Blanco Quintana, Andrés

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    Design and optimization of puzzle-based storage systems with unidimensional movements
    (2023-12-14) Blanco Quintana, Andrés; Carlo-Colón, Héctor J.; College of Engineering; Bartolomei-Suárez, Sonia M.; Pagán-Parés, Omell; Department of Industrial Engineering; Rodríguez-Román, Daniel
    Puzzle-Based Storage Systems (PBS) are very high-density parts-to-person storage systems for unit loads. This type of system is composed of a grid with 𝑚 rows and 𝑛 columns. The grid is composed of cells that may carry loads on top of them. Retrieving a load from a PBS requires sequentially moving loads to cells without a load until the required load reaches the output point. Since loads need to be slid into cells without a load, these cells are commonly referred to as escorts. A paradigm for Puzzle-Based Storage Systems (PBS) is that all cells are designed with the capability to transport loads horizontally and vertically. This study challenges this paradigm by proposing unidimensional PBS (UPBS), where some cells are limited to transporting loads either horizontal or vertical movements. UPBS require a lower investment cost, compared to traditional PBS, at the expense of lower throughput capacity. This thesis introduces the concept of UPBS and presents a linear program (LP) formulation to find the optimal load retrieval path for a single load using a single escort in a UPBS. The LP is solved recursively to understand the cost-to-throughput tradeoffs of unidimensional designs for a 4×4 grid system. It is concluded that it is possible to design UPBS with 25% of the possible unidimensional cells, while reducing the throughput by approximately 10%. A multi-escort formulation for the single load problem is also proposed and used in combination with an existing PBS formulation to understand UPBS design tradeoffs for systems with multiple escorts and a single input/output point. It is concluded that UPBS can be designed such that the capital investment cost to throughput tradeoff is favorable when retrieving a single load. An existing decentralized PBS algorithm for retrieving multiple loads considering multiple input/output points was coded in Python and modified for UPBS. Upon proper validation of the code, it was used to develop managerial insights for designing UPBS. For UPBS systems with simultaneous retrievals, multiple escorts, and multiple I/O Points, the layout depends on the number of loads requested at the same time (i.e., WIP level). For low WIP levels, it is possible to design UPBS with 33.33% of unidimensional rows, which would have implications of a 9.82% increase in throughput and for medium WIP levels with 41.66% of unidimensional rows would have implications of a 9.29% increase in throughput. The increase of throughput is a consequence of the decentralized PBS algorithm forcing some unrequested loads out of the system to prevent gridlocks. Therefore, UPBS with single and multiple escorts can maintain their throughput, with a lower investment cost.