A branch-and-price algorithm for the parallel-line lot-sizing and scheduling problem in flat-panel display manufacturing process

In this paper, we address a lot-sizing and scheduling problem with parallel production lines originating from a flat-panel display manufacturing process. Due to the use of high-tech equipment and expensive materials, as well as high demand levels, it is crucial to establish efficient production plans for this process. We present two integer optimization models for the problem. The first one is an extension of a model proposed in previous literature. Although the model shows satisfactory performance for problems with a single production line, it does not scale well with an increasing number of production lines. To address the scalability issue, we propose an integer optimization approach that can deal with parallel production lines efficiently. Specifically, we introduce a pattern-based model utilizing the concept of a single-line production schedule pattern. To deal with the exponential number of pattern variables in the model, we develop a branch-and-price algorithm. Additionally, we devise an efficient labeling algorithm to solve pricing subproblems, based on a time-expanded network structure of the problem. The performance of the proposed models and algorithms is investigated through computational experiments using real-world data. The test results demonstrate the effectiveness and efficiency of our approaches, particularly showing that the branch-and-price algorithm scales well with an increasing number of production lines.