• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.91-97
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• 2018

In this paper, we show that there exists an optimal investment policy for the surplus in a risk model, in which the surplus is continuously invested to other business at a constant rate a > 0, whenever the level of the surplus exceeds a given threshold V > 0. We assign, to the risk model, two costs, the penalty per unit time while the level of the surplus being under V > 0 and the opportunity cost per unit time by keeping a unit amount of the surplus. After calculating the long-run average cost per unit time, we show that there exists an optimal investment rate $a^*$>0 which minimizes the long-run average cost per unit time, when the claim amount follows an exponential distribution.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1165-1172
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• 2016

In this paper, a surplus process with investments is introduced. Whenever the level of the surplus reaches a target value V > 0, amount S($0{\leq}S{\leq}V$) is invested into other business. After assigning three costs to the surplus process, a reward per unit amount of the investment, a penalty of the surplus being empty and the keeping (opportunity) cost per unit amount of the surplus per unit time, we obtain the long-run average cost per unit time to manage the surplus. We prove that there exists a unique value of S minimizing the long-run average cost per unit time for a given value of V, and also that there exists a unique value of V minimizing the long-run average cost per unit time for a given value of S. These two facts show that an optimal investment policy of the surplus exists when we manage the surplus in the long-run.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.65-71
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• 2003

We consider the finite dam with compound Poisson inputs which is called M/G/1 finite dam. We assign some costs related to operating the dam and calculate the long-run average cost per unit time. Then, we find the optimal dam capacity under which the average costs is minimized.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.147-154
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• 1997

An infinite dam with a compound Poisson input having exponential jumps is considered. As an output policy, we adopt the $P_{\lambda}$$^{M}$ Policy. After assigning costs to the dam we obtain the long-rum average cost per unit time of operating the dam and find the optimal values of .lambda. and M which minimize the long-run average cost.t.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1345-1352
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• 2008

An inventory with constant demand is studied. We adopt a renewal argument to obtain the transient and stationary distribution of the level of the inventory. We show that the stationary distribution can be also derived by making use of either the level crossing technique or the renewal reward theorem. After assigning several managing costs to the inventory, we calculate the long-run average cost per unit time. A numerical example is illustrated to show how we optimize the inventory.

• Journal of the Korean Data and Information Science Society
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• v.8 no.1
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• pp.85-89
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• 1997

In this paper, we consider a random replacement model with minimal repair, which is a generalization of the random replacement model introduced Lee and Lee(1994). It is assumed that a system is minimally repaired when it fails and replaced only when the accumulated operating time of the system exceeds a threshold time by a supervisor who arrives at the system for inspection according to Poisson process. Assigning the corresponding cost to the system, we obtain the expected long-run average cost per unit time and find the optimum values of the threshold time and the supervisor's inspection rate which minimize the average cost.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1089-1096
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• 2011

We consider an infinite dam with inputs formed by a compound Poisson process and adopt a $P^M_{\lambda}$-policy to control the level of water, where the water is released at rate M when the level of water exceeds threshold ${\lambda}$. We obtain interesting stationary properties of the level of water, when the amount of each input independently follows an exponential distribution. After assigning several managing costs to the dam, we derive the long-run average cost per unit time and show that there exist unique values of releasing rate M and threshold ${\lambda}$ which minimize the long-run average cost per unit time. Numerical results are also illustrated by using MATLAB.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.773-782
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• 2004

In this paper, a random shock model for a system is considered. Each shock arriving according to a Poisson process decreases the state of the system by a random amount. A repairman arriving according to another Poisson process of rate $\lambda$ repairs the system only if the state of the system is below a threshold $\alpha$. After assigning various costs to the system, we calculate the long-run average cost and show that there exist a unique value of arrival rate $\lambda$ and a unique value of threshold $\alpha$ which minimize the long-run average cost per unit time.

• 한국데이터정보과학회:학술대회논문집
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• 2004.10a
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• pp.33-42
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• 2004

In this paper, a random shock model for a system is considered. Each shock arriving according to a Poisson process decreases the state of the system by a random amount. A repairman arriving according to another Poisson process of rate $\lambda$ repairs the system only if the state of the system is below a threshold $\alpha$. After assigning various costs to the system, we calculate the long-run average cost and show that there exist a unique value of arrival rate $\lambda$ and a unique value of threshold $\alpha$ which minimize the long-run average cost per unit time.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.725-733
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• 2005

A system subject to random shocks is considered. The shocks arrive according to a Poisson process and the amount of each shock is exponentially distributed. In this paper, a periodic inspection policy for the system is compared with a random inspection policy. After assigning several maintenance costs to the system, we calculate and compare the long-run average costs per unit time under two policies.