• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.10a
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• pp.10-26
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• 2005

In our model, we keep inventory to satisfy uncertain demands which arrives irregularly. In this situation, we have additional two constraints. First, we need to have certain amount of order consolidation (consolidation constraint) for the orders to replenish the inventory because of production or purchase constraint. And also, if we order at a certain date which was set by administrative convenience, we have amount constraint to order the consolidated order demands (capacity constraint). We showed this variant inventory policy is needed in steel industry and note that there will be possible similar case in industry. To deal with this case, we invented a variant replenishment policy and show this policy is superior to other possible polices in the consolidation constraint case by extensive simulation. And we derive a combined solution method for dealing with the capacity constraints in addition to the consolidation constraints. For this, we suggest a combined solution method of integer programming and simulation.

• Journal of the Korean Operations Research and Management Science Society
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• v.31 no.2
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• pp.99-112
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• 2006

In our model, we keep inventory to satisfy uncertain demands which arrives irregularly. In this situation, we have additional two constraints. First, we need to have certain amount of order consolidation (consolidation constraint) for the orders to replenish the inventory because of production or purchase amount constraint. And also, if we order at a certain date which was set by administrative convenience, we have capacity constraint to order the consolidated order demands (capacity constraint). We show this variant inventory policy is needed in steel industry and note that there will be possible similar case in industry. To deal with this case, we invent a variant replenishment policy and show this policy is superior to other possible polices in the consolidation constraint case by extensive simulation. And we derive a combined solution method for dealing with the capacity constraints in addition to the consolidation constraints. For this, we suggest a combined solution method of integer programming and simulation.

• 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.2
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• pp.145-151
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• 2015

As order quantity is increased, the ordering cost per item will be cheaper due to saving of transportation and material handling costs. In this paper, two realistic assumptions such as quantity discount and budget limit are considered. Quantity discount means that all units in the order will be discounted according to the predetermined order levels. Budget limit represents that the costs for inventory investments are bounded. This paper develops a Lagrangian relaxation approach for a continuous review inventory model with a budget constraint and quantity discounts. Computational results indicate that the proposed approach provides a good solution. Sensitivity analysis is done to get some insights on budget limit and quantity discount. As budget limit or the amount of discount according to order quantity is increased, order quantity is increased, whereas reorder point is not always increased.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.31 no.4
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• pp.134-139
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• 2008

Most approaches for continuous review inventory problem need tables for loss function and cumulative standard normal distribution. Furthermore, it is time-consuming to calculate order quantity (Q) and reorder point (r) iteratively until required values are converged. The purpose of this paper is to develop a direct method to get the solution without any tables. We used approximation approaches for loss function and cumulative standard normal distribution. The proposed method can get the solution directly without any iterative procedure for Q, r and without any tables. The performance of the proposed approach is tested by using numerical examples. The budget constraint of this paper assumes that purchasing costs are paid at the time an order is arrived. This constraint can be easily replaced by capacity constraint or budget constraint in which' purchasing costs are paid at the time an order is placed.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.2
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• pp.40-46
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• 2015

The modular assembly system can make it possible for the variety of products to be assembled in a short lead time. In this system, necessary components are assembled to optional components tailor to customers' orders. Budget for inventory investments composed of inventory and purchasing costs are practically limited and the purchasing cost is often paid when an order is arrived. Service cost is assumed to be proportional to service level and it is included in budget constraint. We develop a heuristic procedure to find a good solution for a continuous review inventory system of the modular assembly system with a budget constraint. A regression analysis using a quadratic function based on the exponential function is applied to the cumulative density function of a normal distribution. With the regression result, an efficient heuristics is proposed by using an approximation for some complex functions that are composed of exponential functions only. A simple problem is introduced to illustrate the proposed heuristics.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.4
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• pp.211-218
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• 2012

We analyzed the effect of inventory pooling on the system where multiple depot was used to replenish retailers and where inventories are kept only on the depots. Inventory pooling consists of inventory integration and inventory exchange. We used simulation for checking the cost saving effect of reducing the number of depot (Inventory Integration) for the case when inventories kept on every depots are commonly used for all retailers when certain depot have stock out for their retailer assigned to them (Inventory Exchange) with the constraint of service level. Simulation on wide range of parameter settings results show that cost saving effect from inventory integration diminishes when transportation cost between depot and retailers or stock out cost, or retailer number increases. The effect becomes stronger when the demands on retailers have bigger variance or average. Also the results show that the cost saving effect from inventory exchange becomes stronger on the same situation when inventory integration effect becomes stronger.

• Journal of Korean Institute of Industrial Engineers
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• v.12 no.1
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• pp.43-48
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• 1986

In this paper, the one period multi-item inventory model is considered in which it is required to determine the production quantity and selling price of each item which maximize the probability of realizing predetermined level of profit. The objective function of this model is the sum of weighted probabilities which represent the possibility of obtaining the predetermined level of profit for each item. Budget constraint, inventory site constraint and constraints of price are considered. Finally this paper shows a numerical example in which random demand of each item has exponential distribution.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.36 no.4
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• pp.31-37
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• 2013

In this paper, we develop an efficient approach to solve a continuous review inventory system with a budget constraint when the semi-finished product and optional components are required to be assembled. We are, in particular, interested in a budget constraint that includes a service level. The service cost, such as labor and facility costs, tends to increase as the service level increase, and it makes the problem difficult to solve. Assuming that the reorder point for a semi-finished product is given, we show that the order quantity for the semi-finished product and the order quantity and reorder point for optional components can be determined by minimizing the total cost that includes setup cost, inventory holding cost, and shortage cost. The performance of the proposed approach is tested by numerical examples. By using sensitivity analysis, we conclude that, as the reorder point for semi-finished product increases, the order quantity for semi-finished product increases, whereas the order quantity and reorder point of optional components decreases.

• Journal of the Korean Operations Research and Management Science Society
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• v.15 no.1
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• pp.63-72
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• 1990

This problem in this paper concerns the determination of safety stock for multi-echelon invenetory system. In this model the criterion is to minimize system safety stock subject to a service level constraint and expected annual total cost. Then, safety stock is determined by minimizing expected annual total cost and satisfying given service level. This expected annual total cost is obtained by expected total inventory holding cost plus the expected total stockout cost. Numerical example is given in a three-echelon inventory system. The results obtained by the use of the Hill Algorithm.