By Paul Tillich
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The VRPB involves both a set of customers to whom products are to be delivered and a set of vendors whose products need to be transported back to the depot, and the critical assumption is that all deliveries must be made on each route before any pickups can be made. In this paper, we consider a new extension of the classical VRP motivated by a real-world routing situation, called the Pickup and Delivery for Moving Objects (PDMO) problem: Given manufacture products initially located on numbers of convey belts in arbitrary positions, the robot arm must grasp and deliver the products to the ﬁxed position (depot).
Ii) (Pickup) R can start from O at time sj , move onto the path of bij , and then grasp bij . Namely, bij arrives at the point where R is waiting for bij to come. (iii) (Delivery) R can move back to O at time gj , and gj ≤ sj+1 (except for the last one). We simply call a turn of pickup and delivery of an object, collect the object. A scheduling is valid if the three conditions (i), (ii), and (iii) are satisﬁed. We assume that the robot arm can stop only at the origin and makes no detour to move to any position, because a general scheduling can be transformed easily to such a scheduling without decreasing the number of objects to be collected.