In the present paper, a multi-item inventory problem with the capacity to replenish carriers is considered. In the present study, we propose a model that considers truck capacity, truck cost, and receiving inspection cost with inventories and shortages in inventory management simultaneously. A number of studies have examined the minimum total cost while considering the ordering cost as fixed and not considering the carrier capacity or receiving inspection cost. However, we consider the stepwise ordering cost, which changes in a stepwise manner according to the ordered quantity and the capacity of the carrier. In addition, we consider a receiving inspection cost that is defined not only by ordered quantity but also by ordered item variety. The problem considered herein was formulated as a mathematical programming problem in a finite planning period, and valid inequalities were considered. We could consider individual objective functions for ordering, holding, lost sales, and receiving inspection cost together. We can observe that the receiving inspection cost could be reduced by aggregating the order quantity.