• 한국경영과학회지
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• 제40권3호
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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.

• 대한산업공학회지
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• 제32권2호
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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.

• 대한산업공학회지
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• 제31권3호
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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.

• Management Science and Financial Engineering
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• 제14권2호
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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.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2008년도 추계학술대회 및 정기총회
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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).

• 대한산업공학회지
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• 제36권1호
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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.

• 한국산학기술학회논문지
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• 제13권7호
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• pp.2955-2963
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• 2012

본 논문은 다품종 동적 로트사이징 문제를 풀기 위하여 열생성 기법에 기반한 알고리즘을 제안한다. 제안한 알고리즘의 기본 개념은 한정된 생산 용량을 주문제를 통하여 n개의 제품에 할당하고, 주문제에 의하여 할당된 생산용량을 기반으로 하여 각각의 제품에 대하여 최적화된 로트사이징 문제를 반복적으로 풀어나감으로써 해를 구해나가는 것이다. 부문제를 풀기 위해 본 논문은 로트사이즈, 재공재고 그리고 생산량 간에 존재하는 비선형관계를 기반으로 한 M/G/1모델 기반의 최적화 로트사이징 모델을 제안한다. 실험을 통하여 제안한 알고리즘이 비교적 짧은 시간안에 좋은 해를 생성함을 보여준다.

• 산업공학
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• 제13권3호
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• pp.378-387
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• 2000

As the globalization of manufacturing companies continues, the scope of dependence between these companies and distributors, and other suppliers are growing very rapidly since no one company manufactures or distributes the whole product by themselves. And, the need to increase the efficiency of the whole supply chain is increasing. This paper deals with a multi-plant lot-sizing problem(MPLSP) which happens in a decentralized manufacturing system of a supply chain. In this study, we assume that the whole supply chain is driven by a single source of independent demand and many levels of dependent demands among manufacturing systems in the supply chain. We consider setup cost, transportation cost and time, and inventory holding cost as a decision factor in the MPLSP. The MPLSP is decomposed into two sub-problems: a planning problem of the whole supply chain and a lot-sizing problem of each manufacturing system. The supply chain planning problem becomes a pure linear programming problem and a Generalized Goal Decomposition method is used to solve the problem. Its result is used as a goal of the lot-sizing problem. The lot-sizing problem is solved using the CPLEX package, and then the coefficients of the planning problem are updated reflecting the lot-sizing solution. This procedure is repeated until termination criteria are met. The whole solution process is similar to Lagrangian relaxation method in the sense that the solutions are approaching the optimum in a recursive manner. Through experiments, the proposed closed-loop hierarchical planning and traditional hierarchical planning are compared to optimal solution, and it is shown that the proposed method is a very viable alternative for solving production planning problems of decentralized manufacturing systems and in other areas.

• 한국산학기술학회논문지
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• 제7권1호
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• pp.89-95
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• 2006

공급사슬망에서 분산되어있는 제조시스템에 대한 생산 계획수립은 공급사슬관리의 주요 연구분야 중의 하나이다. 본 논문은 공급사슬망에서 자원제약을 갖는 다단계 다품목 로트사이즈 결정 문제(Multi-Level, multi-item Capacitated Lot Sizing Problem: MLCLSP)를 위한 알고리즘을 제시한다. MLCLSP는 MIP(mixed integer program) 문제에 해당한다. 제안된 알고리즘은 휴리스틱과 최적화 패키지인 LINGO를 이용해 서로 반복적인 방식으로 해를 풀어나가는 혼성적인 성격을 갖는다. 휴리스틱을 이용하여 정수형 변수를 결정한 후, 얻게 되는 LP(linear program) 문제를 LINGO를 이용하여 해를 개선해 나가는 방식을 기본으로 한다. 본 논문에서는 탐색 휴리스틱 기법으로 임의 재시작 타부탐색 알고리즘을 제시한다. 다양한 시나리오의 실험을 통해 제안된 알고리즘들의 성능을 평가한다.

• 품질경영학회지
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• 제18권1호
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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.