• Journal of Korean Institute of Industrial Engineers
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• v.24 no.1
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• pp.127-136
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• 1998

This paper presents a stochastic partial backorder inventory model for the situation in which demand follows normal distribution and back order ratio during that stockout period decreases exponentially according to the length of backorder period. In the paper, an objective function is formulated to minimize the average annual cost, which is the sum of the ordering, carrying, time-proportional backordering, and lost sales cost. And then sensitivity analysis for various exponential backorder ratios and standard deviations of leadtime demand are presented. The inventory model in the paper is reduced to a backorder model and lost sales model, when backorder ratio is 1 and 0, respectively.

• Journal of Korean Institute of Industrial Engineers
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• v.20 no.3
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• pp.105-116
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• 1994

This paper presents an inventory model with partial backorders for the situation in which demand is deterministic, lead time follows normal distribution and back order ratio during the stockout period varies in proportion to the length of backorder period In this situations, an objective function is formulated to minimize a time-proportional backorder cast and a fixed penalty cost per unit lost. And then the procedure of iterative solution method for the model is developed to find optimal reorder paint and order quantity and a numerical example to illustrate the proposed method is presented.

• Journal of the Korean Operations Research and Management Science Society
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• v.21 no.1
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• pp.71-80
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• 1996

This paper presents a stochastic partial inventory model for the situation in which demand is deterministic, lead time follows normal distribution and backorder ratio during the stockout period decreases exponentially according to the length of backorder period. In this situation, an objective function is formulated to minimize the average annual cost, which is the sum of the ordering, carrying time-proportional backordering, quantity-proportional backordering and lost sales costs. And then the procedure of iterative solution method for the model is developed to find optimal reorder point and order quantity and numerical example to illustrate the proposed method is presented.

• 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 Society of Industrial and Systems Engineering
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• v.18 no.36
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• pp.93-103
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• 1995

This paper des with an economic production quantity model with partial backorders for the situation in which production lead time is deterministic and demand during lead time follows a continuous distribution. In the model, an objective function is formulated In minimize an average annual inventory cost. And then the procedure of iterative solution method for the model is developed to find both production reorder point and production quantity. Finally, sensitivity analysis for various partial backorder ratios and standard deviations of demand during production lead time are presented.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.3
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• pp.81-91
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• 1994

This paper is to build an economic production quantity model for situations, in which, during the stockout period, a fraction .betha.(backorder ratio) of the demand is backordered and remaining fraction (1-.betha.) is lost. This paper develops an objective function representing the average annual cost of a production system by defining a time-weighted backorder cost and a lost sales penalty cost per unit lost under the assumptions of deterministic demand rate and deterministic production rate, and provides an algorithm for its optimal solution. At the extreme .betha.= 1, the presented model reduces to the Fabrycky's model with complete backorders.

• 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.