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In this paper we investigate a problem associated with operating a roboticmobile fulfilment system (RMFS). This is the problem of allocating orders andmobile storage racks to pickers.  We present a two-stage formulation of the problem. In our two-stage approachwe, 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 chosenso as to (collectively) contain sufficient product to satisfy all orders. Inthe second-stage we restrict attention to those racks chosen in the first-stagesolution in terms of allocating second-stage orders.  We present three different strategies for first-stage order selection; one ofthese strategies minimises the requirement to make decisions as to the racksequence (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 tobe considered. Extensive computational results are presented for test problemsthat are made publicly available; including test problems that aresignificantly larger than previous problems considered in the literature.

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