Puzzle-based storage (PBS) is one of the most spaceefficient types of storage systems. In a PBS unit, loads are stored in a grid of cells, where each cell may be empty or contain a load. A load can move only to adjacent empty cells using four-way conveyors. When loads are requested for retrieval, a sequence of load movements is performed in order to bring them to the input/output (I/O) points of the unit. In this paper, we present a time-expanded-graph based integer-linear-programming (MILP) formulation that aims to minimize the time to retrieve a set of target loads (makespan). Note that other objectives, such as the flowtime or the number of moves, can be minimized as well. Experiments show that the proposed formulation can solve small to medium size instances, especially when the storage density is not extremely high. Additionally, we show that parallel load retrieval significantly decreases the makespan compared to serial load retrieval.
Progress in Material Handling Research
Bukchin, Yossi and Raviv, Tal, "An efficient MILP formulation for the parallel load retrieval in puzzle based storage systems with simultaneous load movements" (2023). 16th Proceedings (Dresden, Germany- 2023). 10.