould's version, we have to assign all n missiles to salvos. In the Big Bomb version, a cost of B is incurred when all salvo's are unsuccessful. Finally, we consider the Quota version in which the kill probability should exceed some quota Q. We discuss the computational complexity and the approximability of these problem versions. In particular, we show that Gould's version and the Big Bomb version admit pseudopolynomial time exact algorithms and fully polynomial time approximation schemes. We also present an iterative approximation algorithm for the Quota version, and show that a related problem is NP-complete.     

模糊时滞系统控制器依赖于状态时滞的H∞控制

针对一类非线性时滞系统,研究了该系统基于T—S模糊模型的H∞控制器设计问题。采用线性矩阵不等式LMI的方法,设计一个依赖于状态时滞的模糊控制器,得到了系统存在模糊控制器的充分条件,此充分条件等价于一类线性矩阵不等式的可解性,最后通过仿真说明了控制器的有效性。     

Optimal disposal policies for a single-item inventory system with returns

We consider a single-item inventory system in which the stock level can increase due to items being returned as well as decrease when demands occur. Returned items can be repaired and then used to satisfy future demand, or they can be disposed of. We identify those inventory levels where disposal is the best policy. It is shown that this problem is equivalent to a problem of controlling a single-server queue. When the return and demand processes are both Poisson, we find the optimal policy exactly. When the demand and return processes are more general, we use diffusion approximations to obtain an approximate model, which is then solved. The approximate model requires only mean and variance data. Besides the optimal policy, the output of the models includes such characteristics as the operating costs, the purchase rate for new items, the disposal rate for returned items and the average inventory level. Several numerical examples are given. An interesting by-product of our investigation is an approximation for the steady-state behavior of the bulk GI/G/1 queue with a queue limit.     

多智能体信息一致性在机器人编队控制中的应用

对固定拓扑结构下多智能体有向网络一致性问题进行了研究,提出了一类协调控制器并证明了使多智能体网络在固定拓扑结构下取得全局渐进一致的充要条件,考虑到智能体之间通讯过程中存在的时延问题,给出了最大固定延时时间的紧凑上界,取得了满意效果,最后将信息一致性思想应用于多机器人的编队控制。结果表明,基于信息一致性的方法可成功应用于机器人编队控制。     

分组坐标轮换法与机械优化设计

minimax 问题是工程优化设计中普遍存在的问题。本文首次采用分组坐标轮换法求解该问题,通过分析获得了该算法收敛的充分条件(如果收敛,还可计算最大轮换次数)。一些数值计算验证了文中的结论,本文还把该算法用于四连杆实现函数机构的优化设计.     

When is a base stock policy optimal in recovering disrupted cyclic schedules?

The extended economic lot scheduling problem (EELSP) is concerned with scheduling the production of a set of items in a single facility to minimize the long-run average holding, backlogging, and setup costs. Given an efficient cyclic production schedule for the EELSP, called the target schedule, we consider the problem of how to schedule production after a single schedule disruption. We propose a base stock policy, characterized by a base stock vector, that prescribes producing an item until its inventory level reaches the peak inventory of the target schedule corresponding to the item's position in the production sequence. We show that the base stock policy is always successful in recovering the target schedule. Moreover, the base stock policy recovers the target schedule at minimal excess over average cost whenever the backorder costs are proportional to the processing times. This condition holds, for example, when the value of the items is proportional to their processing times, and a common inventory carrying cost and a common service level is used for all the items. Alternatively, the proportionality condition holds if the inventory manager is willing to select the service levels from a certain set that is large enough to guarantee any minimal level of service, and then uses the imputed values for the backorder costs. When the proportionality condition holds we provide a closed-form expression for the total relevant excess over average cost of recovering the target schedule. We assess the performance of the base stock policy when the proportionality condition does not hold through a numerical study, and suggest some heuristic uses of the base stock policy. © 1994 John Wiley & Sons, Inc.     

Optimal FCFS allocation rules for periodic‐review assemble‐to‐order systems

In Assemble‐To‐Order (ATO) systems, situations may arise in which customer demand must be backlogged due to a shortage of some components, leaving available stock of other components unused. Such unused component stock is called remnant stock. Remnant stock is a consequence of both component ordering decisions and decisions regarding allocation of components to end‐product demand. In this article, we examine periodic‐review ATO systems under linear holding and backlogging costs with a component installation stock policy and a First‐Come‐First‐Served (FCFS) allocation policy. We show that the FCFS allocation policy decouples the problem of optimal component allocation over time into deterministic period‐by‐period optimal component allocation problems. We denote the optimal allocation of components to end‐product demand as multimatching. We solve the multi‐matching problem by an iterative algorithm. In addition, an approximation scheme for the joint replenishment and allocation optimization problem with both upper and lower bounds is proposed. Numerical experiments for base‐stock component replenishment policies show that under optimal base‐stock policies and optimal allocation, remnant stock holding costs must be taken into account. Finally, joint optimization incorporating optimal FCFS component allocation is valuable because it provides a benchmark against which heuristic methods can be compared. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 158–169, 2015     

Note: Remarks on theory of the core

This note proposes a necessary and sufficient condition for the existence of an undominated core and a necessary and sufficient condition for coincidence of the intersection core and the undominated core. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 455–458, 2000     

Allocation policies and cost approximations for multilocation inventory systems

Consider a central depot that supplies several locations experiencing random demands. Periodically, the depot may place an order for exogenous supply. Orders arrive after a fixed leadtime, and are then allocated among the several locations. Each allocation reaches its destination after a further delay. We consider the special case where the penalty-cost/holding-cost ratio is constant over the locations. Several approaches are given to approximate the dynamic program describing the problem. Each approach provides both a near-optimal order policy and an approximation of the optimal cost of the original problem. In addition, simple but effective allocation policies are discussed.     

Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems

We consider the classical problem of whether certain classes of lifetime distributions are preserved under the formation of coherent systems. Under the assumption of independent and identically distributed (i.i.d.) component lifetimes, we consider the NBUE (new better than used in expectation) and NWUE (new worse than used in expectation) classes. First, a necessary condition for a coherent system to preserve the NBUE class is given. Sufficient conditions are then obtained for systems satisfying this necessary condition. The sufficient conditions are satisfied for a collection of systems which includes all parallel systems, but the collection is shown to be strictly larger. We also prove that no coherent system preserves the NWUE class. As byproducts of our study, we obtain the following results for the case of i.i.d. component lifetimes: (a) the DFR (decreasing failure rate) class is preserved by no coherent systems other than series systems, and (b) the IMRL (increasing mean residual life) class is not preserved by any coherent systems. Generalizations to the case of dependent component lifetimes are briefly discussed.     

火炮火控系统命中解的分布和存在性

定义了火控系统中问题联立方程应满足的“基本假设”,从理论上讨论了在“基本假设”条件下诸命中解的分布特性 ,证明临近的命中解 (如果存在的话 )是唯一的 ,给出了临近解存在的充分必要条件。用一个简单的实例表出不同目标速度下诸命中解分布的实验数据     

连续变结构系统单步法数字仿真的步长计算

在研究固定结构的连续变结构控制系统单步法数字仿真问题基础上,提出保证准滑模运动精度的仿真步长选择思想和计算方法,并给出仿真实例.研究表明,文中的方法是正确可行的.     

双正常算子及其性质

讨论Hilbert空间上具有A A与AA可交换的算子类的性质及其刻画,考察这类算子与其它算子类的关系,并给出了一些例子,用以说明有关算子类的包含关系.