• Journal of Korean Society of Industrial and Systems Engineering
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• v.37 no.1
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• pp.165-171
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• 2014

We develop an optimization algorithm for a periodic review inventory system under a stochastic budget constraint. While most conventional studies on the periodic review inventory system consider a simple budget limit in terms of the inventory investment being less than a fixed budget, this study adopts more realistic assumption in that purchasing costs are paid at the time an order is arrived. Therefore, probability is employed to express the budget constraint. That is, the probability of total inventory investment to be less than budget must be greater than a certain value assuming that purchasing costs are paid at the time an order is arrived. We express the budget constraint in terms of the Lagrange multiplier and suggest a numerical method to obtain optional values of the cycle time and the safety factor to the system. We also perform the sensitivity analysis in order to investigate the dependence of important quantities on the budget constraint. We find that, as the amount of budget increases, the cycle time and the average inventory level increase, whereas the Lagrange multiplier decreases. In addition, as budget increases, the safety factor increases and reaches to a certain level. In particular, we derive the condition for the maximum safety factor.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.3
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• pp.8-13
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• 2015

One of the most usual indicators to measure the performance of any inventory policy is the mean physical stock. In general, when estimating the mean physical stock in periodic review inventory systems, approximate approaches are often utilized by practitioners and researchers. The mean physical stock is generally calculated by a simple approximation. Still these simple methods are frequently used to analyze various single stockpoint and multi-echelon inventory systems. However, such a simple approximation can be very inaccurate. This is particularly true for low service levels. Even though exact methods to calculate the mean physical stock have been derived, they are available for specific cases only and computationally not very efficient, and therefore less useful in practice. In literature, approximate approaches, such as the simple, the linear, and Simpson approximations, were derived for the periodic review inventory systems that allow backorders. This paper modifies the approximate approaches for the lost sales case and evaluates the modified approximate approaches. Through computational experiments, average (and maximum) percentage deviations of mean physical stock between the exact method and the modified approximations are compared in the periodic review inventory system with lost sales. The same comparison between the modified and the original approximations are also conducted, in order to examine the performance of modified approximations. The results show that all modified approximations perform well for high service levels, but also that the performance may deteriorate fast with decreasing service level. The modified Simpson approximation is clearly better. In addition, the comparison between the modified and the original approximations in the periodic review inventory system with lost sales shows that the modified approximation outperforms the original approximation.

• Journal of Korean Institute of Industrial Engineers
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• v.8 no.1
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• pp.22-28
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• 1982

Under a continuous-review inventory system, the inventory position process was proved to be asymptotically independent of the general renewal demand processes, when the two processes form an asymptotic unimodel joint distribution. The analytical technique implemented through this work seems to be more like general, and so the periodic-review system can be similarly investigated. In conclusion, the results may be evaluated to direct to the analytical analyses of some inventory systems which have been treated under some restrictions on demand processes.

• Journal of the Korean Operations Research and Management Science Society
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• v.31 no.4
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• pp.125-138
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• 2006

This paper considers a periodic review, two-echelon inventory system with one central warehouse and several re-tailers facing normally distributed demand. The goal is to attain target fill rates, while the systemwide total holding costs are minimized. An important aspect of this problem is material rationing in the case of shortages. If a central warehouse has insufficient inventory to deliver all replenishment orders to retailers, all order quantities are should be adjusted according to some rationing rule. A simple but efficient rationing rule is proposed and compared with the Balanced Stock (BS) rationing as introduced by Heijden which is known to be the best rationing policy in the literature. Numerical results show that the proposed rationing rule is more cost effective than BS rationing, especially for the differences in holding costs between retailers are large.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.43 no.1
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• pp.70-78
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• 2020

Under the situation which customer orders are cancelled unless all products in the order are delivered all at once, this paper concentrates on the purchase dependent demands and explores the systematic approach to implant the purchase dependence into the multi-product inventory model. First, by acknowledging that it is a challenging task to formulate a suitable inventory model for the purchase dependence, we derive the optimal solution condition using an EOQ model and extend the optimal solution condition to periodic review models. Then, through the comparison simulation of four inventory policies regarding several degrees of purchase dependence, we demonstrate that the inventory models which consider the purchase dependence generate less total cost than the inventory models which ignore the purchase dependence. In general, the inventory models which consider the purchase dependence reduce the loss of sales by maintaining more inventories, which results in reducing the total cost. Consequently, the simulation result supports the effectiveness of this paper's approach. In addition, this paper uses the individual order period and joint order period obtained from the EOQ model for the multi-product inventory model. Through the in-depth analysis of comparing the two models, we observe that the model of using the joint order period produces less total cost when the degree of purchase dependence is high, but the model of using the individual order period produces less total cost when the degree of purchase dependence is low.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.46 no.4
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• pp.93-100
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• 2023

