Abstract
We study the mixed storage and retrieval scheduling problem of multi-shuttle automated storage and retrieval systems (AS/RSs), considering heterogeneous unit loads to minimize energy consumption. Different from travel time, the energy consumption incurred by crane movement between any two locations is not fixed and can not be easily calculated beforehand. As energy consumption is related to the weight of all unit loads on shuttles, the energy consumed between any two locations is not constant but a variable affected by the scheduling of both storage and retrieval operations at other locations. Considering this aspect of the objective, we formulate the energy-efficient mixed storage and retrieval scheduling problem as a mixed integer nonlinear programming model and propose a branch-and-price algorithm framework to solve the problem. In the pricing subproblem of the framework, we tailor a labeling algorithm based on a proposed dominance judgment policy and embed the Kuhn-Munkres algorithm in the labeling algorithm. The results of computational experiments show that the proposed algorithm outperforms the Gurobi solver in terms of both solution quality and computational efficiency. Based on the results, we give suggestions on the design and operation of warehouses. Our work will be insightful for warehouse managers aiming to operate multi-shuttle AS/RSs with reduced energy consumption and carbon emission and contribute to sustainable warehousing practices.
