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Driven by globalization and e-commerce, the demand for logistics space is rising. However, logistics space is limited and costly, which is especially true for urban areas. Therefore, available storage space must be used with the utmost efficiency. Grid-based storage systems consist of densely stored unit loads on a square grid. Each grid location may be either empty or occupied by a single item. Items are simultaneously and independently movable in the four cardinal directions. This makes high-density storage possible without using fixed aisles. To move an item to an occupied location, other items must move. Thus, one or more empty locations must be available. In this work, we present an approach for the planning of simultaneous storage and retrieval processes of multiple items in a grid-based storage. For this purpose, a decoupled multi-agent route planning approach is proposed in which planning is done at two essentially decoupled levels. At the first level, the order of items and their movement paths are computed, which is collision-free with respect to the stored items in the grid, excluding the moved items. Special attention is paid to the puzzle-based retrieval planning. Similar to the classical 15-puzzle children's game with one empty location, items can be maneuvered from one location to another in the grid using the minimum number of item moves. While previous research showed optimal solutions for one or two empty locations, this thesis provides an optimal solution approach for configurations where multiple empty locations are arbitrarily positioned in the grid. To this end, the problem is formulated as a state space problem and solved using a graph search. At the second level, collisions between the moved items are resolved by scheduling (i.e., the occupancy time of each item along their paths, computed at the first level, are selected in such a way that they avoid collision with each other along their respective movement paths). Finally, we evaluate the approaches that were developed in this thesis in a simulation study by designing and analyzing a grid-based early baggage storage system at a major international airport.