2019 Volume 26 Issue 1 Pages 109-116
In this paper, we deal with parallel processing (thread parallel) using shared memory type multi-core CPU in order to accelerate calculation speed on solving solution in a multi-item multi-stage dynamic lot size scheduling model. This model uses the Lagrangian decomposition and coordination method which decompose the original problem into item-based sub-problems and solve them independently with dynamic programming, and coordinate constraint violations that occur among sub-problems. If processing can be assigned to different threads for each item or for some items, the overall processing acceleration can be expected. Therefore in this study, first, we newly code a parallel processing program by OpenMP with the policy to reduce the memory usage using of the structure of the existing program created by us in about two decades ago, and verify the calculation time by numerical calculation. As a result, it was found that the overhead for parallelizing arrays is actually large, and that the effect of speeding-up could not be obtained, and the computation will be slower compared to sequential processing. Therefore, in order to reduce the overhead, we considered that sharing of the main arrays, which are an array for holding functional equations used in dynamic programming and arrays for holding states, etc., is effective. As a result in the numerical calculation using the improved program, the calculation time decreased as the number of threads increased, and acceleration of at least 3 times was achieved at maximum.
