In recent years, some e-commerce companies such as Amazon have adopted the cargo-to-person picking mode to improve their pickup efficiency. Under this mode, a shelf can store several types of goods and a type of goods can be placed on some shelves. When orders arrive, the warehouse robots move one shelf or more containing the ordered items to a fixed platform, and the pickers select the items from the shelves. It is very important to decide which shelves should be moved to increase picking efficiency. This paper addresses the problem of optimal movable-shelf selection for the cargoto-person picking mode. The goal of this study is to minimize the total time (costs) of moving the selected shelves to finish a batch of orders. We model this problem using 0-1 linear programming and show that the problem is NP-hard. Furthermore, we propose a three-stage hybrid heuristic algorithm with polynomial complexity to solve it. We conduct numerical experiments to show the efficiency of this algorithm.

Based on the dynamic properties of main and secondary structures and the orthogonality condition of structural mode shapes, dynamic responses and response spectra of the two structures are investigated in the frequency domain using the modal truncation technique. Transfer functions and root-mean-square of acceleration response of equipment are directly derived from the dynamic properties of structure and equipment, in which influence factors, such as tuning, interaction and non-classical damping etc., are considered. This analysis is free from the complex eigenvalue problem and the ill-conditioned equation of motion due to the significant different stiffness between main and secondary structures. Power spectral density function of acceleration responses and floor response spectrum are also analyzed by considering the influence of both the natural frequency of equipment and the modal truncation technique. A 10-story main building and equipment with single degree of freedom is used as an example. The results demonstrate the high accuracy of the approach proposed in this paper, where the response spectrum can be obtained only by a few lower modes of the main structure.