• International Journal of Reliability and Applications
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• v.10 no.1
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• pp.33-42
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• 2009

In most of literatures of age replacement policy, the authors consider the case that a new item starts operating at time zero and is to be replaced by new one at time T. It is, however, often to purchase used items because of the limited budget. In this paper, we consider age replacement policy of a used item whose age is $t_0$. The mathematical formulas of the expected cost rate per unit time are derived for both infinite-horizon case and finite-horizon case. For each case, we show that the optimal replacement age exists and is finite and investigate the effect of the age of the used item.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.15-15
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• 2003

We provide some recent results of approximation algorithms for solving Markov Games and discuss their applications to problems that arise in Computer Science. We consider a receding horizon approach as an approximate solution to two-person zero-sum Markov games with an infinite horizon discounted cost criterion. We present error bounds from the optimal equilibrium value of the game when both players take “correlated” receding horizon policies that are based on exact or approximate solutions of receding finite horizon subgames. Motivated by the worst-case optimal control of queueing systems by Altman, we then analyze error bounds when the minimizer plays the (approximate) receding horizon control and the maximizer plays the worst case policy. We give two heuristic examples of the approximate receding horizon control. We extend “parallel rollout” and “hindsight optimization” into the Markov game setting within the framework of the approximate receding horizon approach and analyze their performances. From the parallel rollout approach, the minimizing player seeks to combine dynamically multiple heuristic policies in a set to improve the performances of all of the heuristic policies simultaneously under the guess that the maximizing player has chosen a fixed worst-case policy. Given $\varepsilon$>0, we give the value of the receding horizon which guarantees that the parallel rollout policy with the horizon played by the minimizer “dominates” any heuristic policy in the set by $\varepsilon$, From the hindsight optimization approach, the minimizing player makes a decision based on his expected optimal hindsight performance over a finite horizon. We finally discuss practical implementations of the receding horizon approaches via simulation and applications.

• International Journal of Reliability and Applications
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• v.12 no.2
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• pp.131-143
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• 2011

In most of literatures of age replacement policy, the authors consider the case that a new item starts operating at time zero and is to be replaced by new one at time T. It is, however, often to purchase used items because of the limited budget. In this paper, we consider age replacement policy of a used item whose age is $t_0$. The mathematical formulas of the expected cost rate per unit time are derived for both infinite-horizon case and finite-horizon case. For each case, we show that the optimal replacement age exists and is finite and investigate the effect of the age of the used item.

• Journal of Communications and Networks
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• v.16 no.3
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• pp.293-300
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• 2014

As energy harvesting communication systems emerge, there is a need for transmission schemes that dynamically adapt to the energy harvesting process. In this paper, after exhibiting a finite-horizon online throughput-maximizing scheduling problem formulation and the structure of its optimal solution within a dynamic programming formulation, a low complexity online scheduling policy is proposed. The policy exploits the existence of thresholds for choosing rate and power levels as a function of stored energy, harvest state and time until the end of the horizon. The policy, which is based on computing an expected threshold, performs close to optimal on a wide range of example energy harvest patterns. Moreover, it achieves higher throughput values for a given delay, than throughput-optimal online policies developed based on infinite-horizon formulations in recent literature. The solution is extended to include ergodic time-varying (fading) channels, and a corresponding low complexity policy is proposed and evaluated for this case as well.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.424-427
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• 1995

In this paper, a control law based on the receding horizon concept which robustly stabilizes time-varying discrete linear systems, is proposed. A dynamic game problem minimizing the worst case performance, is adopted as an optimization problem which should be resolved at every current time. The objective of the proposed control law is to guarantee the closed loop stability and the infinite horizon $H^{\infty}$ norm bound. It is shown that the objective can be achieved by selecting the proper terminal weighting matrices which satisfy the inequality conditions proposed in this paper. An example is included to illustrate the results..

• Journal of Korean Society of Industrial and Systems Engineering
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• v.15 no.26
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• pp.173-179
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• 1992

This paper is concerned with preventive maintenance model for the items whose failures are dependent on their wear level. The previous maintenance models have used time as their decision variable, but it is not appropriate for the case which have wear dependent processes for their failures. In this paper, we consider an operating item which is under periodic review and which is subject to degradation. The scheduled maintenance (overhaul ) is based on the level of item degradation rather time. A functional equation for the total expected cost over an infinite horizon period is formulated and solved.

• Journal of the Korean Operations Research and Management Science Society
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• v.4 no.1
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• pp.25-31
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• 1979

We consider the optimal ordering policy for a single-product two-stage inventory system where the main assumptions are as follows: (i) constant continuous demand only at stage 2, (ii) constant input (production) rate at stage 1, (iii) instantaneous delivery (transportation) from stage 1 to stage 2, (iv) backlogging is allowed only at stage 2, (v) an infinite planning horizon. Costs considered are ordering and linear holding costs at both stages, and linear shortage cost only at stages 2. By solving 9 different case problems, we have observed the general from of the optimal ordering policies for our model which minimizes the total cost per unit time. It is noticeable from this observation that the questionable but more often than not adopted assumption by many authors in determining the optimal potimal policy for multistage inventory systems, that the ordering (lot) sizes at each stage remain constant thruout the planning horizon, is not valid.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1901-1904
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• 2003

MPC or model predictive control is representative of control methods which are able to handle physical constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed only on the input, global aymptotic stability can be obtained; until recently, use of infinite horizons was thought to be inevitable in this case. A globally stabilizing finite-horizon MPC has lately been suggested for neutrally stable continuous-time systems using a non-quadratic terminal cost which consists of cubic as well as quadratic functions of the state. The idea originates from the so-called small gain control, where the global stability is proven using a non-quadratic Lyapunov function. The newly developed finite-horizon MPC employs the same form of Lyapunov function as the terminal cost, thereby leading to global asymptotic stability. A discrete-time version of this finite-horizon MPC is presented here. The proposed MPC algorithm is also coded using an SQP (Sequential Quadratic Programming) algorithm, and simulation results are given to show the effectiveness of the method.