• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.889-900
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• 2008

The problem of scheduling n jobs on a single machine is considered when the machine is subject to stochastic breakdowns. The objective is to minimize the weighted squared deviation of job completion times from a common due date. Two versions of the problem are addressed. In the first one the common due date is a given constant, whereas in the second one the common due date is a decision variable. In each case, a general form of deterministic equivalent of the stochastic scheduling problem is obtained when the counting process N(t) related to the machine uptimes is a Poisson process. It is proved that an optimal schedule must be V-shaped in terms of weighted processing time when the agreeable weight condition is satisfied. Based on the V-shape property, two dynamic programming algorithms are proposed to solve both versions of the problem.

• Journal of Advanced Marine Engineering and Technology
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• v.24 no.2
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• pp.90-96
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• 2000

The technology of preventive maintenance and corrective maintenance is widely applied to ships in order to maintain the good voyageable condition. One of the most important fields of marine engineering is to seek the maximum availability and to solve the stochastic maintenance problem such that the cost for corrective maintenance is minimized. Accordingly, for the purpose of making the most suitable maintenance schedule which minimizes the expected cost function, this paper suggests the method to grasp the failure characteristics by the ship's maintenance data that are collected from the past. And, suggests the method to estimate the optimal maintenance interval by using the dynamic programming and the cumulative hazard rate function attained from the maintenance data.

• Journal of Korean Society of Water and Wastewater
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• v.11 no.3
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• pp.87-95
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• 1997

A river water quality management model was made by Dynamic programming. This model optimizes the wastewater treatment cost of the application area, and computed water quality with it must meet the water quality standard. And this model takes into consideration tributary input, wastewater treatment plant effluent, withdrawls for several purposes. Modified Streeter-Phelps equation was used to calculate BOD and DO. Optimization problem was solved with particular exceedance probability flow, and the water quality of each point was calculated with the decided treatment efficiencies. At that time, the probability satisfying the water quality standard of constraints to the exceedance probability of the flow. The developed model was applied to the lower part of the Han-River. The reliability to meet the water quality standard is 70 % when 4 wastewater treatment plants of Seoul City are operated by activated sludge system at autumn of the year 2001. Treatment cost of this case is 121.288 billion won per year.

• Journal of Korea Water Resources Association
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• v.43 no.1
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• pp.67-79
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• 2010

Korea water resources corporation (K-Water) has developed the real-time water resources management system for the Nakdong and the Geum River basin to efficiently operate multi-purpose dams in the basins. This study has extended to the Han River basin for providing an effective ending target storage of a month to the real-time water resources management system using Sampling Stochastic Dynamic Programming (SSDP), consequently increasing the efficiency of the reservoir system. The optimization model were developed for three reservoirs, named Soyang, Chungju, and Hwacheon, with high priority in terms of the amounts of effective capacity and water supply for the basin. The number of storage state variable for each dam to set an optimization problem has been assigned from the results of sensitivity analysis. Compared with the K-water operating policy with the target water supply elevations, the optimization model suggested in this study showed that the shortfalls are decreased by 37.22 MCM/year for the required water demands in the basin, even increasing 171 GWh in hydro electronic power generation. In addition, the result of a reservoir operating system during the drawdown period applied to real situation demonstrates that additional releases for water quality or hydro electronic power generation would be possible during the drawdown period between 2007 and 2008. On the basis of these simulation results, the applicability of the SSDP model and the reservoir operating system is proved. Therefore, the more efficient reservoir operation can be achieved if the reservoir operating system is extended further to other Korean basins.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.2
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• pp.39-60
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• 1995

In this paper, an integration of stochastic dynamic programming (SDP), integer goal programming (IGP) and analytic hierarchy process (AHP) is proposed to handle multiobjective-multicriteria sequential decision making problems under uncertainty inherent in R & D investment planning. SDP has its capability to handle problems which are sequential and stochastic. In the SDP model, the probabilities of the funding levels in any time period are generated using a subjective model which employs functional relationships among interrelated parameters, scenarios of future budget availability and subjective inputs elicited from a group of decision makers. The SDP model primarily yields an optimal investment planning policy considering the possibility that actual funding received may be less than anticipated one and thus the projects being selected under the anticipated budget would be interrupted. IGP is used to handle the multiobjective issues such as tradoff between economic benefit and technology accumulation level. Other managerial concerns related to the determination of the optimal project portifolio within each stage of the SDP model. including project selection, project scheduling and annual budget allocation are also determined by the IGP. AHP is proposed for generating scenario-based transformation probabilities under budgetary uncertainty and for quantifying the environmental risk to be considered.

