• Journal of the Korean Operations Research and Management Science Society
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• v.40 no.3
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• pp.23-38
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• 2015

In this paper, we evaluate the strength of three families of cutting planes for a lot-sizing problem. Lot-sizing problem is very basic MIP model for production planning and many strong valid inequalities have been developed for a variety of relaxations in the literature. To use three families of cutting planes in Branch-and-Cut framework, we develop separation algorithms for each cut and implement them in CPLEX. Then, we perform computational study to compare the effectiveness of three cuts for randomly generated instances of the lot-sizing problem.

• Journal of Korean Society for Quality Management
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• v.18 no.1
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• pp.65-76
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• 1990

A lot-sizing model for multi-stage MRP systems is proposed, in which known demands must be satisfied. In this model, an approach with considerations of initial inventory and limited production capacity is involved. Most of the studies on the lot-sizing techniques for multi-stage material requirement planning systems have been focused upon two basic approaches. One approach is to develope an algorithm yielding an optimal solution. Due to the computational complexity and sensitivity of the optimal solution to the problem of lot sizing, heuristic approaches are often employed. In this paper, the heuristic approach is used by sequential application of a single-stage algorithm with a set of modified cost by the concept of multi-echelon costs. The proposed method is compared with an lot-sizing method(Florian-Klein Model) to prove its effectiveness by numerical examples.

• 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.

• Management Science and Financial Engineering
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• v.14 no.2
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• pp.13-23
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• 2008

The pricing/lot-sizing problem of determining the robust optimal order quantity and selling price is discussed. The uncertainty of parameters characterized by an ellipsoid is explicitly incorporated into the problem. An approximation scheme is proposed to transform the problem into a geometric program, which can be efficiently and reliably solved using interior-point methods.

• 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.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.

• 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 Korean Society of Industrial and Systems Engineering
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• v.12 no.19
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• pp.79-88
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• 1989

This characteristics of process industries are high capital intensity, relatively long and sequence dependent setup times, and extremely limited capacity resources. The lot sizing, sequencing and limited capacity resources factors must he considered for production scheduling in these industries. This paper presents a mixed integer programming model for production scheduling. The economic trade offs between capacitated lot sizing flow shop scheduling and sequence dependent setup times also be compared with SMITH-DANIELS's model. As a results, it is shown that this paper has lower total cost, more efficient throughput than SMITH-DANIELS's model.

• Journal of Korean Institute of Industrial Engineers
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• v.32 no.2
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• pp.98-103
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• 2006

In this research, the single machine capacitated lot-sizing and scheduling problem with sequence- dependent setup costs and setup times (CLSPSD) is considered. This problem is the extension of capacitated lot-sizing and scheduling problem (CLSP) with an additional assumption on sequence-dependent setup costs and setup times. The objective of the problem is minimizing the sum of production costs, inventory holding costs and setup costs satisfying customers' demands. It is known that the CLSPSD is NP-hard. In this paper, the MIP formulation is presented. To handle the problem more efficiently, a conceptual model is suggested, and one of the well-known meta-heuristics, the simulated annealing approach is applied. To illustrate the performance of this approach, various instances are tested and the results of this algorithm are compared with those of the CLPEX. Computational results show that this approach generates optimal or nearly optimal solutions.