An applied column generation approach for solving large-scale uncapacitated dynamic lot sizing problems

Abstract

This study aims to improve performance of the simplex-based method for solving large-scale uncapacitated dynamic lot sizing problems with the column generation technique. This method has determined the entering basic variable with the minimal negative reduced cost value. If all reduced cost are negative, an optimal solution will be reached. The least cost basic variables were introduced to construct its restricted master problem (RMP) matrix with only 2n-1 variables. The operating of the column generation-simplex method provided good performance in less time consuming than the traditional simplex method with 39% and 44% at problem sizes 1,000 and 1,500. While this proposed method could still utilize less memory space used about 7.08% at problem size 1500. The maximum problem size of dynamic programming, column generation and classical simplex algorithm could be achieved by their corresponding empirical equation on test computer at problem size 34000, 21500 and 17900, respectively.