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

TL;DR

This paper introduces a two-stage method for order and rack allocation in robotic mobile fulfilment systems, optimizing order fulfillment and rack selection to improve efficiency, supported by extensive computational testing on large problems.

Contribution

It proposes a novel two-stage formulation and three strategies for order selection, including a heuristic to reduce rack consideration, addressing larger problem instances than prior studies.

Findings

The two-stage approach effectively manages order and rack allocation.

Heuristic reduces computational complexity for large problems.

Strategies improve order fulfillment efficiency.

Abstract

In this paper we investigate a problem associated with operating a robotic mobile fulfilment system (RMFS). This is the problem of allocating orders and mobile storage racks to pickers. We present a two-stage formulation of 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 those racks chosen in the first-stage solution in terms of allocating second-stage orders. We present three different strategies for first-stage order selection; 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.