• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.183-199
• /
• 2007

In this paper we research the problem in which the objective is to minimize the sum of squared deviations of job expected completion times from the due date, and the job processing times are stochastic. In the problem the machine is subject to stochastic breakdowns and all jobs are preempt-repeat. In order to show that the replacing ESSD by SSDE is reasonable, we discuss difference between ESSD function and SSDE function. We first give an express of the expected completion times for both cases without resampling and with resampling. Then we show that the optimal sequence of the problem V-shaped with respect to expected occupying time. A dynamic programming algorithm based on the V-shape property of the optimal sequence is suggested. The time complexity of the algorithm is pseudopolynomial.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.39 no.1
• /
• pp.113-127
• /
• 2014

The stochastic dominance approach is to form a portfolio that stochastically dominates a predetermined benchmark portfolio such as KOSPI. This study is to search a set of portfolio weights for the first-order stochastic dominance with maximum utility defined in terms of mean and variance by managing the constraint set and the objective function in an iterative manner. A nonlinear programming algorithm was developed and tested with promising results against Korean stock market data sets.

• IE interfaces
• /
• v.10 no.3
• /
• pp.179-187
• /
• 1997

The efficiency of material flow systems in terms of optimal network flow and minimum cost flow has always been an important design and operational goal in material handling and distribution system. In this research, an attempt was made to develop a new algorithm and the model to solve a stochastic material flow network with bidirectional and uncertain flows. A stochastic material flow network with bidirectional flows can be considered from a finite set with unknown demand probabilities of each node. This problem can be formulated as a special case of a two-stage linear programming problem which can be converted into an equivalent linear program. To find the optimal solution of proposed stochastic material flow network, some terminologies and algorithms together with theories are developed based on the partitioning and subgradient techniques. A computer program applying the proposed method was developed and was applied to various problems.

• Smart Structures and Systems
• /
• v.9 no.3
• /
• pp.231-251
• /
• 2012

The stochastic optimal control for a piezoelectric spherically symmetric shell subjected to stochastic boundary perturbations is constructed, analyzed and evaluated. The stochastic optimal control problem on the boundary stress output reduction of the piezoelectric shell subjected to stochastic boundary displacement perturbations is presented. The electric potential integral as a function of displacement is obtained to convert the differential equations for the piezoelectric shell with electrical and mechanical coupling into the equation only for displacement. The displacement transformation is constructed to convert the stochastic boundary conditions into homogeneous ones, and the transformed displacement is expanded in space to convert further the partial differential equation for displacement into ordinary differential equations by using the Galerkin method. Then the stochastic optimal control problem of the piezoelectric shell in partial differential equations is transformed into that of the multi-degree-of-freedom system. The optimal control law for electric potential is determined according to the stochastic dynamical programming principle. The frequency-response function matrix, power spectral density matrix and correlation function matrix of the controlled system response are derived based on the theory of random vibration. The expressions of mean-square stress, displacement and electric potential of the controlled piezoelectric shell are finally obtained to evaluate the control effectiveness. Numerical results are given to illustrate the high relative reduction in the root-mean-square boundary stress of the piezoelectric shell subjected to stochastic boundary displacement perturbations by the optimal electric potential control.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10b
• /
• pp.155-159
• /
• 1993

In this paper, we consider the problem of a stochastic optimal switching control, which can be applied to the control of a system with uncertain demand such as a control problem of a power plant. The dynamic programming method is applied for the formulation of the optimal control problem. We solve the system of Quasi-Variational Inequalities(QVI) using an algoritlim which involves the finite difference approximation and contraction mapping method. A mathematical example of the optimal switching control is constructed. The actual performance of the algorithm is also tested through the solution of the constructed example.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.22 no.1
• /
• pp.1-24
• /
• 1997

In this paper, we have proposed new solution methods to solve TSLP (two-stage stochastic linear programming) problems. One solution method is to combine the analytic center concept with Benders' decomposition strategy to solve TSLP problems. Another method is to apply an idea proposed by Geoffrion and Graves to modify the L-shaped algorithm and the analytic center algorithm. We have compared the numerical performance of the proposed algorithms to that of the existing algorithm, the L-shaped algorithm. To effectively compare those algorithms, we have had computational experiments for seven test problems.

