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In this paper we investigate the problem of simultaneously allocating ordersand mobile storage racks to static pickers. Here storage racks are allocated topickers to enable them to pick all of the products for the orders that havebeen allocated to them. Problems of the type considered here arise infacilities operating as robotic mobile fulfilment systems.  We present a formulation of the problem of allocating orders and racks topickers as an integer program and discuss the complexity of the problem. Wepresent two heuristics (matheuristics) for the problem, one using partialinteger optimisation, that are directly based upon our formulation.  We also consider the problem of how to sequence the racks for presentation ateach individual picker and formulate this problem as an integer program. Weprove that, subject to certain conditions being satisfied, a feasible racksequence for all orders can be produced by focusing on just a subset of theorders to be dealt with by the picker.  Computational results are presented, both for order and rack allocation, andfor rack sequencing, for randomly generated test problems (that are madepublicly available) involving up to 500 products, 150 orders, 150 racks and 10pickers.

Order allocation, rack allocation and rack sequencing for pickers in a mobile rack environment