• Journal of the Korean Institute of Intelligent Systems
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• v.25 no.4
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• pp.319-326
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• 2015

Recently in the fields o f stochastic optimal control ( SOC) and reinforcemnet l earning (RL), there have been a great deal of research efforts for the problem of finding data-based sub-optimal control policies. The conventional theory for finding optimal controllers via the value-function-based dynamic programming was established for solving the stochastic optimal control problems with solid theoretical background. However, they can be successfully applied only to extremely simple cases. Hence, the data-based modern approach, which tries to find sub-optimal solutions utilizing relevant data such as the state-transition and reward signals instead of rigorous mathematical analyses, is particularly attractive to practical applications. In this paper, we consider a couple of methods combining the modern SOC strategies and approximate inference together with machine-learning-based data treatment methods. Also, we apply the resultant methods to a variety of application domains including financial engineering, and observe their performance.

• Journal of the Korean Operations Research and Management Science Society
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• v.30 no.3
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• pp.81-93
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• 2005

This paper models supply chain uncertainties in the dynamic Newsboy Problem context. The system consists of one supplier and one retailer who place an order to the supplier every period. Demand uncertainty is modeled as stochastic period demand, and supply uncertainty as the uncertainty in quantities delivered by the supplier. The supplier delivers exactly the amount ordered by the retailer with probability of $\beta$ and the amount minus K with probability of $(1-\beta)$ We formulate the problem as a dynamic programming problem and derive the first-order optimality condition. Through a numerical study, we measure the extent to which the cost decrease due to the reduction in supply uncertainty depends on the level of demand uncertainty. One of the most important findings In this paper is that this cost decrease is relatively small if demand uncertainty is kept high, and vice versa. We also backup this numerical result by analyzing the distribution of ending Inventory under the supply and demand uncertainties.

• Journal of Korea Water Resources Association
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• v.33 no.5
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• pp.593-601
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• 2000

Analyzing monthly inflows of the Chung-Ju Dam associated with EI Nino Southern Oscillation (ENSO), Kim and Lee(2000) reported that the fall and winter inflows in EI Nino years tended to be low while those in La Nina years tended to be high. This study proposes a methodology of employing such a teleconnection between ENSO and inflow in reservoir operations. The ENSO information is used as a hydrologic state variable in stochastic dynamic programming (SDP) to derive a monthly optimal rule for operating the Chung- Ju Dam. An alternative operating rule is also derived with the SDP with no hydrologic state variable. Both of the SDP operating rules are simulated and compared to examine the value of using the ENSO information in operations of the Chung-Ju Dam. The simulation results show that the operating rule using the ENSO information increases energy generation and reliability of water supply as well as reduces spill. spill.

• Journal of Korea Water Resources Association
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• v.38 no.9 s.158
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• pp.737-746
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• 2005

Optimization is a process that searches an optimal solution to obtain maximum or minimum value of an objective function. Many researchers have focused on effective search algorithms for the optimum but few researches were interested in establishing the objective function. This study compares two approaches for the objective function: one allows a tradeoff among the objectives and the other does not allow a tradeoff by assigning weights for the absolute priority between the objectives. An optimization model using sampling stochastic dynamic programming was applied to these two objective functions and the resulting optimal policies were compared. As a result, the objective function with no tradeoff provides a decision making process that matches practical reservoir operations than that with a tradeoff allowed. Therefore, it is more reasonable to establish the objective function with no a tradeoff among the objectives for multi-purpose dam operation plan in Korea.

• Journal of Digital Convergence
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• v.17 no.9
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• pp.127-133
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• 2019

A callable product is one of service derivatives using options to generate demand and reduce risk. This paper compares two booking admission controls for callable products, the online and the batch admission controls. To this end, the paper computes the optimal booking policy by using the backward dynamic programming and the stochastic optimization method. Intuitively, the provider should outperform under the batch control by utilizing demand information. The contribution of the paper is to show that the two controls are equivalent in terms of the booking strategy and the expected profit, which enables the provider to keep its current control method. The paper develops the closed-form solutions for the three fare classes. The future work is to extend the result to the model with complicated fare structures.