• IE interfaces
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• v.13 no.3
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• pp.438-443
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• 2000

In this paper, we suggest a new backorder policy for stockout which is occurred in each regional distribution centers of distribution chain for capital-goods product. In backorder process of backorder policy, minimize expected stockout through the balancing-division module, and has occured stockout is backordering through the emergency supply from central distribution center and regional distribution center. Simulation tests show that our backorder policy is on the decrease of backorder cost and improvement of customer service. Our backorder policy has two important benefit. First, customer service level is improved by realization of minimum stockout. Second, the backorder process by allowance of the same level supply is to decrease system operating cost.

• Journal of Industrial Technology
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• v.21 no.B
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• pp.37-44
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• 2001

Distribution System is considered as the most important part of SCM when the satisfaction of customer demand is considered. This paper focus on the backorder policies for stockout which is occurred in each regional distribution center of two-echelon distribution system facing stochastic demand process. Four concepts for the efficient system operation are suggested. First, at least 30% reduction of stockout is achieved by introduction of 50/25 allocation policy to distribution system. Second, transportation cost and lead-time of backorder are decreased by allowance of internal supply between regional distribution centers. Third, the frequency of emergency supply is minimized by application of Ship-up-to- expected-demand backorder policies. Finally we suggest several effective rules to select multi-internal suppliers. Simulation tests show the efficiency of our backorder policies and enhancement of customer service level.

• Proceedings of the Korea Society for Simulation Conference
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• 2003.06a
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• pp.129-134
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• 2003

In this paper, we determine optimal reduction in the lead time and setup cost for some stochastic inventory models. And we propose more general model that allow the backorder rate as a control variable. We first assume that the lead time demand follows a normal distribution. And we assume that the backorder rate is dependent on the length of lead time through the amount of shortages. The stochastic models analyzed in this paper are the classical continuous and periodic review policy models with a mixture of backorders and lost sales. For each of these models, we provide a sufficient conditions for the uniqueness of the optimal operating policy. We also develop algorithms for solving these models and provide illustrative numerical examples.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.1
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• pp.26-32
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• 2007

This study deals with waiting-time dependent backordering rate during stock-out period in the EconomicProduction Quantity (EPQ) model. Assuming that the backordering rate follows an exponentially decreasingfunction of the waiting time, the backorder rate is developed under First-Come-First-Served (FCFS) andLast-Come-First-Served (LCFS) Policy. The mathematical models are developed based on differential equations.Through numerical examples, the validity of the developed models is illustrated.

• Journal of Korean Institute of Industrial Engineers
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• v.17 no.1
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• pp.51-58
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• 1991

This paper presents a single-echelon, single item, stochastic lead time and static demand inventory model for situations in which, during the stockout period, a fraction ${\beta}$ of the demand is backordered and the remaining fraction $(1-{\beta})$ is lost. In this situations, an objective function representing the average annual cost of inventory system is obtained by defining a time-proportional backorder cost and a fixed penalty cost per unit lost. The optimal operating policy variables minimizing the average annual cost are calculated iteratively. At the extremet ${\beta}=1$, the model presented reduces to the usual backorder case. A numerical example is solved to illustrate the algorithm developed.

• Journal of the military operations research society of Korea
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• v.9 no.1
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• pp.69-74
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• 1983

This article presents a deterministic inventory model for situations in which, during the stockout period, a fraction ${\beta}$ of the demand is backordered and the remaining fraction $1-{\beta}$ is lost. By defining a time proportional backorder cost and a fixed penalty cost per unit lost, a convex objective function representing the average annual cost of operating the inventory system is obtained. The optimal operating policy variables are calculated directly. At the extremes ${\beta}\;=\;1$ and ${\beta}\;=\;0$ the model presented reduces to the usual backorders and lost sales case, respectively.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.17 no.31
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• pp.59-72
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• 1994

