Optimal risk probability for first passage models in semi-Markov decision processes

This paper studies the risk minimization problem in semi-Markov decision processes with denumerable states. The criterion to be optimized is the risk probability (or risk function) that a first passage time to some target set doesn't exceed a threshold value. We first characterize such risk functions and the corresponding optimal value function, and prove that the optimal value function satisfies the optimality equation by using a successive approximation technique. Then, we present some properties of optimal policies, and further give conditions for the existence of optimal policies. In addition, a value iteration algorithm and a policy improvement method for obtaining respectively the optimal value function and optimal policies are developed. Finally, two examples are given to illustrate the value iteration procedure and essential characterization of the risk function.     

The randomized threshold for the discrete-time Geo/G/1 queue

This paper discusses a discrete-time Geo/G/1 queue, in which the server operates a random threshold policy, namely 〈p, N〉 policy, at the end of each service period. After all the messages are served in the queue exhaustively, the server is immediately deactivated until N messages are accumulated in the queue. If the number of messages in the queue is accumulated to N, the server is activated for services with probability p and deactivated with probability (1 − p). Using the generating functions technique, the system state evolution is analyzed. The generating functions of the system size distributions in various states are obtained. Some system characteristics of interest are derived. The long-run average cost function per unit time is analytically developed to determine the joint optimal values of p and N at a minimum cost.     

An analytical study of the modification ability of distribution centers

This paper considers a two-level vendor managed inventory (VMI) system comprising a distribution center (DC) and a retailer. Both the DC’s and the retailer’s replenishment decisions follow the order-up-to-level policy and aim at maximizing the profit of the overall system. We critically examine the potential of the DC’s ability to modify delivery decisions, identify and quantify the cost factors that influence the DC’s modification ability, establish a relationship between the DC’s location and its modification ability, and show the trade-off between the DC’s modification ability and related costs. Our analysis provides a new insight into the role of the DC and reveals the full potential of the VMI system. Our findings and their practical implications, demonstrated with the aid of computational examples, are helpful for enhancing the practice of VMI at both strategic and operational levels.     

Optimal policy for a dynamic,non-stationary,stochastic inventory problem with capacity commitment

This paper studies a single-product, dynamic, non-stationary, stochastic inventory problem with capacity commitment, in which a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer’s total cumulative order quantity over the planning horizon is constrained with the capacity. The objective of the buyer is to choose the capacity at the beginning of the planning horizon and the order quantity in each period to minimize the expected total cost over the planning horizon. We characterize the structure of the minimum sum of the expected ordering, storage and shortage costs in a period and thereafter and the optimal ordering policy for a given capacity. Based on the structure, we identify conditions under which a myopic ordering policy is optimal and derive an equation for the optimal capacity commitment. We then use the optimal capacity and the myopic ordering policy to evaluate the effect of the various parameters on the minimum expected total cost over the planning horizon.     

不透明销售的顾客退货政策选择

本文探讨从事不透明销售的零售商对顾客退货政策的选择问题。分别针对零售商垄断和竞争两种市场情况,建立不透明零售商与其它供应链成员(制造商或普通零售商)之间的博弈模型,获得唯一均衡解;对均衡结果进行结构化分析,给出不透明销售方式下采用全额退款政策的判别条件;针对均衡结果,分析零售商垄断情况下产品不透明参数的最优设计,以及零售商竞争情况下的市场分化情况;鉴于净残值参数在退货政策选择中的决定性作用,本文进一步探讨了净残值为正时全额退款政策对各参与方利润及产品需求和价格的影响,分析了净残值在其中的作用机理。本研究能够为不透明零售商制定退货政策和价格以及其它供应链成员制定相关决策提供支持。     

On the Hamiltonicity Gap and doubly stochastic matrices

We consider the Hamiltonian cycle problem embedded in singularly perturbed (controlled) Markov chains. We also consider a functional on the space of stationary policies of the process that consists of the (1,1)‐entry of the fundamental matrices of the Markov chains induced by these policies. We focus on the subset of these policies that induce doubly stochastic probability transition matrices which we refer to as the “doubly stochastic policies.” We show that when the perturbation parameter, ε, is sufficiently small, the minimum of this functional over the space of the doubly stochastic policies is attained at a Hamiltonian cycle, provided that the graph is Hamiltonian. We also show that when the graph is non‐Hamiltonian, the above minimum is strictly greater than that in a Hamiltonian case. We call the size of this difference the “Hamiltonicity Gap” and derive a conservative lower bound for this gap. Our results imply that the Hamiltonian cycle problem is equivalent to the problem of minimizing the variance of the first hitting time of the home node, over doubly stochastic policies. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

Cooperation between scientists and the government in the US: benefits and problems

This paper discusses the importance of maintaining close working relations between scientists and their government. Several examples of this cooperation in the U.S. are presented to illustrate the benefits, as well as problems, that result from such cooperation, or lack thereof. These examples include government support of scientific research, as well as contributions by science to help governments understand both the possibilities and the limitations of science as they formulate national policy.     

Sensitivity analysis of the moments of the profit on an Income Protection Policy

The main purpose of this paper is to perform a sensitivity analysis where we quantify and analyse the effects on the mean of the profit on an Income Protection policy and two risk measures of changing the values of the transition intensities. All the calculations carried out are based on a multiple state model for Income Protection proposed in Continuous Mortality Investigation Committee (Continuous Mortality Investigation Reports 1991; 12 ). Within this model, we derive a formula for the mean of the profit, which enables to evaluate it more efficiently. In order to calculate the two risk measures we use the numerical algorithms for the calculation of the moments of the profit proposed by Waters (Insurance: Mathematics and Economics 1990; 9 :101–113). We carry out the sensitivity analysis considering two different situations: in the first situation, we update the premium rates used to calculate the moments of the profit, according to the changes in the values of the transition intensities; in the second one, we do not update the premium rates. Both analyses are of practical interest to insurance companies selling Income Protection policies. Copyright © 2009 John Wiley & Sons, Ltd.     

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.