Minimum-Time Travel for a Vehicle with Acceleration Limits: Theoretical Analysis and Receding-Horizon Implementation

A methodology is proposed to generate minimum-time optimal velocity profiles for a vehicle with prescribed acceleration limits along a specified path. The necessary optimality conditions are explicitly derived, allowing the construction of the optimal solution semianalytically. A receding horizon implementation is also proposed for the on-line implementation of the velocity optimizer. Robustness of the receding horizon algorithm is guaranteed by the use of an adaptive scheme that determines the planning and execution horizons. Application to a real-life scenario with a comparison between the infinite and finite receding horizon schemes provides a validation of the proposed methodology. This work has been supported in part by the US Army Research Office, Awards DAAD19-00-1-0473 and W911NF-05-1-0331. The authors thank an anonymous reviewer for his insightful comments regarding the results in Sect. 5.     

Infinite horizon stopping problems with (nearly) total reward criteria

We study an infinite horizon optimal stopping Markov problem which is either undiscounted (total reward) or with a general Markovian discount rate. Using ergodic properties of the underlying Markov process, we establish the feasibility of the stopping problem and prove the existence of optimal and ε$\epsilon$-optimal stopping times. We show the continuity of the value function and its variational characterisation (in the viscosity sense) under different sets of assumptions satisfied by large classes of diffusion and jump–diffusion processes. In the case of a general discounted problem we relax a classical assumption that the discount rate is uniformly separated from zero.     

多货栈及变质情形下两种可替代物品的经济订货批量模型

研究了多货栈及变质情形下两种可替代物品的经济订货批量问题.在计划期内,若某一种易变质物品发生缺货,则可以被另一种易变质物品以一定的替代率代替补充,不同物品有不同的变质率,且要决定租用货栈的数量.以库存系统的总费用最小为目标函数,分别对货栈容量无限与有限的情形建立模型,证明了最优策略存在的唯一性,并分别给出了求解最优订购策略的算法,最后通过一个算例验证了算法的最优性.     

从接受理论看《红楼梦》英译文中的创造性叛逆现象

中国四大名著之一《红楼梦》在国内外都享有盛名,许多学者都曾经对这部小说进行过翻译,其中最具有代表性的两种译本:一个是杨宪益夫妇的译本,另一个是霍克斯的译本。本文将从接受理论的角度去分析,比较这两种译本当中的一些创造性叛逆现象。     

Two storage inventory model with fuzzy deterioration over a random planning horizon

An inventory model for a deteriorating item with stock dependent demand is developed under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. For crisp deterioration rate, the expected profit is derived and maximized via genetic algorithm (GA). On the other hand, when deterioration rate is imprecise then optimistic/pessimistic equivalent of fuzzy objective function is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to maximize the optimistic/pessimistic return and finally fuzzy simulation-based GA is developed to solve the model. The models are illustrated with some numerical data. Sensitivity analyses on expected profit function with respect to distribution parameter λ and confidence levels α₁ and α₂ are also presented.     

On the computation of the optimal cost function for discrete time Markov models with partial observations

We consider several applications of two state, finite action, infinite horizon, discrete-time Markov decision processes with partial observations, for two special cases of observation quality, and show that in each of these cases the optimal cost function is piecewise linear. This in turn allows us to obtain either explicit formulas or simplified algorithms to compute the optimal cost function and the associated optimal control policy. Several examples are presented.Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-86-0029, in part by the National Science Foundation under Grant ECS-8617860, in part by the Advanced Technology Program of the State of Texas, and in part by the DoD Joint Services Electronics Program through the Air Force Office of Scientific Research (AFSC) Contract F49620-86-C-0045.     

The membrane picture of Hawking radiation

The effect of a black hole on the classical physics of exterior electromagnetic fields can be expressed by replacing the black hole by a conducting membrane. We show that when we introduce quantum mechanics the currents in this membrane must also satisfy a quantum Langevin equation and that this, together with the nonzero transmission coefficient for the potential barrier around the hole in the membrane picture, gives rise to the Hawking radiation.     

Contractivity of Bellman operator in risk averse dynamic programming with infinite horizon

The paper deals with a risk averse dynamic programming problem with infinite horizon. First, the required assumptions are formulated to have the problem well defined. Then the Bellman equation is derived, which may be also seen as a standalone reinforcement learning problem. The fact that the Bellman operator is contraction is proved, guaranteeing convergence of various solution algorithms used for dynamic programming as well as reinforcement learning problems, which we demonstrate on the value iteration and the policy iteration algorithms.     

Price-sensitive demand for perishable items - an EOQ model

This paper develops a finite time-horizon deterministic EOQ (Economic Order Quantity) model where the rate of demand decreases quadratically with selling price. Prices at different periods are considered as decision variables. The objective is to find the optimal ordering quantity and optimal sales prices that maximizes the vendor’s total profit. The results are discussed with numerical examples. Sensitivity analysis of the optimal solution with respect to the key parameters of the system is carried out.