This paper deals with ordering policies of consumable goods which have large demand rates in a multi-level distribution system. The system we are concerned consists of one Central Distribution Center(CDC) and N non-identical Regional Distribution Centers(RDCs) which have different demand rates, minimum fillrates, leadtimes, etc. The customer demand on the RDC is stationary poisson and the RDCs demand on the CDC is superposition of Q-stage Erlang distributions. We approximate the RDCs and CDC demand distribution to nomal in order to enhance the efficiency of algorithm. The relevant costs include a fixed ordering cost and inventory holding cost, and backorder cost. The objective is to find a continuous-review ordering policy that minimizes the expected average costs under constraints of minimum fill rates of RDCs and maximum allowable mean delay of CDC. We developed an algorithm for determining the optimal ordering policies of the CDC and the RDCs. We verified and compared the performance of the algorithm through the simulation using the algorithm result as the input parameters.

• Journal of the Korea Safety Management & Science
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• v.8 no.3
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• pp.115-123
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• 2006

The main focus of this study is to investigate the performance of a clark-scarf type multi-echelon serial supply chain operating with a base-stock policy and to optimize the inventory levels in the supply chains so as to minimize the systemwide total inventory cost, comprising holding and backorder costs as all the nodes in the supply chain. The source of supply of raw materials to the most upstream node, namely supplier, is assumed to have an infinite raw material availability. Retailer faces random customer demand, which is assumed to be stationary and normally distributed. If the demand exceeds on-hand inventory, the excess demand is backlogged. Using the echelon stock and demand quantile concepts and an efficient simulation technique, we derive near optimal inventory policy. Additionally we discuss the derived results through the extensive experiments for different supply chain settings.

• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.3
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• pp.27-46
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• 1992

This paper considers an (r, Q) policy for operation of a multipurpose facility. It is assumed that whenever the inventory level falls below r, the model starts to produce the fixed amount of Q. The facility can be utilized for extra production during idle periods, that is, when the inventory level is still greater than r right after a main production operation is terminated or an extra production operation is finished. But, whenever the facility is in operation for an extra production, the operation can not be terminated for the main production even though the inventory level falls below r. In the model, the demand for the product is assumed to arrive according to a compound Poisson process and the processing time required to produce a product is assumed to follow an arbitary distribution. Similarly, the orders for the extra production is assumed to accur in a Poisson process are the extra production processing time is assumed to follow an arbitrary distribution. It is further assumed that unsatisfied demands are backordered and the expected comulative amount of demands is less than that of production during each production period. Under a cost structure which includes a setup/ production cost, a linear holding cost, a linear backorder cost, a linear extra production lost sale cost, and a linear extra production profit, an expression for the expected cost per unit time for a given (r, Q) policy is obtained, and using a convex property of the cost function, a procedure to find the optimal (r, Q) policy is presented.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.10a
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• pp.566-569
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• 2004

본 연구에서는 생산능력의 제한이 있는 다계층(multi-echelon) 공급사슬에서의 효과적인 분배계획수립을 목적으로 한다. 수요 정보는 계획 기간(planning horizon) 동안 확정적인 형태로 주어지고 이러한 상황 하에서 전체 공급사슬에서 발생하는 재고유지 비용(holding cost)과 재고이월 비용(backorder cost)의 합을 최소화하는 분배 문제의 해법을 제시하고자 한다. 본 연구에서는 총비용을 최소화하는 각 노드별 분배량을 결정하기 위해서 look-ahead 기법을 사용한다. Look-ahead 기법을 통해 분배 계획 수립 시 해당 기간의 수요 정보뿐만 아니라 미래 수요를 함께 반영함으로써 생산능력 제한에 효과적으로 대처할 수 있도록 하였다. Look-ahead 기법을 적용하기 위해 본 문제를 단일 기계 일정계획(single machine scheduling) 문제로 전환하고 이에 대한 효율적인 발견적 기법을 제시한다. 또한 제안된 발견적 기법의 성능을 평가하기 위해 다양한 실험 조건하에서 제안된 알고리듬과 기존의 미래 수요를 고려하지 않는 계층 재고 정책(echelon stock policy)의 결과를 비교하여 본 연구의 우수성을 입증하였다.