Integrated pallet retrieval and processing in warehouses under uncertainty

We study the problem of integrated pallet retrieval and successive processing in warehouses motivated by a practical company setting. A set of pallets has to be retrieved in a warehouse having a single stacker crane and multiple input/output-points, and the goal is to minimize the makespan. Previous research focuses on minimizing stacker crane travel times, while subsequent pallet processing times at the input/output-points are neglected. A distinction is made between a blocking and buffering variant, in which either no or sufficient buffer space is available at the input/output-points to temporarily store pallets there before they are processed. To hedge against uncertainties in the pallet processing times, we additionally apply robust optimization with budgeted uncertainty sets. We develop dynamic programming algorithms for the worst-case evaluation, identify polynomially solvable cases when there is only a single input/output-point, and present mathematical models for the general case with an arbitrary number of input/output-points. Our extensive computational study reveals that the integrated models yield considerable benefits compared to either ignoring the stacker crane travel times or the pallet processing times. We propose heuristic algorithms that provide good solutions for large instances in a short amount of computational time.