Integrated storage assignment for an E-grocery fulfilment centre: accounting for day-of-week demand patterns

In this paper, we address a storage assignment problem arising in a fulfilment centre of a major European e-grocery retailer. The centre can be characterised as a hybrid warehouse, consisting of a highly efficient and partially automated fast-picking area designed as a pick-and-pass system with multiple stations, and a picker-to-parts area. The storage assignment problem involves the decisions of selecting products to be allocated to the fast-picking area, assigning these products to picking stations, and determining the specific shelves within the designated station. The objective is to achieve high picking efficiency while maintaining balanced workloads across stations and respecting precedence order constraints. We formulate this three-level problem using an integrated mixed-integer linear programming (MILP) model. Computational experiments with real-world data demonstrate that our integrated approach yields significantly better results than a sequential approach, where the selection of products to be included in the fast-picking area is performed before assigning stations and shelves. To enhance computational efficiency, we propose a heuristic solution approach that fixes SKUs to shelves, allowing us to find better solutions in shorter runtimes compared to directly solving the MILP model. Additionally, we extend the integrated storage assignment model to explicitly account for within-week demand variation. In a set of experiments with day-of-week-dependent demands, we show that while a storage assignment based on average demand figures can lead to highly imbalanced workloads on certain days, the augmented model provides well-balanced storage assignments for each day-of-week without compromising the solution quality in terms of picking efficiency. The benefits of accounting for demand variation are further demonstrated through a simulation-based analysis using sampled weekly data.