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

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