• Management Science and Financial Engineering
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• v.18 no.2
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• pp.23-27
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• 2012

The problem of jointly determining a robust optimal bundle of price and order quantity for a retailer in a single-retailer, single supplier, single-product supply chain is considered. Demand is modeled as a decreasing power function of product price, and unit purchasing cost is modeled as a decreasing power function of order quantity and demand. Parameters defining the two power functions are uncertain but their possible values are characterized by ellipsoids. We extend a previous study in two ways; the purchasing cost function is generalized to take into account the economies of scale realized by higher product demand in addition to larger order quantity, and an exact transformation into an equivalent convex optimization program is developed instead of a geometric programming approximation scheme proposed in the previous study.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.139-151
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• 2009

Based on single-vendor single-buyer integrated production-inventory problem, a model considering freight costs discounts is suggested when the cargo capacity is constrained. With the cost function formulated, several properties of the model are derived and analyzed. An efficient algorithm to find solutions such as shipment lot size, number of shipments and number of full truckloads using properties derived is suggested. Numerical results are provided to illustrate the proposed solution procedures and to provide additional insights.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.10
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• pp.867-873
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• 2001

The purpose of this study is to find analytic solution of determining the optimal capacity (lot-size) of multiproduct acyclic multistage production and inventory system to meet the finished product demand under the constraint of finite intermediate storage. Intermediate storage is a practical way to mitigate the material flow imbalance through the line of supply and demand chain. However, the cost of constructing and operating storage facilities is becoming substantial because of increasing land value, environmental and safety concern. Therefore, reasonable decision-making about the capacity of processes and storage units is an important subject for industries. The industrial solution for this subject is to use the classical economic lot sizing method, EOQ/EPQ(Economic Order Quantity/Economic Production Quantity) model, incorporated with practical experience. But EOQ/EPQ model is not suitable for the chemical plant design with highly interlinked processes and storage units because it is developed based on single product and single stage. This study overcomes the limitation of the classical lot sizing method. The superstructure of the plant consists of the network of serially and/or parallelly interlinked non-continuous processes and storage units. The processes transform a set of feedstock materials into another set of products with constant conversion factors. A novel production and inventory analysis method, PSW(Periodic Square Wave) model, is applied to describe the detail material flows among equipments. The objective function of this study is minimizing the total cost composed of setup and inventory holding cost. The advantage of PSW model comes from the fact that the model provides a set of simple analytic solutions in spite of realistic description of the material flows between processes and storage units. the resulting simple analytic solution can greatly enhance the proper and quick investment decision for the preliminary plant design problem confronted with economic situation.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.61-64
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• 2000

This paper analyzes a dynamic lot-sizing problem, in which the order size of multiple products and a single container type are simultaneously considered. In the problem, each order (product) placed in a period is immediately shipped immediately by containers in the period and the total freight cost is proportional to the number of each container type employed. Also, it is assumed that backlogging is not allowed. The objective of this study is to determine the lot-sizes and the shipping policy that minimizes the total costs, which consist of ordering costs, inventory holding costs, and freight costs. Because this problem is NP-hard, we propose a heuristic algorithm with an adjustment mechanism, based on the optimal solution properties. The computational results from a set of simulation experiment are also presented.

• Proceedings of the Safety Management and Science Conference
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• 2000.05a
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• pp.77-86
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• 2000

This paper deals with the problem of determining the retailer's optimal price and order size under the condition of order-size-dependent delay in payments. It is assumed that the length of delay is a function of the retailer's total amount of purchase. The constant price elasticity demand function is adopted which is a decreasing function of retail price. Investigation of the properties of an optimal solution allows us to develop an algorithm whose validity is illustrated through an example problem.

• International Journal of Advanced Culture Technology
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• v.8 no.1
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• pp.62-70
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• 2020

As an effective means of price discrimination, some suppliers offer trade credit to the distributors in order to stimulate the demand for the product they produce. The availability of the delay in payments from the supplier enables discount of the distributor's selling price from a wider range of the price option in anticipation of increased customer's demand. Since the distributor's lot-size is affected by the demand for the customer, the distributor's lot-size and the selling price determination problem is interdependent and must be solved at the same time. Also, in many common business transactions, the distributor pays the shipping cost for the order and hence, the distributor's ordering cost consists of a fixed ordering cost and the shipping cost that depend on the order quantity. In this regard, we deal with the joint lot-size and price determination problem when the supplier allows delay in payments for an order of a product. The positive effects of credit transactions can be integrated into the EOQ (economic order quantity) model through the consideration of retailing situations, where the customer's demand is a function of the distributor's selling price. It is also assumed that the distributor's order cost consists of a fixed ordering cost and the variable shipping cost. We formulate the distributor's mathematical model from which the solution algorithm is derived based on properties of an optimal solution. A numerical example is presented to illustrate the algorithm developed.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.10a
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• pp.174-174
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• 1993

자원제약하의 롯트 사이즈 결정문제(capacitated lot sizing problem: CLSP)는 주어진 생산자원의 제약요건을 만족하면서 모든 계획기간의 수요를 충족시킬수 있는 가동준비와 재고유지비의 총합에 대한 최소화 문제다. CLSP는 NP-hard이기 때문에 그 해를 효율적으로 구하기 위한 휴리스틱 해법이 그동안 꾸준히 개발되어져 왔으며 그 대부분의 알고리즘은 Wagner-Whitin의 해도출원리를 이용한 것이다. 본 연구는 지금까지 개발된 CLSP의 알고리즘을 분석하여 그 특성을 파악한 후 본 연구에서 개발한 알고리즘과 이들 기존 알고리즘을 비교 실험함으로써 개발된 알고리즘이 어느 정도의 효율성을 가지는가를 검토하고자 한다.

• Proceedings of the Safety Management and Science Conference
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• 2002.05a
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• pp.237-241
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• 2002

This paper deals with the problem of determining the buyer's economic lot sizing policy for exponentially deteriorating products under trade credit. It is also assumed that the ordering cost consists of a fixed set-up cost and a freight cost, where the freight cost has a quantity discount offered due to the economies of scale. We formulate the mathematical model and the solution algorithm is developed based on the properties of an optimal solution.

• Proceedings of the Safety Management and Science Conference
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• 2002.05a
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• pp.243-247
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• 2002

This paper deals with the problem of determining the buyer's economic lot sizing policy for exponentially deteriorating products under trade credit. Assuming that the supplier's credit terms are already known and the length of delay is a function of the buyer's order size, we formulate the mathematical model and the solution algorithm is developed based on the properties of an optimal solution.

• Journal of the Korean Operations Research and Management Science Society
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• v.4 no.1
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• pp.53-58
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• 1979

Production lot sizing problem for a system with exponentially decaying inventory is considered. From the exact cost function developed under conditions of constant demand and no shortages permitted, an approximate optimal solution is derived. The formula is compared with those of the exact solution obtained from numerical procedure and other existing approximate solution. Finally some notable properties of the formula are investigated and shown to be consistent.