• Journal of Industrial Technology
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• v.20 no.A
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• pp.219-228
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• 2000

The determination of lot sizes in prevailing inventory problems has been made with constant safety stock over the planning horizon. But, it is more profitable to accommodate the safety stock to dynamically fluctuating demands. The objective of this paper is to study the method to determine the dynamic safety stock and lot sizing rules depending on the actual customer demands. The last period or highly fluctuating period during the consumption of a lot is the most critical one to stock-out. It means that such periods must be given more attentions. Some dynamic methods to control safety stock are proposed with viewpoints of the time, quantity, and time-quantity. Simulation results show that lot sizing methods with dynamic safety stock reduce about 10% of average total cost compared to those with constant safety stock.

• Journal of Korean Institute of Industrial Engineers
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• v.31 no.3
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• pp.194-200
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• 2005

A stochastic dynamic lot sizing problem for multi-item is suggested in the case that the distribution of the cumulative demand is known over finite planning horizons and all unsatisfied demand is fully backlogged. Each item is produced simultaneously at a variable ratio of input resources employed whenever setup is incurred. A dynamic programming algorithm is proposed to find the optimal production policy, which resembles the Wagner-Whitin algorithm for the deterministic case problem but with some additional feasibility constraints.

• Journal of Korean Institute of Industrial Engineers
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• v.36 no.1
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• pp.7-12
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• 2010

This paper considers a dynamic lot-sizing problem with backlogging under a minimum replenishment policy. For general concave production costs, we propose an O($T^5$) dynamic programming algorithm. If speculative motive is not allowed, in this case, a more efficient O($T^4$) algorithm is developed.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2008.10a
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• pp.290-296
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• 2008

This paper considers a two-stage dynamic lot-sizing problem constrained by a supplier's production capacity. We derive an improved O($T^6$) algorithm over the O($T^7$) algorithm in van Hoesel et al. (2005).

• Journal of Korean Institute of Industrial Engineers
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• v.40 no.4
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• pp.435-441
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• 2014

This paper considers a single-product problem for inbound lot-sizing and outbound dispatching at a third-party warehouse, where the demand is dynamic over the discrete time horizon. Each demand must be delivered into the corresponding delivery time window which is the time interval characterized by the earliest and latest delivery dates of the demand. Ordered products are shipped by heterogeneous container types. Each container type has type-dependent carrying capacity and the unit freight cost depends on each container type. Total freight cost is proportional to the number of each container type used. Also it is assumed that related cost functions are concave and backlogging is not allowed. The objective of the paper is to simultaneously determine the optimal inbound lot-sizing and outbound dispatching plans that minimize total costs which include ordering, shipping, and inventory holding costs. The optimal solution properties are characterized for the problem and then a dynamic programming algorithm is presented to find the optimal solution.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.8 no.12
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• pp.89-95
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• 1985

MRP System에서 시스템 성능을 향상시킬 수 있는 하나의 인자는 우수한 Lot-Sizing rule의 선택과 발견이다. 널리 사용되고 있는 Lot-Sizing rule 들 중 Wagner-Whitin 알고리즘은 생산준비 비용과 재고 유지비용이 가변적일 경우 동적 로트크기 결정에 우수한 forward 알고리즘이다. 본 연구에서는 Wagner-Whitin 알고리즘의 중요 원리들을 응용하여 LDS 알고리즘이라 명명한 backward 알고리즘을 개발한다. 그리고 개발된 알고리즘을 Wagner-Whitin 알고리즘과 비교함으로 그 유효성을 테스트하고 backward 알고리즘이 가지는 계산상의 장점을 고찰한다.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.7
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• pp.2955-2963
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• 2012

This study presents a column generation approach for multiple product dynamic lot-sizing problem. The basic idea of this approach is to have a master problem which allocates limited capacity among n different products and a sub-problem that performs the optimal lot sizing for each product subject to capacity allocation given by the master problem. In the sub-problem, we develop M/G/1 queuing model based clearing function which captures nonlinear relationship between the lot size, the work in process level and the throughput. A large number of test problems are randomly generated to evaluate the performance. Computational results show that the proposed model can find better solutions within reasonable CPU times.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.05a
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• pp.133-136
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• 2006

We consider dynamic lot-sizing model with production time windows where each of n demands has earliest due date and latest due date and it must be satisfied during the given time window. For the case of nonspeculative cost structure, an O(nlog n) time procedure is developed and it is shown to run in O(n) when demands come in the order of latest due dates.

• Industrial Engineering and Management Systems
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• v.11 no.3
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• pp.288-298
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• 2012

Lot sizing and shipment scheduling are two interrelated decisions made by a manufacturing plant and a third-party logistics distribution center. This paper analyzes a dynamic inbound ordering problem and shipment problem with a freight container cost, in which the order size of multiple products and single container type are simultaneously considered. In the problem, each ordered product placed in a period is immediately shipped by some freight containers in the period, and the total freight cost is proportional to the number of containers employed. It is assumed that the load size of each product is equal and backlogging is not allowed. The objective of this study is to simultaneously determine the lot-sizes and the shipment schedule that minimize the total costs, which consist of production cost, inventory holding cost, and freight cost. Because the problem is NP-hard, we propose three meta-heuristic algorithms: a simulated annealing algorithm, a genetic algorithm, and a new population-based evolutionary meta-heuristic called self-evolution algorithm. The performance of the meta-heuristic algorithms is compared with a local search heuristic proposed by the previous paper in terms of the average deviation from the optimal solution in small size problems and the average deviation from the best one among the replications of the meta-heuristic algorithms in large size problems.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.4
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• pp.331-341
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• 2011

This paper considers an inbound lot-sizing and outbound dispatching problem for a single product in a thirdparty logistics (3PL) distribution center. Demands are dynamic and finite over the discrete time horizon, and moreover, each demand has a delivery time window which is the time interval with the dates between the earliest and the latest delivery dates All the product amounts must be delivered to the customer in the time window. Ordered products are shipped by multiple vehicle types and the freight cost is proportional to the vehicle-types and the number of vehicles used. First, we formulate a mixed integer programming model. Since it is difficult to solve the model as the size of real problem being very large, we design a conventional genetic algorithm with a local search heuristic (HGA) and an improved genetic algorithm called adaptive genetic algorithm (AGA). AGA spontaneously adjusts crossover and mutation rate depending upon the status of current population. Finally, we conduct some computational experiments to evaluate the performance of AGA with HGA.