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Puzzle-based storage systems are a new type of automated storage systems that allow storage of unit loads (e.g. cars, pallets, boxes) in a rack on a very small footprint with individual accessibility of all loads. They resemble the famous 15-sliding tile puzzle. Current models for such systems study retrieving loads one at a time. However, much time can be saved by considering multiple retrieval loads simultaneously. We develop an optimal method to do this for two loads and heuristics for three or more loads. Optimal retrieval paths are constructed for multiple load retrieval, which consists of moving multiple loads first to an intermediary 'joining location'. We find that, compared to individual retrieval, optimal dual load retrieval saves on average 17% move time, and savings from the heuristic is almost the same. For three loads, savings are 23% on average. A limitation of our method is that it is valid only for systems with a very high space utilisation, i.e. only one empty location is available. Future research should investigate retrieving multiple loads for systems with multiple empty slots.

In e-commerce fulfilment centres, storage assignment is critical to ensure short response times. To achieve this, many online retailers have moved to product dispersion in combination with product turnover-based slotting. However, commonly used policies do not fully utilise the historical customer demand information to optimise the storage assignment. This paper addresses a comprehensive approach to estimate the joint effects of 'turnover frequency', 'product correlation', and 'inventory dispersion' storage strategies on the expected order picking travel time in automated (robotic), partsto-picker systems. Additionally, it provides a thorough analysis of the impact of product correlation and turnover frequency on storage policies' performance. We develop a mixed-integer linear program for optimal product-to-cluster and cluster-to-zone allocation to minimise the robot's expected travel time. The travel time expressions are developed for different zone and station configurations. An efficient construction and improvement heuristic method is proposed and applied to a real dataset of a personal care products distributor. The analytical results show that the correlated dispersed assignment leads to a shorter expected travel time than the benchmark policies for order sets with sufficiently large order size. The demand correlation plays a major role in the performance of the models in the cases we tested.

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