• 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 Society of Industrial and Systems Engineering
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• v.18 no.33
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• pp.153-160
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• 1995

This paper presents the parallel-type inventory structure using an order-up-to level inventory control system for analyzing the approximation of the expected units backordered and the measure of service. The rate of total expected backorders which is the measure of disservise, 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. Total backorder model for the system without redistribution and the system with redistribution is described.

• 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 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 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 Society of Industrial and Systems Engineering
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• v.21 no.48
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• pp.15-23
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• 1998

This paper concerns the problem of determining the spare inventory level for multi-echelon repairable-item inventory system with finite number of operating items. We consider the system which 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 is used to fill a backorder or is stored at a spare inventory point. Using queueing network, we develop an algorithm to find the spare inventory level which minimizes the total expected cost and, simultaneously, satisfies a specified minimum fill rate. The results of the algorithm clearly indicate that the algorithm successfully generate output with optimal solution.

• 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.

• Korean Management Science Review
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• v.31 no.2
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• pp.1-13
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• 2014

In almost all of the organizations, the cost for acquiring and maintaining the inventory takes a considerable portion of the management budget, and thus a certain constraint is set upon the budget itself. The previous studies on inventory control for each item that aimed to improve the fill rate, backorder, and the expenditure on inventory are fitting for the commercially-operated SCM, but show some discrepancies when they are applied to the spare parts for repairing disabled systems. Therefore, many studies on systematic approach concept considering spare parts of various kinds simultaneously have been conducted to achieve effective performance for the inventory control at a lower cost, and primarily, METRIC series models can be named. However, the past studies were limited when dealing with the probability distributions for representing the situation on demand and transportation of the parts, with the (S-1, S) inventory control policy, and so on. To address these shortcomings, the Continuous Time Markov Chain (CTMC) model, which considers the phase-type distributions and the (s, Q) inventory control policies to best describe the real-world situations inclusively, is presented in this study. Additionally, by considering the cost versus the system availability, the optimization of the inventory level, based on this model, is also covered.