Summary: Aiming at the problem that customer demands generally consist of several discrete batches or orders, in this paper, we describe this problem and present a mathematical model of the discrete split delivery vehicle routing problem (DSDVRP). We have studied the features of the DSDVRP in comparison to the case of continuously split demands, and analyzed and considered solutions to the problem. Here, we propose a tabu search algorithm for the problem, in which we design two individual operations that address the demands of the same customer to avoid unnecessary travel cost, speed up the search process, and enhance the algorithmic search ability. We provide our computational results and compare them with those of other methods reported in the literature. Our findings indicate that the proposed algorithm can find better solutions than those reported in the literature.