Abstract

The Buffer Allocation Problem (BAP) in production flow lines is very relevant from a practical point of view and very challenging from a scientific perspective. For this reason, it has drawn great attention both in industry and in the academic community. However, despite the problem’s relevance, no exact method is available in the literature to solve it when long production lines are being considered, i.e., in practical settings. This work proposes a new Mixed-Integer Linear Programming (MILP) formulation for exact solution of sample-based BAP. Due to the huge number of variables and constraints in the model, an algorithm based on Benders decomposition is proposed to increase the computational efficiency. The algorithm iterates between a simulation module that generates the Benders cuts and an optimization module that involves the solution of an updated MILP model. Multiple Benders cuts after each simulation run are generated by exploiting the structural properties of reversibility and monotonicity of flow line throughput. The new MILP formulation is tighter than the state-of-the-art model from a theoretical point of view, and order of magnitude of computation time saving is also observed in the numerical results.

摘要

从实践的角度来看，生产流水线中的缓冲区分配问题 (BAP) 非常相关，从科学的角度来看非常具有挑战性。正因如此，它引起了工业界和学术界的高度重视。然而，尽管该问题具有相关性，但在考虑长生产线时（即在实际环境中），文献中没有可用的确切方法来解决该问题。这项工作提出了一种新的混合整数线性规划 (MILP) 公式，用于基于样本的 BAP 的精确解。由于模型中存在大量变量和约束，提出了一种基于Benders分解的算法来提高计算效率。该算法在生成 Benders 切割的模拟模块和涉及更新 MILP 模型的解决方案的优化模块之间迭代。通过利用流线吞吐量的可逆性和单调性的结构特性，在每次模拟运行后生成多个 Benders 切割。从理论的角度来看，新的 MILP 公式比最先进的模型更严格，并且在数值结果中也观察到了计算时间节省的数量级。