A two stage approach for order and rack allocation with order backlog in a mobile rack environment

In this paper we investigate a problem associated with operating a robotic mobile fulfilment system (RMFS). This is the problem of simultaneously allocating both orders and racks to multiple pickers with inventory constraints and order backlog. We present a two stage optimisation based approach for the problem. In our two stage approach we, in the first-stage, deal with the orders which must be definitely fulfilled (picked), where the racks chosen to fulfil these first-stage orders are chosen so as to (collectively) contain sufficient product to satisfy all orders. In the second-stage we restrict attention to the racks chosen in the first-stage solution in terms of allocating second-stage orders. We present three different strategies with regard to splitting the orders into a set of first-stage orders and a set of second-stage orders. One of these strategies minimises the requirement to make decisions as to the rack sequence (i.e. the sequence in which racks are presented to each picker). We present a heuristic procedure to reduce the number of racks that need to be considered. Extensive computational results are presented for test problems that are made publicly available; including test problems that are significantly larger than previous problems considered in the literature.