This dissertation focuses on production planning problems in an light-emitting diode (LED) manufacturing system in which multiple types of products are produced at a given or uncertain yield ratio (range) through the same production process. There is a target chip type for each type of wafer; however, by-products that deviate from the target chip type are also produced, significantly. The key features of these LED production environment occur not only in wafer fabrication but also in package assembly. In high-tech industries or manufacturing sites where yields are unstable, these production environmental features may appear. In this thesis, we consider three production planning problems with different number of stage and period, and develop algorithms for the problems.
First, we consider a problem of production planning on a single-stage and single-period case with the objective of minimizing the sum of excess and shortage costs. In this problem, we assumed that the yield ratio is given and determine the number of wafers to be released into the stage. We present mathematical formulation, exact algorithm, dynamic programming algorithm, and a two-phase heuristic algorithm in which an initial solution is obtained first with system decomposition and demand redefinition and then the solution is improved in the second phase.
Secondly, we consider a problem of production planning on a two-stage and single-period case with the objective of minimizing the production cost. In this problem, we assumed that the yield ratio is uncertain value and determine the number of input materials to be released into each stages without allowing shortage. We first present deterministic mathematical model and develop a robust optimization model for the problem.
Finally, we consider a problem of production planning on a two-stage and multi-period case with the objective of minimizing the sum of setup cost, production cost, chip/package inventory holding costs, package lost sales cost. In this problem, we assumed that the yield ratio is given and determine the number of input materials to be released into each stages. The problem was formulated as an mixed integer programming (MIP) and solved using a Lagrangian relaxation approach. We developed a MIP-based Lagrangian heuristic in which solutions of relaxed problems are used to find acceptably feasible solutions. A subgradient optimization method was employed to obtain good lower bounds.
Performance of the suggested algorithms are evaluated through a series of computational experiments on instances which are obtained from real data or generated randomly but in such a way that resulting problems reflect the real situations relatively well. Results of the experiments show that the algorithms developed in this research give very good solutions in a reasonable amount of computation time. Also, the suggested algorithms in this thesis are expected to be used for production planning problems in real manufacturing systems if they are modified to cope with the practical situations.
본 논문에서는 제품 분화가 중첩되는 발광다이오드의 제조 및 조립 공정에서의 생산계획 문제를 다루고 있다. 발광다이오드 생산은 미성숙한 공정 기술과 양산 및 개발이 혼재하는 복잡한 생산환경으로 인해 목표 제품의 낮은 수율과 목표 제품이 아닌 부산물들이 동시 생산되는 문제를 안고 있다. 하나의 투입물이 수요를 갖는 다양한 제품을 동시 생산하는 특징과 함께 서로 다른 종류의 투입물이 동일한 제품을 생산하는 생산 특징을 보이고 있다. 이 두가지 생산 환경적 특징들은 제품별 수요에 맞는 생산을 사실상 불가능하게 하고 작은 생산량 차이에도 재고 및 수요 부족에 따른 큰 비용 차이를 발생시키므로 반드시 이들을 고려하여 생산량을 결정해야 한다. 본 논문에서는 이러한 특징을 갖는 발광다이오드의 생산 공정의 단계, 계획 대상 기간, 생산 수율의 특성에 따라 세 가지의 생산계획 문제를 고려하였고, 각 주제별 고려하는 생산관련 비용을 최소화하는 것을 목적으로 하여 생산량을 결정해주는 생산계획 방법론을 개발하였다. 본 논문에서 제안된 생산계획 문제들에 대한 알고리듬들의 성능은 실제 현장의 상황을 잘 반영할 수 있도록 생성된 문제들을 이용하여 많은 계산 실험을 통해 평가되었다. 실험 결과를 통해, 제안된 알고리듬들은 논문에서 다루고 있는 발광다이오드 생산계획 문제들에 대해 현실적인 시간 내에 우수한 해를 찾아낼 수 있음을 확인하였다.
