An adaptive O(log n)‐optimal policy for the online selection of a monotone subsequence from a random sample

Given a sequence of n independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing selections made by such a policy is within of optimal. Our construction provides a direct and natural way for proving the ‐optimality gap. An earlier proof of the same result made crucial use of a key inequality of Bruss and Delbaen [5] and of de‐Poissonization.     

Inventory control with fixed cost and price optimization in continuous time

We continue to study the problem of inventory control, with simultaneous pricing optimization in continuous time. In our previous paper [8], we considered the case without set up cost, and established the optimality of the base stock-list price (BSLP) policy. In this paper we consider the situation of fixed price. We prove that the discrete time optimal strategy (see [11]), i.e., the (s, S, p) policy can be extended to the continuous time case using the framework of quasi-variational inequalities (QVIs) involving the value function. In the process we show that an associated second order, nonlinear two-point boundary value problem for the value function has a unique solution yielding the triplet (s, S, p). For application purposes the explicit knowledge of this solution is needed to specify the optimal inventory and pricing strategy. Se- lecting a particular demand function we are able to formulate and implement a numerical algorithm to obtain good approximations for the optimal strategy.     

Numerical investigation of finite-source multiserver systems with different vacation policies

Systems with vacations are usually modeled and analyzed by queueing theory, and almost all works assume that the customer source is infinite and the arrival process is Poisson. This paper aims to present an approach for modeling and analyzing finite-source multiserver systems with single and multiple vacations of servers or all stations, using the Generalized Stochastic Petri nets model. We show how this high level formalism, allows a simple construction of detailed and compact models for such systems and to obtain easily the underlying Markov chains. However, for real vacation systems, the models may have a huge state space. To overcome this problem, we give the algorithms for automatically computing the infinitesimal generator, for the different vacation policies. In addition, we develop the formulas of the main exact stationary performance indices. Through numerical examples, we discuss the effect of server number, vacation rate and vacation policy on the system’s performances.     

On contracts for VMI program with continuous review (r, Q) policy

Based on continuous review (r, Q) policy, this paper deals with contracts for vendor managed inventory (VMI) program in a system comprising a single vendor and a single retailer. Two business scenarios that are popular in VMI program are “vendor with ownership” and “retailer with ownership”. Taking the system performance in centralized control as benchmark, we define a contract “perfect” if the contract can enable the system to be coordinated and can guarantee the program to be trusted. A revenue sharing contract is designed for vendor with ownership, and a franchising contract is designed for retailer with ownership. Without consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the other one is a perfect contract. With consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the performance of the other one depends on system parameters.     

Swedish employment offices: A new model for evaluating effectiveness

We measure how well Swedish employment offices perform in delivering the services required of them by the Swedish government. In contrast to earlier studies we use a dynamic efficiency framework, which allows us to better model the intertemporal nature of these services, explicitly allowing for placements of intermediate nature across periods. Rather than using second stage analysis to assess the effects of varying local labor market conditions and differences in client characteristics on performance, we include a measure of the office’s expected work load directly in the model. This measure, derived from duration analysis, is designed to capture the variation across offices in resources needed before an average individual can obtain employment. It is estimated from the characteristics of all unemployed individual and local labor market conditions.     

均值-方差准则下的多期最优保险投资(英文)

近年来,最优保险投资问题吸引了越来越多的注意。一般这个问题是在连续时间框架下来研究的。本文针对这一问题建立离散时间的最优控制模型。应用动态规划原理求解模型对应的近似问题,得到了最优投资策略和投资有效边界的解析表达形式。本文得到的最优投资策略和投资有效边界均依赖于承保参数。通过数值例子分析了承保参数对最优投资策略和有效边界的影响。     

报童模型的最优解及其解空间研究

文章从经典报童模型出发,找到了使收益最大化的报童模型最优解及其存在的解空间。在分析最优解存在条件的基础上,研究了单位生产成本和单位缺货惩罚成本对最优解的解空间的影响。在此基础上,进一步分析了如何通过控制单位生产成本和单位缺货惩罚成本,影响最优解存在条件的方法。最后,在该领域其他学者的实际算例的基础上,提出了分别通过调节单位生产成本和单位缺货惩罚成本,以及同时调节单位生产成本和单位缺货惩罚成本,从而影响企业生产决策的三种方法。文章结果可以指导相关学者选择适当的报童模型算例,且实际算例表明该方法在企业管理方面也有较好的效果和应用前景。     

Monotone optimal replacement policies for a Markovian deteriorating system in a controllable environment

We consider the optimal replacement of a periodically inspected system under Markov deterioration that operates in a controlled environment. Provided are sufficient conditions that characterize an optimal control-limit replacement policy with respect to the system’s condition and its environment. The structure of the optimal policy is illustrated by a numerical example.     

Asymptotically optimal dividend policy for regime-switching compound Poisson models

This work develops asymptotically optimal dividend policies to maximize the expected present value of dividends until ruin.Compound Poisson processes with regime switching are used to model the surplus and the switching（a continuous-time controlled Markov chain） represents random environment and other economic conditions.Assuming the switching to be fast varying together with suitable conditions,it is shown that the system has a limit that is an average with respect to the invariant measure of a related Markov chain.Under simple conditions,the optimal policy of the limit dividend strategy is a threshold policy.Using the optimal policy of the limit system as a guide,feedback control for the original surplus is then developed.It is demonstrated that the constructed dividend policy is asymptotically optimal.     

Stochastic impulse control with regime switching for the optimal dividend policy when there are business cycles,taxes and fixed costs

We consider the problem of finding the optimal dividend policy for a company whose cash reserve follows a Brownian motion with drift and volatility modulated by an observable finite-state continuous-time Markov chain. The Markov chain represents the regime of the economy. We allow fixed costs and taxes associated with the dividend payments. This optimization problem generates a stochastic impulse control problem with regime switching. We solve this problem and obtain the first analytical solutions for the optimal dividend policy when there are simultaneously fixed costs, taxes and business cycles. Our results show that the optimal dividend policy depends strongly on the regime of the economy, on fixed costs and on taxes.