Abstract: A procurement system may include a dual solution computation unit that creates a qualification problem limited to a delivery schedule and computes a dual solution for a qualification problem. The system includes a schedule search unit that creates a function that constrains a dual solution of constraint equations for a linear relaxation problem of the delivery schedules and searches for a delivery schedule exhibiting constraints that violate the dual solution of the qualification problem. The system further includes a schedule adding unit that creates a new qualification problem by adding and setting a delivery schedule and computes a dual solution to a new qualification problem using the dual solution computation. The system further includes an integer solution computation unit that outputs the number of delivery means and the amount of commodity to be purchased.