In this paper, an alternative inventory policy that trades off the bullwhip effect at an upstream facility with cost minimization at a current facility, with the goal of reducing system wide total expected inventory costs, when external demand distributjon is autocorrelated, is considered. The alternative inventory policy has a form that is somewhere between one that completely neglects the autocorrleation and one that actively utilizes the autocorrelation. For this purpose, a mathematical model that allows us to evaluate system wide total expected inventory costs for a periodic review system is developed. This model enables us to identify an optimal inventory policy at a current facility that minimizes system wide total expected inventory costs by the best tradeoff of the bullwhip effect at an upstream facility with cost minimization at a current facility. From numerical experiments, it has been found that (i) when the autocorrelation is negative, the optimal policy is one that actively utilizes the autocorrelation, (ii) when the autocorrelation is small and positive, the optimal policy is one that neglects the autocorrelation, and (iii) when the autocorrelation is large and positive, the optimal policy is somewhere between one that actively utilizes the autocorrelation and one that neglect the autocorrelation.

• Journal of the Korean Operations Research and Management Science Society
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• v.36 no.3
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• pp.61-74
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• 2011

The objective of this study is to evaluate the effects of sharing uncertain yield information with a downstream supply chain player. We are interested in understanding how the amount of yield uncertainty affects the supply-side benefits and/or costs, which has not been considered in the literature, in addition to the customer-side benefits. With that purpose, this work evaluates a supplier who provides yield information in comparison with another supplier who shares no information. We simulate an order-up-to type heuristic policy that is adapted from the literature and reasonably modified to represent yield information sharing with error. From the simulation study, we argue that the customer would experience cost reduction, but the cost for supplier's inventory is increasing when sharing yield information. Furthermore, the amount of benefits and costs are situational and affected by level of yield uncertainty and demand variance. Based on the simulation study, we finally make several recommendations for the supply-side approaches to yield information sharing.

• Journal of the Korea Safety Management & Science
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• v.9 no.4
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• pp.121-127
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• 2007

CSP(Concurrent Spare Parts) is supplied with the procurement of new equipment or weapon system and is used to sustain the equipment without resupply during the initial coverage period. This study is concerned with a problem of determining the near optimal inventory level of the spare parts, especially Concurrent Spare Parts. For this, we utilize the mixed periodic and continuous review polices considering the CSP and (r,Q) Policies concurrently in a two-echelon distribution system. We propose the mathematical model to minimize the total cost which is composed with ordering cost, purchasing cost, holding cost, and stickout cost. If the mixed policy is compared to other policies(CSP, (r,Q)), the proposed methodology performs well and is best policy in the equipment maintenance expenses.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.31 no.1
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• pp.83-91
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• 2008

기업이 수요에서 자기상관을 인식하지 못하게 되면, 이 기업은 수요가 서로 독립이면서 동일한 분포를 따른다는 가정 하에 개발된 전통적인 재고주문방법을 시행하게 된다. 따라서 이 경우에 안전재고량, 재고부족 확률, 재고부족량 등과 같은 성과지표의 관점에서 전통적인 재고주문방법이 정확한 재고주문방법에 비하여 얼마만큼 비효율적인가를 알아보는 것은 기업경영의 측면에서 의미 있는 일이다. 이 논문에서는 정기주문시스템 하에서의 두 가지 재고 관리방법을 비교하기 위한 수리적 모형을 개발하고 이를 통하여 어떠한 상황 하에서 정확한 재고주문방법이 전통적인 재고주문방법에 비하여 더 절실한지를 살펴본다.

• Industrial Engineering and Management Systems
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• v.3 no.1
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• pp.38-51
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• 2004

Over the years, most or many companies have focused their attention to the effectiveness and efficiency of their business units. As a new way of doing business, these companies have begun to realize the strategic importance of planning, controlling, and designing their own supply chain system. This paper analyzes the coordination issues in supply chains that consist of one manufacturer and multiple retailers operating under uncertain end customer demand and delivery lead-time. We use the Genetic Algorithm (GA) to determine the appropriate ordering and inventory level at which the manufacturer and multiple retailers can maximize the profit of the chain. This is performed under three controlling policies: the traditionally centralized controlling policy under the manufacturer's perspective, the entire chain’s perspective, and lastly the coordinating controlling policy with an incentive scheme. The outcome from the study reveals that the coordinating controlling policy with an incentive scheme can outperform the traditional centralized controlling policies by creating a win-win situation in which all members of the chain benefit from higher profit, thus resulting in more willingness from all members to join the chain.