• Journal of Korea Water Resources Association
• /
• v.31 no.4
• /
• pp.407-413
• /
• 1998

This study reviewed the recent studies for the climate change impact on water resource systems and applied one of the techniques to a real reservoir system - the Skagit hydropower system in U.S.A. The technique assumed that the climate change results in ±5% change in monthly average and/or standard deviation of the observed inflows for the Skagit system. For each case of the altered average and standard deviation, an optimal operating policy was derived using s SDP(Stochastic Dynamic Programming) model and compared with the operating policy for the non-climate change case. The results showed that the oparating policy of the Skagit system is more sensitive to the change in the streamflow average than that in the streamflow standard deviation. The derived operating policies were also simulated using the synthetic streamflow scenarios and their average annual gains were compared as a performance index. To choose the best operating policy among the derived policies, a Bayesian decision strategy was also presented with an example. Keywords : climate change, reservoir operating policy, stochastic dynamic programming, Bayesian decision theory.

• Journal of Korea Society of Industrial Information Systems
• /
• v.28 no.1
• /
• pp.27-34
• /
• 2023

The optimal assignment problem between agents and tasks is known as one of the representative problems of combinatorial optimization and an NP-hard problem. This paper covers multi agent-multi task assignment problems with uncertain completion probability. The completion probabilities are generally uncertain due to endogenous (agent or task) or exogenous factors in the system. Assignment decisions without considering uncertainty can be ineffective in a real situation that has volatility. To consider uncertain completion probability mathematically, a mathematical formulation with stochastic programming is illustrated. We also present an algorithm by using the sample average approximation method to solve the problem efficiently. The algorithm can obtain an assignment decision and the upper and lower bounds of the assignment problem. Through numerical experiments, we present the optimality gap and the variance of the gap to confirm the performances of the results. This shows the excellence and robustness of the assignment decisions obtained by the algorithm in the problem with uncertainty.

• Journal of Korea Water Resources Association
• /
• v.37 no.5
• /
• pp.353-361
• /
• 2004

Effective storage in agricultural reservoir has been determined through the reservoir simulation operation based on the water budget analysis. Since each watershed has the native property for runoff, considering the runoff yielding from the basin is feasible to the determination of reservoir effective storage. In this study the stochastic linear programming model considering mainly runoff from watershed has been also formulated to analyze the effective storage of the exiting reservoir. The linear decision rule coupled with chance-constrained model in the linear programming model contributes to reduce the size of linear program model without considering the period of analysis. The Geum-Gang reservoir located in Ansung have been adopted to evaluate the effective storage. It has been shown that the effective storage based on the linear programming model is greater than that based on the water budget analysis. It has been also desired that once the effective storage is obtained through the linear programming model, operation of the reservoir should be performed to check the designed capacity.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1996.04a
• /
• pp.525-529
• /
• 1996

Decision environments involve a high degree of uncertainty as well as multiple, conflicting goals. Although traditional goal programming offers a means of considering multiple, conflicting goals and arrives at a satisficing solution in a deterministic manner, its major drawback is that decision makers often specify aspiration level of each goal as a single number. To overcome the problem of setting aspiration levels, chance constrained programming can be incorporated into goal programming formulation so that sampling information can be utilized to describe uncertainty distribution. Another drawback of goal programming is that it does not provide a systematic approach to set priorities and trade-offs among conflicting goals. To overcome this weekness, the analytic hierarchy process(AHP) is used in the model. Also, most goal programming models in the literature are of a linear form, although some nonlinear models have been presented. Consideration of risk in technological coefficients and right hand sides, however, leads to nonlinear goal programming models, which require a linear approximation to be solved. In this paper, chance constrained reformulation with linear approximation is presented for a 0-1 goal programming problem whose technological coefficients and right hand sides are stochastic. The model is presented with a numerical example for the purpose of demonstration.