With severe global competitions, how to control inventory so as to reduce the material storage space plays a pivotal role in reducing the daily cost resulted from the land rental. The goal of this article is to develop a periodic material delivering schedule to minimize the space required for inventory. We take a leading home appliance manufacturing system in China as a case problem to study the material delivery scheduling optimization problem so as to ensure the synchronization between production and material delivering. The problem can be divided into a number of subproblems with each of them served by a turnover vehicle (TV) and this article investigates one of its subproblems. We build a mixed-integer linear programming (MILP) model for the problem and use the CPLEX optimizer to solve small-size problems. With the combinatorial nature, we design a Grey Wolf Optimizer (GWO) algorithm to solve large-size problems. Extensive experiments are done, and comparisons are made with existing metaheuristics to validate the proposed algorithm. Results demonstrate the efficiency and effectiveness of the proposed method.