• 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 Korean Society for Quality Management
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• v.17 no.1
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• pp.11-18
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• 1989

A one-upper level warehouse n-Iower level retailer inventory distribution model is discussed. This paper presents the parallel-type inventory structure using an order-up-to-level invertory control system for analyzing the approximation of the expected units back ordered and the measure of service. We find that the total expected backorder units in system can substitute the expected back orders in the last two periods for the expected back orders in total periods. The rate of total expected back orders which is the measure of disservice, is given by dividing the improved units of total expected backorder into the total demand during an order cycle. The average annual total cost in system is obtained by considering the results, but from the viewpoint of this study the cost analysis is not described.

• 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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.10a
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• pp.607-610
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• 2004

The purpose of this study is finding a solution to optimal quantities of concurrent spare parts(CSP) which are acquired for using considerably long time. To solve the problem, this paper proposes a new CSP model which can be used in permitting backorder flexibly. Through the simple experiment, we validate the mathematical model which is suggested in this paper. Also, we determine the purchasing quantities of each item minimizing total system costs under an available budget constraints.

• 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.

• IE interfaces
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• v.16 no.4
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• pp.441-449
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• 2003

In this paper we propose a distribution planning method aiming the use in the real-life situations. The assumed form of the distribution network is arborescence. At every node in the distribution network, orders are placed periodically. At each renewal of planning horizon, demand informations of periods in the horizon are updated. The objective of the problem is to minimize the total cost, which is the sum of holding and backorder costs of all sites during planning horizon. For such a situation, this study addressed an effective distribution plan when demands for demand-sites are provided for a given planning horizon.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.3
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• pp.81-90
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• 1993

This article concerns the problem of determining the optimal spare inventory level for multiechelon repairable-item inventory system. The system we are concerned has several bases and a central depot. When an item fails, it is dispatched to a repair facility and, a spare, if available, is plugged in immediately. When the failed item is repaired, it is sent to the base and either used to fill a backorder or stored at a spare inventory point. We develop an optimal algorithm to find the spare inventory level at each base spareswhich minimizes the total expected cost and, simultaneously, satisfies a specified minimum service rate. The algorithm is applied to examples with good results.

• Journal of Korean Port Research
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• v.14 no.1
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• pp.37-45
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• 2000

Centralized safety stock in a periodic replenishment system which consists of one central warehouse and m regional warehouse can reduce backorders allocating the centralized safety stocks to regional warehouse in a certain instant of each replenishment cycle. If the central warehouse can not monitoring inventories in the regional warehouse, then we have to predetermine the instant of allocation according to demand distribution and this instant must be same for all different replenishment cycle. However, transition of inventory level in each cycle need not to be same, and therefore different instant of the allocation may results reduced shortage compare to the predetermined instant of allocation. In this research, we construct a dynamic model based on the assumption of monitoring inventories in the regional warehouse everyday, and develop an algorithm minimize shortage in each replenishment cycle using dynamic programming approach.

• Korean Management Science Review
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• v.28 no.1
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• pp.117-127
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• 2011

In the Multi-Echelon maintenance environment, METRIC(Multi-Echelon Technique for Repairable Item Control) has been used in several different inventory level selection models, such as MOD-METRIC, Vari-METRIC, and Dyna- ETRIC. While this model's logic is easy to be implemented, a critical assumption of infinite maintenance capacity would deteriorate actual values, especially Expected Back Order(EBO)s for each item. To improve the accuracy of EBO, we develop two models using simulation and queueing theory that calculates EBO considering finite capacity. The result of our numerical example shows that the expected backorder from our model is much closer to the true value than the one from Vari-METRIC. The queueing model is preferable to the simulation model regarding the computational time.