Parallelization of Lagrangian Decomposition and Coordination Method for a Multi-Item Single-Machine Dynamic Lot Size Scheduling Problem

Abstract

　An iterative solution method using the Lagrangian decomposition and coordination method has already been proposed for amulti-item single-machine dynamic lot size scheduling problem.However, reducing the computation time until the solution converges has become a practical problem. In order to resolve this problem, parallelization has been attempted in models that extend the problem to multi-stage processes,but the nature of the time required forsolution convergence with data froma single-machine (single-process)has not been clarified so far. In this study,we conducted numerical experiments using OpenMP parallelization with single-machine data and varying the number of threads.As a result, we obtained the same results as in the case of sequential processing,and also found that we could obtain the data approximately twice to less than four times faster depending on the number of threads in the parallel processing.Furthermore,by introducing a quadratic overhead term into Amdahl's law,we estimated the limit curve of computational performance by polynomial approximation and clarified its properties of the parallelization. These results suggest that it is expected to improve operational efficiency in production planning operations.