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.