Novel time-space network flow formulation and approximate dynamic programming approach for the crane scheduling in a coil warehouse

This article proposes an efficient event-based time-space network flow model with side constraints for the crane scheduling problem in a coil warehouse where the crane should carry out a set of coil storage, retrieval and shuffling requests, and determine the sequence of handling these requests as well as the positions to which the coils are moved. The model is formulated based on a graph such that each node represents a location in the warehouse at the end of a specific scheduling stage, and each edge indicates a crane's move between two locations in a stage. Variables reduction strategies are presented to accelerate solving the model. In order to solve large-sized instances of the problem, an exact dynamic programming approach based on optimal assignments between coils and positions in a bipartite network with cuts is designed by exploiting the problem structure. Then an approximate dynamic programming (ADP) approach is developed, in which an affine value function approximation is defined as the estimation of crane's traveling time for handling each coil, and updated via iterations by collecting information from the solutions of separate subproblems. Computational results show that the proposed model is tighter and can be solved much more quickly than a traditional model for a reduced crane scheduling problem in the literature and the standard time-space network flow model. Besides, the proposed algorithm can obtain high quality solutions for large-sized instances in a few minutes and is more efficient in solving the problem than a commercial software package.