Multiple-suction-cup grasping can improve the efficiency of bin picking in cluttered scenes. In this paper, we propose a grasp planner for a vacuum gripper to use multiple suction cups to simultaneously grasp multiple objects or an object with a large surface. To take on the challenge of determining where to grasp and which cups to activate when grasping, we used 3D convolution to convolve the affordable areas inferred by neural network with the gripper kernel in order to find graspable positions of sampled gripper orientations. The kernel used for 3D convolution in this work was encoded including cup ID information, which helps to directly determine which cups to activate by decoding the convolution results. Furthermore, a sorting algorithm is proposed to find the optimal grasp among the candidates. Our planner exhibited good generality and successfully found multiple-cup grasps in previous affordance map datasets. Our planner also exhibited improved picking efficiency using multiple suction cups in physical robot picking experiments. Compared with single-object (single-cup) grasping, multiple-cup grasping contributed to 1.45x, 1.65x, and 1.16x increases in efficiency for picking boxes, fruits, and daily necessities, respectively.