A genetic algorithm for determining optimal replenishment cycles to minimize maximum warehouse space requirements

In a supply chain, it is an important issue for logistic managers to offset the replenishment cycles of multiple products sharing a warehouse so as to minimize the maximum warehouse space requirement (MWSR). Most of the studies in the literature assume that warehouses replenish at the beginning of some basic planning period. In this paper, we relax this assumption by allowing the warehouse to replenish at any time. In order to solve this problem, we conduct theoretical analysis based on Fourier series and Fourier transforms and propose a procedure that is used to calculate MWSR efficiently for any given replenishment schedule. Then, we employ this procedure in a genetic algorithm (GA) to search for the optimal replenishment schedule. Using randomly generated instances, we show that the proposed GA significantly outperforms a previously published heuristic.